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08 Feb 2018, 19:28
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D
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Difficulty:
65%
(hard)
Question Stats:
53% (02:00) correct
47%
(02:26)
wrong
based on 81
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If a^5 + 7a + 2b + b^2 is even and a and b are integers, is a even integer?
(1) a + 2b is even.
(2) a + b is even.
(1) a + 2b is even.
(2) a + b is even.
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
rahul16singh28
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08 Feb 2018, 19:56
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chetan2u
From Statement 1: We have \(a + 2b = Even,\) 2b will be always even irrespective of b = odd/even. Hence, a = Even.
From Statement 2: We have \(a + b = Even.\)
I. a= Odd, b = Odd
\(a^5 + 7a + 2b + b^2 = Even\)---> b = Even(But as per our assumption b has to be Odd). So, this is ruled out.
II. a = Even, b = Even
\(a^5 + 7a + 2b + b^2 = Even\)
The only case possible is a = Even.
Hence, D.
08 Feb 2018, 22:50
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chetan2u
In a^5 + 7a + 2b + b^2, since a & b are integers:
2b is always going to be even.
a^5 + 7a will also always be even (if a is odd, we get odd+odd = even; and if a is even, we get even+even = even)
Since a^5 + 7a + 2b is always even, for entire sum to be even, b^2 also must be even. This means b is even.
Thus we know that 'b' is even for sure, we need to establish whether 'a' is even or not.
Statement 1
a+2b is even, 2b is anyway even; so for this sum to be even, 'a' also must be even. Sufficient.
Statement 2
a+b is even. We have already established that 'b' is even, so for this sum to be even, 'a' also must be even. Sufficient.
Hence D answer
