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If x, y, and z are positive integers, is x+y divisible by 3? 1) x+z is

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Math Revolution GMAT Instructor
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If x, y, and z are positive integers, is x+y divisible by 3? 1) x+z is  [#permalink]

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New post 12 Jul 2017, 01:09
00:00
A
B
C
D
E

Difficulty:

  35% (medium)

Question Stats:

76% (01:15) correct 24% (01:28) wrong based on 69 sessions

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If x, y, and z are positive integers, is x+y divisible by 3?

1) x+z is divisible by 3
2) y+z is divisible by 3

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Re: If x, y, and z are positive integers, is x+y divisible by 3? 1) x+z is  [#permalink]

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New post 12 Jul 2017, 07:33
2
Clicked C in haste. Then realised I didn't check other numbers. I shouldn't do this in Exam. :cry:

Clearly, individually, both A and B are insufficient.

Combining both:
    Let x=1 and z=2. So x+z=1+2=3 which is divisible by 3. (Satisfying A)
    From B, and z=2 from above, we can take y=7 so that y+z=7+2=9 which is divisible by 3. (Satisfying B)
    So, x+y=1+7=8 and not divisible by 3. (Not Satisfying Question stem x+y is not divisible by 3)
I stopped here.
I should have checked this too: (nowhere mentioned they are distinct)
    Let x=y=z=3. So This satisfies A, B and question stem.
So Answer to DS question is E.
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Re: If x, y, and z are positive integers, is x+y divisible by 3? 1) x+z is  [#permalink]

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New post 14 Jul 2017, 00:59
==> In the original condition, there are 3 variables (x,y,z) and in order to match the number of variables to the number of equations, there must be 3 equations. Since there is 1 for con 1) and 1 for con 2), you need 1 more equation, so E is most likely to be the answer. By solving con 1) and con 2), if x=y=z=3 yes, but if z=2, x=y=1 no, hence it is not sufficient.

Therefore, the answer is E.
Answer: E
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If x, y, and z are positive integers, is x+y divisible by 3? 1) x+z is  [#permalink]

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New post 14 Jul 2017, 01:09
MathRevolution wrote:
If x, y, and z are positive integers, is x+y divisible by 3?

1) x+z is divisible by 3
2) y+z is divisible by 3


1) (x+z)/3 = int.
Nothing about y. Insufficient.

2) (y +z)/3 - int.
Nothing about x. Insufficient.

1+2)
(x+y+2z)/3 = int.
x = 1, y=1, z=2
(x+y)/3 = not int.

x=2, y=1, z=3
(x+y+2z)/3 = int.
(x+y)/3 = int.

Insufficient. E is the answer.
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If x, y, and z are positive integers, is x+y divisible by 3? 1) x+z is   [#permalink] 14 Jul 2017, 01:09
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