Lsat Ar Preview

8/2/2019 Lsat Ar Preview

http://slidepdf.com/reader/full/lsat-ar-preview 1/28

tototototoANANANANANALALALALALYTICALYTICALYTICALYTICALYTICAL

REASONINGREASONINGREASONINGREASONINGREASONING

AMERICAN EDUCATION AIDS

OVER 850 AUTHENTIC

EXAMPLES

LUCID EXPLANATIONS

THE ULTIMATE GUIDE

RAMKI 'S

f f f f f or or or or or

LSALSALSALSALSATTTTT



Only about 1/3 of the num ber of pages in a typical LSAT Guide Book

is de vot ed to ANALYTICAL REASONING.

THIS IS THE FIRST BOOK D EDICATED ENTIRELY

TO THIS SUBJ ECT!

Again, the oth er guide books usu ally explain WHY A PARTICULAR

CHOICE IS THE COR RECT ANS WER TO THE GIVEN QUES TION - ON AN

EX POS T FACTO BASIS!

They do not guide you step-by-step on HOW TO ARRIVE AT THE

CORRECT ANSWER TO THE GIVEN QUESTION BY YOURS ELF, WHICH

IS WHAT YOU ARE EXPECTED T O D O IN THE EXAMINATION HALL.

This boo k te ach es you jus t tha t - THE STEP-BY-STEP P ROCESS OF

WORKING OUT THE CORRECT ANSWER, that too IN THE QUICKEST

P OSSIBLE TIME!

AND WITH AUTHEN TIC EXAMPLESOF THE SAME PATTERN S AN D LEVELS OF DIFFICULTY

AS THOSE ASK ED IN LSAT!

THAT IS WHY THIS IS

THE ULTIMATE GUIDETO AN ALYTICAL REAS ON ING!!



Copyright 2006 K. S. Rama krish na n

Amer ican Edu cat ion Aids

CONTENTS

Chapter 1: Int roduct ion 5

Chapter 2: Easier Quest ions 30

Chapter 3: Quest ions of Medium Difficu lty 54

Chapter 4: More Difficu lt Quest ions 81

Answers & Analysis - Chapter 2 112





3

Chapter 1

INTRODUCTION

The m ult iple-choice sections of Law School Admission Test (LSAT) featu re 3 d ifferen t t ypes of ques tions –

Reading Compreh ension, Ana lytical Rea soning an d Logical Rea soning.

The following are t he nu mbers of quest ions u nder each type:

Reading Compreh ension: 26 or 27

Analyt ical Reas oning: 24

Logical Rea soning (2 s ections ): 25 or 26 ea ch

Ther e will be an addit iona l section in ea ch test contain ing quest ions from a ny of th e above 3 types. Known

as t he experiment al or the var iable section, the pur pose of th is additional section is to pretest qu estions for

possible inclusion in futu re t ests. Your per form an ce in t his section is n ot ta ken into considera tion for your

score. You will, however, not be t old which am ong th e 5 sections is th e var iable section, and you will have to

an swer each of th em with equa l seriousn ess.

You ar e allowed 35 minu tes t o an swer ea ch section in L SAT..

Your score in LSAT is given in t he r an ge 120 to 200.

This book dea ls with th e Ana lytical Reasoning qu estions in LS AT.

In troduc t ion to Analy t ica l ReasoningThe pur pose of th e Ana lytical Reasoning questions is to test your ability to underst an d a given stru ctu re of

relat ionsh ips am ong persons, places, things or events, and to logically deduce new relationships a mong th em.

Ea ch Ana lytical Reasoning quest ion will consist of a set of 3 to 7 r elated st at ement s or conditions or r ules

describing a st ru ctu re of relat ionsh ips.

Below th em will be a set of 3 to 8 quest ions that test your un derstandin g of that structure and its

implications.

Thes e quest ions ar e, in fact, of ‘pu zzle’ type, an d no kn owledge of form al logic or ma th ema tics is requ ired t o

answer t hem.

They can be solved usin g th e knowledge, skills, vocabulary a nd t he a bility t o perform simple addition a ndsubtraction.

Most of the Ana lytical Reasoning questions ar e mu ch easier t o solve than th ey initially appear to be. Do not

feel intimida ted by a group of questions mer e becau se th e conditions look long an d complicat ed.

You do no t ha ve to answer the ques t ions menta l l y bu t ca n , and should , use a pen an d pap er for

work ing out the a nswer s.

We sha ll first expose you t o some t ypical quest ions in Analytical Reasoning, and a nswer an d an alyse them

before advising you of the genera l stra tegies tha t you should adopt for a nswerin g these quest ions.

Examp le 1

Questions 1-6 are based on th e following:

A far mer plant s only five differen t kin ds of vegeta bles: beans, corn, kale, peas a nd squ ash . Every year t hefarmer plant s exactly thr ee kinds of vegetables according to th e following rest rictions:

If the farmer plants corn, he a lso plants bean s th at year.

If the farmer plant s kale one year, he does not plant it th e next year.

In a ny year, th e far mer p lant s no more th an one of th e vegeta bles he plan ted in th e previous year.

Qn. 1: If the far mer plant s bean s, corn , and pea s one year, which of the following combinations can he plan t

the next year?

(A) Corn , kale, and p eas

(B) Kale, peas, and squas h

(C) Beans, corn, and squa sh

(D) Bean s, corn , and k ale

(E) Bean s, peas, and squa sh



American Education Aids - LSAT - Analytical Reasoning

4

Qn. 2: Which of th e following is a possible sequen ce of combin at ions for t he far mer to plan t in t wo successive

years?

(A) Beans, corn , ka le Corn, peas, squash

(B) Beans corn,peas Beans, corn , squash

(C) Bea ns, pea s, squ ash Bea ns, cor n, ka le

(D) Cor n, pea s, squ ash Bea ns, ka le, pea s

(E ) Kale, peas, squash Beans, cor n, ka le

Qn. 3: If the farmer plants beans, corn, and peas one year, and peas the second year, which two of thefollowing must h e plant with th e peas th e second year ?

I. Bean s

II. Corn

III. Kale

IV. Squash

(A) I an d II

(B) I and III

(C) II and II I

(D) II an d IV

(E) III an d IV

Qn. 4: Which of th e following is (ar e) tru e?I. The farm er mu st plan t each vegetable at least once in an y two-year per iod

II. Every year a fter th e first year, th e far mer m ust p lant exactly one of th e vegeta bles he plan ts

in th e previous year

III. The farm er never plan ts t he sam e vegetable in thr ee consecut ive years.

(A) I on ly

(B) II only

(C) III only

(D) I an d II only

(E) I an d III only

Qn. 5: If the far mer plant s bean s, corn, and kale in t he first year, which of the following combinat ions m ust

be plant ed in the th ird year?

(A) Beans, corn, an d ka le(B) Bean s, corn , an d pea s

(C) Bean s, kale a nd pea s

(D) Beans, peas, an d squa sh

(E) Kale, peas, and squash

Qn. 6: If the farm er pla nt s bean s, corn, an d ka le one year, which of the following pairs of vegeta bles can not be

planted together a gain as long as th e farm er plants a garden each year?

(A) Peas and squ ash

(B) Kale an d squa sh

(C) Bean s an d kale

(D) Beans a nd peas

(E) Beans and squa sh

Analysis

This is a typical set of quest ions often as ked in LSAT, an d is cons idered to be of th e least difficulty.

Rules under Analytical Reasoning questions are worded in a simple and unambiguous manner, and you

should first r ead th em more tha n once till you ha ve clearly und erst ood what t hey stipulat e.

In t his quest ion, the first t wo lines just give the set ting, an d th is setting is followed by three r ules.

The setting says tha t a farm er h as a choice of five differen t kin ds of vegeta bles, of which he pla nt s only three

in a ny given year.

But he is n ot free to choose an y three am ong the five, but is restricted in his choice by the three rules that

follow.

Rule 1 says that if he plan ts one par ticular vegetable (corn), he should also plan t an oth er par ticular vegetable

(beans).




5

Rules 2 and 3 r estr ict h is choice of the th ree vegetables in any year on t he basis of what he ha d plant ed th e

previous year .

Having u nder stood t he set ting a nd t he r ules, let us now tr y to solve the ‘puzzles’ th at follow.

As sta ted a bove, you do not have to ans wer th e questions ment ally, but should use a pen an d a pa per.

(In th e exam ina tion cent er, you w ill be given a s m an y sheets of paper as you requir e for your rough w ork.)

While doing rough work, you do not h ave to write down th e full names of the vegetables, but can use t heir first

letter s. Thu s, beans, corn, kale, peas an d squa sh can be repr esented by b, c, k, p and s respectively.

(While giving n am es to vegetables, persons, flowers, th ings, anim als etc involved in such qu estions, the qu estion

setters invariably ensu re that n o two of th em st art w ith the sam e letter.)

Qn. 1: Five an swer choices ar e given u nder th is question, of which four can be seen t o violate one or m ore of

th e thr ee given ru les, and only one does not incorporat e any violation. The an swer to th is question should be the

choice wh ich d oes not violate any of the thr ee rules.

There a re two meth ods of an swering such questions.

First Method

Th e first m ethod is to consi der each choice serially, and exami ne wh ether it violates any of th e given ru les, and

stop wh en you spot a choice which d oes not violate an y ru le.

Let us first tr y to answer this question u sing the first m ethod.

(A) violates Ru le 1 tha t, if th e farm er plan ts c in a year, he should also plant b in t ha t year. So, (A) is not the

answer.

(B) does not violat e Rule 1, becau se th ere is n either c nor b in it.(B) does not violate Ru le 2 also, becau se th e far mer ha d not plan ted k th e previous year.

Among th e thr ee vegetables (b, c, p) that the farm er ha d planted t he previous year, he is planting only p this

year accord ing to (B), an d he does not violate t he Ru le 3 also.

So, (B) does not violat e an y of th e th ree given ru les, an d is t he a nswer.

(In th e exam ina tion, you can s top here an d go over to the next question. But , for the sake of comp letion, we sha ll

analyse the other three choices also here.)

(C) does not violate Rule 1 or Ru le 2, but it violates Rule 3 by r epeatin g two vegeta bles - b and c - which h ad

been plant ed in the pr evious year.

(D) also violates Rule 3 by repeating b and c in t he second year.

(E) also violates Rule 3 by repea ting b and s.

{(E) does not violat e Rule 1 because th e stipula tion th at ‘b must be plant ed if c is pla nt ed’ does not mean tha t

‘c must be plant ed if b is plant ed’. If th e latt er was t he int ent ion, the r ule would have been ‘If eith er b or c is

plant ed, th e oth er m ust also be plant ed’ or ‘b and c mu st both be plant ed or n either of th em should be planted’.}

S econd Method

Th e second m ethod is to tak e each of the given ru les serially, apply th em t o each choice and verify wh ether the

rule is satisfied or violated.

Takin g Rule 1, we can see th at (A) violat es it, while th e other choices do not violat e it. So, (A) can be scored out ,

and need not be tested for th e oth er ru les.

Taking Rule 2 next, we can see tha t it is not relevan t to this question at all because th e farm er ha d not planted

k th e previous year.

Takin g Rule 3 next , we can see t ha t (B) does not violat e it, while (C), (D) an d (E) all violat e it.

So, we can choose (B) as t he a ns wer.

Qn. 2: (A) is wrong since, in th e second year, c is proposed without b, which violat es Rule 1.(B) implies t he pla nt ing of two vegetables - b and c - in t wo successive years, which is aga inst Rule 3.

(C) does not violat e an y of the r ules an d is th e corr ect a nswer.

(In th e exam ina tion, you can stop here and go over to the next question.)

(D) violat es Rule 1 in t he first year

By plant ing k in t wo successive year s, (E) violat es Rule 2.

Qn. 3: (To avoid having to look at the question paper again and again, write the question number as 3, and

write d own b, c, k and s on your rough sheet of pap er, an d score off pr ogressively what is inad missible.) It is given

that the farmer h as planted b, c and p in th e first year, and he h as chosen to plan t p in t he second year a lso.

So, to satisfy Rule 3, he can not plan t b and c in th e second yea r. So, score off b and c from your list. What ar e

now left behin d ar e k and s.

It is (E) which sta tes th is, an d is the an swer.




6

{While abbreviating t he n am es, use small letter s if the n am es sta rt with A, B, C, D or E (since oth erwise you

may get confused between t he na mes a nd t he choices). If the na mes st ar t with letter s other t ha n a , b, c, d, e, you

may use capita l lett ers.}

Qn. 4: For a nswerin g such questions, you m ust ta ke an y typical case subject t o the given r ules. Ther e can be

two typical cases in t his qu estion - the first to which Rule 1 is app licable, and t he second to which Ru le 1 is not

applicable.

Taking th e first case, let th e vegetables plan ted by him in t he first year be (b, c, k ). Then, he can plant only one

of th em in t he second year. But th is can not be c, becau se of th e firs t condition.So, what he can plant in the second year can be either (b, p, s) or (k, p, s). In both th e cases, each of the five

vegeta bles is plant ed at l east once in a t wo-year p eriod .

If the vegetables plant ed by him in th e first year are (k , p, s) (which does not involve Rule 1), th ose plan ted by

him in t he second year can be ( p, c, b) or (s, c, b). In t his case a lso, each of th e five vegeta bles is plant ed at least once

in a t wo-year p eriod .

Thus, I is true in both cases.

Since th ere ar e only 5 vegetables and t he farm er ha s to plant 6 vegetables in two years, at least one of th em

ha s to be repea ted. The th ird condition says tha t only one of them can be r epeated. Combining t hese t wo, we can

conclude th at , every year after t he first year, th e far mer must plant exactly one of th e vegeta bles he plan ts in t he

previous year.

S o, II is true.

Let us t ake th e sequence (k , p, s) and ( p, c, b) tha t we foun d possible while an alysing I above. In t he t hird year,the farmer can plant ( p, s, k ) with out violating a ny of th e ru les. In th is case, p is being planted in th ree consecutive

years consisten t with all the given rules.

So, III n eed n ot be true.

Therefore, (D) is the answer.

Qn. 5: Vegetable k cannot be plan ted in t he second year becau se of Rule 2.

Vegetable c cannot be plan ted in t he second year since, in t ha t case, b must also be planted a s per Rule 1, but

then Ru le 3 will be violated.

Therefore, he ha s to plant (b, p, s) in t he second year.

In the third year, therefore, only (A) among the given choices is possible, because all the other choices will

violat e Ru le 3. So, (A) is t he an swer.

Qn. 6: It is given in th is question th at t he farm er ha s planted (b, c, k ) in t he first year.Now, because k cannot be r epeated becau se of Rule 2, and c cann ot be planted without b, he has t o necessar ily

plant (b, p, s) in t he second year.

(Remember t ha t Rule 1 only prohibits c being plant ed with out b, but does not prohibit b being plant ed with out

c.)

The only possible combina tion in th e th ird year t hen is (b, k, c) which was the sa me a s in th e first year.

Once again, he has t o plant in th e fourt h year what he ha d plant ed in th e second year, and so on.

Thu s th e only two possible combinat ions for him ar e (b, c, k ) and (b, p, s).

Thu s, am ong th e given choices, it is (k , s) which can never be plan ted t ogeth er.

So, (B) is th e an swer.

Examp le 2

Questions 1-3 are based on th e followin g data :F, G, H, I, K, L, M and N spoke in a meetin g, but not n ecessar ily in t ha t order. Only one person spoke at a t ime.

F spoke after L, an d took more time th an H.

I spoke before M, but after H, an d took less time th an K.

J spoke after N, but before H, and t ook less time tha n N and more time tha n K.

N spoke after F, an d took less time th an H.

Qn. 1. Of th e following, who spoke first ?

(A) H (B) I (C) J (D) L (E) N

Qn. 2. Of the following speaker s, who took th e most time?

(A) F (B) H (C) J (D) K (E ) N




7

Qn. 3. Which of the following mu st be tr ue?

(A) F was t he second speak er an d gave the th ird length iest speech.

(B) H spoke before I, an d took m ore time t ha n N.

(C) I spoke last , and gave th e shortest speech.

(D) J spoke after M, and t ook less time t ha n F.

(E) N spoke after L, and took more time th an F.

Analysis

Five factual sta tements have been given, and we ha ve to answer th e th ree questions based on th em.The five statem ents give two sets of inform at ion about t he speaker s in a meeting:

(a) th e sequence in which they spoke in the m eeting, an d

(b) the com parative durations of th e var ious speeches.

The inform at ion, as given, looks a bit confusing. So, you sh ould rewrite th em in such a m an ner t ha t t he

inform at ion becomes m uch clearer.

(You will be given an y nu m ber of sheets of paper for your rough work w hen you ta ke LS AT.)

First t ry to rewrite the first par t of the st atement s and establish th e sequence of the speeches, not bothering

for a mom ent a bout t heir durations .

Stipulate the ru le tha t th e name of an earlier speaker will be written to th e left of th e na me of a later speaker.

(For exam ple, K L will mean th at K spoke earlier tha n L).

Stat ement 2 (first ha lf) can then be written as L F

Sta tem ent 3 (first ha lf) can be reduced to H I M

Stat ement 4 (first h alf) can be reduced to N J H

Sta tem ent 5 (first ha lf) can be reduced to F N

You can easily see t ha t, if you combine all these statements, you get the ar ran gement L F N J H I M, as th e

sequence in w hich th e seven speak ers spoke in th e m eetin g. (There is no inform at ion regar ding K’s place in t he

sequence, but we need not both er about it .)

Similarly, rewrite the information given in the second half of each statement to arrive at the comparative

duration of th e speeches, not bothering n ow about th e sequence in w hich they were mad e.

Again, stipu late th e rule th at t he na me of a person who spoke for a shorter dura tion will be put t o the left of

th e na me of a person who spoke for a longer dur at ion. (For exam ple, K L will mean t ha t K took less time for h is

speech th an L).

Sta tem ent 2 (second half) can th en be redu ced to H F

Sta tem ent 3 (second ha lf) can be reduced to I K

Sta tem ent 4 (second half) can be redu ced to K J NSta tem ent 5 (second ha lf) can be reduced to N H

Now, combining all these st at ement s, we get I K J N H F as t he ascend ing order of the d ura tion of th e speeches.

Qn. 1. Fr om the sequence of speaker s L F N J H I M, we stra ightaway get th e answer t o th is question as (D).

Qn. 2. Fr om the a scendin g order of th e dur at ion of speeches I K J N H F , we get t he an swer to Qn. 2 as (A).

Qn. 3. Using both t he sequen ces above, we get th e an swer to quest ion 3 a s (B).

In all th e other choices for t his quest ion, one h alf of the a nswer is wrong.

You can th us n otice how a seemin gly difficult or confusing quest ion h as been ren dered ea sy through a

reinterpretation of th e given inform ation .

Examp le 3

To apply t o a college, a st uden t m ust see th e school coun selor, obta in a tr an script from t he t ra nscript office,

an d obtain a r ecommenda tion from Teacher A or Teacher B.

The stu dent m ust see the counselor before obtaining a t ran script.

The counselor is available only on Fr iday morn ings, and Tu esday, Wednesday, and Th ur sday a fternoons.

The t ra nscript office is open only on Tuesday a nd Wednesday morn ings, Thu rsda y aftern oons a nd F riday

mornings.

Teacher A is available only on Monday a nd Wednesday morn ings.

Teacher B is available only on Monday after noons a nd F riday m ornings.




8

Qn. 1. A student has already seen the counselor and does not care from which teacher she obtains her

recommen da tion. Which of th e following is a complete an d accur at e list of th ose days when s he could possibly

complete th e app licat ion process in one day?

(A) Frida y

(B) Monday, Wednesday

(C) Mond ay, Fr iday

(D) Wedn esda y, Fr iday

(E) Monda y, Wednes day, Fr iday

Qn. 2. A student completed h is applicat ion pr ocedur e in one day. Which of the following stat ement s mu st be

true?

I. He obtained h is recomm enda tion from Teacher A.

II. He obtained h is recomm enda tion from Teacher B.

III. He completed the pr ocedur e in th e mornin g.

(A) I only

(B) II only

(C) III only

(D) I an d III only

(E) II an d III only.

Qn. 3. A student h as a lready obtained his t ran script a nd does not care from which t eacher h e obtains h is

recommen da tion. Which of th e following is a complete an d accur at e list of th ose days when he could possibly

complete t he applicat ion process?

(A) Frida y

(B) Monday, Wednesday

(C) Mond ay, Fr iday

(D) Wedn esda y, Fr iday

(E) Monda y, Wednes day, Fr iday

Analysis

The inform at ion, as given, first m entions th e various services, an d sta tes the days on which each service is

available. Let us n ow rewr ite it so as t o show the services availa ble on ea ch day.

Let C represen t t he coun selor, TO represen t t he tr an script office and AM an d PM repr esent t he foren oons a nd

afternoons respectively.Using t he a bove symbols, you sh ould rewrite th e given informa tion as below:

AM PM

Monday A B

Tuesday TO C

Wednesday TO, A C, B

Thursday – C, TO

Fr iday C, TO, B –

It is now quite easy to an swer th e questions by referr ing to the a bove table.

Qn. 1. Since th e student has already seen th e counselor, he has to now get t he t ran script from th e TO and get

a r ecommenda tion either from A or B. Both th ese are possible on Wednesday or Fr iday. (Though h e can get a

tr an script on Tuesday, he can not meet either A or B on t ha t da y.) So, (D) is th e an swer.

Qn. 2. The only day on which th e stu dent could have seen th e counselor, got t he tr an script an d also obta ined

th e teacher’s recomm enda tion is Friday, an d he could ha ve done all th ese in the m orn ing itself. The tea cher

concern ed in t his case would have been B.

It is easy to see tha t II and III in Qn. 2 are tr ue, while I is not true.

So, the a nswer is (E).

Qn. 3. The da ys on which either or both th e teachers ar e available ar e Monda y, Wednesday an d Fr iday. He

could complete th e application form alities on an y of these t hr ee days.

So, (D) is the an swer. (Since he has alr eady got t he tr an script, we can pr esum e tha t h e has m et th e counselor

already).




9

Examp le 4

Professor Green is choosing a four-member research team from graduate s tudents F, G and H, and

un dergra dua te st uden ts W, X, Y an d Z.

There are to be at least two gradu ate stu dents on the team.

Student F refuses to work with stu dent Y.

Student G refuses to work with stu dent W.

Student Y refuses to work with stu dent Z.

Qn. 1. If studen t Y is chosen, which of the following mu st be t he other mem bers of th e resear ch t eam?(A) F, G and X

(B) G, H a nd W

(C) G, H a nd X

(D) G, H a nd Z

(E) H, W an d X

Qn. 2. If studen t Z is chosen, and stu dent F is r ejected, which of the following mu st be t he m embers of the

research team?

(A) G, H, W an d X

(B) G, H , X an d Z

(C) G, H , Y an d Z

(D) G, X, Y and Z

(E) H , W, X and Z

Qn. 3. If student G is chosen, and student H is rejected as a member of the research team, which of the

following statement s mu st be tru e?

I. Studen t X is chosen.

II. Studen t Z is chosen.

(A) I on ly

(B) II only

(C) Either I or II, but n ot both

(D) Both I an d II

(E) Neither I nor II

Qn. 4. Which of the following mu st be tr ue?I. Studen t W and Y never work t ogeth er.

II. Studen t X and Y always work together.

III. If stu dent W work s, stu dent H a lso works.

(A) I on ly

(B) I an d II only

(C) I an d III only

(D) II a nd I II only

(E) I, II and II I

Qn. 5. Which of the following mu st be tr ue?

I. If student F works, stu dent Z work s

II. If stu dent F does not work , stu dent W does not work.III. If stu dent F does not work , stu dent H work s.

(A) I on ly

(B) III only

(C) I an d II only

(D) I an d III only

(E) II an d III only.

Analysis

(For ta ckling su ch examples, you should m ake a cur sory read ing of th e quest ions first . You would ha ve noticed

tha t all the questions in th e set relate to the various groupin gs tha t are possible. Ther efore, instea d of answerin g

each quest ion independen tly, write down first al l th e possible team s tha t can be form ed consistent with th e given

conditions, and t hen t ake u p th e questions one by one.)




10

One of th e conditions is th at th ere should be at least two gradu ate stu dents on the team. There is therefore no

objection to all th e three graduat e students being on t he team also.

If (F, G, H) all a re on t he t eam , th e four th mem ber can be only be X or Z (since F will not work with Y, and G

will not work wit h W).

Ther efore the t wo possible teams with all th ree gr ad ua te st ud ent s ar e (F, G, H, X) and (F, G, H, Z).

Write th em down on your paper first un der t he h eading ‘possible team s’. (Write the nam es in a group with in

brackets in order to avoid confusion later.)

The only ways in which tw o graduate student s can be grouped to form the stipulated m inimum in t he team

ar e (F, G), (F, H) a nd (G, H).For each one of these cases, we mu st choose two more un dergraduate student s to serve in t he t eam, consistent

with t he given prejudices.

You can easily s ee t ha t the possible combinat ions a re (F, G, X, Z); (F, H, W, Z); (G, H, X, Y); and (G, H, X, Z).

Add th ese four also to your list of ‘possible tea ms’. We th us h ave 6 possible combina tions of tea ms consist ent

with th e given conditions, and can sta rt an swering th e given questions.

Qn. 1. Y occur s only in th e combin at ion (G, H, X, Y.) So, (C) is t he an swer.

Qn. 2. The only combination possible for a team with Z but without F is (G, H, X, Z). So, (B) is the an swer.

Qn. 3. The only tea m wit h G bu t wit hout H is (F, G, X, Z). So, (D) is th e an swer.

Qn. 4. You can easily see tha t I is tr ue.

II is not tr ue, becau se of th e possib le combin at ions (F, G, H, X); (F, G, X, Z) and (G, H, X, Z).

W is available only in t he combina tion (F, H, W, Z). Sta tem ent III is t her efore tr ue.

Since I and III a re alone tr ue, (C) is the a nswer.

Qn. 5. The statement I is not tr ue becau se of the p ossible combina tion (F, G, H, X).

The only combinations in which F is not foun d a re (G, H, X, Y) an d (G, H, X, Z). We do not fin d W in eit he r

of th ese. So, Sta tem ent II is tru e.

In both th ese combinations, we find H as a mem ber. So, III is t ru e. Thu s, (E) is th e an swer.

Exam ple 5

Disease X is cau sed only by contam inat ed food, mosquito bites, or cont act with someone wh o has th e disease,

but none of th ese exposur es necessarily cau ses th e disease.Ther e is a th ree-day interval, from t he tim e of exposur e to disease X to th e first a ppear an ce of the sympt oms,

dur ing which an infected per son is cont agious.

Mike was bitt en by a mosquito on Monda y.

Mike met with Joe on Tuesday.

Joe at e cont am inat ed food on Monday a nd Wednesday

These wer e th eir only possible exposur es t o disease X.

All th ese events occurr ed within one week.

Qn. 1. If Joe developed disease X as a resu lt of eating contam inat ed food, which of th e following sta tem ents

must be true?

I. Joe first exhibited th e sympt oms of disease X on Th ur sday.

II. Mike will get disea se X.III. Joe first exhibited the sym ptoms of disease X on Sa tu rda y.

A. I only

B. II only

C. III only

D. Eith er I or III, but not both.

E. Eith er, I or III, but n ot both .

Qn. 2. If Joe exhibited t he symp toms of disease X on Sa tu rda y, which of the following sta tem ent s mu st be

true?

I. Joe was cont agious wh en h e met Mike.

II. Joe developed disease X as a result of eat ing cont am inat ed food.

III. Mike gave disease X to Joe when t hey met .




11

A. I only

B. II only

C. III only

D. I an d II only

E. II and III only

Qn. 3. If Mike first exhibited th e sympt oms of disease X on Th ur sday, which of the following sta tem ents mu st

be tr ue?

I. Mike may h ave given disea se X to J oe on Tu esday.II. Mike developed disease X as a resu lt of being bitten by a m osquito.

III. If Joe developed disease X, it r esulted from ea ting cont am inat ed food or m eeting with Mike.

A. II only

B. I an d II only

C. I an d III only

D. II a nd I II only

E. I, II and III.

Qn. 4. If Mike first exhibited th e sympt oms of disease X on Fr iday, which of th e following sta tem ents mu st be

true?

I. Joe first exhibited th e sympt oms of disease X on Thu rsda y.

II. Mike got disease X as a resu lt of being bitten by a m osquito.

III . Mike was infected on Tuesd ay.

A. II only

B. III only

C. I an d III only

D. II a nd I II only

E. I, II and III

Analysis

Th is is an in terestin g set of questions, which you sh ould tr y to answ er by yourself before readin g furth er.

Qn. 1. Joe had eaten contam inat ed food on Monda y an d Wednesday. If he had cont acted th e disease on Monda y,

he would develop the symptoms on Thursday (From the answer choices, we have to infer that the incubation

period of thr ee days should include t he da y on wh ich t he disease was cont acted by an y one of th e th ree given

methods.)If, on the other hand, he had escaped the disease on Monday, but had contacted it only on Wednesday, he

would h ave developed sympt oms on Sat ur day.

Therefore, either I or III of the given possibilities can be tr ue. Obvious ly, if I is tru e, III can not be t ru e, an d vice

versa . So, (E) is th e an swer.

II says that Mike will get the disease, which need not be true, because the given narration says that an

exposure does not n ecessarily cause the d isease.

Qn. 2. Since Joe developed t he symp toms only on Sat ur day, he mu st ha ve contacted it on Wednesday. This

mu st h ave been due t o his ta king cont am inat ed food on th at da y.

So, II is tr ue.

I is not tr ue, since Joe and Mike ha d met on Tuesday, a da y earlier th an J oe ha d been exposed to disease X.

If III is t ru e, Joe mu st ha ve developed sympt oms of X on F riday it self, and not on Sa tu rda y. So, III is not true.So, (B) is th e an swer.

Qn. 3. Since Mike was bitt en by a m osquito on Mond ay, he m ay ha ve become contagious on th at day, and m ay

have given it t o Mike when th ey met on Tuesday. So, I is tr ue.

Since Mike developed th e symptoms on Thu rsda y, he must ha ve contacted t he disease on Monda y itself and

not on Tuesday wh en h e met J oe. So, he could have got it only from the m osquito bite on M onday. So, II is tr ue.

It is not given when Joe developed the symptoms. So, he could have got it either from the food he ate on

Monda y or Wednesday, or when he m et Mike on Tu esday when Mike was contagious. So, III is also tr ue.

Ther efore, (E) is the an swer.

Qn. 4. If Mike developed symptoms of the disease on Frida y, he mu st h ave contacted it on Tuesday. So, (III ) is

true.




12

Since Mike ha d met Joe on Tuesda y, he must have got th e disease from J oe, and not from a mosquito bite on

Monda y. So, II is not true.

Joe mus t h ave been contagious on Tuesday t o have passed on the disease t o Mike, an d th at could ha ve only

been due to his ha ving eaten cont am inat ed food on Mond ay. In t his case, he would ha ve developed symptoms of

the disease on Th ursday. So, I is tru e.

So, (C) is th e an swer.

Exam ple 6

Juniors at Lambert University can choose from among seven courses - Biology, Astronomy, English,Mathematics, History, Chemistry and Psychology.

A jun ior cann ot tak e both En glish a nd Astronomy.

Chemist ry is a prer equisite for Biology and can not be t aken concurr ent ly with Biology.

A jun ior m ust ta ke at least t wo of the t hr ee courses, En glish, History an d Psychology.

No course ma y be repeated.

Qn. 1. What is the m aximum nu mber of cour ses a junior can ta ke without violatin g any of th e conditions?

(A) 3

(B) 4

(C) 5

(D) 6

(E) 7

Qn. 2. A student who took Biology during his sophomore year and who chooses Chemistry, Psychology, and

one other cour se as a jun ior could be violat ing which of th e following cond itions?

I. A jun ior can not t ake both En glish a nd Astr onomy.

II. A junior mu st ta ke a t least two of th e th ree cour ses, English, History, and Psychology.

III. No course ma y be repeat ed.

(A) I on ly

(B) II only

(C) I and II

(D) II an d III

(E) Neither I,II nor III

Qn. 3. If a junior is tak ing Astr onomy an d Mat hem at ics an d wishes to ta ke four cour ses, in how may differentways can th e oth er two courses be taken ?

(A) one

(B) two

(C) thr ee

(D) four

(E) five

Analysis

(These questions can be answered straightway with out any need to rewrite the given stipulations in any other

form . Att emp t th e questions by yourself before read ing fu rth er.)

Qn. 1. The only incompa tible pairs of subjects a re (En glish an d Astronomy) and (Chemistr y an d Biology).

One can th erefore t ake En glish, Chemistr y, Mathem at ics, History and Psychology, with out violatin g an y of the given conditions.

The ma ximum nu mber of subjects h e can ta ke is th us 5. So, (C) is th e ans wer.

Qn. 2. (Sophomore year mean s th e pre-junior year, and what a stu dent h ad stu died in a sophomore year is

irrelevant to this set of questions, an d is given only to trip you.) This stu dent ha s alrea dy chosen Chemist ry an d

Psychology, and wishes to choose just one more subject .

Condition 1 th at he cann ot choose both En glish a nd Astronomy can not th erefore be violated by him .

Condition 3 stat es that he should take at least two of the three courses English, History and Psychology. By

deciding to ta ke only one more su bject, he will be violatin g this conditi on.

If h e chooses Bi ology , he would be violat ing cond ition 2.

So, it is possible for th e stu den t t o violat e Cond itions 2 an d 3. So, (D) is th e an swer.




13

Qn. 3. This stu dent h as a lready chosen Astr onomy an d Math ema tics, an d wishes to choose two more subjects.

Remember th at he h as t o take t wo of the t hr ee compulsory subjects, nam ely, English, History and Psychology.

But , since he h as chosen Astr onomy, he cannot t ake En glish. Therefore, he ha s to necessarily choose Hist ory

and Psychology.

Thus th ere is only one way he can choose th e rem ain ing two sub jects. So, (A) is the a ns wer.

Exam ple 7

The E ast -West r oads of New City ar e laid out r egularly, with a dist an ce of one-ha lf mile from one t o the n ext.

Dwyer Road is 1/2 mile nort h of Tru ro Road. Tru ro Road is 1 mile south of Exeter Road. Monroe Road is 1 milesouth of Tru ro Road. Elm Road is 1 mile south of Monr oe Road. Jupit er Road is 1/2 mile north of Elm Road.

Qn. 1. An add itiona l road, Cromwell, could be in a ny of th e following locat ions EXCEP T

(A) 1/2 mile n orth of Exet er

(B) 1/2 mile nort h of Monr ce

(C) 1/2 mile sout h of Elm

(D) 1 m ile south of Dwyer

(E) 1 mile sout h of Tru ro

Qn. 2. Which r oad is far th est from Trur o Road?

(A) Elm

(B) Exet er

(C) Ju piter

(D) Dwyer

(E) Monroe

Qn. 3. What is the dista nce between Dwyer Road an d Monr oe Road?

(A) 1 mile

(B) 1 1/2 mile s

(C) 2 miles

(D) 2 1/2 mile s

(E) 3 miles

Analysis

If the given data is reduced to an intelligible form, we can locate all the roads relative to each othergeographically.

Let us a dopt the convent ion t ha t, when we write th e nam es of an y two roads, th e north ern one will be written

above an d th e souther n one will be writt en below, and t ha t if the t wo roads a re with in 1/2 a mile of each oth er,

th ere can be no oth er r oad in between th em. With th is convention, you can eas ily see tha t t he given st at ement s

can be u sed t o give the following ord er of the r oads:

The first in form at ion ma y therefore be written a s

Dwyer

Truro

When t he second inform at ion is incorpora ted, th is becomes

Exeter

Dwyer

TruroThe t hird inform at ion is t ha t Monroe Road is 1 m ile sout h of Tru ro Road. So, let u s leave one line vacant , and

writ e M below it.

Exeter

Dwyer

Truro

–

Monroe

The four th inform at ion is t ha t E lm road is 1 m ile sout h of Monroe Road. So, let u s again leave one line vacant

an d write Elm below it, gett ing

Exeter

Dwyer

Truro




14

–

Monroe

–

Elm

From th e last condition, we learn tha t J upiter is between Monroe and E lm.

Exeter

Dwyer

Truro

–Monroe

Jupiter

Elm

The a bove is the final configur at ion a ccording t o the given dat a. The data does not pr ovide us inform at ion

regar ding th e nam e of the road lying between Trur o Road a nd Monroe Road.

You ar e now ready t o answer t he given questions.

Qn.1. You can ea sily see tha t it is possible to have a n ew road sa tisfying an y of the four cond itions (A), (B), (C)

an d (D).

But it is not possible to have a n ew road one mile to th e south of Tru ro Road, since we already ha ve Monr oe

Road th ere.

So, (E) is the a ns wer.

Qn. 2. Elm Road is t he far th est from Tru ro Road. So, (A) is th e an swer.

Qn. 3. It is easy t o see from t he above tha t t he dista nce between Dwyer Road an d Monr oe Road is 1 1/2 miles.


Exam ple 8

Sta tem ent 1: There a re five houses th at occupy the ent ire length of a block, and in front of each house is a car

belonging to th e owner of th e house. The five owners a re Clar k, Jones, Smith, Thomas, and Williams, and th e

colours of the car s ar e blue, green , mar oon, red a nd yellow.

Sta tem ent 2: The person wh o owns t he fifth house owns th e yellow car.

Sta tem ent 3: The house J ones owns h as h ouses on both sides of it.

Stat ement 4: Clark owns th e ma roon car.

Sta tem ent 5: The person who owns t o the second h ouse owns t he r ed car.Sta tem ent 6: William s owns t he middle house.

Sta tem ent 7: Smit h does not own th e yellow car.

Sta tem ent 8: The person who owns th e first h ouse owns th e green car.

Qn. 1. Which of th e following sta temen ts can be derived from st at ement s (1), (3), and (6)?

(A) Jones owns th e first or second house.

(B) Jones owns th e first or fourt h h ouse.

(C) Jones owns t he first or fifth h ouse.

(D) J ones owns t he second or four th house.

(E) Jones owns th e second or fifth h ouse.

Qn. 2. What is the colour of th e car th at Jones owns?(A) Red

(B) Yellow

(C) Green

(D) Blue

(E) Mar oon

Qn. 3. Which h ouse and car belong t o Thomas?

(A) The first h ouse a nd t he green car.

(B) The second h ouse a nd th e blue car.

(C) The second house an d t he r ed car.

(D) The four th house an d th e blue car.

(E) The fifth house a nd th e yellow car.




15

Qn. 4. Which of th e following st at emen ts can be derived from st at emen ts (1), (5), (6) an d (8)?

I. The yellow car is in front of either th e th ird, or t he four th or th e fifth h ouse.

II. Williams owns eit her th e blue, or th e yellow, or t he m ar oon car.

(A) I on ly

(B) II only

(C) Either I or II, but n ot both

(D) Both I an d II

(E) Neith er I nor II

Analysis

We should tr y to match t he nu mbers of the houses, th e nam es of the owners an d th e colours of th e car. Let us

th erefore form a t able as follows, an d tr y to fill it u p usin g the given dat a. (You can use t he init ial letter s of th e

na mes an d the colour s to save time)

House No. Nam e of owner Colour of car

Sta tem ent (2) means t ha t we can put down Y as t he colour of th e car against House No. 5

Sta tem ent s (3) an d (4) do not immediat ely help us to make an y entries in th e table. Let us ignore them for th e

present.

Fr om Stat ement (5), we can put R as th e colour of th e car in th e second house.

Fr om Stat ement (6), we can wr ite down W as the na me of th e owner of th e thir d house.

Sta tem ent (7) is not of an y help now, and we can pass it over.

Sta tem ent (8) ena bles us to put down G as t he colour of th e car in th e first h ouse.

We now ha ve th e following t able:

1. G

2. R

3. W

4.

5. Y

The rem ainin g colours ar e M an d B. Now, sta tem ent (4) says th at C owns the car M.

W must th erefore own car B.

This ena bles us to put B in No. 3 an d M in No. 4.

The owner of house No. 4 can a lso be put down as C.

We now get th e ta ble:

1. G

2. R3. W B

4. C M

5. Y

It is men tioned in (3) that J ’s house ha s houses on both sides of it. Since the only houses ha ving houses on

both sides are 2, 3 and 4, and the occupants of 3 and 4 have already been identified as W and C, J must be

occupying house No. 2. Pu t down his na me accord ingly.

Sta tem ent (7) says th at S does not own car Y. Therefore S cann ot be th e occupant of th e fifth house. He mu st

th erefore be t he occupant of th e first house.

This leaves only T who mu st be t he occupant of th e fifth h ouse.

Our ta ble is now complete a nd looks as follows:

House No. Nam e of owner Colour of car

1. S G2. J R

3. W B

4. C M

5. T Y

Qn. 1. (Note that this qu estion has to be answ ered from the partial in form ation available in S tatements (1), (3)

an d (6) only, and not from th e above table.) The only houses which ha ve houses on both sides ar e th e second, th ird

an d the four th . Since sta tem ent (6) says th at Williams owns th e middle house, J ones can own either t he second

or th e fourt h hous e. This is wha t follows from (3). So, (D) is th e ans wer.

Qn. 2. Fr om th e above table, we can sa y th at J ones’ car is r ed in colour. So, (A) is th e an swer.




16

Qn. 3. The a nswer is (E) from t he a bove table.

Qn. 4. (This qu estion ha s to be answered from the partial in form ation available in S tatements (1), (5), (6) and

(8), and not from th e above table.) Fr om st at ement s (5) an d (8), we know that car R is in t he second h ouse and car

G is in th e first h ouse. Car Y mu st th erefore be in the t hird, fourth or the fifth house.

We also know from (6) th at W lives in th e th ird house. He cann ot th erefore own either car R or car G. He mu st

own car B, or car Y or car M.

Thu s, we can der ive both I a nd II from st at ement s (5), (6) and (8). So, (D) is t he a nswer.

Exam ple 9

In a certa in Society, th ere ar e thr ee mar riage groups J, R and G.

A ma n a nd a woman ma y mar ry only if th ey belong to the sam e group.

The sons of Group-J pa ren ts belong to Group R; th e dau ghter s belong t o Group G.

The sons of Group R par ent s belong to Group G; the da ught ers belong to group J.

The sons of Group-G paren ts belong to group J ; the da ught ers belong t o Group-R.

Qn.1. Which of th e following kin ds of gra nd children is it possible for a coup le belongin g to group J to ha ve?

(A) Group J only

(B) Group J an d R only

(C) Groups J an d G only

(D) Groups R a nd G only

(E) Groups J, R and G.

Qn. 2. Under t he ru les given, may a ma n m arr y his niece?

(A) No

(B) Yes, if sh e is h is br other ’s da ugh ter.

(C) Yes, if she is h is sist er’s da ugh ter.

(D) Yes, if sh e is h is wife’s br oth er ’s da ugh ter.

(E) Yes, if sh e is h is wife’s sist er ’s da ugh ter.

Qn. 3. Which of th e following kinds of au nt ma y a ma n m ar ry?

I. His moth er’s sist er.

II. His fath er’s sister.

III . The widow of his fat her ’s brot her.(A) I on ly

(B) II only

(C) III only

(D) I an d II only

(E) I, II and I II

Qn. 4. Which of th e following sta temen ts can be inferr ed from t he given ru les?

I. A brother a nd sister m ay not ma rr y.

II. A woman may n ot m arr y her father.

III. A man may not mar ry his granddau ghter.

(A) I on ly

(B) II only(C) III only

(D) I and III only

(E) I, II and I II.

Analysis

For th e sak e of clarit y, reduce the given da ta as a ta ble as given below:

Pa ren ts Sons Daughters

J R G

R G J

G J R

Qn. 1. Group J parent s can ha ve Group R sons, or Gr oup G da ughters.

Group R sons will mar ry other Gr oup R girls. They can have eith er Group G sons, or Gr oup J dau ghter s.




17

Similarly, the Group G daughters will marry other Group G men, and can produce either Group J sons or

Group R dau ghters.

Thu s, th e gran dchildren of th e original Group J couple can belong to any one of G, J, or R.

So, (E) is the a ns wer.

Qn. 2: Let us ta ke th e example of a m an belonging to R Group. His broth er will also belong to R group, an d his

brother ’s dau ghter will belong to J gr oup. He cannot th erefore m ar ry h is brother ’s dau ghter. So, (B) is incorr ect.

A Group R ma n’s sister will belong to G group an d her dau ghter will belong to R group. He can therefore

ma rr y her. So, (C) is the an swer.This mea ns t ha t (A) is wrong.

(A Group R m an ’s wife will also belong to Group R, an d her broth er will belong t o Group J . He will mar ry

an other Gr oup J woma n, and th eir dau ghter will belong to Group G. So, a Gr oup R man can not ma rr y her. So, (D)

is wrong.

A Group R m an ’s wife an d sister will both belong to Group R. So, the latt er will mar ry an other Gr oup R man ,

an d th eir dau ghter will belong to Group J. So, the Group R m an cannot m ar ry h er. So, (E) is wrong.)

Qn. 3: Let us again ta ke the example of an R man . His mother would be a J and h er sister would also be a J.

He cannot th erefore m ar ry h is mother ’s sister. So, I is not possible

His father would be a J a nd h is fat her ’s sister would be a R. He can th erefore ma rr y his fat her ’s sister. So, II

is possible.

His fat her ’s broth er would be a J, an d his widow would also be a J. So, R cannot ma rr y her. So, III is n ot

possible.


Qn. 4: It can be seen from t he above table tha t a brother an d sister always belong to different groups, an d

th erefore cann ot ma rr y. So, I is tru e.

It can also be seen th at a dau ghter a nd her fat her a lways belong to different groups. Thu s, II is also tr ue.

Now, if we take a R ma n, his son will belong to G, and h is gran ddau ghter will belong t o R. So, he can ma rr y his

gran ddau ghter. So, III is not true.

So, (D) is th e an swer

Example 10

Lau ra ha s agr eed to feed a friend’s dog for a full week, ru nn ing from Mond ay to Sun day. A tota l of seven

bra nd s of dog food is a vailable, of which exactly five – M, N, O, P, an d Q – a re p rotein -enriched, an d exactly t wo,R and S, ar e vitam in-enriched. Lau ra m ust a dher e to th e following feeding inst ru ctions:

On ea ch of th e seven days, a different bra nd of dog food m ust be fed.

Pr otein-enr iched d og food cann ot be fed for more t ha n two consecutive days.

R must be fed earlier in the week tha n S.

M must be fed earlier in the week th an R.

N mu st be fed earlier in th e week than Q, an d exactly four of th e oth er bra nds m ust be fed between N an d

Q.

Qn. 1: Which of the following bra nds mu st be schedu led to be fed on Wednesday

(A) M

(B) O

(C) P(D) R

(E) S

Qn. 2: If Q is sched uled t o be fed on Su nd ay, which of the following could also be tr ue?

(A) R an d O ar e schedu led to be fed on consecut ive days

(B) N is schedu led to be fed ear lier t ha n M

(C) Two days intervene bet ween th e day O is fed an d th e day P is fed

(D) P is schedu led to be fed on Tuesda y

(E) S is schedu led to be fed on Thur sday




18

Qn. 3: Which of th e following pa irs of bran ds could be s ched uled t o be fed on cons ecutive da ys?

(A) M an d O

(B) N and P

(C) O an d S

(D) Q an d R

(E) R an d S

Analysis

Let us first write down th e following table to show the weekdays an d tr y to fill it consisten t with th e giveninstructions.

Mon Tue Wed Thu Fri Sa t Sun

R and S a re th e only two vitam in enr iched foods, an d it is stipula ted t ha t R mu st come before S.

If you pu t down R un der Monday, th en S h as t o be necessar ily put down u nder Th ur sday to satisfy the second

condition.


R S

This will mean that protein-enriched food will have to be given on the next three consecutive days which

violat es condition 2. Ther efore, R cannot be fed on Monday.

If R is put down u nder Tu esday, S has t o be put down un der F riday. Condition 2 is now tak en care of.

Mon Tue Wed Thu Fri Sa t SunR S

In ord er t o satisfy condition 4, M must be fed on Monda y.


M R S

Ther efore the ear liest tha t N can be fed is Wednesday, and th e latest th at Q can be fed is Sunda y.


M R N S Q

This will leave only thr ee clear days between N a nd Q, which violates th e last condit ion. Th erefore, R cannot

be given on T uesda y either .

If R is fed on Wednes day, S has to be fed on S at ur da y.


R S

Ther efore N cann ot be fed on Monday, but h as to be fed on Tuesday. This will mean th at M is fed on Monda y,an d Q is fed on S un day.


M N R S Q

Ther efore, th e possibilities a re (sta rt ing from Monday) ( M, N, R, O, P, S, Q) or

(M, N, R, P, O, S, Q).

The th ree quest ions can be easily answer ed now.

Qn. 1: It can be easily see tha t R is to be fed on Wedn esda y. So, th e an swer is (D).

Qn. 2: (Notice tha t t he phr ase used is ‘could be tr ue’ an d not ‘should be tr ue’.)

A is the only possibility among the given choices, and is the answer.

Qn. 3: (Here a lso, note th at the phra se is ‘could be scheduled’ an d n ot ‘should be schedu led’) (C) is t he only

possibility a mong t he given choices, and is th e an swer.

(Note what we did in th is case. Between th e two groups protein-enriched an d vit am in-enriched, we took th e one

wit h th e sm aller nu m ber, and tested serially wh ether one of th em could be fed on M onda y, Tu esday, Wednesda y etc.

Th e first tw o were elim ina ted becau se of the other condit ions, an d w e could z ero in on th e th ird a s a possibility.

S ince we have not tested the possibility of vitam in-enriched foods being fed on T hu rsday, Friday and S aturd ay,

the answ ers to th e last two questions are m ere possibilities, and need not be m and atory. That is wh y th e questions

us e the ph rase ‘could be’, and not ‘m ust be’.)

(We shall n ow give you a set of m ore difficult questions of the types th at h ave been asked in LS AT )




19

Example 11

A swimm ing inst ru ctor is plann ing th e orga nizat ion of her cour se. The cour se will include only str okes selected

from st rokes F, G, H, I, J, K an d L. The str okes must be ta ught in a sequence subject to th e following rest rictions.

F m ust be ta ught before H can be tau ght

Both G a nd H m ust be tau ght before K can be ta ught

Both H and I m ust be tau ght before L can be ta ught

Qn. 1: Which of the following is an accepta ble order of str okes t o be tau ght?

(A) F, H, K, L, I, G, J(B) F, I, H , L, G, J, K

(C) G, K, H, I, L , J, F

(D) I, H , L, F, G, K, J

(E) L , G, K, F, H, J , I

Qn. 2: If only th ree str okes are t au ght in th e cour se, which of the following CANNOT be ta ught ?

(A) G

(B) H

(C) I

(D) J

(E) K

Qn. 3: If only four str okes are t au ght in th e cour se, which of the following must be tr ue?

(A) F is ta ught

(B) H is tau ght

(C) If G is tau ght, th en K is tau ght

(D) If I is tau ght, then J is taught

(E) If G and I ar e taught , then H is tau ght

Qn. 4: If only four st rokes ar e ta ught in t he cour se, which of the following must be tr ue?

(A) If F is ta ught , it is tau ght first

(B) If G is tau ght, it is t au ght before H

(C) If H is ta ught , it is tau ght second

(D) If J is tau ght, it is tau ght before I

(E) If K is ta ught, it is ta ught last

Qn. 5: If J an d I a re t he first t wo strokes ta ught in a five-str oke course, which of the following is a possible

order for t he rema ining three str okes?

(A) F, H, K

(B) F, H, L

(C) G, H, K

(D) G, H, L

(E) H, K, F

Qn. 6: If strokes K and L are ta ught in t he course, what is the least n umber of strokes that can be ta ught?

(A) 3

(B) 4(C) 5

(D) 6

(E) 7

Qn. 7; If only five strokes ar e ta ught in t he cour se, which of the following mu st be t au ght?

(A) G

(B) H

(C) I

(D) J

(E) K




20

Analysis

Rule 2, when r ead with Ru le 1, mean s th at K can be tau ght only after (F, G, H) ha ve been ta ught . The relat ive

orders in which (F, G) or (G, H) can be ta ught is not st ipulat ed.

Similarly, Rule 3, when r ead with Rule 1, mean s th at L can be tau ght only after (F, H, I) have been t au ght.

Again, the r elative order s in which (F, I) or (H, I) can be tau ght ar e not st ipulat ed.

There is also no stipulation about J.

Let us n ow answer t he questions.

Qn. 1: (A) violat es Rule 2 a nd Ru le 3, an d is n ot an accepta ble order.(B) satisfies all the t hr ee rules, an d is an a ccepta ble order. In t he exam inat ion, you can st op here an d ma rk (B)

as th e answer.

(You can easily see th at t he rem ain ing th ee choices violate one or m ore of the th ree given cond itions.)

Qn. 2: We have already seen tha t K can be tau ght only after F, G and H have been t au ght. Therefore, if only

three strokes are tau ght, K cannot be one of them . So, th e an swer is (E).

Qn. 3: Fr om the given conditions, we can see tha t t her e are at least three str okes H, K, L which can be ta ught

only after F h as been t aught . Therefore, the lat est position a t wh ich F can be tau ght is 4. So, F must always be

within th e first four strokes tha t a re ta ught. Thus, (A) must be t ru e, and is the an swer.

Qn. 4: The an swer to th is question easily follows from our a nswer t o Qn. 2. Since at least t hr ee strokes ha veto be tau ght before K, K has to be th e last to be tau ght in an y combination of four in which it occur s. So, (E) is th e

answer.

Qn. 5: (A) is not possible since K cannot be taught without G having been taught earlier as per the second

condition.

(B) is possible since it sat isfies the first an d t he t hird conditions, and t he second condition is n ot relevant .

So, (B) is th e an swer. You can st op here, an d go over t o the n ext qu estion.

(The rem aining th ree choices violate th e first condition.)

Qn. 6: We have seen t ha t (F, G, H) must ha ve been t au ght before K, and (F, H, I) must have been t au ght before

L. Therefore, if (K, L) ar e ta ught , then (F, G, H, I) mu st a lso have been ta ught . Thu s at least 6 strokes must have

been ta ught in t his cour se. Therefore, th e an swer is (D).

Qn. 7: There a re at least t wo str okes (K, L) which can be tau ght only after H h as been ta ught. Therefore H

cann ot be either t he sixth or the seventh stroke to be taught. It h as t o be necessarily with in th e first five. So, (B)

is the answer.

Example 12

Five ad ult acrobat s – M, N, O, P, an d Q – a nd five child acrobat s – V, W, X, Y, and Z – form a h um an pyra mid

with four levels, as follows:

There a re four of th e acrobats on th e lowest or first level; thr ee on t he n ext higher or second level; two on t he

level above tha t, th e thir d; and one on t he highest or four th level.

Except for t he a crobats on th e first level, who stan d on th e floor, each acrobat st an ds on th e shoulders of two

adjacent a crobat s on th e next lower level.

Whenever an y acrobat falls, th e acrobat s who are st an ding on eith er of th at acrobat’s shoulders mu st a lso fall.Child acrobat s cannot be in th e first level of the pyra mid, nor can th ey occupy an y position tha t r equires th e

use of more th an one shoulder t o support oth er acrobats.

Analysis

Qn. 1. If X sta nds on V’s shoulder, an d M a nd W sta nd side by side on t he sa me level as one an other, which

of the following is a possible arrangement for the second level?

(A) V, M, W

(B) V, W, M

(C) X, M, W

(D) Y, N, Z

(E) Y, O, V




21

Qn. 2. If Q and W ar e sta ndin g on N ’s shou lders a nd M falls, which of th e following set s of acrobat s could be

left st an ding after a ll the a crobat s who must fall as a r esult of M’s fall have fallen?

(A) N, O, P, Q, V, and W

(B) N, O, P, V, X, an d Y

(C) N, P, V, W, X, and Y

(D) O, P, Q, V, X, an d Y

(E) O, P, Q, W, X, and Y

Qn. 3. If V an d W sta nd on differen t levels, an d X and Z stan d on t he sa me level, which of th e following is acomplete an d a ccur at e list of the levels on which Y could possibly stan d?

(A) Second

(B) Thir d

(C) Fourth

(D) Second , th ird

(E) Third, fourt h

Qn. 4. If V and W stan d on O’s shoulders, and M sta nds on th e same level as N an d P a nd is th e only acrobat

between t hem, which of the following must be tr ue?

(A) If M falls, all five of th e child acrobat s m us t fall

(B) If N falls, exactly four of th e child acrobat s mu st fall

(C) If O falls, exactly two of the child a crobat s mu st fa ll(D) If P falls, exactly th ree of th e child a crobats m us t fall

(E) If Q falls, exactly th ree of th e child a crobats m us t fall

Qn. 5. If W sta nd s on V’s sh oulder, an d V stan ds on M’s sh oulder, which of the following CANNOT be t ru e?

(A) N and V sta nd side by side on t he sa me level

(B) W and X sta nd side by side on t he sa me level

(C) X an d Y stand side by side on th e sam e level

(D) M stan ds on t he same level as N a nd P and is t he only acrobat between th em

(E) M stan ds on th e same level as Y an d Z and is th e only acrobat between th em

Qn. 6. If W sta nds on th e shoulders of N an d P, an d X stan ds on t he sh oulders of M an d V, which of the

following mu st be t ru e?

(A) M sta nds on th e same level as V an d W and is th e only acrobat between th em(B) N sta nds on th e same level as P a nd Q a nd is th e only acrobat between t hem

(C) O stan ds on t he sam e level as P an d Q and is only acrobat bet ween them

(D) P stan ds on the sa me level as M an d V an d is the only acrobat bet ween th em

(E) Q stands on t he same level as N a nd O an d is the only acrobat between t hem

Qn. 7. If N an d Y stand on M’s shoulders, and Z stan ds on t he sh oulders of P a nd O, which of the following

mu st be sta nding side by side on th e same level as one anoth er?

(A) M an d O

(B) M an d P

(C) N and Z

(D) P and Q

(E) W an d X Analysis

You should un derst an d th at t he levels are num bered in sequence not from top to bottom but from bottom to

top . The bottom level is th e first level, an d will consist of four per sons. The second, th ird a nd fourt h levels will

cons ist of 3, 2, and 1 p ers ons. The p yra mid will look a s follows:

C

C C

C A C

A A A A

(C: Ch ild A: Adult )

You can easily see that it is only in t he case of th ose standin g in th e 2nd and 3rd position in the bottom row,

and th e one standing in t he m idd le position in t he second row, tha t both sh oulders will be occup ied. Ther efore, as

per t he last condition, th e five adult a crobats m ust be occupying th e four positions in th e bott om r ow an d th e




22

middle position in t he second row. The child acrobat s mu st be occupying the t wo extrem e positions in t he second

row, both th e positions in th e th ird r ow an d also the t op position.

Before a nswer ing each qu est ion, wr it e “M, N, O, P, Q”, an d “V, W, X, Y, Z” in two differen t rows one be low th e

other to rem ind you th at th ey belong t o the a dult s’ an d t he children’s group r espectively.)

Qn. 1: The only row in which there can be an adult and a child acrobat together is the second row from the

bottom, and M mu st t her efore be occupying th e middle position in t his. The only possible answer s for t his quest ion

ar e th erefore (A) an d (C).

But (C) is not possible becaus e, in t his case, V sh ould be in t he bott om row, which is n ot possible.So, (A) is th e a ns wer.

Qn. 2. In t his case also, Q an d W must be in th e second row with Q in th e middle.

M, who falls, mu st t her efore be in t he bott om row. If M ha d occupied one of th e extrem e positions, the acrobat

sta nding on his sh oulder will be a child.

When t his child falls, a child in t he t hird row will also fall, and t her efore th e child in th e top row will also fall.

Thus, th ree child acrobats will fall in t his case.

If M ha d occupied one of the t wo middle positions in t he bott om row, Q and an other child acrobat will be

sta ndin g on his shoulders.

When h e falls, both th ese will also fall, an d bring down with t hem both th e children on the t hird row as well

as th e child at th e top. In th is case, four children will fall.

In eith er case, th e num ber of children left stan din g can not exceed 2.(A) is th us t he only possibility, and is the answer.

Qn. 3. It h as been given tha t X and Z stan d on the sa me level. If both th ese are st an ding in th e second row,

th en Y can occupy only th e th ird r ow and can not be on top, since, in t his case, eith er V or W will be occupying t he

top position.

If X and Z are occupying the two positions in the third row, Y will have to occupy one of the two extreme

positions in t he second r ow, leavin g th e top position t o eith er V or W.

Thu s, Y can not a t a ll occupy t he t op position, an d can be only in t he second or th e th ird levels.

So, (D) is th e an swer.

Qn. 4. In t his case, V and W mu st be occupying t he t wo positions in th e th ird r ow, and O m ust be occupying th e

midd le position in t he second row. th e following will be th e form at ion in t his case:

–V W

– O –

N M P Q

In (A), if M falls, th e child at t he r ight extr eme of th e second r ow will still sta nd . So, (A) is not t ru e.

In (B), when N falls, one child in th e second r ow, one child in t he t hir d r ow, and t he child a t t he t op will fall. So,

(B) is not tr ue.

In (C), if O falls, all th e th ree childr en a bove him will fall. So, (C) is not tr ue.

In (D), when P falls, O, as well as four out of the five children (except t he one a t th e extrem e left in t he second

row) will fall. So, (D) is n ot t ru e.

When Q falls, th e child right of O, W and an d t he child at th e top will fall.

So, (E) must be tru e, an d is the a nswer.

Qn. 5. The th ree possibilities ar e shown here.

W – –

V – W – W –

– M – V – – V – –

– – – – M – – – – M – –

It is possible for N t o occup y th e midd le position in t he second r ow in (2) an d (3) above, sat isfying (A).

It is possible for X to occupy th e other position in t he t hir d r ow in (1), (2), (3) above, sat isfying (B).

Since the m iddle position in th e second row has to be occupied by an adu lt, an d one of th e positions in t he

th ird r ow is alr ead y occup ied in all th e possibilities, (C) is not possible, and is t he a nswer.

You can easily see t ha t (D) is possible in (3) above, and (E ) is possible in (1) above.




23

Qn. 6: The following will be th e possible ar ra ngemen ts to sat isfy th e given conditions.

– –

– X – X

W M V W M V

N P – – P N – –

You can easily see that (A) has to be necessarily tru e, an d can h appily stop here. (Satisfy your self why th e

other choices need n ot be t ru e.)

Qn. 7: The following will be th e possible arr an gement s in t his case.V W

W X V X

Z N Y Z N Y

P O M Q O P M Q

You can easily see that (C) is wha t is m an dat ory, and is th e an swer.

Example 13

Seven persons – N, Q, R, S, T, U, and W – are all the persons present at a party. All of them join distinct

conversat iona l groups th at form dur ing the pa rt y and t ha t consist of two, th ree, or four persons at a time. At a ny

tim e dur ing th e par ty, each of th e persons pr esent is considered t o be a mem ber of exactly one of th e conversat iona l

groups. Dur ing th e par ty t he following conditions a re sa tisfied.

N can never be in th e same coversat iona l group a s S.

T mu st be in a conversat iona l group t ha t includes either S or W, but T can not be in a conversa tional group

with both S a nd W.

W must be in a conversa tional group th at consists of exactly th ree persons.

Qn. 1: Which of the following lists three conversational groups that can exist at the same time during the

party?

(A) N and S Q, T, and W R and U

(B) N and T R and S Q, U, and W

(C) N and U R and S Q, T, and W

(D) N and W S and U Q, R, and T

(E ) N, U, and W S and Q R and T

Qn. 2: If, at a cert ain point dur ing th e par ty, R, T, and W ar e mem bers of th ree distin ct conversational groups,S mu st at tha t point be in a conversational group tha t includes

(A) Q

(B) R

(C) T

(D) U

(E) W

Qn. 3: If, at a cert ain p oint dur ing th e par ty, a group of thr ee persons an d a group of four persons h ave form ed

an d W is in t he sa me conversa tional group as U, which of the following must at th e point be in th e group with W

and U?

(A) N

(B) Q(C) R

(D) S

(E) T

Qn. 4: If, at a cert ain p oint du rin g th e par ty, one of th e conversa tiona l groups consist s only of Q, R, an d W, at

th at point N m ust be part of a group of exactly

(A) two persons, whose other mem ber is T

(B) two persons, whose oth er m ember is U

(C) four per sons, whose oth er m embers include S

(D) four per sons, whose oth er m embers include T

(E) four per sons, whose oth er m embers include U




24

Analysis

The given nar ra tive implies tha t t he seven persons can divide into groups either as (2,2,3) or (3,4).

The first condition is th at N an d S cann ot be in t he sa me group. Write (N x S) on your paper to indicat e this.

Write the second condition as (T, S) and (T, W) and (T x (S, W)), meaning that T must always be present if

either S or W is present , but T m ust not be present if S an d W are both pr esent r espectively.

Writ e th e th ird condition a s (W, –, –,)}

Qn. 1: (A) violat es th e firs t condition.

(B) violat es th e second condit ion t ha t T m ust always be with eith er S or W.(C) does not violat e any of th e given cond itions, an d is th e ans wer. You can st op here and go over to the next

question.

(D) violates the last condition, and (E) violates the second condition.

Qn. 2: It is given t hat R, T and W a re m embers of three distinct groups. So, the gr oups mu st consist of 2, 2 a nd

3 per sons r espectively.

Write t he n am es of th ose left out as N, Q, S, U on your pa per, an d score out each of th em a s soon a s you a ssign

him t o an y group.

Because of the t hir d condit ion, (W, –, –) mus t be one gr oup.

Because W, R an d T are given t o be in dist inct gr oups, the oth er t wo groups m us t be (R, –) and (T, –).

Now write down on your paper th e thr ee possible groups a s

(W, –, –) (R, –) (T, –)

To fulfil th e second cond ition, writ e t he t hir d gr oup a bove as (T, S), an d score off S from t he list N, Q, S, U.

You can now wr ite (W, N, Q); (R, U) with out violat ing a ny of the cond itions.

So, (C) is th e an swer.

Qn. 3: The last condition is th at W mu st be in a group t ha t cont ains exactly 3 persons. This question says th at

W and U are t ogether.

So, writ e th e first t eam in t his case is (W, U, –)

Now, th e first condit ion implies th at N an d S can not both be in the sa me tea m. So, th e thir d mem ber in th e

first team must be either S or N.

If the third member in this team is S, it implies that T will be in the second team. This will contradict the

second condition t ha t T mu st a lways be with eith er W or S. So, th e th ird mem ber of th e first team cannot be S, but

mu st be N.

So, (A) is th e a ns wer.

Qn. 4: This qu estion says t ha t (Q, R, W) are in one tea m. Those who are left out ar e N, S, T, U. Write t hese

na mes on your paper for r eady reference.

The first condition says th at N an d S can not be togeth er in th e same t eam. So, th e division in t his case can not

be as 3 persons + 4 persons, but mu st be 3 persons + 2 persons + 2 persons.

Therefore, in order to fulfil the first an d th e second conditions, the r ema ining two team s mu st be (N, U) and (S,

T).


Example 14

The consu mer complain t d epar tm ent of a firm employs exactly six people who answer letter s: G, H, I, J, K and

L, Every complaint let ter received by the depa rt men t is classified as eith er r ed or blue. The following procedur esfor a nswering the letters a re used:

Red letters a re given first t o G or H.

Blue let ter s ar e given first to an y one of the following: G, J, or I.

If a letter r aises a pr oblem t ha t cann ot be resolved by the per son to whom it is given, it mu st be forwar ded

until it reaches someone who can resolve the problem and answer the letter. A letter must be forwarded as

follows:

By G to I if th e letter is red, but to J if the lett er is blue;

By H to eith er G or I;

By I to J if th e letter is red, but to K if the letter is blue;

By J t o either I or K wheth er th e letter is red or blue;

By K to L whether t he letter is red or blue;

L answer s every lett er given t o him.




25

Qn. 1: Any of the following can be tr ue E XCEP T:

(A) G forwards a red lett er t o I.

(B) H forwar ds a r ed letter to G.

(C) H forwards a red lett er t o I.

(D) I forwards a red lett er t o K.

(E) J forwards a red letter t o I.

Qn. 2: A blue lett er could rea ch L via which of the following sequen ces of people?

(A) G to H t o K(B) G to I to J

(C) G to J to K

(D) I t o H t o J

(E) I to G to J t o K

Qn. 3: Any letter th at reaches L mu st ha ve been previously given to

(A) G

(B) H

(C) I

(D) J

(E) K

Qn. 4:Which of the following could be given to each of th e six member s of th e consum er comp laint depa rt men t

in turn?

(A) A red letter th at is first given t o H

(B) A red letter th at is first given to G

(C) A blue lett er t ha t is first given t o G

(D) A blue lett er t ha t is first given t o I

(E) A blue letter th at is first given t o J

Qn. 5. Any letter that reaches L must have been handled by a minimum of how many members of the

consumer complaint depa rt ment before reaching L?

(A) 1

(B) 2

(C) 3(D) 4

(E) 5

Qn. 6 . If a m ember of the consum er complaint depar tmen t is given a letter tha t h e or sh e had previously

given t o some oth er m ember of th e depart ment , the per son who is given t he letter a second t ime could be

(A) G

(B) H

(C) J

(D) K

(E) L

Analysis(Quest ions like t his which involve the m ovement of some items a re m ost easily answered by first dr awing a

diagra m incorpora ting t he given conditions)

The initia l nar ra tion ta lks of two different t ypes of complaint letter s - red an d blue, an d pr escribe different

routes for t hem. So, draw two independent diagra ms for r ed an d blue letter s as follows. The ar row mar k sh ows

the direction in which the letter is forwarded. Put a circle around the name of the persons who can receive a

comp lain t in itia lly. )

Qn. 1: Since th is questions involves th e movement of th e red letter, we should r efer t o the first diagra m. You

G H

I

JK

L

G J

LK

I




26

can ea sily see (A), (B), (C) and (E) ar e tr ue, while (D) is not t ru e. So, (D) is th e an swer.

Qn. 2: We should refer t o the second d iagram for a nswerin g th is question. You can easily see that , among th e

choices, th e blue lett er can ta ke t he r oute G t o J t o K to L. So, (C) is the a nswer.

Qn. 3: We can see t ha t, in both dia gram s, L gets t he lett er from only K. So, (E) is th e an swer.

Qn. 4: You can easily see from the first diagram tha t it is a red letter t hat is given to H t hat can go in tur n t o

G, I, J, K an d L. So, (A) is th e a nswer.

Qn. 5:We can see from th e second diagram th at a lett er given t o J or I reaches L with only K in between. In all

th e oth er cases ther e is more th an one person between t he recipient of th e complaint a nd L. So, th e minimum

nu mber of persons wh o han dle a complain t before it r eaches L is 2. So, (B) is t he a nswer.

Qn. 6: The only two-way route for th e complain t is bet ween I a nd J . So, it is only I a nd J who can receive a

letter a second t ime. Of these t wo, J is m ent ioned in (C), which is th e an swer.

MEANINGS OF EXPRES SIONS USED IN ANALYTICAL REASON ING QUESTIONS

You should clearly u nderst an d t he m eanin gs of some of the expressions used often in t he Analytical Reasoning

questions:

1. The expression ‘Monday through Fr iday’ mea ns t he a ll th e five days Monda y, Tuesd ay, Wednesd ay, Thu rsd ay

an d Fr iday, including M onday and Friday.

Simila rly, th e nu mber s ‘1 through 8’ mea ns all the 8 numbers including 1 and 8.

2. ‘D occurs before C’ implies th at D can and should occur a nywh ere before C.

‘D occur s im m ediately before C’ implies t ha t (D, C) mu st occur next to each other in th at ord er.

Simila rly ‘D occurs after C’ implies t ha t D can and should occur an ywhere after C.

‘D occur s im m ediately after C’ implies tha t (C, D) mu st occur n ext to each other in th at order.

3. ‘C a nd D occur next to each other ’ mean s th at th e order in which th ey occur can be either (C, D) or (D, C).

4. ‘Whenever C occurs D also occurs’ does not necessa rily imply t he converse ‘When ever D occurs C a lsooccurs’. If th e latt er is t he int ention, the qu estion will state ‘C an d D alw ays occur togeth er ’.

5. ‘Which of th e followin g could be an a rra ngement?’ means th at t he given arra ngement is a possibility (and is

one of th e many possible ar ra ngemen ts), an d is not man datory.

On t he oth er h an d, ‘Which of th e following must be the arr angement?’ means th at th e arran gement is

mandatory, an d no other arr angement is possible.

The following ar e some inferences you can immediat ely draw from t he st at ed condit ions:

1. Th e condit ion ‘X always occur s after Y’ implies t ha t X can never occupy th e first position.

Th e cond ition ‘X alwa ys occur s after Y an d Z’ implies t ha t X can never occupy th e first or th e second position.

2. Simila rly, the condit ion ‘X alwa ys occur s before Y’ implies t ha t X can never occupy th e last position.

Th e condition ‘X alwa ys occurs before Y an d Z’ implies t ha t X can never occup y the last or th e penultimate

position.

RULES YOU SH OULD FOLLOW

1. While reading th e conditions, do not int roduce unwar ra nt ed assu mpt ions. For exam ple, in a set relat ing to

th e relationships of height a nd weight a mong th e member s of a group, do not assu me th at X is taller t ha n Y, X

mu st a lso weigh m ore t ha n Y.

2. The conditions are stated in as clear manner as possible; you should not interpret them as if they are

designed to trip you. For example, if a question asks how many person could be eligible for being selected as



Documents

Lsat Ar Preview