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15 Feb 2021, 01:15
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C
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Difficulty:
85%
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Question Stats:
45% (01:51) correct
55%
(01:47)
wrong
based on 119
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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.
(1) x is an integer.
(2) The product of x and positive integer y is not x.
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
Data Sufficiency Forum
15 Feb 2021, 04:58
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The expression \((4^x)^(5 - 3x)\) can be equal to 1, only if (a) x = 0 or (b) 5 - 3x = 0 i.e x = 5/3
Statement 1: x is an integer.
With this statement, x can be 0, in which case, the expression is = 1. but if x is any other value than 0, then it is not equal to 1.
Therefore Statement 1 Alone is Insufficient. Answer options could be B, C or E
Statement 2: The product of x and positive integer y is not x.
From this statement, we can conclude that x cannot be -1, 0 or +1. In this case, any integer value of x will not give a value of 1 for the above expression.
What we cannot conclude from this statement is whether x is an integer, and therefore it could be possible for x to be 5/3 in which case the expression being equal to 1 can be an option.
Therefore Statement 2 Alone is Insufficient. Answer Options could be C or E.
Combining Both Statements:
Here we know that x cannot be 0 and x cannot be 5/3 and hence NO, the value of the expression cannot be 1.
Therefore Both Statements together are Sufficient.
Option C
Arun Kumar
Statement 1: x is an integer.
With this statement, x can be 0, in which case, the expression is = 1. but if x is any other value than 0, then it is not equal to 1.
Therefore Statement 1 Alone is Insufficient. Answer options could be B, C or E
Statement 2: The product of x and positive integer y is not x.
From this statement, we can conclude that x cannot be -1, 0 or +1. In this case, any integer value of x will not give a value of 1 for the above expression.
What we cannot conclude from this statement is whether x is an integer, and therefore it could be possible for x to be 5/3 in which case the expression being equal to 1 can be an option.
Therefore Statement 2 Alone is Insufficient. Answer Options could be C or E.
Combining Both Statements:
Here we know that x cannot be 0 and x cannot be 5/3 and hence NO, the value of the expression cannot be 1.
Therefore Both Statements together are Sufficient.
Option C
Arun Kumar
15 Feb 2021, 10:44
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Given expression, (4^x)^(5−3x)=1 or, x*(5−3x) = 1 or, x= 0 or 5/3
Stat1: x is an integer. So, x= 0 and not equal to 5/3.
But x= 0, expression = 1; at x= other integer, expression not equal to 1. Not sufficient.
Stat2: The product of x and positive integer y is not x.
So, x not equal to -1, 0 and +1. Now, x can be 5/3/
But x= 5/3, expression = 1; at x= other value, expression not equal to 1. Not sufficient.
Combining both, x not equal to 0 or 5/3. So, expression not equal to 1. Sufficient.
So, I think C.
Stat1: x is an integer. So, x= 0 and not equal to 5/3.
But x= 0, expression = 1; at x= other integer, expression not equal to 1. Not sufficient.
Stat2: The product of x and positive integer y is not x.
So, x not equal to -1, 0 and +1. Now, x can be 5/3/
But x= 5/3, expression = 1; at x= other value, expression not equal to 1. Not sufficient.
Combining both, x not equal to 0 or 5/3. So, expression not equal to 1. Sufficient.
So, I think C.
