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Is x/y>1?

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by Max@Math Revolution » Wed Dec 19, 2018 4:47 am

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[Math Revolution GMAT math practice question]

Is x/y>1?

1) x>y
2) x-y>1
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Source: — Data Sufficiency |

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by Brent@GMATPrepNow » Wed Dec 19, 2018 6:04 am
Max@Math Revolution wrote:Is x/y > 1?
1) x > y
2) x - y > 1
Target question: Is x/y > 1?

Statement 1: x > y
Let's TEST some values.
There are several values of x and y that satisfy statement 1. Here are two:
Case a: x = 3 and y = 1. In this case, x/y = 3/1 = 3. So, the answer to the target question is YES, x/y IS greater than 1
Case b: x = 3 and y = -1. In this case, x/y = 3/(-1) = -3. So, the answer to the target question is NO, x/y is NOT greater than 1
Since we can answer the target question with certainty, statement 1 is SUFFICIENT

Statement 2: x - y > 1
Let's TEST some values.
There are several values of x and y that satisfy statement 2. Here are two:
Case a: x = 3 and y = 1. In this case, x/y = 3/1 = 3. So, the answer to the target question is YES, x/y IS greater than 1
Case b: x = 3 and y = -1. In this case, x/y = 3/(-1) = -3. So, the answer to the target question is NO, x/y is NOT greater than 1
Since we can answer the target question with certainty, statement 2 is 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 = 3 and y = 1. In this case, x/y = 3/1 = 3. So, the answer to the target question is YES, x/y IS greater than 1
Case b: x = 3 and y = -1. In this case, x/y = 3/(-1) = -3. So, the answer to the target question is NO, x/y is NOT greater than 1
Since we cannot answer the target question with certainty, the combined statements are NOT SUFFICIENT

Answer: E

Cheers,
Brent
Brent Hanneson - Creator of GMATPrepNow.com
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by Max@Math Revolution » Thu Dec 20, 2018 11:26 pm
=>

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.

x/y>1
=> xy>y^2
=> xy-y^2>0
=> y(x-y)>0
By condition 2), x-y > 1 > 0, but we can't determine whether y is positive from condition 1).

Therefore, E is the answer.
Answer: E
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