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# If y is negative, what is the value of x ?

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Math Expert
Joined: 02 Sep 2009
Posts: 47219
If y is negative, what is the value of x ?  [#permalink]

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12 Sep 2017, 05:08
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65% (hard)

Question Stats:

54% (01:10) correct 46% (01:33) wrong based on 57 sessions

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If y is negative, what is the value of x ?

(1) x + y = -(|y| - x)
(2) x - y = 2

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Joined: 02 Nov 2015
Posts: 170
GMAT 1: 640 Q49 V29
Re: If y is negative, what is the value of x ?  [#permalink]

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12 Sep 2017, 07:10
A... Statement 1 alone is sufficient.

On solving statement 1 we get x=0.

Statement 2. Tells nothing about y.. insufficient..

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Joined: 02 Jul 2017
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GMAT 1: 730 Q50 V38
Re: If y is negative, what is the value of x ?  [#permalink]

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12 Sep 2017, 08:43
1
y = -ve,
Find: x ?

Lets put value of y with its sign so y=-a where "a" is a positive number

(1) x + y = -(|y| - x)
=> x-a =-(|-a|-x)
=> x-a = -(a-x)
=> x-a =-a+x => x-a = x-a
we don't get any value. It just tell equality
Not sufficient

(2) x - y = 2
x-(-a) = 2 => x+a =2
We dont know value of a so we cannot find value of x. So insufficient

1+2
we don't get anything from equation 1 and combining it with 2 will not give us anything extra.

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Re: If y is negative, what is the value of x ?  [#permalink]

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12 Sep 2017, 08:58
Bunuel wrote:
If y is negative, what is the value of x ?

(1) x + y = -(|y| - x)
(2) x - y = 2

Statement 1: $$x+y = -|y|+x$$. As $$y$$ is negative hence $$y = -|y|$$. So adding same value $$x$$ to both sides of the equation will not change the value of the Equality $$y = -|y|$$. Hence $$x$$ can be any real number. Insufficient

Statement 2: Cannot be solved as we have two variable and one equation. Hence Insufficient

Combining 1 & 2. we cannot find the value of $$x$$ as we have only one equation and two variables. Hence Insufficient

Option E
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Re: If y is negative, what is the value of x ?  [#permalink]

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13 Sep 2017, 12:49
Bunuel wrote:
If y is negative, what is the value of x ?

(1) x + y = -(|y| - x)
(2) x - y = 2

Forget conventional ways of solving math questions. In DS, Variable approach is the easiest and quickest way to find the answer without actually solving the problem. Remember equal number of variables and independent equations ensures a solution.

There 2 variables and 0 equation. Thus we need 2 equations to solve for the variables; the conditions provide 2 equations, so there is high chance that (C) will be the answer.

Condition 1) & 2)

$$x + y = -(|y| - x)$$ is equivalent to $$x+y = -(-y-x)$$ since y is negative.
Then we have $$x + y = x + y$$.
We don't have any equation.

The only equation $$x - y = 2$$ from the condition 2) is not sufficient.

Both conditions together, they are not sufficient.

Normally for cases where we need 2 more equations, such as original conditions with 2 variables, or 3 variables and 1 equation, or 4 variables and 2 equations, we have 1 equation each in both 1) and 2). Therefore C has a high chance of being the answer, which is why we attempt to solve the question using 1) and 2) together. Here, there is 70% chance that C is the answer, while E has 25% chance. These two are the key questions. In case of common mistake type 3,4, the answer may be from A, B or D but there is only 5% chance. Since C is most likely to be the answer according to DS definition, we solve the question assuming C would be our answer hence using 1) and 2) together. (It saves us time). Obviously there may be cases where the answer is A, B, D or E.
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Re: If y is negative, what is the value of x ? &nbs [#permalink] 13 Sep 2017, 12:49
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