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.
Thank you for using the timer!
We noticed you are actually not timing your practice. Click the START button first next time you use the timer.
There are many benefits to timing your practice, including:
Join the live F2F session with the Admission Directors from Rotman School of Management and Ivey Business School to find out why Canada is increasingly becoming the go-to destination for several MBA aspirants, and gain critical insights....
A live session in which Greg Guglielmo, Haas MBA & Founder of Avanti Prep, analyses resumes of MBA applicants, and suggests ways of improvement in one on one talk with concerned applicants.
Leadership is one of the most important characteristics schools look for in applicants. This session will help define exactly what leadership is and how you can best showcase it in your essays.
Start by taking a free, full-length practice test—at your convenience. Receive a detailed score analysis to understand your strengths and see where you need to improve.
GMAT tests your ability to think critically by presenting "tricky" arguments that require you to notice flaws or vulnerabilities in the construct. e-GMAT is conducting a free webinar in which you can learn the art to decode difficult CR questions.
Re: If y is the smallest positive integer such that 3,150 multiplied by y
[#permalink]
Show Tags
28 Jan 2012, 17:00
19
16
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 \(3,150y=(2*3^2*5^2*7)*(2*7)=(2*3*5*7)^2=perfect \ square\).
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 >
Re: If y is the smallest positive integer such that 3,150 multiplied by y
[#permalink]
Show Tags
08 Mar 2011, 06:27
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.
Re: If y is the smallest positive integer such that 3,150 multiplied by y
[#permalink]
Show Tags
23 Mar 2012, 20:27
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
Re: If y is the smallest positive integer such that 3,150 multiplied by y
[#permalink]
Show Tags
13 Jun 2013, 01:07
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.
Re: If y is the smallest positive integer such that 3,150 multiplied by y
[#permalink]
Show Tags
29 Aug 2013, 00:35
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
Re: If y is the smallest positive integer such that 3,150 multiplied by y
[#permalink]
Show Tags
22 Jul 2014, 03:18
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."
Re: If y is the smallest positive integer such that 3,150 multiplied by y
[#permalink]
Show Tags
22 Jul 2014, 03:31
4
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."
Re: If y is the smallest positive integer such that 3,150 multiplied by y
[#permalink]
Show Tags
11 May 2016, 06:24
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
Re: If y is the smallest positive integer such that 3,150 multiplied by y
[#permalink]
Show Tags
24 Aug 2017, 11:03
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.
Re: If y is the smallest positive integer such that 3,150 multiplied by y
[#permalink]
Show Tags
25 Aug 2018, 23:30
1
1
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.
Re: If y is the smallest positive integer such that 3,150 multiplied by y
[#permalink]
Show Tags
05 Sep 2018, 07:15
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
_________________
If you enjoy my solutions, you'll love my GMAT prep course.
In order to make powers of all distinct prime factors even we need one 2 and one 7 because their power are 1 each in 3150
i.e. We need to multiply (2*7=14) in 3150 in order to make it a perfect square
hence, y = 14
Answer: Option E
_________________
Prepare with PERFECTION to claim Q≥50 and V≥40 !!! GMATinsight .............(Bhoopendra Singh and Dr.Sushma Jha) e-mail: info@GMATinsight.com l Call : +91-9999687183 / 9891333772 One-on-One Skype classes l Classroom Coaching l On-demand Quant course l Admissions Consulting
Re: If y is the smallest positive integer such that 3,150 multiplied by y
[#permalink]
Show Tags
29 Jan 2020, 20:15
GMATPrepNow wrote:
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
Thank you for your explanation. I was struggling to understand this question because I didn't understand what the question is asking (the wording of this question is confusing to me). With your explanation, I now understand the question and the solution to it.
gmatclubot
Re: If y is the smallest positive integer such that 3,150 multiplied by y
[#permalink]
29 Jan 2020, 20:15