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# What is the value of y, if both x and y are integers and xy<0?

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Math Expert
Joined: 02 Aug 2009
Posts: 8180
What is the value of y, if both x and y are integers and xy<0?  [#permalink]

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05 Dec 2018, 04:55
1
2
00:00

Difficulty:

95% (hard)

Question Stats:

44% (02:06) correct 56% (01:59) wrong based on 100 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) $$x+y=0$$

Chetan's questions

tricky

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Joined: 05 Nov 2018
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Re: What is the value of y, if both x and y are integers and xy<0?  [#permalink]

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05 Dec 2018, 05:33
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

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Re: What is the value of y, if both x and y are integers and xy<0?  [#permalink]

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05 Dec 2018, 05:02
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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Re: What is the value of y, if both x and y are integers and xy<0?  [#permalink]

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05 Dec 2018, 05:26
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.
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Re: What is the value of y, if both x and y are integers and xy<0?  [#permalink]

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03 Jan 2019, 10:49
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.
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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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