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If x and y are positive integers, are x and y consecutive?

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by Max@Math Revolution » Wed Jun 12, 2019 12:16 am

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[GMAT math practice question]

If x and y are positive integers, are x and y consecutive?

1) x+y=3
2) xy=2
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Source: — Data Sufficiency |

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by Brent@GMATPrepNow » Wed Jun 12, 2019 4:34 am
Max@Math Revolution wrote:[GMAT math practice question]

If x and y are positive integers, are x and y consecutive?

1) x+y=3
2) xy=2
Given: x and y are positive integers

Target question: Are x and y consecutive?

Statement 1: x+y=3
Since x+y=3 are x positive integers, we know that one number must be 1 and the other number must be 2.
The answer to the target question is YES, x and y ARE consecutive
Since we can answer the target question with certainty, statement 1 is SUFFICIENT

Statement 2: xy=2
Since x+y=3 are x positive integers, we know that one number must be 1 and the other number must be 2.
The answer to the target question is YES, x and y ARE consecutive
Since we can answer the target question with certainty, statement 2 is SUFFICIENT

Answer: D

Cheers,
Brent
Brent Hanneson - Creator of GMATPrepNow.com
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by Max@Math Revolution » Thu Jun 13, 2019 10:49 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. We should simplify conditions if necessary.

Since x and y are positive integers, condition 1) tells us that either x = 1 and y = 2, or x = 2 and y= 1. Thus, x and y are consecutive integers.

Since x and y are positive integers, condition 2 tells us that either x = 1 and y = 2, or x = 2 and y= 1. Thus, x and y are consecutive integers.

Therefore, D is the answer.

Note: Tip 1) of the VA method states that D is most likely to be the answer if condition 1) gives the same information as condition 2).
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