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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: 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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20 Dec 2017, 00:53
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65% (hard)

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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 $$y<1$$

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MathRevolution: Finish GMAT Quant Section with 10 minutes to spare
The one-and-only World’s First Variable Approach for DS and IVY Approach for PS with ease, speed and accuracy.
"Only $79 for 1 month Online Course" "Free Resources-30 day online access & Diagnostic Test" "Unlimited Access to over 120 free video lessons - try it yourself" Manager 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] ### Show Tags 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 Answer D Retired Moderator 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] ### Show Tags 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. Hence D answer Math Revolution GMAT Instructor 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] ### Show Tags 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. Therefore, the answer is D. Note: Since conditions 1) and 2) are similar, D is most likely to be the answer by Tip 1). Answer: D _________________ MathRevolution: Finish GMAT Quant Section with 10 minutes to spare The one-and-only World’s First Variable Approach for DS and IVY Approach for PS with ease, speed and accuracy. "Only$79 for 1 month Online Course"
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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