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09 Aug 2023, 01:30
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D
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Difficulty:
15%
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Question Stats:
83% (01:08) correct
17%
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wrong
based on 41
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If x is an integer and p is an odd integer, is x even?
(1) x^p is even.
(2) p*x = 24
(1) x^p is even.
(2) p*x = 24
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
13 Aug 2023, 22:58
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Some of the General Rules
For Any integer or Function the Addition Rule:
ODD+EVEN = ODD
ODD+ODD = EVEN
EVEN+EVEN= EVEN
For Any integer or Function the Multiplication Rule:
ODD* ODD= ODD
ODD*EVEN= EVEN
EVEN*EVEN=EVEN
The Exponent Rule
\(ODD^{Any Integer} = ODD\\
EVEN^{Any Integer}=EVEN\)
Statement(1)
\(x^p is even\)
From the above rules it is implied, if the expression \(x^p\) is even then irrespective of p, x is always even.
Statement(2)
p*x = 24
if p is Odd then x has to be even as per the above rules.
So can be answered with any of the statements independently.
Option D.
For Any integer or Function the Addition Rule:
ODD+EVEN = ODD
ODD+ODD = EVEN
EVEN+EVEN= EVEN
For Any integer or Function the Multiplication Rule:
ODD* ODD= ODD
ODD*EVEN= EVEN
EVEN*EVEN=EVEN
The Exponent Rule
\(ODD^{Any Integer} = ODD\\
EVEN^{Any Integer}=EVEN\)
Statement(1)
\(x^p is even\)
From the above rules it is implied, if the expression \(x^p\) is even then irrespective of p, x is always even.
Statement(2)
p*x = 24
if p is Odd then x has to be even as per the above rules.
So can be answered with any of the statements independently.
Option D.
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