carcass wrote:
If a and b are constants, what is the value of a ?
1. a < b
2. (t − a)( t − b) = t² + t − 12, for all values of t.
Target question: What is the value of a? Statement 1:a < b Definitely NOT SUFFICIENT
Statement 2: (t − a)( t − b) = t² + t − 12 Factor: t² + t − 12 = (t + 4)(t - 3)
Rewrite in terms of (t - a) and (t - b) to get: t² + t − 12 = (t -
-4)(t -
3)
There are two possible cases:
Case a: a = -4 and b = 3, in which case
a = -4Case b: a = 3 and b = -4, in which case
a = 3Since we cannot answer the
target question with certainty, statement 2 is NOT SUFFICIENT
Statements 1 and 2 combined Statement 2 tells us that EITHER a = -4 and b = 3 OR a = 3 and b = -4
Statement 2 tells us that a < b, which means it MUST be the case that a = -4 and b = 3
So,
a = -4Since we can answer the
target question with certainty, the combined statements are SUFFICIENT
Answer: C
Since it says in statement B "for all values of t", I just plugged in 0 to get a*b=12 and even combining that with stmt. 1, I figured I can´t get a unique value. Where did I go wrong?