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If c and d are positive integers, is c even?
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21 Jan 2020, 05:50
21 Jan 2020, 05:50
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If c and d are positive integers, is c even?
(1) c^2 - 1 is odd.
(2) (c - 3)(d + 2) is odd.
(1) c^2 - 1 is odd.
(2) (c - 3)(d + 2) is odd.
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Re: If c and d are positive integers, is c even?
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21 Jan 2020, 06:11
21 Jan 2020, 06:11
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Bunuel wrote:
If c and d are positive integers, is c even?
(1) c^2 - 1 is odd.
(2) (c - 3)(d + 2) is odd.
(1) c^2 - 1 is odd.
(2) (c - 3)(d + 2) is odd.
Given: If c and d are positive integers
Question: Is c even?
Statement 1: c^2 - 1 is odd
\(c^2\) = odd + 1 = even
But c must be even because c is an integer hence
SUFFICIENT
Statement 2: (c - 3)(d + 2) is odd
i.e. c-3 = odd i.e. c = odd+3 = even
SUFFICIENT
Answer: Option D
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If c and d are positive integers, is c even?
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21 Jan 2020, 15:42
21 Jan 2020, 15:42
Expert Reply
Bunuel wrote:
If c and d are positive integers, is c even?
(1) c^2 - 1 is odd.
(2) (c - 3)(d + 2) is odd.
(1) c^2 - 1 is odd.
(2) (c - 3)(d + 2) is odd.
Statement 1:
\(c^2 - 1\) is odd, so \(c^2\) is even. In order to have \(c^2\) even we must have \(c\) even, sufficient. (Note c can be negative but negative numbers can also be even).
Statement 2:
A product is odd, in order to have the product to be odd each factor must be odd. So \(c - 3\) is odd and \(c\) is even, sufficient.
Ans: D
