SQC31

7/21/2019 SQC31

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Session Numbers

Factorial based – I

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:

• Factorial n (or n!) is the product of first n natural number i.e.n! = 1 × 2 × 3 × … × (n – 2) × (n – 1) × n.

• Highest power of any prime number x in N! is 2 3 n

N N N N...

x x x x

+ + + +

, where nN x≥ and [X]

represent the greatest integer less than or equal to X.• The number of zeros at the end of N! is equal to the highest power of 5 in N!.

Highlight: This session deals with questions which are based on finding the highest power of a number infactorial of another number, number of zeros at the end of factorial of a number and remainder whenfactorial of a number is divided by a certain number. Questions in the session are of easy to moderatedifficulty level.

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SessionNumbers

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

Q1. What is the greatest power of 5 which can divide 80! exactly?(a) 16 (b) 20 (c) 19 (d) None of these

(CAT 1991)

Q2. The product of all integers from 1 to 100 will have the following numbers of zeros at the end.

(a) 20 (b) 24 (c) 19 (d) 22(CAT 1993)

Q3. ABC is a three-digit number in which A > 0. The value of ABC is equal to the sum of the factorials of

its three digits. What is the value of B?

(a) 9 (b) 7 (c) 4 (d) 2(CAT 1997)

Q4. Let n! = 1 × 2 × 3 × … × n for integer n 1.≥If p = 1! + (2 × 2!) + (3 × 3!) + … + (10 × 10!), then p + 2 when divided by 11! leaves a remainder of

(a) 10 (b) 0 (c) 7 (d) 1(CAT 2005)

Q5. The number of positive integers n in the range 12 n 40≤ ≤ such that the product

(n 1)(n 2) 3.2.1− − is not divisible by n is

(a) 5 (b) 7 (c) 13 (d) 14

(CAT 2003 (L))

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Session Numbers

Errata:

Despite the best of our efforts, minor slips have crept into this session which are elaborated

below for your convenience.

In question no. 2, at 5:13, GP mistakenly writes 19/ 2 8.5(25) (25)= , which should actually be

19/ 2 9.5(25) (25)= .

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SQC31