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GRE Prep Club Team Member
Joined: 20 Feb 2017
Posts: 2506
Given Kudos: 1053
GPA: 3.39
If n and y are positive integers and 450y = n^3, which of the followin
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13 Apr 2022, 09:28
13 Apr 2022, 09:28
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If n and y are positive integers and \(450y = n^3\), which of the following must be an integer ?
I. \(\frac{y}{3 * 2^2 * 5}\)
II. \(\frac{y}{3^2 * 2 * 5}\)
III. \(\frac{y}{3 * 2 * 5^2}\)
A. None.
B. I only.
C. II only.
D. III only.
E. I, II, and III
I. \(\frac{y}{3 * 2^2 * 5}\)
II. \(\frac{y}{3^2 * 2 * 5}\)
III. \(\frac{y}{3 * 2 * 5^2}\)
A. None.
B. I only.
C. II only.
D. III only.
E. I, II, and III
GRE Prep Club Team Member
Joined: 20 Feb 2017
Posts: 2506
Given Kudos: 1053
GPA: 3.39
Re: If n and y are positive integers and 450y = n^3, which of the followin
[#permalink]
17 Apr 2022, 03:25
17 Apr 2022, 03:25
Expert Reply
"Must be an integer" means the lowest possible value of \(y\).
\(450y=n^3\) --> \(2*3^2*5^2*y=n^3\). As \(n\) and \(y\) are integers, \(y\) must complete the powers of 2, 3, and 5 to cubes (generally to the multiple of 3).
Thus \(y_{min}=2^2*3*5\), in this case \(2*3^2*5^2*y=(2*3*5)^3=n^3\).
Notice that for this value of \(y\) only the first option is an integer: \(\frac{y}{{3*2^2*5}}=\frac{2^2*3*5}{{3*2^2*5}}=1\).
Answer: B.
\(450y=n^3\) --> \(2*3^2*5^2*y=n^3\). As \(n\) and \(y\) are integers, \(y\) must complete the powers of 2, 3, and 5 to cubes (generally to the multiple of 3).
Thus \(y_{min}=2^2*3*5\), in this case \(2*3^2*5^2*y=(2*3*5)^3=n^3\).
Notice that for this value of \(y\) only the first option is an integer: \(\frac{y}{{3*2^2*5}}=\frac{2^2*3*5}{{3*2^2*5}}=1\).
Answer: B.
gmatclubot
Re: If n and y are positive integers and 450y = n^3, which of the followin [#permalink]
17 Apr 2022, 03:25
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