Session Numbers

Cyclicity

Numbers is one of the most important topics for CAT and other management entrance exams, questionsfrom which have appeared consistently and in significant numbers in all these exams.

Key concepts discussed:

• The cyclicity of unit digits 0,1, 5 and 6 is 1.• The cyclicity of unit digits 4 and 9 is 2.• The cyclicity of unit digits 2, 3, 7 and 8 is 4.• When a natural number A ends with 0, Ak will always end with 00, where k is a natural number

greater than 1.• When a natural number A ends with 5, Ak will always end with 25, where k is a natural number

greater than 1.

Highlight: This session deals with questions which are based on finding unit digit of a number, unit digit ofsum of two or more numbers, product of two or more numbers (in the exponential form). Questions in thesession are of easy to moderate difficulty level.

SessionNumbers

The questions discussed in the session are given below along with their source.

Q1. What is the digit in the unit’s place of 251?(a) 2 (b) 8 (c) 1 (d) 4

(CAT 1998)

Q2. The unit digit in the product of (8267)153 × (341)72 is(a) 1 (b) 2 (c) 7 (d) 9

(IIFT 2013-15)

Q3. Suppose the English alphabet letters A, B, C,..., Z are denoted by the remainders obtained ondividing the numbers 20, 21, 22,..., 225, respectively, by 29, then the letter “K” would be denoted by(a) 6 (b) 7 (c) 8 (d) 9

(JMET 2011)

Q4. Find the units’ digit of 1359 .

(a) 3 (b) 7 (c) 9 (d) 1(CL material)

Q5. Find the last digit of the number 3322117 .

(a) 7 (b) 1 (c) 9 (d) 3(CL material)

Q6. What is the last digit of 5 44 53 32 2 ?−

(a) 0 (b) 2 (c) 4 (d) 6 (e) None of these(CL material)