If n is the product of all the integers from 5 to 20, inclusive, what

Question

If n is the product of all the integers from 5 to 20, inclusive, what is the greatest integer k for which 2^k is a factor of n ?

(A) 11
(B) 12
(C) 13
(D) 15
(E) 16

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2448 · Answer

5-20 = 20!/4!
20! = 20/2 + 20/4 + 20/8 + 20/16 = 10+5+2+1 = 18
4! = 4/2+4/4 = 3
factor of 2 in 20!/4! = 15
therefore ans = 2^15.

LucidGhost · Answer

Let's find the number of 2^k in 20! first and then minus powers of 2 in 4! 
20/2 + 20/4 +20/8 +20/16 +20/32 ...
10+5+2+1+0 
= 18 
20! has 18 twos in it. 
4! has 3 twos in it. 
To get answer minus them. (18-3=15)

Greatest possible value of k= 15

D

SwiftMonk · Answer

20!/4! = 20*19*............*5
2^m in 20!= 20/2 +20/4 +20/8 +20/16=10+5+2+1=18
2^n in 4!= 4/2 +4/4=2+1=3
=2^18/2^3=2^15
hence 15 is the desired ans.

Taidaishar · Answer

An easy way to do this is by calculating the number of 2s in 20!, and subtracting the number of 2s in 1 to 5 from it.

Number of 2s in 20! = 20/2 + 20/4 + 20/8 + 20/16 = 10 + 5 + 2 + 1 = 18

Number of 2s in 1 to 5 = 1x2x3x4 = 2^3

18-3 = 15. Answer is D.

If n is the product of all the integers from 5 to 20, inclusive, what

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GMAT Problem Solving (PS) Questions

If n is the product of all the integers from 5 to 20, inclusive, what

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