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by vinay1983 » Sun Oct 06, 2013 8:36 am
What is the value of (a + b)2 ?

(1) a = 15/b

(2) (a - b)2 = 4
You can, for example never foretell what any one man will do, but you can say with precision what an average number will be up to!
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by Brent@GMATPrepNow » Sun Oct 06, 2013 9:12 am
vinay1983 wrote:What is the value of (a + b)² ?

(1) a = 15/b

(2) (a - b)² = 4

Target question: What is the value of (a + b)²?

Statement 1: a = 15/b
In other words, ab = 15
There are several values of a and b that satisfy this condition. Here are two:
Case a: a = 15 and b = 1, in which case (a + b)² = 16² = 256
Case b: a = 3 and b = 5, in which case (a + b)² = 8² = 64
Since we cannot answer the target question with certainty, statement 1 is NOT SUFFICIENT

Statement 2: (a - b)² = 4
There are several values of a and b that satisfy this condition. Here are two:
Case a: a = 2 and b = 0, in which case (a + b)² = 2² = 4
Case b: a = 3 and b = 1, in which case (a + b)² = 4² = 16
Since we cannot answer the target question with certainty, statement 2 is NOT SUFFICIENT

Statements 1 and 2 combined
NOTICE that if we expand (a + b)² we get a² + 2ab + b². This will come in handy later.

Statement 1 tells us that ab = 15. This means that 4ab = 60

Statement 2 tells us that (a - b)² = 4
Expand to get: a² - 2ab + b² = 4
Add 4ab to both sides to get a² + 2ab + b² = 4 + 4ab
Since, we already know that 4ab = 60, we get a² + 2ab + b² = 4 + 60
In other words, a² + 2ab + b² = 64
Factor to get (a + b)² = 64
Since we can answer the target question with certainty, the combined statements are SUFFICIENT

Answer = C

Cheers,
Brent
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by vinay1983 » Sun Oct 06, 2013 8:44 pm
Brent@GMATPrepNow wrote:
vinay1983 wrote:What is the value of (a + b)² ?

(1) a = 15/b

(2) (a - b)² = 4

Target question: What is the value of (a + b)²?

Statement 1: a = 15/b
In other words, ab = 15
There are several values of a and b that satisfy this condition. Here are two:
Case a: a = 15 and b = 1, in which case (a + b)² = 16² = 256
Case b: a = 3 and b = 5, in which case (a + b)² = 8² = 64
Since we cannot answer the target question with certainty, statement 1 is NOT SUFFICIENT

Statement 2: (a - b)² = 4
There are several values of a and b that satisfy this condition. Here are two:
Case a: a = 2 and b = 0, in which case (a + b)² = 2² = 4
Case b: a = 3 and b = 1, in which case (a + b)² = 4² = 16
Since we cannot answer the target question with certainty, statement 2 is NOT SUFFICIENT

Statements 1 and 2 combined
NOTICE that if we expand (a + b)² we get a² + 2ab + b². This will come in handy later.

Statement 1 tells us that ab = 15. This means that 4ab = 60

Statement 2 tells us that (a - b)² = 4
Expand to get: a² - 2ab + b² = 4
Add 4ab to both sides to get a² + 2ab + b² = 4 + 4ab
Since, we already know that 4ab = 60, we get a² + 2ab + b² = 4 + 60
In other words, a² + 2ab + b² = 64
Factor to get (a + b)² = 64
Since we can answer the target question with certainty, the combined statements are SUFFICIENT

Answer = C

Cheers,
Brent
Brent Thanks!I solved the same way, bit i did not use "4ab". Is there any other way?
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by Brent@GMATPrepNow » Sun Oct 06, 2013 9:05 pm
vinay1983 wrote:
Brent Thanks!I solved the same way, bit i did not use "4ab". Is there any other way?
At the moment, I can't of a second way, but that doesn't mean there isn't a second way.
I'll have to think about that one.

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by varun289 » Sun Oct 06, 2013 9:52 pm
Hi

IMO - E ,
as it clear that A, B , D gone just by seeing two options

so We left with C or E , now
combine - equation - A^2-2.A-15=0 give a= 5 or 3 , so b= -3 or -5

so( A+B ).2= +16 or -16

hence E
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by theCodeToGMAT » Sun Oct 06, 2013 10:01 pm
varun289 wrote:Hi

IMO - E ,
as it clear that A, B , D gone just by seeing two options

so We left with C or E , now
combine - equation - A^2-2.A-15=0 give a= 5 or 3 , so b= -3 or -5

so( A+B ).2= +16 or -16

hence E
Varun, I am not sure how you reached to that equation.

(a-b)^2 = 4

a^2 + b^2 - 2ab = 4
Add 4ab both sides
a^2 + b^2 + 2ab = 4+4ab
(a+b)^2 = 4+4(15) = 54
SUFFICIENT

Answer {C}
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by varun289 » Sun Oct 06, 2013 10:08 pm
(1) a = 15/b

(2) (a - b)2 = 4
a-b=2 , a-15/a=2 => a^2 -2A-15=2 => (A-5) (A+3)=0 , a= 5 or -3 so b= 3 or -5

IMO -E
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by theCodeToGMAT » Sun Oct 06, 2013 10:13 pm
varun289 wrote:(1) a = 15/b

(2) (a - b)2 = 4
a-b=2 , a-15/a=2 => a^2 -2A-15=2 => (A-5) (A+3)=0 , a= 5 or -3 so b= 3 or -5

IMO -E
We are NOT asked about A & B values... don't forget we need SQUARE..

A = 5 & B = 3 ==> (5+3)^2 = 64
A =-3 & B =-5 ==> (-5-3)^2 = 64

64 == 64
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by varun289 » Sun Oct 06, 2013 10:20 pm
what the question - A+B square or 2. (A+B) in case two OA=E in case one OA=C
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by theCodeToGMAT » Sun Oct 06, 2013 10:23 pm
varun289 wrote:what the question - A+B square or 2. (A+B) in case two OA=E in case one OA=C
Its SQUARE
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