It is currently 24 Jun 2017, 08:52

### 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 June
Open Detailed Calendar

# If both 5^2 and 3^3 are factors of n x (2^5) x (6^2) x (7^3)

 new topic post reply Question banks Downloads My Bookmarks Reviews Important topics
Author Message
TAGS:

### Hide Tags

Intern
Joined: 02 Oct 2013
Posts: 2
If both 5^2 and 3^3 are factors of n x (2^5) x (6^2) x (7^3) [#permalink]

### Show Tags

13 Oct 2013, 20:13
1
KUDOS
2
This post was
BOOKMARKED
00:00

Difficulty:

25% (medium)

Question Stats:

69% (01:58) correct 31% (01:09) wrong based on 150 sessions

### HideShow timer Statistics

If both 5^2 and 3^3 are factors of n x (2^5) x (6^2) x (7^3), what is the smallest possible positive value of n?

A. 25
B. 27
C. 45
D. 75
E. 125
[Reveal] Spoiler: OA

Last edited by Bunuel on 17 Nov 2013, 13:56, edited 2 times in total.
Renamed the topic and edited the question.
Manager
Joined: 18 Dec 2012
Posts: 96
Location: India
Concentration: General Management, Strategy
GMAT 1: 660 Q49 V32
GMAT 2: 530 Q37 V25
GPA: 3.32
WE: Manufacturing and Production (Manufacturing)
Re: Factor/exponent question [#permalink]

### Show Tags

13 Oct 2013, 21:10
2
KUDOS
john4 wrote:
If both 5^2 and 3^3 are factors of n x (2^5) x (6^2) x (7^3), what is the smallest possible positive value of n?

A.) 25
B.) 27
C.) 45
D.) 75
E.) 125

I don't understand how to tackle this question. Thanks!

Hi John,

Solution :
$$(2^5) * (6^2) * (7^3) * n$$ is the given number.

If both 5^2 & 3^3 are factors, then they must be present in the number.

Leaving rest of the prime factors and splitting 6^2 into 3^2 * 2^3.

The number is lacking 5^2 & a 3, so that 5^2 and 3^3 is a factor.

Hence the smallest number is 5^2 * 3 = 75

Hope it is clear

Cheers
Qoofi
_________________

I'm telling this because you don't get it. You think you get it which is not the same as actually getting it. Get it?

Intern
Joined: 31 Aug 2013
Posts: 15
Re: Factor/exponent question [#permalink]

### Show Tags

17 Nov 2013, 13:55
Hello qoofi,

Please explain me more clearer.
Please check I dont get the answer of this question,

If both 5^2 and 3^3 are factors of n x (2^5) x (6^2) x (7^3) :

It means that n*2^5*6^2*7^3 his number is dicvisible by these 2 factors.
If it is divisible so we can write the equation as,

n*5^2*6^2*7^3/5^2*3^3
= n*5^2*(2^2*3^2) *7^3/5^2*3^3=so after this how to get the answer I dont get it.
Intern
Status: preparing for the GMAT
Joined: 16 Jul 2013
Posts: 39
Concentration: Technology, Entrepreneurship
GMAT Date: 10-15-2013
GPA: 3.53
Re: Factor/exponent question [#permalink]

### Show Tags

26 Nov 2013, 09:19
1
KUDOS
sumit88 wrote:
Hello qoofi,

Please explain me more clearer.
Please check I dont get the answer of this question,

If both 5^2 and 3^3 are factors of n x (2^5) x (6^2) x (7^3) :

It means that n*2^5*6^2*7^3 his number is dicvisible by these 2 factors.
If it is divisible so we can write the equation as,

n*5^2*6^2*7^3/5^2*3^3
= n*5^2*(2^2*3^2) *7^3/5^2*3^3=so after this how to get the answer I dont get it.

First, if a number, lets say X, is a factor of another number, lets say Y . Then Y is divisible by X

In the question, both 5^2 and 3^3 are factors of n x (2^5) x (6^2) x (7^3), so n x (2^5) x (6^2) x (7^3) must be divisible by 5^2 and 3^3

we can rewrite n x (2^5) x (6^2) x (7^3) as n x (2^5) x (2^2) x (3^2) x (7^3)

so to make (2^5) x (2^2) x (3^2) x (7^3) divisible by 5^2 and 3^3, we need 5^2 and 3^1 ( if Y is divisible by X, then all prime factors of X must also be prime factors of Y)

so n= 5^2 and 3^1 which equals 75.

hope you find it helpful.
_________________

لا الله الا الله, محمد رسول الله

You never fail until you stop trying ,,,

SVP
Status: The Best Or Nothing
Joined: 27 Dec 2012
Posts: 1857
Location: India
Concentration: General Management, Technology
WE: Information Technology (Computer Software)
Re: If both 5^2 and 3^3 are factors of n x (2^5) x (6^2) x (7^3) [#permalink]

### Show Tags

26 Feb 2014, 01:46
Just compare 5^2 and 3^3 with >>>>>>>> (2^5) x (6^2) x (7^3)

5^2 = 25 is not present; also 3^2 is present instead of 3^3, so one additional 3 is required as well

So, n= 25x3 = 75 = Answer = D
_________________

Kindly press "+1 Kudos" to appreciate

GMAT Club Legend
Joined: 09 Sep 2013
Posts: 15945
Re: If both 5^2 and 3^3 are factors of n x (2^5) x (6^2) x (7^3) [#permalink]

### Show Tags

08 Jun 2015, 14:40
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.
_________________
GMAT Club Legend
Joined: 09 Sep 2013
Posts: 15945
Re: If both 5^2 and 3^3 are factors of n x (2^5) x (6^2) x (7^3) [#permalink]

### Show Tags

14 Sep 2016, 01:29
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: If both 5^2 and 3^3 are factors of n x (2^5) x (6^2) x (7^3)   [#permalink] 14 Sep 2016, 01:29
Similar topics Replies Last post
Similar
Topics:
1 If 5^x+5^x+5^x+5^x+5^x=25^n, x=? 5 10 Jun 2017, 00:03
3 If the expression x^2 – xy/5 + 25 can be expressed by (x – 5)^2, what 4 21 May 2017, 22:30
What is the greatest value of x such that 5^x is a factor of 25! ? 2 08 Dec 2016, 10:57
13 If x^2−5x+6=2−|x−1|, what is the product of all possible values of x? 7 29 May 2016, 21:50
4 If x ,y, and z are all factors of 25, which of the following 4 09 Jan 2016, 08:29
Display posts from previous: Sort by

# If both 5^2 and 3^3 are factors of n x (2^5) x (6^2) x (7^3)

 new topic post reply Question banks Downloads My Bookmarks Reviews Important topics

 Powered by phpBB © phpBB Group and phpBB SEO Kindly note that the GMAT® test is a registered trademark of the Graduate Management Admission Council®, and this site has neither been reviewed nor endorsed by GMAC®.