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

It is currently 16 Dec 2019, 00:33

Close

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
Your Progress

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

Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.

Close

Request Expert Reply

Confirm Cancel

If y is the smallest positive integer such that 3,150 multiplied by y

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

Hide Tags

Find Similar Topics 
Intern
Intern
User avatar
Joined: 17 May 2008
Posts: 9
If y is the smallest positive integer such that 3,150 multiplied by y  [#permalink]

Show Tags

New post Updated on: 21 Aug 2019, 00:05
4
33
00:00
A
B
C
D
E

Difficulty:

  15% (low)

Question Stats:

79% (01:21) correct 21% (01:51) wrong based on 1454 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

Originally posted by mrwaxy on 12 Jun 2008, 05:00.
Last edited by Bunuel on 21 Aug 2019, 00:05, edited 4 times in total.
Added the OA
Most Helpful Expert Reply
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 59739
Re: If y is the smallest positive integer such that 3,150 multiplied by y  [#permalink]

Show Tags

New post 28 Jan 2012, 18:00
12
12
mrwaxy 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

Detailed explanation would be appreciated.


\(3,150=2*3^2*5^2*7\), 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 \(3,150y=(2*3^2*5^2*7)*(2*7)=(2*3*5*7)^2=perfect \ square\).

Answer: E.

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
can-someone-answer-this-and-tell-me-why-92066.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.
_________________
General Discussion
Veritas Prep GMAT Instructor
User avatar
V
Joined: 16 Oct 2010
Posts: 9880
Location: Pune, India
Re: Arithmetic properties  [#permalink]

Show Tags

New post 23 Feb 2011, 19:32
Baten80 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


This question is based on the concept that when you prime factorize a perfect square, the power of every distinct prime factor is even. The reason for this is given in the following blog posts:
http://www.veritasprep.com/blog/2010/12/quarter-wit-quarter-wisdom-writing-factors-of-an-ugly-number/
http://www.veritasprep.com/blog/2010/12/quarter-wit-quarter-wisdom-factors-of-perfect-squares/

3150 is not a perfect square i.e. square of an integer because
\(3150 = 2*3^2*5^2*7\)

Note that 3 and 5 have even powers (2 each) while 2 and 7 have a power of 1 each. Hence to make 3150 a perfect square, we need to make all powers even. So if we multiply 3150 by 2*7, powers of all prime factors will become even.
\(3150*2*7 = 2^2*3^2*5^2*7^2\) - A perfect square

Answer (E).

Similarly, if you had to divide 3150 by the smallest number to get a perfect square, you would have divided it by 2*7 to get rid of 2 and 7 completely so that the remaining prime factors have even powers,
\(3150/(2*7) = 3^2*5^2\) - A perfect square
_________________
Karishma
Veritas Prep GMAT Instructor

Learn more about how Veritas Prep can help you achieve a great GMAT score by checking out their GMAT Prep Options >
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 59739
Re: If y is the smallest positive integer such that 3,150 multiplied by y  [#permalink]

Show Tags

New post 08 Mar 2011, 07:27
6
14
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.

Answer: E.

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
can-someone-answer-this-and-tell-me-why-92066.html
og-quantitative-91750.html
division-factor-88388.html
if-5400mn-k4-where-m-n-and-k-are-positive-integers-109284.html
_________________
Manager
Manager
User avatar
Joined: 27 Oct 2011
Posts: 116
Location: United States
Concentration: Finance, Strategy
GPA: 3.7
WE: Account Management (Consumer Products)
Re: If y is the smallest positive integer such that 3,150 multiplied by y  [#permalink]

Show Tags

New post 28 Jan 2012, 17:42
2
2
answer E. factor out the number and find any prime numbers that are not paired. 7 & 2.
Manager
Manager
User avatar
Joined: 27 Oct 2011
Posts: 116
Location: United States
Concentration: Finance, Strategy
GPA: 3.7
WE: Account Management (Consumer Products)
Re: If y is the smallest positive integer such that 3,150 multiplied by y  [#permalink]

Show Tags

New post 23 Mar 2012, 21:27
2
2
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
Manager
Manager
avatar
Joined: 28 Feb 2012
Posts: 103
Concentration: Strategy, International Business
Schools: INSEAD Jan '13
GPA: 3.9
WE: Marketing (Other)
GMAT ToolKit User
Re: If y is the smallest positive integer such that 3,150 multiplied by y  [#permalink]

Show Tags

New post 13 Jun 2013, 02:07
1
1
mrwaxy 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


In such questions we need to break the number into the smallest possible prime factors. So the smallest prime factors of 3150 are:
315*10=63*5*2*5=7*9*5*2*5=7*3*3*5*2*5. In order to get a square of an integer we have to have at least two identical primes. In our case we have 3*3 and 5*5 corresponding to this condition but not 2*7 so our smallest number should be 14.

Answer is E
Manager
Manager
avatar
Joined: 29 Mar 2010
Posts: 113
Location: United States
Concentration: Finance, International Business
GMAT 1: 590 Q28 V38
GPA: 2.54
WE: Accounting (Hospitality and Tourism)
GMAT ToolKit User
Re: If y is the smallest positive integer such that 3,150 multiplied by y  [#permalink]

Show Tags

New post 17 Jul 2013, 21:09
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
User avatar
V
Joined: 02 Sep 2009
Posts: 59739
Re: If y is the smallest positive integer such that 3,150 multiplied by y  [#permalink]

Show Tags

New post 17 Jul 2013, 22:26
1
1
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
can-someone-answer-this-and-tell-me-why-92066.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.
_________________
Director
Director
User avatar
Joined: 14 Dec 2012
Posts: 687
Location: India
Concentration: General Management, Operations
GMAT 1: 700 Q50 V34
GPA: 3.6
GMAT ToolKit User
Re: If y is the smallest positive integer such that 3,150 multiplied by y  [#permalink]

Show Tags

New post 29 Aug 2013, 01:35
1
kumar83 wrote:
if y is the smallest positive interger such that 3150 multiplied by y is the square of an interger, that Y must be

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


Kindly Explain.


3150 =\(2*3^2*5^2*7\)
For it to be perfect square all the prime number should be least raised to the power 2
in 3150 ...only 2 and 7 needs to be multiplied so that all prime will be raised power 2
hence least value of \(4y = 2*7 = 14\)

hence E
_________________
When you want to succeed as bad as you want to breathe ...then you will be successfull....

GIVE VALUE TO OFFICIAL QUESTIONS...



GMAT RCs VOCABULARY LIST: http://gmatclub.com/forum/vocabulary-list-for-gmat-reading-comprehension-155228.html
learn AWA writing techniques while watching video : http://www.gmatprepnow.com/module/gmat-analytical-writing-assessment
: http://www.youtube.com/watch?v=APt9ITygGss
Intern
Intern
avatar
Joined: 04 Jun 2014
Posts: 46
Re: If y is the smallest positive integer such that 3,150 multiplied by y  [#permalink]

Show Tags

New post 22 Jul 2014, 04:18
Hello,

can anyone help me with this type of question? I don't get it why the remaining numbers, 7 and 2, are the smallest positive integer y. Which chapter in the MGMAT books should i restudy to deal with this kind of problem? I don't understand the explanation in the OG which says: "To be a perfect square, 3,150y must have an even number of each of its prime factors."

Any help is appreciated!
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 59739
Re: If y is the smallest positive integer such that 3,150 multiplied by y  [#permalink]

Show Tags

New post 22 Jul 2014, 04:31
lou34 wrote:
Hello,

can anyone help me with this type of question? I don't get it why the remaining numbers, 7 and 2, are the smallest positive integer y. Which chapter in the MGMAT books should i restudy to deal with this kind of problem? I don't understand the explanation in the OG which says: "To be a perfect square, 3,150y must have an even number of each of its prime factors."

Any help is appreciated!


Have you checked this: if-y-is-the-smallest-positive-integer-such-that-65323.html#p1035828

Similar questions to practice:
if-n-is-a-positive-integer-and-n-2-is-divisible-by-96-then-127364.html
if-n-is-a-positive-integer-and-n-2-is-divisible-by-72-then-90523.html
a-certain-clock-marks-every-hour-by-striking-a-number-of-tim-91750.html
if-m-and-n-are-positive-integer-and-1800m-n3-what-is-108985.html
if-x-and-y-are-positive-integers-and-180x-y-100413.html
n-is-a-positive-integer-and-k-is-the-product-of-all-integer-104272.html
if-x-is-a-positive-integer-and-x-2-is-divisible-by-32-then-88388.html
if-n-and-y-are-positive-integers-and-450y-n-92562.html
if-5400mn-k-4-where-m-n-and-k-are-positive-integers-109284.html
if-a-and-n-are-integers-and-a-2-24n-then-n-must-be-173533.html
if-n-and-y-are-positive-integers-and-450y-n-92562.html
if-n-and-y-are-positive-integers-and-450y-n-92562.html

Hope this helps.
_________________
Target Test Prep Representative
User avatar
V
Status: Founder & CEO
Affiliations: Target Test Prep
Joined: 14 Oct 2015
Posts: 8715
Location: United States (CA)
Re: If y is the smallest positive integer such that 3,150 multiplied by y  [#permalink]

Show Tags

New post 11 May 2016, 07:24
5
1
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

Answer is E.
_________________

Scott Woodbury-Stewart

Founder and CEO

Scott@TargetTestPrep.com
TTP - Target Test Prep Logo
122 Reviews

5-star rated online GMAT quant
self study course

See why Target Test Prep is the top rated GMAT quant course on GMAT Club. Read Our Reviews

If you find one of my posts helpful, please take a moment to click on the "Kudos" button.

GMAT Club Legend
GMAT Club Legend
User avatar
V
Joined: 12 Sep 2015
Posts: 4158
Location: Canada
Re: If y is the smallest positive integer such that 3,150 multiplied by y  [#permalink]

Show Tags

New post 24 Aug 2017, 12:03
1
Top Contributor
mrwaxy 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


Key concept: The prime factorization of a perfect square (the square of an integer) will have an EVEN number of each prime.
For example, 36 = (2)(2)(3)(3)
And 400 = (2)(2)(2)(2)(5)(5)

Likewise, 3150y must have an EVEN number of each prime in its prime factorization.
So, 3150y = (2)(3)(3)(5)(5)(7)y
We have an EVEN number of 3's and 7's, but we have a single 2 and a single 7.
If y = (2)(7), then we get a perfect square.

That is: 3150y = (2)(2)(3)(3)(5)(5)(7)(7)

So, if y = 14, then 3150y is a perfect square.

Answer:

RELATED VIDEO FROM OUR COURSE

_________________
Test confidently with gmatprepnow.com
Image
Intern
Intern
User avatar
B
Joined: 28 Apr 2016
Posts: 43
Location: United States
GMAT 1: 780 Q51 V47
GPA: 3.9
Re: If y is the smallest positive integer such that 3,150 multiplied by y  [#permalink]

Show Tags

New post 26 Aug 2018, 00:30
I wanted to share my GMAT Timing Tips for this question (the links below include growing lists of questions that you can use to practice these tips):

Prime factors of a perfect square, perfect cube, etc.: As others in this thread have pointed out, we need to know that all prime factors of a perfect square have exponents that are even. If we find that any of the prime factors of 3,150 do not have even exponents, y will need to contain each of those prime factors, so that the prime factorization of 3,150*y will have an even exponent for each of those prime factors.

Prime factorization: In order to determine the prime factors of y, we need to do the prime factorization of 3,150, so let's try to do it as efficiently as possible. Because factors of 10 and 5 are easy to see, I recommend starting by factoring 3,150 into 315*10, then 63*5*2*5. We can also recognize that 63 = 9*7 = 3^2 *7. This means that the prime factorization of 3,150 is 2 * 3^2 * 5^2 * 7. Since there are odd powers of 2 and 7, y must contain factors of 2 and 7, and the smallest possible value of y is 2*7 = 14.

Please let me know if you have any questions, or if you would like me to post a video solution!
_________________
Online GMAT tutor with a 780 GMAT score. Harvard graduate.

Please read and share my free GMAT Timing Strategy Guide!
GMAT Club Legend
GMAT Club Legend
User avatar
V
Joined: 12 Sep 2015
Posts: 4158
Location: Canada
Re: If y is the smallest positive integer such that 3,150 multiplied by y  [#permalink]

Show Tags

New post 05 Sep 2018, 08:15
Top Contributor
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


Key concept: The prime factorization of a perfect square (the square of an integer) will have an EVEN number of each prime.
For example, 36 = (2)(2)(3)(3)
And 400 = (2)(2)(2)(2)(5)(5)
Likewise, 3150y must have an EVEN number of each prime in its prime factorization.


So, 3150y = (2)(3)(3)(5)(5)(7)y
We have an EVEN number of 3's and 7's, but we have a single 2 and a single 7.
If y = (2)(7), then we get a perfect square.

That is: 3150y = (2)(2)(3)(3)(5)(5)(7)(7)

So, if y = 14, then 3150y is a perfect square.

Answer: E

Cheers,
Brent
_________________
Test confidently with gmatprepnow.com
Image
Non-Human User
User avatar
Joined: 09 Sep 2013
Posts: 13743
Re: If y is the smallest positive integer such that 3,150 multiplied by y  [#permalink]

Show Tags

New post 13 Sep 2019, 16:59
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 Bot
Re: If y is the smallest positive integer such that 3,150 multiplied by y   [#permalink] 13 Sep 2019, 16:59
Display posts from previous: Sort by

If y is the smallest positive integer such that 3,150 multiplied by y

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





Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne