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02 May 2021, 04:15
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C
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
65%
(hard)
Question Stats:
48% (01:43) correct
52%
(02:21)
wrong
based on 44
sessions
History
Date
Time
Result
Not Attempted Yet
Is \((4^x)^{(5-3x)}=1\)?
(1) x is an integer.
(2) The product of x and positive integer y is not x.
(1) x is an integer.
(2) The product of x and positive integer y is not x.
09 May 2021, 04:00
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Bunuel
First of all \((4^x)^{(5-3x)}=4^{x*(5-3x)}\)
For this expression to be equal to 1, \(x*(5-3x)\) must be equal to 0.
\(x*(5-3x)=0\) --> \(x=0\) or \(x=\frac{5}{3}\).
So basically the question asks whether \(x=0\) or \(x=\frac{5}{3}\).
(1) x is an integer, hence x is not 5/3. But we don't know whether x is 0 or any other integer. Not sufficient.
(2) \(xy\neq{x}\), hence x is not equal to 0. But x can be any other number, integer or not integer. Not sufficient.
(1)+(2) x is an integer but not 0. So, x is not 0, not 5/3. Hence \(x*(5-3x)\neq{0}\), hence \((4^x)^{(5-3x)}\) does not equal to 1. Sufficient.
Answer: C.
General Discussion
02 May 2021, 04:24
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Bunuel
Question: Is \((4^x)^{(5-3x)}=1\)?
Question: Is \((4)^{(5x-3x^2)}=1\)?
Property: \(a^0 = 1\)
Question: Is \(5x-3x^2=0\)?
Question: Is \(x(5-3x)=0\)?
Question: Is \(x=0\) OR Is \(x=\frac{5}{3}\)?
Statement 1: x is an integer.
x may be 0 or non zero both hence
NOT SUFFICIENT
Statement 2: The product of x and positive integer y is not x.
i.e. x is non-zero but x maybe 5/3 hence
NOT SUFFICIENT
COmbining the statements
x is a non zero integer i.e. x≠0 and x≠5/3
Answer is always NO
SUFFICIENT
Answer: Option C
