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Root/ Exponents...easy way?

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Manager
Manager
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Joined: 14 Dec 2011
Posts: 65
GMAT 1: 630 Q48 V29
GMAT 2: 690 Q48 V37
Followers: 1

Kudos [?]: 5 [0], given: 24

GMAT Tests User
Root/ Exponents...easy way? [#permalink] New post 29 Dec 2011, 21:31
00:00
A
B
C
D
E

Difficulty:

  5% (low)

Question Stats:

75% (01:37) correct 25% (02:40) wrong based on 8 sessions
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!
[Reveal] Spoiler: OA
Manager
Manager
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Joined: 17 Oct 2011
Posts: 241
Location: United States
Concentration: Strategy, Marketing
GMAT 1: 720 Q51 V36
Followers: 4

Kudos [?]: 71 [0], given: 36

GMAT Tests User
Re: Root/ Exponents...easy way? [#permalink] New post 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
Answer: B

Hope this helps.
Senior Manager
Senior Manager
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Joined: 13 May 2011
Posts: 324
WE 1: IT 1 Yr
WE 2: Supply Chain 5 Yrs
Followers: 19

Kudos [?]: 118 [0], given: 11

GMAT Tests User
Re: Root/ Exponents...easy way? [#permalink] New post 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
Re: Root/ Exponents...easy way?   [#permalink] 30 Dec 2011, 02:01
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