If 2^z is a factor of 25!, which of the following could be the value

Question

If 2^z is a factor of 25!, which of the following could be the value of z?

I. 22
II. 23
III. 24

A. I ​ only 
B. II only 
C. I​ and II 
D. I, II, and III 
E. None

OptimusPrepJanielle · Accepted Answer

2^z is a factor of 25!, what values can z take.

Powers of 2 in 25! =   +   +  +   , where   is the integral part of x
Powers of 2 in 25! = 12 + 6 + 3 + 1 = 22

Hence the maximum value of 2^z in 25! = 2^22
Only Statement I satisfies

Correct Option: A

prashant212 · Answer

25! contains all numbers from 1 to 25. To find the factor with the highest power of 2, we count the number of multiples of 2,4,8 and 16

Multiples of 2 = 12
Multiples of 4 = 6
Multiples of 8 = 3
Multiples of 16 = 1
Total count = 22

A is the answer.

law258 · Answer

(25/2)+(25/4)+(25/8)+(25/16) = 12+6+3+1 = 22

A

Abhishek009 · Answer

25/2 = 12
12/6 = 3
3/2 = 1

12+3+1 = 22
 
So, Answer will be (A) Only I

cavana · Answer

1) To paraphrase the question we need to find the total number of prime factors 2 in 25!
2) We need to count all the multiples of 2, add an additional two for every multiple of 2 that is also a multiples of 4, add an additional two for everything multiple of 2 that is also a multiple of 4 and multiple of 8, and add an additional two for every multiple of 2 that is also a multiple of 4, 6, 8, and 24.
3) 25/2=12; 25/4=6; 25/8=3; 25/24=1; 12+6+3+1=22

orangebicycle5 · Answer

25/2 = 12, 25/4 = 6, 25/8 = 3, 25/16 = 1

12+6+3+1 = 22

DanTheGMATMan · Answer

https://www.youtube.com/watch?v=gpIo9TELc-s

bumpbot · Answer

Automated notice from GMAT Club BumpBot:

A member just gave Kudos to this thread, showing it’s still useful. I’ve bumped it to the top so more people can benefit. Feel free to add your own questions or solutions.

This post was generated automatically.

If 2^z is a factor of 25!, which of the following could be the value

Prep Toolkit

Top 5 GMAT Debrief Videos

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards

GMAT Problem Solving (PS) Questions

If 2^z is a factor of 25!, which of the following could be the value

Prep Toolkit

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards