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If x, y, z are positive integers and x<y<z, which of the following mus

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Math Revolution GMAT Instructor
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If x, y, z are positive integers and x<y<z, which of the following mus  [#permalink]

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New post 08 Aug 2018, 02:12
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A
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C
D
E

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[Math Revolution GMAT math practice question]

If \(x, y, z\) are positive integers and \(x<y<z\), which of the following must be greater than \((z^x)(z^y)\)?

\(A. y^{2z}\)
\(B. y^{2y}\)
\(C. x^{2y}\)
\(D. x^{zx}\)
\(E. z^{2y}\)

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If x, y, z are positive integers and x<y<z, which of the following mus  [#permalink]

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New post 08 Aug 2018, 02:20
MathRevolution wrote:
[Math Revolution GMAT math practice question]

If \(x, y, z\) are positive integers and \(x<y<z\), which of the following must be greater than \((z^x)(z^y)\)?

\(A. y^{2z}\)
\(B. y^{2y}\)
\(C. x^{2y}\)
\(D. x^{zx}\)
\(E. z^{2y}\)



Note : x, y, z are positive integers. x<y<z.

plug value for z, y, z.

x = 2
y = 3
z=4.

Given

\((z^x)(z^y)\)

=\(z^{(x+y)}\)

= \(4^{(3+2)}\)

= \(4^{5}\)

= \(2^{10}\)

we need to find an option which will provide a value greater than \(2^{10}\)

As we have z its base, we also start with option having base z.

Option E)

\(z^{2y}\)

= \(4^{(2*3)}\)

=\(2^{12}\)

The best answer is E.
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Re: If x, y, z are positive integers and x<y<z, which of the following mus  [#permalink]

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New post 08 Aug 2018, 02:30
1
MathRevolution wrote:
[Math Revolution GMAT math practice question]

If \(x, y, z\) are positive integers and \(x<y<z\), which of the following must be greater than \((z^x)(z^y)\)?

\(A. y^{2z}\)
\(B. y^{2y}\)
\(C. x^{2y}\)
\(D. x^{zx}\)
\(E. z^{2y}\)


\((z^x)(z^y)\) can also be written as
\(z^{x+y}\)

My first choice would be option E as it is the only one with base as Z.
E. \(z^{2y}\)

as x<y<z
x+y<y+y
x+y<2y
Therefore
\(z^{x+y}\) < \(z^{2y}\)
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Math Revolution GMAT Instructor
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Joined: 16 Aug 2015
Posts: 7609
GMAT 1: 760 Q51 V42
GPA: 3.82
Re: If x, y, z are positive integers and x<y<z, which of the following mus  [#permalink]

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New post 10 Aug 2018, 02:34
=>

Since \(z^x < z^y,\) we have \((z^x)(z^y)< (z^y)(z^y) = z^{2y}\).

Therefore, the answer is E.
Answer: E
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Re: If x, y, z are positive integers and x<y<z, which of the following mus   [#permalink] 10 Aug 2018, 02:34
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