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Is xy>0?

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Is xy>0?  [#permalink]

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New post 28 Aug 2018, 02:06
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[Math Revolution GMAT math practice question]

Is \(xy>0\)?

\(1) x+y>0\)
\(2) |x|+|y|<1\)

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Re: Is xy>0?  [#permalink]

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New post 28 Aug 2018, 02:44
1
From statement 1:

No info about X and Y.
If X is +0.9 and Y is -0.4 Then X+Y = 0.5>0
But XY<0 and,
If X = 1 and Y is 2 then X+Y = 3>0
and XY>0. Both cases possible.
Insufficient.

From statement 2:

|x|+|y|<1
|X|<1 and |Y|<1
Same cases as statement 1.
Insufficient.

Combining also doesn't give a unique answer.

E is the answer.
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Re: Is xy>0?  [#permalink]

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New post 28 Aug 2018, 08:11
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MathRevolution wrote:
[Math Revolution GMAT math practice question]

Is \(xy>0\)?

\(1) x+y>0\)
\(2) |x|+|y|<1\)


Target question: Is xy>0?

Statement 1: x + y > 0
This statement doesn't FEEL sufficient, so I'll TEST some values.
There are several values of x and y that satisfy statement 1. Here are two:
Case a: x = 1 and y = 1. In this case, xy = (1)(1) = 1. So, the answer to the target question is YES, xy IS greater than 0
Case b: x = 2 and y = -1. In this case, xy = (2)(-1) = -2. So, the answer to the target question is NO, xy is NOT greater than 0
Since we cannot answer the target question with certainty, statement 1 is NOT SUFFICIENT

Aside: For more on this idea of testing values when a statement doesn't feel sufficient, read my article: http://www.gmatprepnow.com/articles/dat ... lug-values

Statement 2: |x| + |y| < 1
Let's test values again.
Case a: x = 0.2 and y = 0.2. In this case, xy = (0.2)(0.2) = 0.04. So, the answer to the target question is YES, xy IS greater than 0
Case b: x = -0.8 and y = 0.1. In this case, xy = (-0.8)(0.1) = -0.08. So, the answer to the target question is NO, xy is NOT greater than 0
Since we cannot answer the target question with certainty, statement 2 is NOT SUFFICIENT

Statements 1 and 2 combined
There are still several values of x and y that satisfy BOTH statements. Here are two:
Case a: x = 0.2 and y = 0.2. In this case, xy = (0.2)(0.2) = 0.04. So, the answer to the target question is YES, xy IS greater than 0
Case b: x = 0.8 and y = -0.1. In this case, xy = (0.8)(-0.1) = -0.08. So, the answer to the target question is NO, xy is NOT greater than 0
Since we cannot answer the target question with certainty, the combined statements are NOT SUFFICIENT

Answer: E

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Re: Is xy>0?  [#permalink]

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New post 28 Aug 2018, 08:49
MathRevolution wrote:
[Math Revolution GMAT math practice question]

Is \(xy>0\)?

\(1) x+y>0\)
\(2) |x|+|y|<1\)
Answer is E
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Re: Is xy>0?  [#permalink]

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New post 28 Aug 2018, 09:56
MathRevolution wrote:
[Math Revolution GMAT math practice question]

Is \(xy>0\)?

\(1) x+y>0\)
\(2) |x|+|y|<1\)

I think the quickest way to solve this question is number plugging.
When the question is whether xy > 0 or xy < 0, I usually select number 0 to test the statement.

(1) x+y>0. If x=0, y=0.5 -> No. If x=0.1, y=0.5 -> Yes. --> Not sufficient.
(2) |x|+|y|<1. If x=0, y=0.5 -> No. If x=0.1, y=0.5 -> Yes. --> Not sufficient.

(1) + (2) Two possible answers still exist. --> Not sufficient.

Answer E.
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Re: Is xy>0?  [#permalink]

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New post 30 Aug 2018, 00:49
=>

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.

Since we have 2 variables (\(x\) and \(y\)) and \(0\) equations, C is most likely to be the answer. So, we should consider conditions 1) & 2) together first. After comparing the number of variables and the number of equations, we can save time by considering conditions 1) & 2) together first.

Conditions 1) & 2)
If \(x = \frac{1}{2}\) and \(y = \frac{1}{4}\), then \(xy > 0\) and the answer is ‘yes’.
If \(x = \frac{1}{2}\) and \(y = -(\frac{1}{4})\), then \(xy < 0\) and the answer is ‘no’.

Since the answer is not unique, both conditions are not sufficient, when taken together.

Therefore, E is the answer.
Answer: E

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Re: Is xy>0?   [#permalink] 30 Aug 2018, 00:49
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