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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] New post 01 Mar 2011, 09:56
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A
B
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E

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76% (02:13) correct 24% (01:02) wrong based on 72 sessions
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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Kudos [?]: 37033 [0], given: 4627

Re: If x, y, and z are consecutive even positive integers, which [#permalink] New post 01 Mar 2011, 10:03
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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] New post 23 Nov 2013, 02:57
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] New post 27 Dec 2014, 03:23
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Re: If x, y, and z are consecutive even positive integers, which [#permalink] New post 27 Dec 2014, 10:41
Expert's post
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] 27 Dec 2014, 10:41
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