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Math Revolution GMAT Instructor V
Joined: 16 Aug 2015
Posts: 9006
GMAT 1: 760 Q51 V42
GPA: 3.82
If x, y, z are positive integers and x<y<z, which of the following mus  [#permalink]

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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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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)

$$z^{2y}$$

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

=$$2^{12}$$

Manager  G
Joined: 19 Nov 2017
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Location: India
Schools: ISB
GMAT 1: 670 Q49 V32
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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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2
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 V
Joined: 16 Aug 2015
Posts: 9006
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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=>

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

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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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_________________ Re: If x, y, z are positive integers and x<y<z, which of the following mus   [#permalink] 15 Mar 2020, 06:06

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