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Joined: 20 Feb 2017
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If a and b are positive integers such that a b and a/b are both even
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19 Apr 2022, 08:55
19 Apr 2022, 08:55
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If a and b are positive integers such that a – b and a/b are both even integers, which of the following must be an odd integer?
A. a/2
B. b/2
C. (a+b)/2
D. (a + 2)/2
E. (b+2)/2
A. a/2
B. b/2
C. (a+b)/2
D. (a + 2)/2
E. (b+2)/2
Re: If a and b are positive integers such that a b and a/b are both even
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22 Apr 2022, 02:43
22 Apr 2022, 02:43
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\(a-b\) even --> either both even or both odd
\(\frac{a}{b}\) even --> either both even or \(a\) is even and \(b\) is odd.
As both statements are true --> \(a\) and \(b\) must be even.
As \(\frac{a}{b}\) is an even integer --> \(a\) must be multiple of 4.
Options A is always even.
Options B can be even or odd.
Options C can be even or odd.
Options D: \(\frac{a+2}{2}=\frac{a}{2}+1\), as \(a\) is multiple of \(4\), \(\frac{a}{2}\) is even integer --> even+1=odd. Hence option D is always odd.
Options E can be even, odd.
Answer: D.
\(\frac{a}{b}\) even --> either both even or \(a\) is even and \(b\) is odd.
As both statements are true --> \(a\) and \(b\) must be even.
As \(\frac{a}{b}\) is an even integer --> \(a\) must be multiple of 4.
Options A is always even.
Options B can be even or odd.
Options C can be even or odd.
Options D: \(\frac{a+2}{2}=\frac{a}{2}+1\), as \(a\) is multiple of \(4\), \(\frac{a}{2}\) is even integer --> even+1=odd. Hence option D is always odd.
Options E can be even, odd.
Answer: D.
gmatclubot
Re: If a and b are positive integers such that a b and a/b are both even [#permalink]
22 Apr 2022, 02:43
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