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Math Expert V
Joined: 02 Aug 2009
Posts: 7999
What is the value of y, if both x and y are integers and xy<0?  [#permalink]

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1
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Difficulty:   95% (hard)

Question Stats: 44% (02:05) correct 56% (01:58) wrong based on 130 sessions

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What is the value of y, if both x and y are integers and xy<0?
(1) $$\frac{2^x}{2^y}=4$$
(2) $$x+y=0$$

New question!!!..
tricky

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Manager  G
Joined: 23 Aug 2016
Posts: 101
Location: India
Concentration: Finance, Strategy
GMAT 1: 660 Q49 V31 GPA: 2.84
WE: Other (Energy and Utilities)
Re: What is the value of y, if both x and y are integers and xy<0?  [#permalink]

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A.
1. Says that x-y=2
As we know both x and y are integers and one is positive and one is negative i.e none of them is zero, we can safety find value of x and y which satisfies the equation x-y=2
There is only one set of points that are at a distance of 2 units of each other and have different signs i.e. 1 and -1.
Sufficient.

2. Not sufficient. X and y can be (2,-2),(3,-3) etc.

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Manager  B
Joined: 01 Nov 2018
Posts: 81
GMAT 1: 690 Q48 V35 GPA: 3.88
Re: What is the value of y, if both x and y are integers and xy<0?  [#permalink]

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Took me 7:30min to get A.... Had to realize from Statement 1, you get x-y=2 and the only way for XY to be negative is for Y to be negative. The only values that work to satisfy this conditions are 1 and -1 respectively for X and Y. Any tips on how to realize this much faster? I knew 2 was insufficient but on the actual exam, a question like this would destroy my timing as I would never spend more than 3/3:30 tops for a single question.
Intern  B
Joined: 05 Nov 2018
Posts: 7
What is the value of y, if both x and y are integers and xy<0?  [#permalink]

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1
Statement 1

$$2^{x-y}$$= $$2^2$$

x-y=2

$$x\leq{-2}$$ => $$xy\leq{0}$$
x=-1 y=-3 xy>0
x=0 y=-2 xy=0
x=1 y=-1 xy<0
$$x\geq{2}$$ => $$xy\geq{0}$$

as xy<0 only x=1 and y=-1 fits.

Statement 1 Sufficient

Statement 2

x+y=0
x=-y

xy<0 for all non zero values

Not sufficient

LBS Moderator D
Joined: 04 Jun 2018
Posts: 649
Location: Germany
Concentration: General Management, Finance
GMAT 1: 730 Q47 V44 GPA: 3.4
WE: Analyst (Transportation)
Re: What is the value of y, if both x and y are integers and xy<0?  [#permalink]

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st1gg3r wrote:
Statement 1

$$2^{x-y}$$= $$2^2$$

x-y=2

$$x\leq{-2}$$ => $$xy\leq{0}$$
x=-1 y=-3 xy>0
x=0 y=-2 xy=0
x=1 y=-1 xy<0
$$x\geq{2}$$ => $$xy\geq{0}$$

as xy<0 only x=1 and y=-1 fits.

Statement 1 Sufficient

Statement 2

x+y=0
x=-y

xy<0 for all non zero values

Not sufficient

Thank you for the detailed explanation.
I was actually unable to spot the possibility to make use of exponent rules and transform the equation accordingly.
_________________ Re: What is the value of y, if both x and y are integers and xy<0?   [#permalink] 03 Jan 2019, 10:49
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