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

Question

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

AkshayKS21 · Answer

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.

MathRevolution · Answer

==> 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

Therefore, the answer is E.
Answer: E

akshayk · Answer

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.

Kinshook · Answer

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

1) x+z is divisible by 3
x + z mod 3 = 0
Since y is unknown
NOT SUFFICIENT

2) y+z is divisible by 3
y + z mod 3 = 0
Since x is unknown
NOT SUFFICIENT

(1) + (2) 
1) x+z is divisible by 3
x + z mod 3 = 0
2) y+z is divisible by 3
y + z mod 3 = 0
x + y + 2z mod 3 = 0
x - y mod 3 = 0
There is no way to find x+ymod3
NOT SUFFICIENT

IMO E

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

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GMAT Data Sufficiency (DS) Questions

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

Prep Toolkit

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More than Quant/Verbal Abilities: Speed vs. Accuracy

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My Rewards