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If a and b are constants, what is the value of a ?
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Updated on: 29 Oct 2019, 08:10
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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
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?)
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
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!
Re: If a and b are constants, what is the value of a ?
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25 Nov 2019, 09:18
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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
Answer: C
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?
(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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(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
gmatclubot
Re: If a and b are constants, what is the value of a ?
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01 Dec 2019, 08:03
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69% (01:28) correct 
