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# If s is the sum of consecutive even integers w, x, y, and z

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Manager
Joined: 22 Apr 2011
Posts: 112
If s is the sum of consecutive even integers w, x, y, and z  [#permalink]

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05 Jun 2012, 18:10
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Difficulty:

35% (medium)

Question Stats:

76% (01:52) correct 24% (01:44) wrong based on 188 sessions

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If s is the sum of consecutive even integers w, x, y, and z, where w < x < y < z, all of the following must be true EXCEPT

A. z - w = 3(y - x)
B. s is divisible by 8
C. The average of w, x, y, and z is odd
D. s is divisible by 4
E. w + x + 8 = y + z
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06 Jun 2012, 00:15
2
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alchemist009 wrote:
If s is the sum of consecutive even integers w, x, y, and z,
where w < x < y < z, all of the following must be true
EXCEPT
(A) z - w = 3(y - x)
(B) s is divisible by 8
(C) The average of w, x, y, and z is odd
(D) s is divisible by 4
(E) w + x + 8 = y + z

Just assume that the numbers are 2a, 2a+2, 2a+4 and 2a+6.

s = 2a + 2a+2 + 2a+4 + 2a+6 = 8a + 12

Focus on the easiest options first. You see that s is not divisible by 8. Answer (B)

Or you can take values: w = 0, x = 2, y = 4, z = 6. Their sum is 12 = s.
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Karishma
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Re: If s is the sum of consecutive even integers w, x, y, and z  [#permalink]

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21 Jul 2015, 13:08
I am new to the forum, I still do not understand the concept about consecutive integers and inclusive integers and does even numbers factor in? Can someone please explain

thanks Hyder
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Re: If s is the sum of consecutive even integers w, x, y, and z  [#permalink]

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21 Jul 2015, 13:17
hyder27 wrote:
I am new to the forum, I still do not understand the concept about consecutive integers and inclusive integers and does even numbers factor in? Can someone please explain

thanks Hyder

"Consecutive" means one after the other.

1,2,3,4,5,6... are consecutive integers while 1,4,5,6,10,15,20... are non consecutive integers.

I have answered your other post for "inclusive" integers at the location set-a-consists-of-the-integers-from-4-to-12-inclusive-while-set-b-202080.html#p1551976

Even numbers will always be a part of set of consecutive integers (set having more than 1 integers). Any odd integer is followed by an even integer.
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Re: If s is the sum of consecutive even integers w, x, y, and z  [#permalink]

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21 Jul 2015, 13:26
@Enger2012

thanks for a fast response, i understood the concept about consecutive and non and even integers, will look at the post for inclusive integers thanks

Hyder
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Joined: 07 Dec 2014
Posts: 1252
If s is the sum of consecutive even integers w, x, y, and z  [#permalink]

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05 Mar 2020, 20:24
alchemist009 wrote:
If s is the sum of consecutive even integers w, x, y, and z, where w < x < y < z, all of the following must be true EXCEPT

A. z - w = 3(y - x)
B. s is divisible by 8
C. The average of w, x, y, and z is odd
D. s is divisible by 4
E. w + x + 8 = y + z

2+4+6+8=20
s not divisible by 8
B
If s is the sum of consecutive even integers w, x, y, and z   [#permalink] 05 Mar 2020, 20:24