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# If a and b are constants, what is the value of a ?

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Joined: 01 Sep 2010
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If a and b are constants, what is the value of a ?  [#permalink]

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26 Jul 2017, 11:50
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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.

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Re: If a and b are constants, what is the value of a ?  [#permalink]

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26 Jul 2017, 13:15
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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 = -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

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##### General Discussion
Manager
Joined: 01 Feb 2017
Posts: 224
Re: If a and b are constants, what is the value of a ?  [#permalink]

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26 Jul 2017, 13:13
1
Ans C:
St. 2: Solving Quadratic, we get
(t-a)(t-b) = (t+4)(t-3)
St. 1: a<b
Therefore, a=-4 and b= +3
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Joined: 20 Oct 2017
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If a and b are constants, what is the value of a ?  [#permalink]

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26 Oct 2018, 10:03
Isn't it possible for a=-6 and b=2?

(t-a)(t-b) = (t--6)(t-2) = t^2 + 6t - 2t -12 = t^2+4t -12. This solution appears to be consistent with the given constraints, and since it says a and b are "constants" the answer would be E.

Am i missing something?
If a and b are constants, what is the value of a ?   [#permalink] 26 Oct 2018, 10:03
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