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Updated on: 08 Oct 2012, 04:18
Originally posted by jeeteshsingh on 21 Feb 2010, 14:20.
Last edited by Bunuel on 08 Oct 2012, 04:18, edited 2 times in total.
Last edited by Bunuel on 08 Oct 2012, 04:18, edited 2 times in total.
Edited the question.
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B
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Question Stats:
48% (02:26) correct
52%
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If x, y, and z are integers greater than 1, and \(3^{27}*5^{10}*z = 5^8*9^{14}*x^y\), then what is the value of x?
(1) y is prime.
(2) x is prime.
(1) y is prime.
(2) x is prime.
28 Jun 2012, 02:53
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If x, y, and z are integers greater than 1, and \(3^{27}*5^{10}*z = 5^8*9^{14}*x^y\), then what is the value of x?
\(3^{27}*5^{10}*z = 5^8*9^{14}*x^y\);
\(3^{27}*5^{2}*z =3^{28}*x^y\);
\(5^{2}*z = 3*x^y\);
\(\frac{x^y}{z}=\frac{5^2}{3}\), so \(x^y\) is a multiple of 25 and \(z\) is a multiple of 3.
(1) y is prime. We can have that \(x=5\), \(y=2=prime\) and \(z=3\) OR \(x=10\), \(y=2=prime\) and \(z=12\)... Not sufficient.
(2) x is prime. Since \(x^y\) is a multiple of \(5^2\) and \(x\) is a prime, then \(x=5\). Sufficient.
Answer: B.
Hope it's clear.
\(3^{27}*5^{10}*z = 5^8*9^{14}*x^y\);
\(3^{27}*5^{2}*z =3^{28}*x^y\);
\(5^{2}*z = 3*x^y\);
\(\frac{x^y}{z}=\frac{5^2}{3}\), so \(x^y\) is a multiple of 25 and \(z\) is a multiple of 3.
(1) y is prime. We can have that \(x=5\), \(y=2=prime\) and \(z=3\) OR \(x=10\), \(y=2=prime\) and \(z=12\)... Not sufficient.
(2) x is prime. Since \(x^y\) is a multiple of \(5^2\) and \(x\) is a prime, then \(x=5\). Sufficient.
Answer: B.
Hope it's clear.
General Discussion
06 Nov 2020, 05:43
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jeeteshsingh
\(3^{27}*5^{10}*z = 5^8*9^{14}*x^y\)
\(3^{27}*5^{10}*z = 5^8*3^{28}*x^y\)
\(5^{2}*z = 3x^y\)
\(z = 3*\frac{x^y}{25}\)
Since z is an INTEGER greater than 1, the resulting equation implies that \(x^y\) is a multiple of 25.
The statements do not discuss \(z\).
Thus, the question stem can be rephrased as follows:
If \(x^y \)is a positive multiple of 25, what is the value of \(x\)?
Statement 1: y is prime
Case 1: x=5 and y=2, with the result that \(x^y\) is a multiple of 25
Case 2: x=25 and y=2, with the result that \(x^y\) is a multiple of 25
Since \(x\) can be different values, INSUFFICIENT.
Statement 2: x is prime
Since \(x^y\) is a multiple of 25 and \(x\) is prime, only x=5 is possible.
SUFFICIENT.
