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Is 0 between x and y?

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Math Revolution GMAT Instructor
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Is 0 between x and y?  [#permalink]

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New post 01 Aug 2018, 02:05
1
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A
B
C
D
E

Difficulty:

  25% (medium)

Question Stats:

75% (01:19) correct 25% (00:57) wrong based on 57 sessions

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[Math Revolution GMAT math practice question]

Is \(0\) between \(x\) and \(y\)?

\(1) x-y>0\)
\(2) x^2-y^2>0\)

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Is 0 between x and y?  [#permalink]

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New post 01 Aug 2018, 05:21
To determine if 0 is between x and y

=> whether x and y have different sign

Statement 1

x-y > 0

=> x can be 10 and y can 2 satisfying x-y>0 10-2 = 8 >0 x and y have same sign

=> x can be 10 and y can -2 satisfying x-y>0 10-(-2) = 12 >0 x and y have different sign

Statement 1 is not sufficient

Statement 2

\(x^2 - y^2 > 0\)

=> \(x^2 > y^2\)

=> x can be 10 and y can 2 satisfying \(x^2 - y^2 > 0\) 100-4 = 96 >0 x and y have same sign

=> x can be 10 and y can -2 satisfying \(x^2 - y^2 > 0\) 100-4 = 96 >0 x and y have different sign

Statement 2 is not sufficient

Combining statements 1 and 2

\(x^2 - y^2 > 0\) and \(x-y > 0\)

=> \((x+y)(x-y) > 0\)

=> \(x+y > 0\)

=> x can be 10 and y can 2 satisfying x+y>0 10+2 = 12 >0 x and y have same sign

=> x can be 10 and y can -2 satisfying x+y>0 10+(-2) = 8 >0 x and y have different sign

Statements 1 and 2 together are insufficient

Hence option E
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Is 0 between x and y?  [#permalink]

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New post 01 Aug 2018, 17:36
MathRevolution wrote:
[Math Revolution GMAT math practice question]

Is \(0\) between \(x\) and \(y\)?

\(1) x-y>0\)
\(2) x^2-y^2>0\)


Question is whether\(X\) and \(Y\) have opposite signs ?

Statement 1: \(X-Y >0\) => \(X>Y\) . Suppose X is positive Y Could be Positive or Negative. For example, X= 5, Y = 3, -3. So no conclusion about signs of \(X and Y\).

Statement 2: \(2) X^2-Y^2>0\) = \((X-Y)(X+Y)>0\)
1. \(X-Y>0\) and \(X+Y>0\) => \(X>Y\) & \(X>-Y\)
2. \(X-Y<0\) and \(X+Y<0\) => \(X<Y\) & \(X<-Y\)

So X and Y could have same sign or could have different signs.

combine statement 1 and 2, still X and Y could have same or different signs. No conclusion. So Answer E.
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Re: Is 0 between x and y?  [#permalink]

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New post 01 Aug 2018, 20:34
Statement 1

x>y we don't know anything that whether zero lies between x and y. Hence insufficient

Statement 2
This could be written as
|x|>|y|
again nothing about zero or the magnitude of x and y. Hence insufficient.

Combining both statements don't say anything about zero, Hence insufficient
The correct answer should be E
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Re: Is 0 between x and y?  [#permalink]

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New post 02 Aug 2018, 11:11
Top Contributor
MathRevolution wrote:
[Math Revolution GMAT math practice question]

Is \(0\) between \(x\) and \(y\)?

\(1) x-y>0\)
\(2) x^2-y^2>0\)


Target question: Is 0 between x and y?

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 = 2 and y = -1. In this case, the answer to the target question is YES, 0 IS between x and y
Case b: x = 2 and y = 1. In this case, the answer to the target question is NO, 0 is NOT between x and y
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^2 - y^2 > 0
This statement doesn't FEEL sufficient, so I'll TEST some values.
IMPORTANT: When testing values always check to see whether you can RE-USE values you used when analyzing the other statement.
We can see that we can RE-USE both of the cases that we used for statement 1. That is the x- and y-values we used for statement 1 also satisfy statement 2.
Case a: x = 2 and y = -1. In this case, the answer to the target question is YES, 0 IS between x and y
Case b: x = 2 and y = 1. In this case, the answer to the target question is NO, 0 is NOT between x and y
Since we cannot answer the target question with certainty, statement 2 is NOT SUFFICIENT

Statements 1 and 2 combined
IMPORTANT: Notice that I was able to use the same counter-examples to show that each statement ALONE is not sufficient. So, the same counter-examples will satisfy the two statements COMBINED.
In other words,
Case a: x = 2 and y = -1. In this case, the answer to the target question is YES, 0 IS between x and y
Case b: x = 2 and y = 1. In this case, the answer to the target question is NO, 0 is NOT between x and y
Since we cannot answer the target question with certainty, the combined statements are NOT SUFFICIENT

Answer: E

Cheers,
Brent
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Re: Is 0 between x and y?  [#permalink]

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New post 03 Aug 2018, 02:04
=>

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. We then recheck the question.

If we modify the question, it asks if xy < 0. Since the two conditions do not give us enough information to determine the sign of xy, both conditions together are not sufficient, and the answer is E.

Since we have 2 variables (x and y) and 1 equation, D is most likely to be the answer. So, we should consider each of the conditions on its own first.

Conditions 1) & 2)
If x = 2 and y = -1, then 0 is between x and y.
If x = 2 and y = 1, then 0 is not between x and y.
Since we don’t have a unique solution, both conditions together are not sufficient.

Therefore, E is the answer.

Answer: E

Normally, in problems which require 2 equations, such as those in which the original conditions include 2 variables, or 3 variables and 1 equation, or 4 variables and 2 equations, each of conditions 1) and 2) provide an additional equation. In these problems, the two key possibilities are that C is the answer (with probability 70%), and E is the answer (with probability 25%). Thus, there is only a 5% chance that A, B or D is the answer. This occurs in common mistake types 3 and 4. Since C (both conditions together are sufficient) is the most likely answer, we save time by first checking whether conditions 1) and 2) are sufficient, when taken together. Obviously, there may be cases in which the answer is A, B, D or E, but if conditions 1) and 2) are NOT sufficient when taken together, the answer must be E.
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