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# If w, x, y and z are integers and w + x = y, is y divisible by z?

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Math Expert
Joined: 02 Sep 2009
Posts: 51101
If w, x, y and z are integers and w + x = y, is y divisible by z?  [#permalink]

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05 Dec 2017, 20:57
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Difficulty:

25% (medium)

Question Stats:

83% (01:28) correct 17% (02:05) wrong based on 82 sessions

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If w, x, y and z are integers and w + x = y, is y divisible by z?

(1) w and x each have a remainder of 1 when divided by z
(2) z = 2

_________________
Manager
Joined: 05 Dec 2016
Posts: 244
Concentration: Strategy, Finance
GMAT 1: 620 Q46 V29
Re: If w, x, y and z are integers and w + x = y, is y divisible by z?  [#permalink]

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06 Dec 2017, 03:01
(1)
w=z*k+1, where k is a constant
x=z*m+1, where m is a constant
y=w+x=z*k+z*m+2
y/z=(z*k+z*m+2)/z=m+k+2/z
Since we don't know whether z=2 we cannot give a definite answer if y/z is an integer
(2) z=2
No information about the divisibility of w and x by 2.
(1)+(2)
y/z=(z*k+z*m+2)/2=m+k+1
Sufficient
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Joined: 21 Aug 2013
Posts: 1412
Location: India
Re: If w, x, y and z are integers and w + x = y, is y divisible by z?  [#permalink]

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06 Dec 2017, 22:56
Bunuel wrote:
If w, x, y and z are integers and w + x = y, is y divisible by z?

(1) w and x each have a remainder of 1 when divided by z
(2) z = 2

(1) We dont know the value of z, so we cant say. Insufficient.

(2) z=2, so now whether y is divisible by z or not depends on whether y is even or odd. y is even if w & x are either both even or both odd. And y is odd if one of w/x is even and the other is odd. But we dont know. So Insufficient.

Combining the two statements, both w/x give a remainder 1 when divided by z, which means both w/x are odd, thus y is even. And hence y is divisible by z. Sufficient.

Re: If w, x, y and z are integers and w + x = y, is y divisible by z? &nbs [#permalink] 06 Dec 2017, 22:56
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