TCS Aptitude Questions With Answers (Www.programminggeek.in)

1) 5 coffee and 4 tea costs rs.96,5 milk and 6 coffee costs rs. 32 and

7 tea and 6 milk costs rs.37. What is the combined price of 1 tea,1

coffee and 1 milk?

Soln:

5C+4T=96 and 5M+6C=32 and 7T+6M=37

add all 3 equations then 11M+11T+11C=165

so M+T+C=15

2) Jack buys 18 sharpeners (white and brown) for rs. 100.If he pays 1

rupee more for each white than brown sharpeners.how many of white and

how many brown sharpeners did he buy?

Soln:

Lets think x brown ones are there so the no of whites are 18-x.

now each brown coast y and each white then coast y+1.

so xy+(18-x)*(y+1)=100

18y-x=82

so one can easily say that y=5 and x=8

we cant take more for sum expectation.

now if brows are x and cost y then the total coast is xy=40 and

the whites are 10 and they coast 1 rs more each so they coast 6 and

6*10 is 60 and

60+40 is 100 so the sum satiesfies

3) a hollow cube of size 5 cm is taken of thickness 1 cm. it is made

of smaller cubes of 1 cm. if 1 face of outer surface of the cube are

painted. find how many total faces of the smaller cube remain

unpainted?

Soln:

hollow cube volume=n^3 - (n-2)^2

n > no of small cubes

n=5 > 5^3-(5-2)^2=98

i.e. 98 small cubes

total surfaces = 6*98=588

if bigger cube is painted 4 sides i.e. 4*25=100 small faces got paint

face does not paint=588-100=488

4) What is the raminder when 222 ^222 divided by 7 ?

Soln:

222=31*7+5

31*1+5 when divided by 7 gives 5 as remainder.

5) 1700 lottery tickets are sold for $25 each, and one grand prize of

$4100 is awarded. If you purchase one ticket, find your expectation

per ticket?

expectation= prob of wining * rewards

here,

expectation =1/1700 * 4100 = 2.41

but ticket cost $25 each

now expectation here = 2.41 - 25 = -22.59(ans)

1! + 2! + ????. + 50!=?

Soln:

1! = 1 (units digit 1)




5!, 6!.... the units digit will be 0 because all the terms will

include 5x2=10

units digit of 1!+2!+... will be 1+2+6+4+0+0+0.... = 3

6) How many different digit number are there which have digit

1,2,3,4,5,6,7,8, such that digit 1 appears exactly once?

Soln:

Digit 1 can appear in any of the 4 positions of a 4 digit number =>

4C1

Further,as repetition is allowed,the othe three digits can have any of

the remaining 7 numbers

So total no of different 4 digit numbers possible = 4C1 * 7 * 7 *7 =

4C1 * 7^3

7) (209*144)^2 + (209*209)+(209*144)+(144*144) = ?

Soln:

905863729 by digit sum method.

8) A pizza shop made pizzas with many flavours. There are 9 different

flavors, in that 2 flavors are taken to make pizza. In how many ways

they can arrange?

Soln:

9c2=36

9) A car manufacturer produces only red and blue TCS Models which come

out of the final testing area at random. What are the odds that five

consecutive cars of same color will come throughthe test area at any

one time?

Soln:

p(5 consecutive cars of same color)=p(5 red)+p(5 blue)

=1/2^5+1/2^5

=1/16

10) Sangakara and Ponting select batting by using a dice, but dice is

biased. So to resolve,Ponting takes out a coin. What is the

probability that coin shows correct option?

Soln:

Coin has 2 Faces, probability of it showing correct option is 1/2

11) How many divisors are there for 1758?

Soln:

1758 = 2*3*293

293 is a prime no.

so the no. of divisors is given by

(1+1)*(1+1)*(1+1) = 8

12) Gold is 19times as heavy as water and copper is 9 times as heavy

as waterIn what ratio should these be mixed to get an alloy 15times as

heavy as water?

Soln:

Using alligation

(15x-9x):(19x-15x)

Ratio is 3:2.

13) How many times do the hands of a clock coincide in 5hrs?

Soln:

5 times.

We start from 1200am, all three hands first coincide at 12:00 clock

and then at 1:5:5, 2:10:10, 3:15:15 and 4:20:20.

14) Raj goes to market to buy oranges If he can bargain and reduce the

price per orange by Rs2 he can buy 30 oranges instead of 20 oranges

with the money he has. How much money does he have?

Soln:

Let price of an orange is x.

if he can reduce the price by rs 2 he can buy 30 oranges...so 30(x-

2)=total money now .

Similarly, if the price is not reduce then he can buy 20 oranges....so

total money he have 20 * X.

So,30(x-2)=20x

so,x=6.

So total money he have 6 *20 = 120 (20*x)

15) If a pipe can fill the tank within 6hrsBut due to leak it takes 30

min moreNow the tank is full then how much time will it take to empty

the tank throught the leak ?

Soln:

Work done by pipe without leak in 1hr = 1/6

Work done by pipe with leak in 1hr = 2/13

So, work done by only leak in 1hr = 1/6 - 2/13= 1/78

So, leak will empty the tank in = 78hrs

16) (209*144)^2 + (209*209)+(209*144)+(144*144) = ?.a)905863729

b)905368729 c)905729368 ?

Soln:

Consider 209=a,144=b

(ab)^2+(a)^2+ab+b^2 add -ab +ab then (a+b)^2+ab(ab-1)

solving we get 905868729

17) A seven digit number is formed by using the digits 3, 3, 4, 5, 5,

8 & 9. Probability that the number formed is great than 57,26,000 is ?

Soln:

Total sample space is 7!/(2!*2!)=1260

total number of numbers formed by 3,3,4,5,5,8,9 which are greater than

5726000 are

when first digit is 5 second digit should be 8 or 9

so 58*****=5!/2!=60

and 59*****=5!/2!=60

or first digit should be 8 or 9

so 8******=6!/(2!*2!)=180

and 9******=6!/(2!*2!)=180

so required probability = (60+60+180+180)/1260=480/1260 = 8/21.

18) In how many ways can seven different objects be divided among

three persons so that either 1 or 2 of them do not get any object?

Soln:

When 1 person does not get any object,

7 objects will be distributed between two persons

no. of ways of distributing 7 objects between two persons=

7c1+7c2+7c3+7c4+7c4+7c5+7c6+7c7 = 126

also two persons can be selected in 3c2 i.e 3 ways

so total no. of ways of distributing objects when 1 person does not

get any object= 3*126=378

when two person does not get any object, all d 7 objects will be given

to 1 person.. and this 0ne person can be

selected from 3 persons in three ways..

so total no. of required ways = 378+3= 381

19) When I acquired my Mercedes-Benz car in Germany, the first thing I

had to do was to get a license plate. The plate I got had a peculiar

number on it. It consisted of 5 different numbers and by mistake when

I fixed it upside down the number could be still read, but the value

had increased by 78633 ?

Soln:

10968

5 differ numbers can be read upside down same are 0 , 1 , 6 , 8 , 9

try with these no.s

number is 10968.

10968

78633

--------

89601

20) If 28a+30b+31c=365 then what is the value of a+b+c = ?

Soln:

No of months in a year having 28 days=1



so,28a+30b+31c=28*1+(30*4)+(31*7)=365

Thus a+b+c=no of months in a year=12.

21) In 4 throws of a pair of dice what is the chance of throwing a

double twice?

Soln:

when a pair of dice is thrown,

probability of getting a double=6/36=1/6

probability of not getting a double will be=5/6

we have to get a double twice that means from 4 throws we have to

select any two throws = 4C2

probability=4c2 *(1/6)^2 * (5/6)^2= 25/216

(1/6)^2*(5/6)^2 means we are getting double 2 times and a non double 2

times.

22) what is the remainder when 46! is divided by 47 ?

Soln:

If (n+1)!/n , then remainder is 1 and if (n-1)!/n , then remainder is

n.

So, answer is 46.

23) If india = 90 and france = 146 then england equals to?

Soln:

I=9 N=14 D=4 I=9 A=1

(9*1)+(14*2)+(4*3)+(9*4)+(1*5) = 90

Multiply code of each lettr wid 1 2 3 in that order...

Similarly france wil be

(6*1)+(18*2)+(1*3)+(14*4)+(3*5)+(5*6)= 146

In that manner, england will be 219.

24) A train travels 50%faster than a car.both start from point a A at

the same time and reaches point B 75 km away from A at the same

time.on the way the train lost about 12.5 min due to stoppages.the

speed of the car?

Soln:

speed of car=x

speed of train=3x/2

75/x-75/3x/2=12.5/60

solving above equation we get x=120

speed of car=120km/h

speed of train=180km/h.

25) A cow and a horse are bought for 200000.the cow is sold at a

profit of 20% and horse at a loss of 10%. The overall gain is 4000.

The cost price of the cow?

Soln:

Let us assume the C.P of cow = x

C.P of horse = y;

Then according to the given condition x+y=200000 --------(1);

Also the S.P of Cow = 1.2x

S.P of horse = 0.9y

So total S.P = 1.2x+0.9y

Given,

(1.2x+0.9y)-(x+y) = 40000 --------(2)

Now two variable two equation, on solving we get x=80000.

26) George does 3/5th of a piece of work in 9 days. He then calls in

Paul , and they finish the work in 4 days. How long would Paul take to

do the work by himself?

Soln:

100% work will be done by George in 15 days

(1/15)9+(1/15+1/x)4=1

solving this eqn.

we get x=30.

27) ((77!(77!-2*54!)^3)/(77!+54!)^3)+(54!((2*77!-54!)^3)/(77!+54!)^3)=

?

Soln:

assume a=77!& b=54!

according to the expression

(a(a-2b)^3)/(a+b)^3 + (b(2a-b)^3)/(a+b)^3)

=(a^4+2*a^3*b -2*a*b^3-b^4)/(a+b)^3

= (a-b)*(a+b)^3/(a+b)^3

= (a-b)

= (77!-54!)

28) Find the probability that a leap year chosen at random has 53

sundays?

Soln:

A leap year has 366 days, therefore 52 weeks i.e. 52 Sunday and 2

days.

The remaining 2 days may be any two days of the week.

For having 53 Sundays in a year, one of the remaining 2 days must be a

Sunday.

n(S) = 7

n(E) = 2

P(E) = n(E) / n(S) = 2 / 7

29) Remainder when 128^1000 is divided by 153?

Soln:

128^1000/153

(128^2)^500/153

(16384) by 153 reminder=13

(13^2)^250/153

=(169)/153 reminder=16

Now 16^250/153

(16^6)^41*(16^4)/153

=(16^6)=16777216/153 Reminder 1

=(16^4)=65536/153 Reminder 52

So 52*1=52.

30) A lady has fine gloves and hats in her closet- 14 blue, 20 red,

and 18 yellow. T he lights are out and it is totally dark. In spite of

the darkness, she can make out the diff erence between a hat and a

glove. She takes out an item out of the closet only if she is sure

that if it is a glove. How many gloves must she take out to make sure

she has a pair of each color?

Soln:

14 blue 20 red and 18 yellow

to make sure that she has a pair of each colour leave the minimum

value which is blue and add 20 and 18 =

20+18 =38

and 2 from blue gives = 38+2=40

so atleast 40 gloves must be taken.

31) (a% of a)+(b% of b)=2% of ab then what % of a is b?

Soln:

(a% of a)+(b% of b)=2% of ab

ie a^2 + b^2 =2ab

ie (a-b)^2 =0

ie a-b=0

a=b

ie 100%.

32) A B and C run a race with A finishing 48 meters ahead of B and 72

meters ahead of C while runner B finishes 32 meters ahead of runner C.

Each runner travels the entire distance at a constant speed. What is

the length of the race ?

Soln:

Let total dist=x

a/b=x/x-48

a/c=x/x-72

b/c=x/x-32=x-48/x-72

by solving we get x=192.

33) There are two qualities of milk Amul and sudha having different

prices per litre , their volumes being 130 litres and 180 litre

respectively. After equal amounts of milk was removed from both . the

milk removed from amul was added to sudha and vice versa . The

resulting two types of milk now have the same price .Find the amount

of milk drawn out from each type of milk ?

Soln:

let A=tank containing Amul milk 130L

and S=tank containing Sudha milk 180L

now suppose x L milk from A ans S is drawn

after mixing milk as perthe condition, it gives same proportion of

Amul milk in both the tanks

in A proportion of Amul milk=(130-x)/130

in S proportion of Amul milk=(x)/180

solve this for x

x=(130*180)/310

x=75.48

34) Three vessels having volumes in the ratio of 1:2:3 are full of

mixture of coke and soda. In the first vessel ratio of coke and soda

is 2:3 in second ,3:& and in the third 1:4 if the liquid in all the

three vessels were mixed in bigger container what is the resulting

mixture of coke and soda ?

Soln:

let volume of 1st can is 10 ltr ,2nd can is 20 ltr and 3rd can is 30

ltr

coke in 1st can is 4 ltr

soda in 1st can is 6 ltr

coke in 2nd can is 6 ltr

soda in 2nd can is 14 ltr

coke in 3rd can is 6 ltr

soda in 3rd can is 24 ltr

resulting ratio of coke and soda=(4+6+6):(6+14+24) = 16:44 = 4:11

35) A mixture of cement, sand ,and gravel in the ratio of 1:2:4 by

volume is required . A person wishes to measure out quantities by

weight .He finds that the weight of one cubic foot of cement is 94 kg,

of sand 100 kg and gravel 110 kg what should be the ratio of all in

order to give proper mixture ?

Soln:

The ratio of cement, sand ,and gravel is 1:2:4 by volume.

if, we assume the total volume is 1 cubic foot

then, by weight the ratio must be,

=> (1*94):(2*100):(4*110)

=> 47:100:220

36) What are the last two digits of expression 5306^214 ?

Soln:

for 5306^214

the last digit will always determined by the expansion of 6^214

hence, 6^214=6^200*6^14

=(6^2)^100*(6^2)^6*6^2

=>>6*6*36

as the expansion of (6^2) must consist 36

so last 2 digit is 96.

37) Find the smallest number such that n! is divisible by 990 ?

Soln:

The factor of 990 is : 11*5*3*3*2

That why the maximum factor of 990 is 11 .

so, n=11

That means n!=11!= (11*10*9*8*7*6*5*4*3*2*1)

And then n!/990 = (11!/990)= (11*10*9*8*7*6*5*4*3*2*1)/(11*5*3*3*2)

So Ans is 11.

38) 48 persons P1, P2, P3,. P48 met and shook hands in a

circular fashion i.e. a total of 48 handshakes among the pairs (P1,

P2), (P2, P3), (P3, P4), ..(P46, P47), (P47, P48) and (P48, P1).

Find the least value of N for which a group of N persons can be formed

such that each of the remaining persons outside the group shook hands

with at least one person in the group ?

Soln:

From this arrangement,the

pair(p1,p2),(p2,p3),(p3,p4),.....(p46,p47),(p47,p48)and(p48,p1). If we

seperate p3,p6,p9......p48.The total 16 person the remaining person

must read have shaked hand with atleast one person.

As P2 shook hands with P1 & P3.. similarly P5 shook hands with P4 &

P6... so on till.. P48..

this gives us series..

2,5,8,11,....48 as an A.P. with n=16

39) p(x)= ( x^2012+x^2011+x^2010+.............x+1)-x^2012

q(x)=(x^2011+x^2010+................x+1)

the remainder when p(x) is divided by q(x) is ?

Soln:

Take x=1

(2013)^2-1^2012 it is divided by 2011 by formula[a^2-b^2]

(2014*2012)/2012

So remainder is 0.

40) In a certain code 253 means 'books are old';546 means 'man is old'

and '378'means 'buy good books' what stands for 'are' in that code?

Soln:

books are old as 253 --eq1

man is old as 546 --eq2

buy good books as 378 --eq3

so comparing eq1 and eq3 we get code for books as 3.

and comparing eq1 and eq2 we get code for old as 5.

now compare again equation 1 with the given code and so code for "are"

is 2.

41) what is the remainder when 46! is divide by 47?

Soln:

From remainder theorem = (p-1)!/p = p-1

so (47-1)!/47 = 47-1 = 46 is remainder.

42) How many four digits are formed such that the digits are in

decreasing order ?

Soln:

0,1,2,3,4,5,6,7,8,9

3C3=1

4C3=4

5C3=10

6C3=20

7C3=35

8C3=56

9C3=84

Total = 210.

43) If INDIA = 90 and FRANCE=146 then ENGLAND=?

Soln:

A=1,B=2,..... Z=26

INDIA= 1*9+2*14+3*4+4*9+5*1=90

FRANCE= 1*6+2*18+3*1+4*14+5*3+6*5=146

ENGLAND= 1*5+2*14+3*7+4*12+5*1+6*14+7*4=219

44) There are certain no. of chocolates in a bag. If they were equally

divided among 14 children,there are 10 chocolates left. If they were

to be equally divided among 15 children,there are 8 chocolates left.

Obviously, this can be satisfied if any multiple of 210 chocolates are

added to the bag. What is the remainder when the minimum feasible

number of chocolates in the bag is divided by 9 ?

Soln:

14*2=28+left 10=38

15*2=30+left 8=38

210+38=248

=248/9=27qu and 5 remainder.

45) Find the average speed, if a man travels at a speed of 24kmph up

and 36kmph down at an altitude of 200m ?

Soln:

Avg speed = 2xy(x+y)= 28.8 kmph

46) A beat B by 15 meters and C by 19 meters in 200 m race. then in

the race of 3700 meters B will defeat C by how much distance ?

Soln:

Distance of A - distance of B = 15 meters //for 200 m race ,

Distance of A - distance of C = 19 meters // for 200 m race,

( Va*t) - ( Vb*t ) = 15 //equation 1

( Va*t ) - ( Vc*t ) = 19 // equation 2

so subtracting equation 1 from 2 , we get

(Vb*t) - (Vc*t) = 4 meters

which means the difference in distance of B and C will be a multiple

of 4 always.

and in the options given , only 80 is the multiple of 4, so ans in 80.

47) Roy is now 4 years older than Erik and 2 years older than Iris. If

in 2 years, Roy will be twice as old as Erik, then in 2 years what

would be Roy's age multiplied by Iris's age ?

Soln:

roy=r

eric=r-4

iris=r-2

r+2=2(r-2)

r=6

iris age is

6-2=4

after 2 years

iris age=6

roy age=8

multiply 6*8=48.

48) Akhilesh, Bernard, Catherine and Dinesh go for a picnic. In a

weighing machine they try to find their weights. When Akhilesh stands

on the machine, without his knowledge Bernard also climbs the machine

and the weight shown was 132kg. When Bernard stands, without his

knowledge Catherine also stands on the machine and the machine shows

130 kg. Similarly the weight of Catherine and Dinesh is found as 102

kg and that of Bernard and Dinesh is 116 kg. What is the weight of

Dinesh?

Soln:

A+B=132

B+C=130---eq1

C+D=102---eq2

B+D=116---eq3

by solving eq1,2 &3

D=44 kg.

49) If 3*y+x>2 and x+2*y -1.

50) Find the number of 0's in 15*32*25*22*40*75*98*112*125 ?

Soln:

The number of zeros in the given expression is 9 because number of

zeroes depends on how many pairs of (5*2) exists.

On expanding the above expression

(5*3)*(2*2*2*2*2)*(5*5)*(11*2)*(2*2*2*5)*(5*5*3)*(7*7*2)*(56*2)*(5*5*5

).

51) The height of triangle is increased by 40%.What can be the maximum

percentage increase in length of the base so that the increase in area

is restricted to a maximum of 60%?

Soln:

Area of triangle is given by a= 0.5*b*h

Increase area by 60% means updated area will be, a+0.6a=1.6a

Also increase height by 40% updated height will be 1.4h

So putting these updated values in area equation will give b=1.1428b

Therefore increase in base will be 14.28%

52) 4 12 x 44 46 132 134.... find x ?

Soln:

2+2=4,4*3=12,12+2=14,14*3=42,42+2=44,44*3=132,132+2=134

so answer is 14.

53) Ram and Shakil run a race of 2000 meters. First, Ram gives Shakil

a start of 200 meters and beats him by one minute. If , Ram gives

Shakil a start of 6 minutes Ram is beaten by 1000 meters. Find the

time in minutes in which Ram and Shakil can run the races separately ?

Soln:

LET r be velocity of ram and s be the velocity of Shakil then

(2000/r)=(1800/s)-60......(1)

second case

distance Shakil travel in 6 min=360s

again equating time for both

1000/r=(2000-360s)/s.......(2)

solving (1) &(2) we get s=20/6

putting value in first we get time =480sec=8min.

54) Two identical circles intersect so that their centres, and the

points at which they intersect, form a square of side 1 cm. The area

in sq.cm of the portion that is common to the two circles ?

Soln:

Area of the common portion can be calculated as = 2(Area of the sector

of a circle having the angle of 90 - Area of the right angled triangle

of side 1 cm).

Here the right angled triangle is obtained by joining the two

intersecting points which is in turn the diagonal of the square.

Now the area of common section is = 2( (90/360)* pi * 1*1 - (1/2)*1*1)

= pi/2 -1.

55) A semicircle is drawn with AB as its diameter. From C, a point on

AB, a line perpendicular to AB is drawn, meeting the circumference of

the semicircle at D. Given that AC=2cm and CD=6cm, the area of the

semicircle in square cm will be ?

Soln:

Let O be center of circle and radius be x.

C can be anywhere on AB.Let us suppose that C is somewhere between A

and O.

AC=2cm....so CO=(x-2)

DO=x,CD=6cm

CDO form a right angled triangle with right angle at C.

Using Pythagoras theorem,

x^2=6^2+(x-2)^2

4x=40

x=10cm

area=[pi(x)^2]/2

area=50pi.

56) A completes 80% of a work in 20 days. Then B also joins and A and

B together finish the remaining work in 3 days. How long does it need

for B if he alone completes the work?

Soln:

A alone can complete the work in (20/80)*100= 25 days

As work completed by A is 80%=80/100=4/5, remaining work= 1/5

If B alone can complete the work in 'x' days, then

3 days work of A & B= 3*[(1/25)+(1/x)]= 1/5

1/x=2/75 or x=75/2 =37.5

57) Let n be a natural number, then n(n*n-1) is always divisible by ?

Soln:

n(n*n-1)

= n*(n^2-1)

= n*(n-1)*(n+1)

= (n-1)*(n)*(n+1)

product of 3 conseutive natural no. is always divisible by 6.

58) What is the remainder when 6^17 + 17^6 is divided by 7?

Soln:

use remainder theorem, (ax +/- b)^n / x => rem = (+/- b )^n

6 ^ 17 / 7 => (7-1)^7 / 7 => (-1)^7 => rem = -1

17^6 / 7 => (2*7+3)^6 / 7 => 3^6 / 7 => 27*27 / 7 => -1*-1 / 7 => 1/7

=> rem = 1

so, 6 ^ 17 + 17 ^ 6 / 7 => rem(-1 + 1)/ 7 => 0

59) In what ratio does milk and water are to be mixed in order to get

a gain of 1333% by keeping selling price constant ?

Soln:

100/(100+1333) : 1333/(100+1333)

=100:1333

60) A rectangle is divided into 4 rectangles of area 70,36,20,x where

x=?

Soln:

36:70 :: 20:x

=> 36*x = 70*20

=> x = 70*20/36

=> x = 350/9

61) What is the distance between two parallel chords of length 24 cm

and 32 cm in a cirle of radius 20 cm, given they are on same side?

Soln:

Let the distances of the chords 24cm and 32cm from the center be x&y.

x^2+12^2=20^2 i.e x=16

y^2+16^2=20^2 i.e y=12

Thus, distance between the chords is 16-12 = 4 cm.

62) A class of 100 students. 24 of them are girls and 32 are not.

Which base am I using?

Soln:

if base be b then

100 = 24 + 32

=> 1*b^2 + 0*b^1 + 0 = (2b+4) + (3b+2)

=> b^2 - 5b -6 = 0

=> (b-6)*(b+1) = 0

=> b = -1,6

base can't negative

so, b = 6.

63) An organisation has 3 committees, only 2 persons are members of

all 3 committee but every pair of committee has 3 members in common.

What is the least possible number of members on any one committee?

Soln:

Let A and B are common in all committee

In 1 and 2 committee ,let say C is common

In 2 and 3 committee,D is common

In 1 and 3 committee, E is common.

so, 1 committe has ABCE

2 commitee has ABCD..so on.

so the answer is minimum 4.

64) J can dig a well in 16 days. P can dig a well in 24 days. J, P, H

dig in 8 days. H alone can dig the well in how many days?

Soln:

j's 1 day work=1/16

p's 1 day work=1/24

so in 1 day j&p can together do (1/16)+(1/24)=5/48 part

in 1 day j,p &h together can do 1/8 part

so h's 1 day work =(1/8)-(5/48)=1/48

so h can do whole work in 48 days.

65) Three non negative numbers, X, Y and Z are such that the mean is M

and the median is 5. If M is 10 more than the smallest number and 15

less than the biggest number, find the value of X+Y+Z ?

Soln:

given median=5,so y=5

x+y+z/3=10+z

x+y+z/3=x-15

solving 2 equations we get,

x=25,y=5,z=0

ans=30.

66) a, b, c are non negitive integers such that 28a+30b+31c = 365. a +

b + c = ?

Soln:

12 month = 365 days

so a=7 (31 days month)

b=4 ( 30 days month)

c=1 (February)

so answer= 7+4+1=12.

67) In how many ways 7 different objects can be divided among 3

persons so that either one or two of them do not get any object?

Soln:

if 2 of them don't get any, all object goes to 3rd person => 3

ways(A/B/C)

if 1 of them don't get any, 7 objects goes to rest 2 persons

(AB,BC,CA)

this can be in 3 ways

(1,6)=> 7c1

(2,5)=> 7c2

(3,4)=> 7c3

(4,3)=> 7c4

(5,2)=> 7c5

(6,1)=> 7c6

(7c1+7c2+7c3+7c4+7c5+7c6)= 2^7-2 = 126

total ways = 3*126 = 378

Total = 3 + 378 = 381.

68) (753 x 753 + 247 x 247 - 753 x 247)/(753 x 753 x 753 + 247 x 247 x

247) = ?

Soln:

if x=753, y=247

then (x^2+y^2-xy)/(x^3+y^3) = 1/(x+y) = 1/1000.

69) Three groups of children contain 3 girls and one boy; 2 girls and

2 boys, one girl and 3 boys. One child is selected at random from each

group. What is the probability that the three selected consists of 1

girl and 2 boys?

Soln:

The probability of selecting of 1 boy from the first group is 1/4, 1

girl 3/4

The probability of selecting of 1 boy from the second group is 1/2, 1

girl 1/2

The probability of selecting of 1 boy from the third group is 3/4, 1

girl 1/4.

The probability of selecting of 1 girl and 2 boys is

P(girl from I group) AND P(boy from II group) AND P(boy from III

group) OR

P(boy from I group) AND P(girl from II group) AND P(boy from III

group) OR

P(boy from I group) AND P(boy from II group) AND P(girl from III

group)

In Math it equals to (AND = "*", OR = "+"):

3/4*1/2*3/4 + 1/4*1/2*3/4 + 1/4*1/2*1/4 = 9/32 + 3/32 + 1/32 = 13/32

70) George does 3/5 of a piece of work in 9 days. He then calls Paul

and they finish the work in 4 days. How long would Paul take to do the

work by himself?

Soln:

George 1 day work=1/15

Let Paul 1 day work be 1/x

work to be done=1-3/5=2/5

then,a/c

4(1/15+1/x)=2/5

x=30.

71) Let A be the two digit number. How many numbers are there, if 18

more the sum of the digits is the same number?

Soln:

let the digit of no. is x and y

unit digit y and tens digit is x hence no. will be 10*x+y

as given 18 more the sum of digit is same no.

so (x+y)+18 = 10*x+y

x=2;

possible two digit no. with x=2 are

20,21,22,23,24,25,26,27,28,29

total 10 numbers.

72) If Jam's age in 1994 is half of his grandmother's age. Sum of

their birth years is 3844. What will be Jam's age in 1999?

Soln:

In 1994, let the ages of GM and Jam = 2x , x

birth yr of GM = (1994 - 2x)

birth year of Jam = (1994 - x)

given,

=> 1994 - 2x + 1994 - x = 3844

=> x = 48

in 1999, the age of Jam = (48 + 5) = 53

73) You have to form a 6 digit even number with numbers from 1 to 7,

the digit second to last should be even ?

Soln:

digit to be even last digit has 3 chances ie:2 or 4 or 6

digit 2nd to last should be also even so after filling last digit ,

this must have 2 chances.

then first place will posses: 5 chances

then second place will posses: 4 chances

then third place will posses: 3 chances

then next place will posses:2 chances

finally product of chances are 5*4*3*2*2*3=720.

74) In the month January , there only are 4 thrusdays and 4 sundays,

then what will be the day of 1st January?

Soln:

Monday

If the week starts on monday.it will end on sunday so four thursday

and four sunday will come in a span of 28 days so the last day is

sunday and january has got 31 days the remaining 3 days will be monday

tuesday and wednesday so therefore there is exctly four sundays and

four thursday.

75) Look at this series: 14, 28, 20, 40, 32, 64, what number should

come next?

Soln:

14*2=28, 28-8=20

20*2=40, 40-8=32

32*2=64, 64-8=56

76) class of 25 students took a science test. 10 students had an

average (arithmetic mean) score of 80. The other students had an

average score of 60. What is the average score of the whole class?

Soln:

10 students had an average of 80.

total=10*80=800

other 15 students had an average score of 60.

total=15*60=900

the average score of the whole class=(800+900)/25 = 68.

77) A car travelling with 5/7th of actual speed covers 42km in

1hr40min48sec.find the speed of the car ?

Soln:

Let speed be s

(5/7)s=42/(1+ 40/60 + 48/(60*60))

s = 35km/hr.

78) A person climbed a hill which was 200m high. The average speed

while climbing was 24 m/sec and while coming down it was 30m/sec. What

is the average speed (in kmph) of his journey?

Soln:

Avg speed=2xy/x+y.

2*24*30/54=80/3m/s

80/3*18/5 = 96km/hr.

79) 14 , 56 , 458 , 860 , 1262, X ?

Soln:

14

56=14*4+0

458=14*32+10

860=14*60+20

1262=14*88+30

14*116+40=1664 will be next number.

80) A man starts a work and one more man joins him everyday. If the

work is thus completed in 11 days, then find the number of days in

which six men working together will finish the work?

Soln:

if one man work 1 unit

two men work 2 unit

3 men work 3 unit and so on upto 11th day

total unit of work done in 11 day are 1+2+3+.........+10+11 =66

now 66 unit of work willbe done by 6 men is 66/6=11.

81) Apple costs L rupees per kilo gram for the first 30 kgs and Q

rupees per kg for each additional kg. If the price of 33 kgs is Rs.

11.67 and for 36 kgs of apples is Rs. 12.48 then the cost of first 10

kgs of apple is ?

Soln:

30L+6Q=12.48

30L+3Q=11.67

=> Q=0.27.

10L=3.62

So, answer is 3.62

82) A polygon has interior angle of 156 degrees. How many diagonal are

their in that polygon ?

Soln:

(n-2)*180/n =156;

n=15;

no of diaognals = 15C2 - 15 = 90

83) What is the remainder of expression 48 ^ 567 /7 ?

Soln:

48 ^ 567 / 7

= (7*7-1)^567 / 7

= (-1)^567 / 7

= -1/7

rem = 7-1 = 6

84) what is the maximum sum of the terms in the arithmetic progression

25, 241/2, 24...?

Soln:

Its a decreasing AP 25,24.5,24,23.5,...

if nth term is zero then

25 + (n-1)*(-.5) = 0

=> n = 51

after 51 terms AP contains -ve terms

so, max sum will be obtained upto 50/51th term

S max = 51/2 *(25+0) = 637.5

85) 30^72^87 divided by 11 gives remainder?

Soln:

unit digit of 72^87 = 8

so,72^87 = (10k + 8)

30^(10k+8)/11

= 3^(10k+8)*10^(10k+8)/11

= 3^10k * 3^8 * 10^(10k+8)/11

= (3^5)^2k * 3^5*3^3 * 10^(10k+8)/11

= (11*22+1)^2k *(11*22+1)*(11*2+5)*(11*1-1)^(10k+8)/ 11

=> rem = 1^2k * 1 * 5 *(-1)^(10k+8) = 5

86) When (1!)^1!+(2!)^2!+(3!)^3!+...............(100!)^100! is divided

by 5,the remainder obtained is ?

Soln:

1 + 2^2 + 6^6 + 24^24 + [(5!)^5! + (6!)^6! + .....+ (100!)^100!] / 5

from (5!)^5! to 100!^100! each term is divisible by 5 & gives rem = 0

[unit digit of 1 + 2^2 + 6^6 + 24^24 = 1+4 +6+6 = 7]

Required remainder = 1 + 2^2 + 6^6 + 24^24 / 5 => rem= 7/5 = 2

87) 123^123! what is the last two digit ?

Soln:

123^123!

(123)^(----28 zeroes)

consider only last two digit

(23)^4)^(--000000000)

(--41)^(---00000000)

unit digit = 1 ,tens place = (tens of 41)*(unit of ---000)= 4*0=0

=> last two digits = 01

88) The ratio b/w the ages of two persons is 6:5.and sum of there ages

is 77 then how many years later there ratio becomes 8:7?

We all know that Arya Bhatta is the greatest mathematics belongs to

India . When his daughter Mayabati was in her teen age he discovered a

problem. At that time the age of Mayabati is a prime number, let that

age is a. After some years her age becomes b. then Arya Bhatta was

able to solve that problem with the help of his daughter Mayabati. If

a-b=5 & product of a& b is 26 then what is the sum of two squares?

Soln:

a-b=5

ab=26

a^2+b^2=?

we know that,(a-b)^2=a^2+b^2-2ab

(5)^2=a^2+b^2-2(26)

25=a^2+b^2-52

a^2+b^2=25+52

a^2+b^2=77

89) Inspired by fibonacci series Sanket decided to create his own

series which is 1,2,3,7,7,22,15,67,. lik dis,then what number will

come immediately before 63?

Soln:

1,2,3,7,7,22,15,67,

its combination of two alternate series

1,3,7,15,31,63,127 => next=(pre*2+1)

2,7,22,67,202,307 => next no.=(pre*3+1)

series is 1,2,3,7,7,22,15,67,31,202,63,307

so, 202 comes immediately before 63.

90) A man goes upstream for a distance of 10 km in 5 hrs. Another man

goes downstream the same distance of 10 km in 3 hrs. what is the

difference in speed of 2 men if the river speed is 0.5 kmph?

Soln:

10/(x-.5) = 5 => x = 2.5

10/(y+.5) = 3 => y = 2.84

(x-y)= 2.83 - 2.5 = .33 km/h

91) Three distinct single digit numbers A,B,C are in GP. If abs(x) for

real x is the absolute value of x(x if x is +ve or zero, -x if x is -

ve), then the number of different possible values of abs(A+B-C) is ?

Soln:

A,B,C may be

(1,2,4) & (4,2,1)

(1,3,9) & (9,3,1)

(2,4,8) & (8,4,2)

(4,6,9) & (9,6,4)

find abs(A+B-c) for these 8 GPs

1, 5, 5, 11 , 2, 10, 1 , 11

we get 5 different values (1,2,5,10,11)

92) 2 vehicles A and B leave for city Y from city X. A overtakes B at

10.30 am and reaches city X at 12.00 pm. It waits for 2 hours and

returns to city Y. On its way it meets B at 3 pm and reaches city at 5

pm. B reaches city X, waits for one hour and returns to city Y. After

how many hours will B reach city Y from the time A overtook him for

the first time?

Soln:

Let total distance be 60m.

A covers that sixty metres in 3hrs such that 20m in 1hr.

When a overtakes b then they were half way means 30m and when they

again meet then they were on 40m such that b covers 10m in 4.30hrs and

b have to cover 90m to reach city Y again.

so (4.5*9)+1hr(b waits for one hour)= 41.5hrs

93) 250 men and 150 women working in a factory,having an average

productivity of 12 units per day. Average productivity of men is 15

units per day,what is the average productivity of women per day?

Soln:

sum of 400 people(250m+150w)= 400*12=4800

sum of 250 men is 250*15=3750

sum of 150 women=4800-3750=1050

therefore 1050/150=7 units per day.

94) How many numbers are there that appear in both of arithmetic

progression 4,11,18,25,...2020 and 4,13,22,31,40.....2020?

Soln:

total terms in 4,11,18,25,....,2020 are 289

total terms in 4,13,22,31,40...,2020 are 225

every comman number in first sequence is at 9th number

every comman number in second sequence is at 7th number

so 225/7=32+1 (4 is first number)

so ans is 33.

95) If all the factors of 5040 are written in ascending order then

which will be 55th factor from beginning?

Soln:

The total factors are 5040=2^4*3^2*5*7=(4+1)(2+1)(1+1)(1+1)=60

so

1*5040

2*2520

3*1680

4*1260

5*1008

6*840

.....

55th factor is 840.

96) M is 30% of Q, Q is 20% of P and N is 50% of P. What is M / N?

Soln:

M/N=30Q/50P

20P=100Q

50P=100/20*50Q=250Q

M/N=30Q/250Q=3/25

97) In how many ways a team of 11 must be selected a team 5 men and 11

women such that the team must comprise of not more than 3 men ?

Soln:

Different combinations for the formation of the team will be

3men,8women; 2men,9women; 1men,10 women; 0men, 11 women.

5C0*11C11+11C10*5C1+11C9*5C2+11C8*5C3

=1+11*5+55*10+165*10

=1+55+550+1650

=2256

98) If 4 men role the same dice simultaneously, what is the

probability that all of them get the same number on the dice?

Soln:

No. of events having all of them same

no={(1111);(2222);(3333);(4444);(5555);(6666)}=6;

total possibility=6^4

prob.=6/6^4

=>1/6^3

99) If taxi fare =15rs/km Train fare= 21rs/km Total dist travelled

=450km, total amount charged= 8320rs. Then distance travelled by

train=?

Soln:

Let x be the distance traveled by taxi, y=distance traveled by train

then total fare charge= 15x+21y=8320

total distance traveled= x+y=450

solving these two equation we get

y=291.67km

100) A travels at 40kmph and B travels at 60kmph. They are traveling

towards each other and start at the same time. By the time they meet,

B would have traveled 120 km more than A. Find the total distance ?

Soln:

s=d/t

let the distance travelled by a=x km

the distance travelled by b=(x+120) km

x=40*t

x+120=60*t

on solving we get t=6

x=240,x+120=360

so total distance=600km.

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