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x is a positive integer and y is a negative integer.

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x is a positive integer and y is a negative integer. [#permalink] New post 06 Mar 2018, 15:46
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x is a positive integer and y is a negative integer.

Quantity A
Quantity B
x - y
y - x


A) Quantity A is greater.
B) Quantity B is greater.
C) The two quantities are equal.
D) The relationship cannot be determined from the information given.

Kudos to the right solution and explanation
[Reveal] Spoiler: OA

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Re: x is a positive integer and y is a negative integer. [#permalink] New post 06 Mar 2018, 18:45
For quantity A, if a positive subtracts a negative, the negatives will cancel, and we will produce a positive plus another positive. So quantity A is positive.

For quantity B, if a negative subtracts a positive, it will produce another negative.

Since quantity A is positive and quantity B is negative, the answer must be A.

METHOD TWO: If using number properties seems a little fuzzy, you could always try choosing values for x and y. For example:

If x = 4 and y = -2,

then quantity A is 4 - (-2) = 6
and quantity B is -2 - 4 = -6

proving that A is the answer.

METHOD THREE: we can also treat the two quantities as an inequality.

x - y >? y - x

add x to both sides

2x - y >? y

add y to both sides

2x >? 2y

We can see that two times a positive will be larger than two times a negative, proving again that the answer is A.
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Re: x is a positive integer and y is a negative integer.   [#permalink] 06 Mar 2018, 18:45
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