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

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Question Stats: 69% (01:28) correct 31% (01:42) wrong based on 901 sessions

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

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Top Contributor
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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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Originally posted by GMATPrepNow on 26 Jul 2017, 13:15.
Last edited by GMATPrepNow on 29 Oct 2019, 08:10, edited 1 time in total.
##### General Discussion
Manager  P
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Re: If a and b are constants, what is the value of a ?  [#permalink]

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

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carcass wrote:
If a and b are constants, what is the value of a?

(1) $$a < b$$

(2) $$(t − a)( t − b) = t ^2 + t − 12$$, for all values of t.

Statement 1: a<b - Clearly not sufficient

Statement 2: Ignore the LHS. $$t ^2 + t − 12$$ The factors of this equation are +4 and -3. Still not sufficient.

Combining 1 and 2:
a=-4 and b=3 since a<b.

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

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GMATPrepNow Could you help me with a small query? For statement 2

Quote:
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

Could we have done this as below and would it be fruitful?

(t − a)( t − b) = t² + t − 12
(t - a) = t² + t − 12
t - a = t² + t − 12
12 = t² + a

and ( t − b) = t² + t − 12
t - b = t² + t − 12
12 = t² + b Therefore since, t² + b = t² + a we get a = b ? (Is this right?)

Thank you
Dablu
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Top Contributor
gurudabl wrote:
GMATPrepNow Could you help me with a small query? For statement 2

Quote:
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

Could we have done this as below and would it be fruitful?

(t − a)( t − b) = t² + t − 12
(t - a) = t² + t − 12
t - a = t² + t − 12
12 = t² + a

and ( t − b) = t² + t − 12
t - b = t² + t − 12
12 = t² + b Therefore since, t² + b = t² + a we get a = b ? (Is this right?)

Thank you
Dablu

I think you're confusing (t − a)( t − b) = t² + t − 12 with (t − a)( t − b) = 0
If (t − a)( t − b) = 0, then we know that either (t − a) = 0 or ( t − b) = 0
We're using the principle that says: If AB = 0, then either A = 0, or B = 0

The same strategy doesn't apply when the quadratic expression does not equal 0.
For example, if AB = 6, we can't conclude that A = 6 or B = 6

So, if (t − a)( t − b) = t² + t − 12, we can't then conclude that either (t - a) = t² + t − 12 or (t - b) = t² + t − 12

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

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Hi GMATPrepNow
Quote:
I think you're confusing (t − a)( t − b) = t² + t − 12 with (t − a)( t − b) = 0
If (t − a)( t − b) = 0, then we know that either (t − a) = 0 or ( t − b) = 0
We're using the principle that says: If AB = 0, then either A = 0, or B = 0

The same strategy doesn't apply when the quadratic expression does not equal 0.
For example, if AB = 6, we can't conclude that A = 6 or B = 6

So, if (t − a)( t − b) = t² + t − 12, we can't then conclude that either (t - a) = t² + t − 12 or (t - b) = t² + t − 12

Cheers,
Brent

Thank you for your reply. Definitely cleared my confusion! Intern  B
Joined: 19 Sep 2019
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Location: Austria
Re: If a and b are constants, what is the value of a ?  [#permalink]

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GMATPrepNow wrote:
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

Hey Brent

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?

Thanks,

Philipp
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Yes, why can we not just plug in 0 for t ?
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philippi Moritz279

(2) (t−a)(t−b)=t^2+t−12 for all values of t.
If you say t=0
then equation becomes (0-a)(0-b)=0+0-12 which is (-a)(-b)=-12 which is ab=-12. We know that a and b are constants, so values must be 3/4 with one of the two being negative.
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Re: If a and b are constants, what is the value of a ?  [#permalink]

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TheNightKing

Yes but another solutions could be -2 and 6 for ab=-12.
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Moritz279 wrote:
TheNightKing

Yes but another solutions could be -2 and 6 for ab=-12.

Moritz279

No. $$t^2+t-12$$ still has to hold true. +6-2 gives you 4. You need 1 which is only possible by +4-3.
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Re: If a and b are constants, what is the value of a ?  [#permalink]

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carcass wrote:
If a and b are constants, what is the value of a?

(1) $$a < b$$

(2) $$(t − a)( t − b) = t ^2 + t − 12$$, for all values of t.

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

(1) $$a < b$$
Since a and b are unknown
NOT SUFFICIENT

(2) $$(t − a)( t − b) = t ^2 + t − 12$$, for all values of t.
t=-4 or t=3
a=-4 or 3
NOT SUFFICIENT

(1)+(2)
(1) $$a < b$$
(2) $$(t − a)( t − b) = t ^2 + t − 12$$, for all values of t.
a=-4 and b=3 since a<b
SUFFICIENT

IMO C

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

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TheNightKing wrote:
philippi Moritz279

(2) (t−a)(t−b)=t^2+t−12 for all values of t.
If you say t=0
then equation becomes (0-a)(0-b)=0+0-12 which is (-a)(-b)=-12 which is ab=-12. We know that a and b are constants, so values must be 3/4 with one of the two being negative.

Thanks, I get it now :D Re: If a and b are constants, what is the value of a ?   [#permalink] 01 Dec 2019, 08:03
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