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If x, y, and z are consecutive even positive integers, which

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If x, y, and z are consecutive even positive integers, which [#permalink]

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If x, y, and z are consecutive even positive integers, which of the following could be equal to x + y + z ?

A. 141
B. 200
C. 318
D. 391
E. 412
[Reveal] Spoiler: OA
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Re: If x, y, and z are consecutive even positive integers, which [#permalink]

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banksy wrote:
If x, y, and z are consecutive even positive integers, which of the following could be equal to x + y + z ?

A. 141
B. 200
C. 318
D. 391
E. 412


The sum of 3 consecutive even numbers must be both even and multiple of 3: x+y+x=(2k-2)+2k+(2k+2)=6k, only option which satisfies this is C.

Answer: C.
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Re: If x, y, and z are consecutive even positive integers, which [#permalink]

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Sum of even integers must be an enven number → A and D out

Consecutive even integers = x - 2 + x + x + 2 = 3x. Therefore, the number must be divisible by 3, hence C.


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Re: If x, y, and z are consecutive even positive integers, which [#permalink]

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Re: If x, y, and z are consecutive even positive integers, which [#permalink]

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New post 27 Dec 2014, 11:41
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Hi All,

The key to answering this question quickly is to realize that X+Y+Z is a multiple of BOTH 2 and 3. With that information, you can quickly eliminate answer choices. If you don't recognize those two Number Properties though, then you can still get to the correct answer (but it will require a bit more work).

We're told that X, Y and Z are CONSECUTIVE EVEN INTEGERS, so we could write them algebraically as...

A + (A+2) + (A+4) = 3A + 6

We know that 3A + 6 COULD equal one of those five answers; we just have to find it...

Could 3A + 6 = 141
3A = 135
A = 45
This is NOT an EVEN INTEGER, so 141 is NOT the answer

Could 3A + 6 = 200
3A = 194
A = 64.6666
This is NOT an EVEN INTEGER, so 200 is NOT the answer

Could 3A + 6 = 318
3A = 312
A = 104
This IS an EVEN INTEGER! The numbers would be 104, 106 and 108. This IS the answer

Final Answer:
[Reveal] Spoiler:
C


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Re: If x, y, and z are consecutive even positive integers, which [#permalink]

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New post 21 Nov 2015, 08:52
Please tag number properties.
Thank you
banksy wrote:
If x, y, and z are consecutive even positive integers, which of the following could be equal to x + y + z ?

A. 141
B. 200
C. 318
D. 391
E. 412

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Re: If x, y, and z are consecutive even positive integers, which [#permalink]

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New post 25 Dec 2015, 12:37
Three consecutive even integers would be (2n - 2), 2n, (2n +2)

The sum is 6n.

Only option C is a multiple of 6.
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Re: If x, y, and z are consecutive even positive integers, which   [#permalink] 25 Dec 2015, 12:37
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