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If x is the sum of n odd integers, which of the following must be true

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Bunuel
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If x is the sum of n odd integers, which of the following must be true [#permalink] New post   24 Mar 2022, 06:15
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A
B
C
D
E

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If x is the sum of n odd integers, which of the following must be true?

A. x is odd.
B. x is even.
C. x≠0
D. If x is even, n is even.
E. If n is odd, x is even.
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D
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IanStewart
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Re: If x is the sum of n odd integers, which of the following must be true [#permalink] New post   24 Mar 2022, 06:27
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A sum of odd integers can be odd (1 + 1 + 1 is odd), it can be even (1 + 1 is even) and it can be zero (1 + (-1) is zero). So A, B and C do not need to be true. Looking at E, if we add an odd number of odd numbers, the sum is always odd, so E is false. So the answer is D.
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Re: If x is the sum of n odd integers, which of the following must be true [#permalink] New post   24 Mar 2022, 06:31
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Bunuel wrote:
If x is the sum of n odd integers, which of the following must be true?

A. x is odd.
B. x is even.
C. x≠0
D. If x is even, n is even.
E. If n is odd, x is even.


x = Sum of n odd integers

A. x is odd. is wrong because for even value of n, x will be even
B. x is even. is wrong because for Odd value of n, x will be Odd
C. x≠0 is wrong because for the odd integers -1 and +1, sum x will be zero
D. If x is even, n is even. CORRECT because sum of even number of Odd integers will be Even
E. If n is odd, x is even.

Answer: Option D

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Re: If x is the sum of n odd integers, which of the following must be true [#permalink] New post   02 Jul 2022, 02:14
Do we consider negative integers to be odd or even ?
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Bunuel
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Re: If x is the sum of n odd integers, which of the following must be true [#permalink] New post   02 Jul 2022, 03:24
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Mayankcy wrote:
Do we consider negative integers to be odd or even ?


An even number is an integer which is divisible by 2 without a remainder, so ..., -4, -2, 0, 2, 4, 6, ... are all even numbers.
An odd number is an integer which is NOT divisible by 2 without a remainder, so ..., -3, -1, 1, 3, 5, 7, ... are all odd numbers.

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Re: If x is the sum of n odd integers, which of the following must be true [#permalink] New post   02 Jul 2022, 15:03
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Plug in sequences. Try to use a kind of back solving in this question.
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