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if y is the smallest +ve integer such that 3150*y is the squ
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04 Sep 2018, 22:14
04 Sep 2018, 22:14
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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
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if y is the smallest +ve integer such that 3150*y is the squ
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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
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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.
