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If y is the smallest positive integer such that 3,150 multip
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14 Aug 2020, 11:07
14 Aug 2020, 11:07
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Question Stats:
77% (01:06) correct
22% (02:19) wrong based on 31 sessions
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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
A. 2
B. 5
C. 6
D. 7
E. 14
Re: If y is the smallest positive integer such that 3,150 multip
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14 Aug 2020, 11:08
14 Aug 2020, 11:08
Expert Reply
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If y is the smallest positive integer such that 3,150 multip
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14 Aug 2020, 11:12
14 Aug 2020, 11:12
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Carcass 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
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 5'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
