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0 as an integer

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0 as an integer

by jswesth » Sun Mar 13, 2016 3:08 pm
Problem #31 in the OG16 Quantitative Review bonus book:

If x and y are integers, what is the value of x?
(1.) xy=1
(2.) x≠1

The answer given is C (both statements together are sufficient), but isn't this overlooking the fact that x could be 0? Making the answer E in my mind...

What am I missing here?
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Source: — Data Sufficiency |

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by [email protected] » Sun Mar 13, 2016 3:22 pm
Hi jswesth,

The prompt starts off by telling us that X and Y are both INTEGERS. We're asked for the value of X.

1) XY = 1

Since X and Y are both integers, there are only two possible options here:

X and Y are both 1
X and Y are both -1
Fact 1 is INSUFFICIENT

2) X does NOT equal 1

This does not tell us the value of X.
Fact 2 is insufficient

Combined, since X CANNOT equal 1, it must be -1.
Combined, SUFFICIENT.

Final Answer: C

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by jswesth » Sun Mar 13, 2016 4:06 pm
But 0 is an integer. If the prompt stated "positive integers", that's a different story. But it just states simply "integer", of which 0 is one.

Because of this, either X or Y could be 0, and the other could be any other positive or negative integer.

Why isn't this the case?
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by [email protected] » Sun Mar 13, 2016 5:38 pm
Hi jswesth,

Each of the two Facts underneath the prompt provide additional information/restrictions that you must use to answer the question that is asked. In Fact 1, we're told that (X)(Y) = 1, so NEITHER of those two variables can equal 0 (since anything multiplied by 0 equals 0). When using that Fact, there are only TWO options (X and Y are both +1 or X and Y are both -1).

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