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.
