vinay1983 wrote:What is the value of (a + b)² ?
(1) a = 15/b
(2) (a - b)² = 4
Target question: What is the value of (a + b)²?
Statement 1: a = 15/b
In other words, ab = 15
There are several values of a and b that satisfy this condition. Here are two:
Case a: a = 15 and b = 1, in which case (a + b)² = 16² = 256
Case b: a = 3 and b = 5, in which case (a + b)² = 8² = 64
Since we cannot answer the target question with certainty, statement 1 is NOT SUFFICIENT
Statement 2: (a - b)² = 4
There are several values of a and b that satisfy this condition. Here are two:
Case a: a = 2 and b = 0, in which case (a + b)² = 2² = 4
Case b: a = 3 and b = 1, in which case (a + b)² = 4² = 16
Since we cannot answer the target question with certainty, statement 2 is NOT SUFFICIENT
Statements 1 and 2 combined
NOTICE that if we expand (a + b)² we get a² + 2ab + b². This will come in handy later.
Statement 1 tells us that ab = 15. This means that 4ab = 60
Statement 2 tells us that (a - b)² = 4
Expand to get: a² - 2ab + b² = 4
Add 4ab to both sides to get a² + 2ab + b² = 4 + 4ab
Since, we already know that 4ab = 60, we get a² + 2ab + b² = 4 + 60
In other words, a² + 2ab + b² = 64
Factor to get (a + b)² = 64
Since we can answer the target question with certainty, the combined statements are SUFFICIENT
Answer = C
Cheers,
Brent
