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# If |x+1|=|y+1|, what is the value of x+y? 1) xy<0

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Math Revolution GMAT Instructor
Joined: 16 Aug 2015
Posts: 4705
GPA: 3.82
If |x+1|=|y+1|, what is the value of x+y? 1) xy<0 [#permalink]

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20 Dec 2017, 00:53
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[GMAT math practice question]

If $$|x+1|=|y+1|$$, what is the value of $$x+y$$?

1) $$xy<0$$
2) $$x>1$$ and $$y<1$$
[Reveal] Spoiler: OA

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Senior Manager
Joined: 05 Dec 2016
Posts: 260
Concentration: Strategy, Finance
GMAT 1: 620 Q46 V29
Re: If |x+1|=|y+1|, what is the value of x+y? 1) xy<0 [#permalink]

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20 Dec 2017, 04:24
opening module we get 2 outcomes:
case 1: x=y
case 2: x+y=-2
So, we need to discover whether x and y are equal or not

(1) xy<0 follows that x and y are not equal, then 2nd case applies only and x+y=-2 Sufficient
(2) x>1; y<1 we see that they are not equal, then 2nd case applies only and x+y=-2 Sufficient

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Re: If |x+1|=|y+1|, what is the value of x+y? 1) xy<0 [#permalink]

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20 Dec 2017, 10:11
MathRevolution wrote:
[GMAT math practice question]

If $$|x+1|=|y+1|$$, what is the value of $$x+y$$?

1) $$xy<0$$
2) $$x>1$$ and $$y<1$$

When we are given that |a| = |b| (or absolute value of a is equal to absolute value of b), then there could be two cases:
Either a = b
Or a = -b

So in the given question, either x+1 = y +1 (which gives us x=y) Or x+1 = -y-1 (which gives us x+y = -2)
Now if its the first case or x=y, then we cannot find x+y (multiple values will be possible)
But if its the second case then x+y will be -2.

(1) xy < 0
If their product is less than 0 then obviously x and y have opposite signs, so they cannot be equal. So definitely we have the second case and x+y = -2. Sufficient.

(2) x > 1 and y < 1
This again tells us that x and y cannot be equal, and thus we have the second case and x+y = -2. Sufficient.

Math Revolution GMAT Instructor
Joined: 16 Aug 2015
Posts: 4705
GPA: 3.82
Re: If |x+1|=|y+1|, what is the value of x+y? 1) xy<0 [#permalink]

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20 Dec 2017, 23:38
=>

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.

The first step of the VA (Variable Approach) method is to modify the original condition and the question, and then recheck the question

Modifying the original condition gives:

$$|x+1|=|y+1|$$
$$⇔ (x+1)^2=(y+1)^2$$
$$⇔ (x+1)^2=(y+1)^2$$
$$⇔ (x+1)^2-(y+1)2=0$$
$$⇔ (x+1+y+1)(x+1-y-1)=0$$
$$⇔ (x+y+2)(x-y)=0$$
$$⇔ x+y=-2$$ or $$x=y$$

As we have 2 variables (x and y) and 1 equation in the original condition, D is most likely to be the answer.

Condition 1)
Since $$xy < 0, x≠y.$$
So, $$x + y = -2$$, and condition 1) is sufficient.

Condition 2)
Since $$x>1$$ and $$y<1, x≠y.$$
So, $$x + y = -2$$.
Condition 2) is sufficient too.

Note: Since conditions 1) and 2) are similar, D is most likely to be the answer by Tip 1).

_________________

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Re: If |x+1|=|y+1|, what is the value of x+y? 1) xy<0   [#permalink] 20 Dec 2017, 23:38
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