GMAT Focus EditionQuantitative ReasoningMedium
If 'a' and 'b' are positive integers, is 'a' divisible by 4? (1) a + b is divisible by 4. (2) b is divisible by 4.
- AEACH statement ALONE is sufficient.
- BStatement (1) ALONE is sufficient, but statement (2) alone is not sufficient.
- CBOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.
- DStatement (2) ALONE is sufficient, but statement (1) alone is not sufficient.
Show answer & explanationAnswer & explanation
Correct answer: C. BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.
Statement (1) alone is insufficient (e.g., a=2, b=2, a+b=4; a=4, b=4, a+b=8). Statement (2) alone is insufficient (e.g., a=2, b=4; a=4, b=4). Together, if a+b is divisible by 4 and b is divisible by 4, then (a+b) - b = a must also be divisible by 4.
Why the other options are wrong
- A. Neither statement alone provides enough information to answer the question.
- B. Statement (1) is insufficient as 'a' can be divisible or not divisible by 4.
- D. Statement (2) is insufficient as 'a' can be divisible or not divisible by 4.
Properties of Divisibility (Sums/Differences)
If two integers are divisible by a number, their sum and difference are also divisible by that number. Conversely, if a sum/difference and one of the integers are divisible, the other integer is too.
- If x is divisible by d and y is divisible by d, then (x + y) is divisible by d.
- If x is divisible by d and y is divisible by d, then (x - y) is divisible by d.
- If (x + y) is divisible by d and x is divisible by d, then y must be divisible by d.
Memory trick: Think of multiples: if parts make a multiple, the missing piece must too!