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Source: — Data Sufficiency |

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by Anurag@Gurome » Tue Feb 26, 2013 3:56 am
anastasios1984 wrote:If X and Y are integers and Y = |x+3| + |4-x| does Y = 7?

i) X<4
ii)X>-3
y = |x + 3| + |4 - x| means y is the sum of the distances of x from -3 and 4 on the number line.

Now the distance between -3 and 4 on the number line is (3 + 4) = 7.
Hence, the sum of the distances of x from -3 and 4 on the number line will be equal to 7 only if x lies between -3 and 4. If it is less than -3 or more than 4, the sum will be obviously greater than 7.

Statement 1: x may or may not be more than -3
Hence, y ≥ 7 ---> Not sufficient

Statement 2: x may or may not be less than 4
Hence, y ≥ 7 ---> Not sufficient

1 & 2 Together: Now we know that -3 < x < 4, hence the sum will be always equal to 7 ---> Sufficient

The correct answer is C.
Anurag Mairal, Ph.D., MBA
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