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If x, y, and z are consecutive integers, and x < y < z , is x even?

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If x, y, and z are consecutive integers, and x < y < z , is x even? [#permalink]

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New post 27 Jul 2011, 03:45
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If x, y, and z are consecutive integers, and x < y < z , is x even?

(1) x + y is odd.

(2) x + z is even.
[Reveal] Spoiler: OA

Last edited by Bunuel on 04 Oct 2017, 00:13, edited 1 time in total.
Renamed the topic, edited the question and added the OA.

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Re: If x, y, and z are consecutive integers, and x < y < z , is x even? [#permalink]

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New post 27 Jul 2011, 04:18
bschool83 wrote:
If x , y , and z are consecutive integers, and x < y < z , is x even?

(1) x + y is odd.

(2) x + z is even.



(1) Insufficient - x, and y are given as consecutive integers, so one number in x and y has to be even and one has to be odd, like x=1 and y =2 or x=2 and y=3....but the sum will always be odd. so this statement doesnt gives any information at all.

2) Insufficient. - It's given that x y and z are consecutive integers in order x ,y, z....so sum of x and z will always be even. you can see for example if x=1 and z=3 sum =4 (even) , similarly if x=2 and z=4, sum = 6 even . so this too doesnt adds any info. even +even = always even and odd + odd = always even.

together too they are insufficient because neither of the statements add any info to what is already given in question. Answer E.

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Re: If x, y, and z are consecutive integers, and x < y < z , is x even? [#permalink]

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New post 03 Oct 2017, 23:53
is x even, with x,y,z being consecutive and x<y<z

St 1: x+ y = odd. And x< y
Case 1: 1+2 = 3 (ODD); 4+5 = ODD; 5+6 (ODD)
Not suff x can be odd or even answer is ODD

St 2: x + z = even. x = 4, y = 5, z = 6 answer is even. x =3, y = 4, z= 6 answer is even.
odd + odd = even and even+ even = even
Not suff

1) + 2) No conclusion. Ans is E

What is the OA?

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Re: If x, y, and z are consecutive integers, and x < y < z , is x even? [#permalink]

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New post 04 Oct 2017, 00:15
Madhavi1990 wrote:
If x, y, and z are consecutive integers, and x < y < z , is x even?

(1) x + y is odd.

(2) x + z is even.

is x even, with x,y,z being consecutive and x<y<z

St 1: x+ y = odd. And x< y
Case 1: 1+2 = 3 (ODD); 4+5 = ODD; 5+6 (ODD)
Not suff x can be odd or even answer is ODD

St 2: x + z = even. x = 4, y = 5, z = 6 answer is even. x =3, y = 4, z= 6 answer is even.
odd + odd = even and even+ even = even
Not suff

1) + 2) No conclusion. Ans is E

What is the OA?


The OA is E. Any set of three consecutive integers will satisfy both of the statements. For example, consider {0, 1, 2} and {1, 2, 3}.
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Kudos [?]: 135451 [0], given: 12695

Re: If x, y, and z are consecutive integers, and x < y < z , is x even?   [#permalink] 04 Oct 2017, 00:15
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