Practice GMAT Data Sufficiency Question
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If b is prime and the symbol # represents one of the following operations: addition, subtraction, multiplication, or division, is the value of b # 2 even or odd?
 (b # 1) # 2 = 5
 4 # b = 3 # (1 # b) and b is even
Correct Answer: D
 This problem deals with the properties of prime numbers. Keep in mind that 1 is not a prime number and that 2 is the only even prime number.

Evaluate Statement (1) alone.
 Try each of the operations in turn. First, try addition:
(b + 1) + 2 = 5
Solve for b.
b = 2.
Under addition, b = 2, which is a prime number; therefore addition is a possibility for the operator.  Next, try subtraction.
(b  1)  2 = 5
Solve for b.
b = 8
But b = 8 is not prime, therefore operator cannot represent subtraction.  Next, try multiplication.
(b * 1) * 2 = 5
Solve for b.
b = 5/2
But b = 5/2 is not prime, therefore operator cannot represent multiplication.  Finally, try division.
(b / 1) / 2 = 5
Solve for b.
b = 10
But b = 10 is not prime, therefore operator cannot represent division.  Since addition is the only operation for which b is prime, # must represent addition. In this case, b = 2 and the value of b # 2 is 4, which is even.
 Statement (1) is SUFFICIENT.
 Try each of the operations in turn. First, try addition:

Evaluate Statement (2) alone.
 Try each of the operations in turn. First, try addition:
4 + b = 3 + (1 + b)
Subtract 4 from each side.
b = b
While this is true, it does not give any information about the value of b. However, addition is still a possible operation.  Next, try subtraction:
4  b = 3  (1  b)
Solve for b.
b = 1
In this case, b = 1 is not a prime number, so subtraction is not a possible operation.  Next, try multiplication:
4 * b = 3 * (1 * b)
Simplify.
4b = 3b
The only value for which this holds true is b = 0, which is not a prime number. Therefore, multiplication is not a possible operation.  Finally, try division:
4 / b = 3 / (1 / b)
Multiply both sides by (1 / b)
4 / b^{2} = 3
Solve for b^{2}.
b^{2} = 4/3
Which means that b = sqrt(4/3) or b = sqrt(4/3). Neither of these is prime, so division is not a possible operation.  The symbol # must represent addition, since this is the only possible operation. By Statement (2), b is even, but b is still prime. Since 2 is the only even prime number, b must be 2. In this case, the value of b # 2 is even because an even number plus 2 is still an even number.
 Statement (2) is SUFFICIENT.
 Try each of the operations in turn. First, try addition:
 Since Statement (1) alone is SUFFICIENT and Statement (2) alone is SUFFICIENT, answer D is correct.
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