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If the sum of three consecutive integers is odd, then the first and th

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Sajjad1994
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If the sum of three consecutive integers is odd, then the first and th [#permalink] New post   05 Jul 2019, 04:24
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If the sum of three consecutive integers is odd, then the first and the last integers must be

(A) odd, even
(B) odd, odd
(C) even, odd
(D) even, even
(E) none of the above

Source: Nova GMAT
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D
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Re: If the sum of three consecutive integers is odd, then the first and th [#permalink] New post   Updated on: 05 Jul 2019, 05:31
Let the consecutive numbers be a-1, a, a+1

Sum = 3a = odd
Then a = odd
Let a = 5
a-1 = 4
a+1 = 6
So first and last are also even.

D is the answer.

Originally posted by Chethan92 on 05 Jul 2019, 05:12.
Last edited by Chethan92 on 05 Jul 2019, 05:31, edited 1 time in total.
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Re: If the sum of three consecutive integers is odd, then the first and th [#permalink] New post   05 Jul 2019, 05:26
SajjadAhmad wrote:
If the sum of three consecutive integers is odd, then the first and the last integers must be

(A) odd, even
(B) odd, odd
(C) even, odd
(D) even, even
(E) none of the above

Source: Nova GMAT


Let the 3 consecutive number be x, x+1, x+2

Sum of these 3 numbers= x+x+1+x+2= 3x+3= odd
3x=ODD-ODD=Even------> x=even
Let x=2, then first and last number will be even
Answer D
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Re: If the sum of three consecutive integers is odd, then the first and th [#permalink] New post   26 Aug 2019, 10:50
X, X+1, X+2

1 + 2 + 3 = 6, even so will not work
2 + 3 + 4 = 9, odd, works,

3 + 4 + 5 = 12 even, again does not work

4 + 5 + 6 = 15, odd, works again

So answer is two evens
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Re: If the sum of three consecutive integers is odd, then the first and th [#permalink] New post   27 Aug 2019, 18:26
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SajjadAhmad wrote:
If the sum of three consecutive integers is odd, then the first and the last integers must be

(A) odd, even
(B) odd, odd
(C) even, odd
(D) even, even
(E) none of the above

Source: Nova GMAT


If the first number is odd, then we have an even sum since

odd + even + odd = even.

If the first number is even, then we have an odd sum since

even + odd + even = odd

Thus, both the first and last numbers must be even.

Answer: D
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Re: If the sum of three consecutive integers is odd, then the first and th [#permalink] New post   27 Aug 2019, 19:06
SajjadAhmad wrote:
If the sum of three consecutive integers is odd, then the first and the last integers must be

(A) odd, even
(B) odd, odd
(C) even, odd
(D) even, even
(E) none of the above

Source: Nova GMAT


There are only 2 possibilities
{Even, odd, even} sum= odd
{odd, even, odd} sum= even

Since sum of 3 consecutive integers is odd, only {even, odd, even} is possible.

First and last integers are both even

IMO D

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Re: If the sum of three consecutive integers is odd, then the first and th [#permalink] New post   25 Oct 2020, 15:13
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Re: If the sum of three consecutive integers is odd, then the first and th [#permalink]
25 Oct 2020, 15:13
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