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If x, y, z, and w are positive integers and all of them are exponents

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If x, y, z, and w are positive integers and all of them are exponents  [#permalink]

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New post 08 Apr 2019, 10:59
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  95% (hard)

Question Stats:

26% (02:19) correct 74% (02:06) wrong based on 39 sessions

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If x, y, z, and w are positive integers and all of them are exponents of 2, what is the largest one of them?

(1) x*y*z*w=2^16
(2) x+y+z+w=170

A. Statement (1) ALONE is sufficient but Statement (2) ALONE is not sufficient.
B. Statement (2) ALONE is sufficient but Statement (1) ALONE is not sufficient.
C. BOTH Statements TOGETHER are sufficient, but NEITHER Statement alone is sufficient.
D. Each Statement ALONE is sufficient.
E. Statements (1) and (2) TOGETHER are NOT sufficient.
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Re: If x, y, z, and w are positive integers and all of them are exponents  [#permalink]

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New post 08 Apr 2019, 11:09
From S1:

\(x*y*z*w = 2^{16}\)
Clearly Insufficient.

From S2:

x+y+z+w = 170
Only possible combination is \(2^7+2^5+2^3+2^1\)
So, the largest is \(2^7\).
Sufficient.

B is the answer.
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Re: If x, y, z, and w are positive integers and all of them are exponents  [#permalink]

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New post 08 Apr 2019, 20:04
I thought the question is asking about which one among X,y,z and w have the largest value....

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If x, y, z, and w are positive integers and all of them are exponents  [#permalink]

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New post 09 Apr 2019, 10:54
Chethan92 wrote:
From S1:

\(x*y*z*w = 2^{16}\)
Clearly Insufficient.

From S2:

x+y+z+w = 170
Only possible combination is \(2^7+2^5+2^3+2^1\)
So, the largest is \(2^7\).
Sufficient.

B is the answer.



But how can we decide which is which?

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If x, y, z, and w are positive integers and all of them are exponents  [#permalink]

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New post 10 Apr 2019, 09:21
Chethan92 wrote:
From S1:

\(x*y*z*w = 2^{16}\)
Clearly Insufficient.

From S2:

x+y+z+w = 170
Only possible combination is \(2^7+2^5+2^3+2^1\)
So, the largest is \(2^7\).
Sufficient.

B is the answer.


Why can't it be 2^10+2^3+2^2+2^1
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Re: If x, y, z, and w are positive integers and all of them are exponents  [#permalink]

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New post 10 Apr 2019, 10:10
1
anmolgmat14 wrote:
Chethan92 wrote:
From S1:

\(x*y*z*w = 2^{16}\)
Clearly Insufficient.

From S2:

x+y+z+w = 170
Only possible combination is \(2^7+2^5+2^3+2^1\)
So, the largest is \(2^7\).
Sufficient.

B is the answer.


Why can't it be 2^10+2^3+2^2+2^1


anmolgmat14, 2^10 = 1024.
Statement says, x+y+w+z = 170.
Hence 2^10 is not possible.
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Re: If x, y, z, and w are positive integers and all of them are exponents   [#permalink] 10 Apr 2019, 10:10
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