December 20, 2018 December 20, 2018 10:00 PM PST 11:00 PM PST This is the most inexpensive and attractive price in the market. Get the course now! December 22, 2018 December 22, 2018 07:00 AM PST 09:00 AM PST Attend this webinar to learn how to leverage Meaning and Logic to solve the most challenging Sentence Correction Questions.
Author 
Message 
TAGS:

Hide Tags

Manager
Joined: 10 Nov 2010
Posts: 189
Location: India
Concentration: Strategy, Operations
GMAT 1: 520 Q42 V19 GMAT 2: 540 Q44 V21
WE: Information Technology (Computer Software)

If y is the smallest positive integer such that 3,150 multip
[#permalink]
Show Tags
Updated on: 17 Dec 2012, 07:53
Question Stats:
75% (01:24) correct 25% (01:44) wrong based on 1174 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
Official Answer and Stats are available only to registered users. Register/ Login.
_________________
The proof of understanding is the ability to explain it.
Originally posted by GMATD11 on 08 Mar 2011, 05:37.
Last edited by Bunuel on 17 Dec 2012, 07:53, edited 1 time in total.
Renamed the topic and edited the question.




Math Expert
Joined: 02 Sep 2009
Posts: 51307

Re: y  the smallest +ve integer
[#permalink]
Show Tags
08 Mar 2011, 06:27
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: ifmandnarepositiveintegerand1800mn3whatis108985.htmlpropertyofintegers104272.htmlifxandyarepositiveintegersand180xy100413.htmlnumberproperties92562.htmlcansomeoneanswerthisandtellmewhy92066.htmlogquantitative91750.htmldivisionfactor88388.htmlif5400mnk4wheremnandkarepositiveintegers109284.html
_________________
New to the Math Forum? Please read this: Ultimate GMAT Quantitative Megathread  All You Need for Quant  PLEASE READ AND FOLLOW: 12 Rules for Posting!!! Resources: GMAT Math Book  Triangles  Polygons  Coordinate Geometry  Factorials  Circles  Number Theory  Remainders; 8. Overlapping Sets  PDF of Math Book; 10. Remainders  GMAT Prep Software Analysis  SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS)  Tricky questions from previous years.
Collection of Questions: PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.
What are GMAT Club Tests? Extrahard Quant Tests with Brilliant Analytics




Retired Moderator
Joined: 20 Dec 2010
Posts: 1818

Re: y  the smallest +ve integer
[#permalink]
Show Tags
08 Mar 2011, 05:49
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
_________________
~fluke
GMAT Club Premium Membership  big benefits and savings



Director
Joined: 01 Feb 2011
Posts: 659

Re: y  the smallest +ve integer
[#permalink]
Show Tags
09 Mar 2011, 16:28
Answer is E.
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: 138
Location: United States
Concentration: Finance, Strategy
GPA: 3.7
WE: Account Management (Consumer Products)

Re: If y is the smallest positive integer such that 3150
[#permalink]
Show Tags
23 Mar 2012, 20:27
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: 120
Location: United States
Concentration: Finance, International Business
GPA: 2.54
WE: Accounting (Hospitality and Tourism)

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: 51307

Re: If y is the smallest positive integer such that 3,150 multip
[#permalink]
Show Tags
17 Jul 2013, 21:26



Intern
Joined: 11 Nov 2014
Posts: 34
Concentration: Marketing, Finance
WE: Programming (Computer Software)

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: 9

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



Target Test Prep Representative
Status: Founder & CEO
Affiliations: Target Test Prep
Joined: 14 Oct 2015
Posts: 4328
Location: United States (CA)

Re: If y is the smallest positive integer such that 3,150 multip
[#permalink]
Show Tags
11 May 2016, 06:24
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 WoodburyStewart
Founder and CEO
GMAT Quant SelfStudy Course
500+ lessons 3000+ practice problems 800+ HD solutions



CEO
Joined: 11 Sep 2015
Posts: 3243
Location: Canada

Re: If y is the smallest positive integer such that 3,150 multip
[#permalink]
Show Tags
05 Sep 2018, 07:15
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




Re: If y is the smallest positive integer such that 3,150 multip &nbs
[#permalink]
05 Sep 2018, 07:15






