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Math Revolution GMAT Instructor V
Joined: 16 Aug 2015
Posts: 8229
GMAT 1: 760 Q51 V42 GPA: 3.82
If x, y, and z are positive integers, is x+y divisible by 7?  [#permalink]

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Difficulty:   35% (medium)

Question Stats: 74% (01:20) correct 26% (01:29) wrong based on 49 sessions

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[GMAT math practice question]

If $$x, y$$, and $$z$$ are positive integers, is $$x+y$$ divisible by $$7$$?

1) $$x+z$$ is divisible by $$7$$
2) $$y+z$$ is divisible by $$7$$

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Math Expert V
Joined: 02 Aug 2009
Posts: 8282
Re: If x, y, and z are positive integers, is x+y divisible by 7?  [#permalink]

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MathRevolution wrote:
[GMAT math practice question]

If $$x, y$$, and $$z$$ are positive integers, is $$x+y$$ divisible by $$7$$?

1) $$x+z$$ is divisible by $$7$$
2) $$y+z$$ is divisible by $$7$$

Statements alone are clearly insuff as we are not told about third variable..
1) x+z is divisible by 7.
2) y+z is div by 7

Combined..
X+z and y+z are div by 7, so we can say for sure x+y+2z is div by 7..
So if z is div by 7, x+y is div by 7..
z=14, both x and y will have to be div by 7 to satisfy the statements and hence their sum is div by 7.

But if z is not div by 7, x+y is not div by 7..
z=4, so x can be 3 as X+z is div by 7..
Similarly y can be 10, as y+z is div by 7..
But x+y =3+10=13 is not
Insufficient

E
_________________
Math Revolution GMAT Instructor V
Joined: 16 Aug 2015
Posts: 8229
GMAT 1: 760 Q51 V42 GPA: 3.82
Re: If x, y, and z are positive integers, is x+y divisible by 7?  [#permalink]

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=>

Forget conventional ways of solving math questions. For DS problems, the VA (Variable Approach) method is the quickest and easiest way to find the answer without actually solving the problem. Remember that equal numbers of variables and independent equations ensure a solution.

Since we have 3 variables ($$x, y$$ and $$z$$) and $$0$$ equations, E is most likely to be the answer. So, we should consider conditions 1) & 2) together first.

Conditions 1) & 2):
If $$x = 7, y = 7,$$ and $$z = 7$$, the answer is ‘yes’, since $$x + y = 14$$ is divisible by $$7$$.
If $$x = 1, y = 1$$, and $$z = 6$$, the answer is ‘no’, since $$x + y = 2$$ is not divisible by $$7$$.
Thus, conditions 1) and 2) together are not sufficient.

In cases where 3 or more additional equations are required, such as for original conditions with “3 variables”, or “4 variables and 1 equation”, or “5 variables and 2 equations”, conditions 1) and 2) usually supply only one additional equation. Therefore, there is an 80% chance that E is the answer, a 15% chance that C is the answer, and a 5% chance that the answer is A, B or D. Since E (i.e. conditions 1) & 2) are NOT sufficient, when taken together) is most likely to be the answer, it is generally most efficient to begin by checking the sufficiency of conditions 1) and 2), when taken together. Obviously, there may be occasions on which the answer is A, B, C or D.
_________________ Re: If x, y, and z are positive integers, is x+y divisible by 7?   [#permalink] 26 Feb 2018, 02:31
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# If x, y, and z are positive integers, is x+y divisible by 7?  