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

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Manager
Joined: 10 Feb 2011
Posts: 112

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

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01 Mar 2011, 10:56
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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

Kudos [?]: 363 [1], given: 10

Math Expert
Joined: 02 Sep 2009
Posts: 41889

Kudos [?]: 129207 [1], given: 12196

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

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01 Mar 2011, 11:03
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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.

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Kudos [?]: 129207 [1], given: 12196

Intern
Joined: 14 Mar 2013
Posts: 48

Kudos [?]: 66 [1], given: 119

Location: United States
GMAT Date: 12-03-2013
WE: General Management (Retail)
Re: If x, y, and z are consecutive even positive integers, which [#permalink]

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23 Nov 2013, 03:57
1
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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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Kudos [?]: 66 [1], given: 119

GMAT Club Legend
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Kudos [?]: 273 [0], given: 0

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

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27 Dec 2014, 04:23
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Kudos [?]: 3413 [1], given: 172

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

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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

[Reveal] Spoiler:
C

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Kudos [?]: 3413 [1], given: 172

Director
Status: Tutor - BrushMyQuant
Joined: 05 Apr 2011
Posts: 622

Kudos [?]: 770 [0], given: 59

Location: India
Concentration: Finance, Marketing
Schools: XLRI (A)
GMAT 1: 700 Q51 V31
GPA: 3
WE: Information Technology (Computer Software)
Re: If x, y, and z are consecutive even positive integers, which [#permalink]

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21 Nov 2015, 08:52
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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Kudos [?]: 770 [0], given: 59

Senior Manager
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GMAT 1: 540 Q39 V26
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Re: If x, y, and z are consecutive even positive integers, which [#permalink]

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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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Kudos [?]: 38 [0], given: 165

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Kudos [?]: 844 [0], given: 595

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

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19 Jan 2017, 14:27
Let the 3 consecutive even integers be represents by -->
2n
2n+2
2n+4

Sum=> 6n+6-> 6(n+1)
Hence the sum must be a multiple of 6.
Only option that fits this criteria is C.

Hence C.

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Kudos [?]: 844 [0], given: 595

Senior Manager
Joined: 25 Mar 2013
Posts: 275

Kudos [?]: 33 [0], given: 101

Location: United States
Concentration: Entrepreneurship, Marketing
GPA: 3.5
Re: If x, y, and z are consecutive even positive integers, which [#permalink]

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20 Jan 2017, 07:43
x + (x+2) + (x+4)
3x + 6 = 318
Only option
C
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Kudos [?]: 33 [0], given: 101

Manager
Joined: 01 Mar 2015
Posts: 61

Kudos [?]: 16 [0], given: 6

Location: India
GMAT 1: 690 Q42 V42
Re: If x, y, and z are consecutive even positive integers, which [#permalink]

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22 Jan 2017, 00:06
Take the three consecutive even numbers as x-2,x and x+2. So the sum is 3x. So the problem boils down to: Which of the answer choices is a multiple of 3. Job done.
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Kudos [?]: 16 [0], given: 6

Re: If x, y, and z are consecutive even positive integers, which   [#permalink] 22 Jan 2017, 00:06
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