If y is the smallest positive integer such that 3,150 multip : GMAT Problem Solving (PS)
Check GMAT Club Decision Tracker for the Latest School Decision Releases http://gmatclub.com/AppTrack

 It is currently 21 Jan 2017, 15:21

### 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 y is the smallest positive integer such that 3,150 multip

Author Message
TAGS:

### Hide Tags

Senior Manager
Joined: 10 Nov 2010
Posts: 267
Location: India
Concentration: Strategy, Operations
GMAT 1: 520 Q42 V19
GMAT 2: 540 Q44 V21
WE: Information Technology (Computer Software)
Followers: 5

Kudos [?]: 301 [1] , given: 22

If y is the smallest positive integer such that 3,150 multip [#permalink]

### Show Tags

08 Mar 2011, 05:37
1
KUDOS
15
This post was
BOOKMARKED
00:00

Difficulty:

15% (low)

Question Stats:

73% (02:09) correct 27% (01:23) wrong based on 791 sessions

### HideShow timer Statistics

If y is the smallest positive integer such that 3,150 multiplied by y is the square of an integer, then y must be

(A) 2
(B) 5
(C) 6
(D) 7
(E) 14
[Reveal] Spoiler: OA

_________________

The proof of understanding is the ability to explain it.

Last edited by Bunuel on 17 Dec 2012, 07:53, edited 1 time in total.
Renamed the topic and edited the question.
Math Forum Moderator
Joined: 20 Dec 2010
Posts: 2021
Followers: 161

Kudos [?]: 1705 [1] , given: 376

Re: y - the smallest +ve integer [#permalink]

### Show Tags

08 Mar 2011, 05:49
1
KUDOS
GMATD11 wrote:
142.) If y is the smallest positive integer such that 3150 multiplied by y is the square of an integer, then y must be

a) 2
b) 5
c) 6
d) 7
e) 14

upon factoring 3150 i got following prime factors 3,3,5,5 nd 2

You missed 7 as a prime factor of 3150.

3150 = 3,3,5,5,2 and 7
_________________
Math Expert
Joined: 02 Sep 2009
Posts: 36590
Followers: 7092

Kudos [?]: 93361 [2] , given: 10557

Re: y - the smallest +ve integer [#permalink]

### Show Tags

08 Mar 2011, 06:27
2
KUDOS
Expert's post
9
This post was
BOOKMARKED
GMATD11 wrote:
142.) If y is the smallest positive integer such that 3150 multiplied by y is the square of an integer, then y must be

a) 2
b) 5
c) 6
d) 7
e) 14

upon factoring 3150 i got following prime factors 3,3,5,5 nd 2

3,150=2*3^2*5^2*7, now 3,150*y to be a perfect square y must complete the odd powers of 2 and 7 to even number (perfect square has even powers of its primes), so the least value of y is 2*7=14. In this case 3,150y=(2*3^2*5^2*7)*(2*7)=(2*3*5*7)^2=perfect square.

Similar questions to practice:

if-m-and-n-are-positive-integer-and-1800m-n3-what-is-108985.html
property-of-integers-104272.html
if-x-and-y-are-positive-integers-and-180x-y-100413.html
number-properties-92562.html
og-quantitative-91750.html
division-factor-88388.html
if-5400mn-k4-where-m-n-and-k-are-positive-integers-109284.html
_________________
Director
Joined: 01 Feb 2011
Posts: 755
Followers: 14

Kudos [?]: 115 [0], given: 42

Re: y - the smallest +ve integer [#permalink]

### Show Tags

09 Mar 2011, 16:28

on prime factorization 3150 can be expressed as 2 *(3^2)*(5^2)*7

to make the above number a perfect square , we know it atleast need to multiply this by 2*7 = 14
Manager
Joined: 27 Oct 2011
Posts: 191
Location: United States
Concentration: Finance, Strategy
GMAT 1: Q V
GPA: 3.7
WE: Account Management (Consumer Products)
Followers: 5

Kudos [?]: 150 [1] , given: 4

Re: If y is the smallest positive integer such that 3150 [#permalink]

### Show Tags

23 Mar 2012, 20:27
1
KUDOS
1
This post was
BOOKMARKED
E.

Create a prime factor tree for 3,150 and see what numbers do not have a pair.
3150 = 5x5x3x3x7x2.... the 7 and 2 do not have a second pair to make it a perfect square of a number. so y must be 7*2 = 14
_________________

DETERMINED TO BREAK 700!!!

Manager
Joined: 29 Mar 2010
Posts: 141
Location: United States
GMAT 1: 590 Q28 V38
GPA: 2.54
WE: Accounting (Hospitality and Tourism)
Followers: 1

Kudos [?]: 114 [0], given: 16

Re: If y is the smallest positive integer such that 3,150 multip [#permalink]

### Show Tags

17 Jul 2013, 20:09
Where can I find the logic of how to answer this question?

Is there a section in the math guide that covers this?

Thanks,
Hunter
_________________

4/28 GMATPrep 42Q 36V 640

Math Expert
Joined: 02 Sep 2009
Posts: 36590
Followers: 7092

Kudos [?]: 93361 [1] , given: 10557

Re: If y is the smallest positive integer such that 3,150 multip [#permalink]

### Show Tags

17 Jul 2013, 21:26
1
KUDOS
Expert's post
hfbamafan wrote:
Where can I find the logic of how to answer this question?

Is there a section in the math guide that covers this?

Thanks,
Hunter

No special section covers this, but I can recommend similar questions:
if-m-and-n-are-positive-integer-and-1800m-n3-what-is-108985.html
property-of-integers-104272.html
if-x-and-y-are-positive-integers-and-180x-y-100413.html
number-properties-92562.html
og-quantitative-91750.html
division-factor-88388.html
if-5400mn-k4-where-m-n-and-k-are-positive-integers-109284.html

Hope it helps.
_________________
GMAT Club Legend
Joined: 09 Sep 2013
Posts: 13489
Followers: 576

Kudos [?]: 163 [0], given: 0

Re: If y is the smallest positive integer such that 3,150 multip [#permalink]

### Show Tags

15 Aug 2014, 13:24
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: 13489
Followers: 576

Kudos [?]: 163 [0], given: 0

Re: If y is the smallest positive integer such that 3,150 multip [#permalink]

### Show Tags

02 Sep 2015, 16:09
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.
_________________
Intern
Joined: 11 Nov 2014
Posts: 42
Concentration: Marketing, Finance
WE: Programming (Computer Software)
Followers: 0

Kudos [?]: 9 [0], given: 101

Re: If y is the smallest positive integer such that 3,150 multip [#permalink]

### Show Tags

10 May 2016, 23:44
3150 = 3 * 1050 = 3*3*350 = 3*3*35*10
= 3*3*5*7*5*2
= (3)^2 * (5)^2 * 14
So we can say
if we want this number to be a perfect square
this has to be multiplied with 14 .
y=14
Intern
Joined: 10 May 2016
Posts: 8
Followers: 0

Kudos [?]: 0 [0], given: 6

Re: If y is the smallest positive integer such that 3,150 multip [#permalink]

### Show Tags

11 May 2016, 01:02
Logic for a number to be square = all its prime factors should have power 2

3150 = (5^2)(3^2)(2*7)

Only 2 and 7 do not have power 2

to make power 2 multiply with 2*7=14
Director
Status: Founder & CEO
Affiliations: Target Test Prep
Joined: 14 Oct 2015
Posts: 511
Location: United States (CA)
Followers: 20

Kudos [?]: 189 [2] , given: 2

Re: If y is the smallest positive integer such that 3,150 multip [#permalink]

### Show Tags

11 May 2016, 06:24
2
KUDOS
GMATD11 wrote:
If y is the smallest positive integer such that 3,150 multiplied by y is the square of an integer, then y must be

(A) 2
(B) 5
(C) 6
(D) 7
(E) 14

Solution:

This problem is testing us on the rule that when we express a perfect square by its unique prime factors, every prime factor's exponent is an even number.

Let’s start by prime factorizing 3,150.

3,150 = 315 x 10 = 5 x 63 x 10 = 5 x 7 x 3 x 3 x 5 x 2

3,150 = 2^1 x 3^2 x 5^2 x 7^1

(Notice that the exponents of both 2 and 7 are not even numbers. This tells us that 3,150 itself is not a perfect square.)

We also are given that 3,150 multiplied by y is the square of an integer. We can write this as:

2^1 x 3^2 x 5^2 x 7^1 x y = square of an integer

According to our rule, we need all unique prime factors' exponents to be even numbers. Thus, we need one more 2 and one more 7. Therefore, y = 7 x 2 = 14

_________________

Jeffrey Miller
Scott Woodbury-Stewart
Founder and CEO

Re: If y is the smallest positive integer such that 3,150 multip   [#permalink] 11 May 2016, 06:24
Similar topics Replies Last post
Similar
Topics:
53 If x is the smallest positive integer that is not prime and 25 30 Jul 2013, 11:07
2 If k is the smallest positive integer such that 2,940k 5 04 May 2013, 09:17
2 What is the smallest positive integer K such that the 6 29 Dec 2010, 14:36
19 What is the smallest positive integer n for which 324 is a 15 19 Jun 2010, 00:09
16 If y is the smallest positive integer such that 3,150 13 12 Jun 2008, 04:00
Display posts from previous: Sort by