BREAKING: Target Test Prep releases Brand New 2026 On Demand GMAT prep course

Redeem

Simple... I think

This topic has expert replies
Post new topic Post Reply
Previous Topic Next Topic
Source: — Problem Solving |
User avatar
GMAT Instructor
Posts: 3225
Joined: Tue Jan 08, 2008 2:40 pm
Location: Toronto
Thanked: 1710 times
Followed by:614 members
GMAT Score:800

Re: Simple... I think

by Stuart@KaplanGMAT » Thu Mar 20, 2008 12:46 pm
HarvardDreamin wrote:q3) What is the maximum integer value of M for which 12!/2^M is an integer?

A. 2 B. 4 C. 6 D. 10 E. 12
We need to figure out how many times "2" goes into the expression in the numerator.

12! = 12 * 11 * 10 * 9 * 8 * 7 * 6 * 5 * 4 * 3 * 2 * 1

Let's start by ignoring the numbers that aren't multiples of 2. For this question, we only care about:

12 * 10 * 8 * 6 * 4 * 2

Next, let's factor into primes:

2*2*3 * 2*5 * 2*2*2 * 2*3 * 2*2 * 2

Count 'em up, we have 10 2s: choose (D).
Image

Stuart Kovinsky | Kaplan GMAT Faculty | Toronto

Kaplan Exclusive: The Official Test Day Experience | Ready to Take a Free Practice Test? | Kaplan/Beat the GMAT Member Discount
BTG100 for $100 off a full course
Top
Senior | Next Rank: 100 Posts
Posts: 93
Joined: Sun Jan 27, 2008 1:35 am
Thanked: 2 times

by HarvardDreamin » Fri Mar 21, 2008 8:51 am
Many Thanks
ON MY WAY TO HBS......
Top
Senior | Next Rank: 100 Posts
Posts: 59
Joined: Sat Mar 08, 2008 5:15 pm
Location: Cincinnati
Thanked: 3 times

by ritz » Fri Mar 21, 2008 6:25 pm
I dont know if you are still searching for the answer, but here is a much easier & faster way to answer these type of questions.
Q. q3) What is the maximum integer value of M for which 12!/2^M is an integer?
A. 2 B. 4 C. 6 D. 10 E. 12
Sol:-
find out how many times
Step 1:- 2 divides 12!
a) 6
Step 2:- 2 square divides 12!
b) 3
Step 3:- 2 cube divides 12!
c) 1
Step 4:- 2 to the power 4 divides 12!
d) 0
STOP
add
a b c d & that is your answer which is 10.
You can solve any such problems this way.
You can also solve that questions like how many zeroes are there at the end of 20!

regards
Ritz[/b]
Top
Senior | Next Rank: 100 Posts
Posts: 34
Joined: Wed Feb 20, 2008 7:15 pm
Thanked: 6 times
Followed by:1 members

by mmukher » Sat Mar 22, 2008 1:43 pm
ritz wrote: You can also solve that questions like how many zeroes are there at the end of 20!

Ritz[/b]

Not sure I understand ritz, how would we find out how many zeroes at the end of 20! ?

Many thanks
Top
Senior | Next Rank: 100 Posts
Posts: 59
Joined: Sat Mar 08, 2008 5:15 pm
Location: Cincinnati
Thanked: 3 times

by ritz » Sat Mar 22, 2008 1:53 pm
20/5= 4
20/25= 0
As we will surely have more 2's than 5,(zeroes will be created by the multiplication of 5 & 2) so we can safely say that there will be 4 zeroes at the end of 20| (sorry, no factorial sign on my handheld)
Let me know if you have some doubt still...
Top
Senior | Next Rank: 100 Posts
Posts: 34
Joined: Wed Feb 20, 2008 7:15 pm
Thanked: 6 times
Followed by:1 members

by mmukher » Sat Mar 22, 2008 2:02 pm
Nice!... thanks a lot pal.
Top
Post new topic Post Reply
• Page 1 of 1