GMAT Question of the Day: Daily via email | Daily via Instagram New to GMAT Club? Watch this Video

 It is currently 22 Feb 2020, 00:53

### GMAT Club Daily Prep

#### Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

# X is the product of integers from 1 to 50, inclusive. If 12^N is a fac

Author Message
TAGS:

### Hide Tags

Math Expert
Joined: 02 Sep 2009
Posts: 61385
X is the product of integers from 1 to 50, inclusive. If 12^N is a fac  [#permalink]

### Show Tags

09 Dec 2019, 01:13
00:00

Difficulty:

55% (hard)

Question Stats:

58% (01:51) correct 42% (01:46) wrong based on 57 sessions

### HideShow timer Statistics

X is the product of integers from 1 to 50, inclusive. If 12^N is a factor of X, what is the greatest possible value of N?

A. 4
B. 12
C. 22
D. 28
E. 57

Are You Up For the Challenge: 700 Level Questions

_________________
Senior PS Moderator
Joined: 26 Feb 2016
Posts: 3265
Location: India
GPA: 3.12
X is the product of integers from 1 to 50, inclusive. If 12^N is a fac  [#permalink]

### Show Tags

09 Dec 2019, 01:33
4
The formula for finding the highest power of a prime number in a factorial

If p is a prime number, then the highest power of p in a factorial n is {$$\frac{n}{p}$$} + {$$\frac{n}{p^2}$$} + {$$\frac{n}{p^3}$$}.....
where {$$\frac{a}{b}$$} is the quotient when integer b divides another integer a

Now coming to the problem at hand.

n = $$50$$
p = $$12 = 2^2*3$$

To find the highest power of 12, we need to find the highest power of 3(which is the bigger prime number)
Here, the bigger the prime number the lower will the frequency of that prime be in the factorial.

Therefore, the highest power of 12 in 50 is $${\frac{50}{3}} + {\frac{50}{3^2}} + {\frac{50}{3^3}} = 16 + 5 + 1 = 22$$(Option C)
_________________
You've got what it takes, but it will take everything you've got
VP
Joined: 24 Nov 2016
Posts: 1224
Location: United States
X is the product of integers from 1 to 50, inclusive. If 12^N is a fac  [#permalink]

### Show Tags

11 Dec 2019, 05:39
1
Bunuel wrote:
X is the product of integers from 1 to 50, inclusive. If 12^N is a factor of X, what is the greatest possible value of N?

A. 4
B. 12
C. 22
D. 28
E. 57

$$50!/{12}^n=50!/(2^23)^n$$
$$quotients(50/[2^1,2^2,2^3…2^x])=25+12+6+3=46$$
$$quotients(50/[3^1,3^2,3^3…3^x])=16+5+1=22$$
$$50!/(12)^n=(2^23)^n=(2^{2n}*3^n)=2^{2(22)}*3^{22}=(12)^{22}$$

Ans (C)
X is the product of integers from 1 to 50, inclusive. If 12^N is a fac   [#permalink] 11 Dec 2019, 05:39
Display posts from previous: Sort by