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655-705 (Hard)|   Exponents|      
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Bunuel
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Is (4^x)^(5-3x) = 1 ? 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:

49% (01:43) correct 51% (02:21) wrong based on 45 sessions

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Is \((4^x)^{(5-3x)}=1\)?

(1) x is an integer.
(2) The product of x and positive integer y is not x.
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Official Answer
C
Pure algebraic questions like this one are no longer part of the GMAT Data Sufficiency syllabus.
For relevant Data Sufficiency questions, please check the Data Sufficiency forum:
Data Sufficiency Forum
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Is (4^x)^(5-3x) = 1 ? 02 May 2021, 04:24
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Bunuel
Is \((4^x)^{(5-3x)}=1\)?

(1) x is an integer.
(2) The product of x and positive integer y is not x.
Show more

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
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Is (4^x)^(5-3x) = 1 ? 02 May 2021, 04:28
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Bunuel
Is \((4^x)^{(5-3x)}=1\)?

(1) x is an integer.
(2) The product of x and positive integer y is not x.
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When will \((4^x)^{(5-3x)}=1\) be true?

It will be when \((4^x)^{(5-3x)}=4^0=1\) or \(x(5-3x)=0\), that is when x is 0 or x is 5/3.

(1) x is an integer.
If x is 0, then yes, otherwise no.
Insufficient

(2) The product of x and positive integer y is not x.
\(xy\neq{x}........xy-x\neq 0......x(y-1)\neq 0\)
So x is not 0 and y is not 1.
But if x=5/3, then yes, otherwise no.
Insufficient


Combined.
X is neither 0 nor 5/3.
So answer is no.
Sufficient

C
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Is (4^x)^(5-3x) = 1 ? 02 May 2021, 04:30
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Bunuel
Is \((4^x)^{(5-3x)}=1\)?

(1) x is an integer.
(2) The product of x and positive integer y is not x.
Show more

Given:
\((4^x)^{(5-3x)}=1\)
\((4)^{5x-3x^2} = 4^0\)(As, \((a^m)^n = (a)^{mn})\)
\(x(5 - 3x) = 0\)
is x = 0, is x = \(\frac{5}{3}\)

1) x could be any integer. 0, 1 ,2...
Not sufficient.
2) x * y ≠ x
x is not zero, y ≠ 1
x could be 1, 2, \(\frac{5}{3}\)
Combining 1 & 2:
x ≠ 0, x≠ 5/3
Sufficient. Hence, C
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Is (4^x)^(5-3x) = 1 ? 09 May 2021, 04:00
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Bunuel
Is \((4^x)^{(5-3x)}=1\)?

(1) x is an integer.
(2) The product of x and positive integer y is not x.
Show more

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.
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