BTGmoderatorDC wrote:If x, y, and d are integers and d is odd, are both x and y divisible by d ?
(1) x + y is divisible by d.
(2) x − y is divisible by d.
OA C
Source: Official Guide
Let's take each statement one by one.
(1) x + y is divisible by d.
Case 1: Say x = y = 3, then x + y = 3 + 3 = 6 as well as x and y are divisible by 3. The answer is yes.
Case 2: Say x = 1 and y = 2, then though x + y = 1 + 2 = 3 is divisible by 3, x and y are not divisible by 3. The answer is no. Insufficient.
(2) x − y is divisible by d.
Case 1: Say x = y = 3, then x - y = 3 - 3 = 0 as well as x and y are divisible by 3. The answer is yes.
Case 2: Say x = 4 and y = 1, then though x - y = 4 - 1 = 3 is divisible by 3, x and y are not divisible by 3. The answer is no. Insufficient.
(1) and (2) together
From (1), say x + y = dp, where p = quotient
From (2), say x - y = dq, where q = quotient
=> x = d(p + q)/2, divisible by d; similarly, y = d(p - q)/2, divisible by d. Sufficient.
The correct answer:
C
Hope this helps!
-Jay
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