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M12-07

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M12-07  [#permalink]

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New post 15 Sep 2014, 23:46
1
1
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A
B
C
D
E

Difficulty:

  15% (low)

Question Stats:

82% (01:03) correct 18% (01:02) wrong based on 74 sessions

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Re M12-07  [#permalink]

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New post 15 Sep 2014, 23:46
Official Solution:


(1) \(a^2-a-2=0\). From this statement it follows that \(a=-1\) or \(a=2\). Not sufficient.

(2) \(b^2+b-2=0\). From this statement it follows that \(b=-2\) or \(b=1\). Not sufficient.

(1)+(2) If \(a=-1\) and \(b=-2\) then the answer is 9 but if \(a=-1\) and \(b=1\) then the answer is 0. Not sufficient.


Answer: E
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Re: M12-07  [#permalink]

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New post 01 Jun 2016, 15:36
Hello,
why is it ok not to specify that "a" and b" are integers?
thank you
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Re: M12-07  [#permalink]

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New post 01 Jun 2016, 21:48
Avigano wrote:
Hello,
why is it ok not to specify that "a" and b" are integers?
thank you


Why should it be specified? We can solve for a and b and get their values. It turns out that both of them are integers but the values could have been non-integers as well.
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Re: M12-07  [#permalink]

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New post 08 Aug 2016, 07:07
Bunuel wrote:
Official Solution:


(1) \(a^2-a-2=0\). From this statement it follows that \(a=-1\) or \(a=2\). Not sufficient.

(2) \(b^2+b-2=0\). From this statement it follows that \(b=-2\) or \(b=1\). Not sufficient.

(1)+(2) If \(a=-1\) and \(b=-2\) then the answer is 9 but if \(a=-1\) and \(b=1\) then the answer is 0. Not sufficient.


Answer: E


Thanks for the elegant solution. I approached it in a different way, and arrived at the same answer.

I expanded the expression in the stem, and for (1), I saw that it gives no information about a, so insufficient. I did the same for (2), as it gives no info about a. I figured both statements together are insufficient as well, since both terms together cannot be manipulated either by addition, multiplyication, subtraction, or division in such a way that is helpul to solving the stem.

Is this a valid aprroach?

Thanks!
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Re: M12-07  [#permalink]

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New post 09 Aug 2016, 15:43
I thought I could get away with not solving for #2, but upon thinking about it, you should solve for both a and b.

In this particular case, of (a+b)^2, what if #1 was the same but #2 was a different equation: b^2 + 5= 5 ? If b = 0, then #1 & #2 is sufficient.
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M12-07  [#permalink]

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New post 07 Jul 2018, 13:44
Hi Bunuel

Can you please help:
Statement 1:
a^2-a-2=0
so a^-a=2
a(a-1)=2
so either a=2 or a-1=2; a=3 (this is where i am wrong, i get different value of a)

similarly
statement 2:
b^2+b-2=0
b(b+1)=2
so either b=2 or b+1=2; b=1 (again different value of b)


Thanks.
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Re: M12-07  [#permalink]

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New post 10 Jul 2018, 01:02
pantera07 wrote:
Hi Bunuel

Can you please help:
Statement 1:
a^2-a-2=0
so a^-a=2
a(a-1)=2
so either a=2 or a-1=2; a=3 (this is where i am wrong, i get different value of a)

similarly
statement 2:
b^2+b-2=0
b(b+1)=2
so either b=2 or b+1=2; b=1 (again different value of b)


Thanks.


a(a - 1) = 2 does not mean than a = 2 or a - 1 = 2. You can do this only when the LHS equals to 0. This is because the product is 0 if either of the multiples is 0. For example, a(a - 1) = 0 to be true either a or a - 1 must be true. But the roots of a^2 - a - 2 = 0 are a = -1 and a = 2.
_________________

New to the Math Forum?
Please read this: Ultimate GMAT Quantitative Megathread | All You Need for Quant | PLEASE READ AND FOLLOW: 12 Rules for Posting!!!

Resources:
GMAT Math Book | Triangles | Polygons | Coordinate Geometry | Factorials | Circles | Number Theory | Remainders; 8. Overlapping Sets | PDF of Math Book; 10. Remainders | GMAT Prep Software Analysis | SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) | Tricky questions from previous years.

Collection of Questions:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


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Re: M12-07 &nbs [#permalink] 10 Jul 2018, 01:02
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