BTGmoderatorLU wrote:Source: GMAT Paper Tests
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.
The OA is C
Given: x, y, and d are integers and d is odd
Target question: Are both x and y divisible by d?
Statement 1: x+y is divisible by d.
Let's TEST some values.
There are several values of x, y and d that satisfy statement 1. Here are two:
Case a: x = 6, y = 9 and d = 3. Notice that 6+9 = 15, and 15 is divisible by 3. In this case, the answer to the target question is
YES, x and y ARE both divisible by d
Case b: x = 2, y = 4 and d = 3. Notice that 2+4 = 6, and 6 is divisible by 3. In this case, the answer to the target question is
NO, x and y are NOT both divisible by d
Since we cannot answer the
target question with certainty, statement 1 is NOT SUFFICIENT
Statement 2: x-y is divisible by d
Let's TEST some values.
Case a: x = 9, y = 3 and d = 3. Notice that 9-3 = 6, and 6 is divisible by 3. In this case, the answer to the target question is
YES, x and y ARE both divisible by d
Case b: x = 10, y = 4 and d = 3. Notice that 10-4 = 6, and 6 is divisible by 3. In this case, the answer to the target question is
NO, x and y are NOT both divisible by d
Since we cannot answer the
target question with certainty, statement 2 is NOT SUFFICIENT
Statements 1 and 2 combined
Here are some nice divisibility rules:
Rule #1. If integers A and B are each divisible by integer k, then (A + B) is divisible by k
Rule #2. If integers A and B are each divisible by integer k, then (A - B) is divisible by k
Statement 1 tells us that x+y is divisible by d
Statement 2 tells us that x-y is divisible by d
By Rule #1, (x+y) + (x-y) is divisible by d
Simplify to get: 2x is divisible by d
Since we're told that d is ODD, we know that
x MUST BE divisible by d
By Rule #2, (x+y) - (x-y) is divisible by d
Simplify to get: 2y is divisible by d
Since we're told that d is ODD, we know that
y MUST BE divisible by d
So, the answer to the target question is
YES, x and y ARE both divisible by d
Answer: C
Cheers,
Brent
