What is the value of (a + b)2 ?
(1) a = 15/b
(2) (a - b)2 = 4
a+b
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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
- vinay1983
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Brent Thanks!I solved the same way, bit i did not use "4ab". Is there any other way?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
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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At the moment, I can't of a second way, but that doesn't mean there isn't a second way.vinay1983 wrote:
Brent Thanks!I solved the same way, bit i did not use "4ab". Is there any other way?
I'll have to think about that one.
Cheers,
Brent
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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
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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Varun, I am not sure how you reached to that equation.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
(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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- theCodeToGMAT
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We are NOT asked about A & B values... don't forget we need SQUARE..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
A = 5 & B = 3 ==> (5+3)^2 = 64
A =-3 & B =-5 ==> (-5-3)^2 = 64
64 == 64
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Its SQUAREvarun289 wrote:what the question - A+B square or 2. (A+B) in case two OA=E in case one OA=C
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