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Math Revolution GMAT Instructor V
Joined: 16 Aug 2015
Posts: 9032
GMAT 1: 760 Q51 V42
GPA: 3.82
If |x+1|=|y+1|, what is the value of x+y? 1) xy<0  [#permalink]

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Difficulty:   65% (hard)

Question Stats: 55% (02:05) correct 45% (02:16) wrong based on 85 sessions

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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 $$y<1$$

_________________
Manager  S
Joined: 05 Dec 2016
Posts: 227
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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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

Retired Moderator P
Joined: 21 Aug 2013
Posts: 1357
Location: India
Re: If |x+1|=|y+1|, what is the value of x+y? 1) xy<0  [#permalink]

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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 V
Joined: 16 Aug 2015
Posts: 9032
GMAT 1: 760 Q51 V42
GPA: 3.82
Re: If |x+1|=|y+1|, what is the value of x+y? 1) xy<0  [#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.

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).

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

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