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If x and y are positive integers, are x and y consecutive? 1

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Source: — Data Sufficiency |
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by DavidG@VeritasPrep » Sun Apr 02, 2017 4:05 pm
ziyuenlau wrote:If x and y are positive integers, are x and y consecutive?

1) x+y=3
2) x-y=1

Source : Math Revolution
Official Answer : D
Statement 1: The only positive integers that will sum to 3 are 1 and 2, so YES x and y must be consecutive. Sufficient.

Statement 2: Add y to both sides to get x = 1 + y. This is the algebraic definition of consecutive integers. If x and y are integers, and x = 1 + y (or y = 1 + x) then x and y must be consecutive integers. You could also see this by plugging in numbers. (y = 1 and x = 2; y = 2 and x = 3, etc.) No matter what, x and y will always be consecutive integers, yielding a definitive YES. Sufficient.

The answer is D
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by Jay@ManhattanReview » Tue Apr 04, 2017 2:30 am
ziyuenlau wrote:If x and y are positive integers, are x and y consecutive?

1) x+y=3
2) x-y=1

Source : Math Revolution
Official Answer : D
Hi ziyuenlau,

Statement 1: x+y=3

We must try with the minimum possible and the maximum possible values of x and y.

The minimum possible of x = 1, thus y = 2. Thus, x and y are consecutive. Yes.

The maximum possible of x = 2 (it cannot be 3 as that will make y = 0), thus y = 1. Thus, x and y are consecutive. Yes. Sufficient.

Statement 2: x-y=1

x-y=1 itself defies that x and y are consecutive if each of them is positive. It basically states that the difference of two positive integers is 1, thus, they are consecutive. Sufficient.

The correct answer: D

Hope this helps!

Relevant book: Manhattan Review GMAT Data Sufficiency Guide

-Jay
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by Jeff@TargetTestPrep » Tue Apr 11, 2017 11:24 am
ziyuenlau wrote:If x and y are positive integers, are x and y consecutive?

1) x+y=3
2) x-y=1
We are given that x and y are positive integers and we need to determine whether x and y are consecutive.

Statement One Alone:

x + y = 3

Since x and y are positive integers and their sum is 3, either x = 2 and y = 1 or x = 1 and y = 2. Either way, x and y are consecutive. Statement one is sufficient to answer the question.

Statement Two Alone:

x - y = 1

Since x = 1 + y, we see that x is one more than y, and thus x and y are consecutive. Statement two alone is also sufficient to answer the question.

Answer D

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