GRE Prep 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
Track
Your Progress
Practice
Pays
Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.
if y is the smallest +ve integer such that 3150*y is the squ
[#permalink]
04 Sep 2018, 22:14
04 Sep 2018, 22:14
1
3
Bookmarks
00:00
Question Stats:
73% (01:10) correct
26% (01:43) wrong based on 46 sessions
Hide Show timer Statistics
if y is the smallest positive integer such that 3150y is the square of an integer then y must be
A) 2
B) 5
C) 6
D) 7
E) 14
A) 2
B) 5
C) 6
D) 7
E) 14
Retired Moderator
Joined: 10 Apr 2015
Posts: 6218
Given Kudos: 136
if y is the smallest +ve integer such that 3150*y is the squ
[#permalink]
05 Sep 2018, 07:15
05 Sep 2018, 07:15
1
amorphous wrote:
if y is the smallest positive integer such that 3150*y is the square of an integer then y must be
A) 2
B) 5
C) 6
D) 7
E) 14
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
ASIDE: This is actually an official GMAT question (see https://gmatclub.com/forum/if-y-is-the- ... 10513.html)
Re: if y is the smallest +ve integer such that 3150*y is the squ
[#permalink]
07 Sep 2018, 20:11
07 Sep 2018, 20:11
1
amorphous wrote:
if y is the smallest +ve integer such that \(3150*y\) is the square of an integer then y must be?
A) 2
B) 5
C) 6
D) 7
E) 14
src: orbit test prep
A) 2
B) 5
C) 6
D) 7
E) 14
src: orbit test prep
3150y = perfect square.
3150 = 2*5*5*3*3*7
In order to make it perfect square y has to be 14 as we only a 2 and a 7. To get a prime square each prime factor must have even exponents.
So y is 14.
3150*14 = 2*5*5*3*3*7*7*2.
It looks like: \(2^25^23^27^2\)
The best answer is E.
