GMAT Question of the Day - Daily to your Mailbox; hard ones only

 It is currently 16 Jan 2019, 12:27

### 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

## Events & Promotions

###### Events & Promotions in January
PrevNext
SuMoTuWeThFrSa
303112345
6789101112
13141516171819
20212223242526
272829303112
Open Detailed Calendar
• ### The winning strategy for a high GRE score

January 17, 2019

January 17, 2019

08:00 AM PST

09:00 AM PST

Learn the winning strategy for a high GRE score — what do people who reach a high score do differently? We're going to share insights, tips and strategies from data we've collected from over 50,000 students who used examPAL.
• ### Free GMAT Strategy Webinar

January 19, 2019

January 19, 2019

07:00 AM PST

09:00 AM PST

Aiming to score 760+? Attend this FREE session to learn how to Define your GMAT Strategy, Create your Study Plan and Master the Core Skills to excel on the GMAT.

# X is the product of integers from 1 to 50

Author Message
TAGS:

### Hide Tags

Current Student
Joined: 19 Aug 2016
Posts: 149
Location: India
GMAT 1: 640 Q47 V31
GPA: 3.82
X is the product of integers from 1 to 50  [#permalink]

### Show Tags

08 Apr 2017, 06:52
1
8
00:00

Difficulty:

65% (hard)

Question Stats:

61% (02:17) correct 39% (01:32) wrong based on 115 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

_________________

Consider giving me Kudos if you find my posts useful, challenging and helpful!

Senior Manager
Status: Countdown Begins...
Joined: 03 Jul 2016
Posts: 289
Location: India
Concentration: Technology, Strategy
Schools: IIMB
GMAT 1: 580 Q48 V22
GPA: 3.7
WE: Information Technology (Consulting)
X is the product of integers from 1 to 50  [#permalink]

### Show Tags

08 Apr 2017, 09:28
1
ashikaverma13 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

$$12^n = 2^(2n)*3^n$$

We have many 2's in the product of 1 to 50. thus we need to find number of 3's in product 1-50

1-30 = 10 + 1(9) + 1(18) +2(27)
31- 50 = 6(33- 48) + 1(36) + 1(45) = 22
Current Student
Joined: 19 Aug 2016
Posts: 149
Location: India
GMAT 1: 640 Q47 V31
GPA: 3.82
Re: X is the product of integers from 1 to 50  [#permalink]

### Show Tags

08 Apr 2017, 09:33
RMD007 wrote:
ashikaverma13 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

$$12^n = 2^(2n)*3^n$$

We have many 2's in the product of 1 to 50. thus we need to find number of 3's in product 1-50

1-30 = 10 + 1(9) + 1(18) +2(27)
31- 50 = 6(33- 48) + 1(36) + 1(45) = 22

Can you explain a bit more? Why is only finding the number of 3s enough?
_________________

Consider giving me Kudos if you find my posts useful, challenging and helpful!

Board of Directors
Status: QA & VA Forum Moderator
Joined: 11 Jun 2011
Posts: 4331
Location: India
GPA: 3.5
Re: X is the product of integers from 1 to 50  [#permalink]

### Show Tags

08 Apr 2017, 10:27
1
ashikaverma13 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

X is the product of integers from 1 to 50, inclusive = 50!

$$12 = 2^2*3$$

Highest power of 2 that will divide 50! is 47

$$\frac{50}{2} = 25$$
$$\frac{25}{2} = 12$$
$$\frac{12}{2} = 6$$
$$\frac{6}{2} = 3$$
$$\frac{3}{2} = 1$$

Highest power of 3 that will divide 50! is 22

$$\frac{50}{3} = 16$$
$$\frac{16}{3} = 5$$
$$\frac{5}{3} = 1$$

Since the highest power of 3 < 2 , the highest power of $$12^n$$ that will divide 50! will be 22 , hence, answer will be (C) 22.
_________________

Thanks and Regards

Abhishek....

PLEASE FOLLOW THE RULES FOR POSTING IN QA AND VA FORUM AND USE SEARCH FUNCTION BEFORE POSTING NEW QUESTIONS

How to use Search Function in GMAT Club | Rules for Posting in QA forum | Writing Mathematical Formulas |Rules for Posting in VA forum | Request Expert's Reply ( VA Forum Only )

Senior Manager
Status: Countdown Begins...
Joined: 03 Jul 2016
Posts: 289
Location: India
Concentration: Technology, Strategy
Schools: IIMB
GMAT 1: 580 Q48 V22
GPA: 3.7
WE: Information Technology (Consulting)
Re: X is the product of integers from 1 to 50  [#permalink]

### Show Tags

08 Apr 2017, 22:45
ashikaverma13 wrote:
RMD007 wrote:
We have many 2's in the product of 1 to 50. thus we need to find number of 3's in product 1-50

1-30 = 10 + 1(9) + 1(18) +2(27)
31- 50 = 6(33- 48) + 1(36) + 1(45) = 22

Can you explain a bit more? Why is only finding the number of 3s enough?

Sure. We have a product of numbers from 1 to 50 and the question says it is divisible by $$12^n$$ = $$2^(2n)*3^n$$

We have two prime factors 2 and 3 and we need to find such maximum value of n for which $$2^(2n)$$and $$3^n$$ both will be part of this product.

Now, as we glance through the product of 1 to 50, we know that number of 2's in the product will be greater than number of 3's present . So we if find the number of 3's, such number will obviously be less than 2's and hence it will be sufficient to say that $$12^n$$ is divisible by product of 1-50.

Hope this helps..
Non-Human User
Joined: 09 Sep 2013
Posts: 9414
Re: X is the product of integers from 1 to 50  [#permalink]

### Show Tags

09 Dec 2018, 08:43
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
_________________
Re: X is the product of integers from 1 to 50 &nbs [#permalink] 09 Dec 2018, 08:43
Display posts from previous: Sort by