Vincen wrote: ↑Tue Oct 05, 2021 6:40 am
If \(a\) and \(b\) are constants, what is the value of \(a?\)
(1) \(a<b\)
(2) \((t-a)(t-b)=t^2+t-12,\) for all values of \(t.\)
Answer:
C
Source: Official Guide
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 = -4
Case b: a = 3 and b = -4, in which case
a = 3
Since 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 = -4
Since we can answer the
target question with certainty, the combined statements are SUFFICIENT
Answer: C
