Bunuel wrote:
GMAT CLUB'S FRESH QUESTION:
If |x - y| = |x - z|, what is the value of x?
(1) y < z
(2) The average (arithmetic mean) of y and z equal to the average (arithmetic mean) of y, z and 2.
Given, |x - y| = |x - z|, which means distance of x from y & distance of x from z are equal.
so we have
(a) if (x - y) > 0 & (x - z) > 0, then y = z, & x can take any value
(b) if (x - y) < 0 & (x - z) < 0, then y = z, & x can take any value
(c) if (x - y) > 0 & (x - z) < 0, then x = (y + z)/2, & x > y , x < z & y < x < z
(d) if (x - y) < 0 & (x - z) > 0, then x = (y + z)/2, & x < y, x > z & z < x < y
Statement 1: y < z , hence case (d) is possible, x lies between y & z, as y < x < z. However not sufficient to find value of x.
Statement 2: \(\frac{(y + z)}{2}\) = \(\frac{(y + z + 2)}{3}\)
Simplifying this we get, y + z = 4, however we cannot say anything about of position of x & hence cannot calculate x.
Since y = z = 2, hence x can take any value
or y = 1, z = 3, then x = 2
Hence statement 2 is not sufficient.
Combining both Statements, we have y < z & y + z = 4. hence we have case (c), y < x < z
Hence x = (y + z)/2 = 4/2 = 2.
Combining both statements is Sufficient.
Answer C.
Thanks,
GyM
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