If (2^x)^y = (x^2)^z, the value of y when x is 16 and z is 32 is how : GMAT Problem Solving (PS)
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# If (2^x)^y = (x^2)^z, the value of y when x is 16 and z is 32 is how

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Manager
Joined: 14 Dec 2011
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If (2^x)^y = (x^2)^z, the value of y when x is 16 and z is 32 is how [#permalink]

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29 Dec 2011, 21:31
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Question Stats:

66% (02:23) correct 34% (01:42) wrong based on 62 sessions

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If (2^x)^y = (x^2)^z, the value of y when x is 16 and z is 32 is how much greater than the value of y when x and z are both 8 ?

A. 6
B. 10
C. 16
D. 17
E. 24

[Reveal] Spoiler:
My Idea

2^(x*y) = x^(2*z)
2^(16y) = 16^64 ---- > no idea how to get y out of this
2^(8y) = 8^16 ---- > and again no idea how to get y

How to I solve those equations?

Thanks a lot!
[Reveal] Spoiler: OA
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Kudos [?]: 95 [0], given: 36

Re: If (2^x)^y = (x^2)^z, the value of y when x is 16 and z is 32 is how [#permalink]

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29 Dec 2011, 22:14
Impenetrable wrote:
If (2^x)^y = (x^2)^z, the value of y when x is 16 and z is 32 is how much greater than the value of y when x and z are both 8 ?

6
10
16
17
24

My Idea

2^(x*y) = x^(2*z)
2^(16y) = 16^64 ---- > no idea how to get y out of this
2^(8y) = 8^16 ---- > and again no idea how to get y

How to I solve those equations?

Thanks a lot!

$$2^(xy)=x^(2z)$$
$$2^(16y)=16^64$$
but,$$16=2^4$$
so, $$2^(16y)=2^(4*64)$$
$$16y=4*64$$
$$y=16$$

similarly,
$$8=2^3$$
so, $$8y=3*2*8$$
or, $$y=6$$

Hope this helps.
Senior Manager
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Kudos [?]: 253 [0], given: 11

Re: If (2^x)^y = (x^2)^z, the value of y when x is 16 and z is 32 is how [#permalink]

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30 Dec 2011, 02:01
for the 1st condition: 2^16y=2^(16*16)
y=16
for the 2nd condition: 2^8y=2^(6*8)
y=6
16-6=10=B
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Re: If (2^x)^y = (x^2)^z, the value of y when x is 16 and z is 32 is how [#permalink]

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19 Aug 2016, 11:17
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Re: If (2^x)^y = (x^2)^z, the value of y when x is 16 and z is 32 is how   [#permalink] 19 Aug 2016, 11:17
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