What is the value of b?

Question

(1) b(b-8) = -16
(2) (b+4)^2 = 64

Zarrolou · Answer

What is the value of b?

(1) b(b-8) = -16 
so  b^2-8b+16=0 
 b=4 
Sufficient

(2) (b+4)^2 = 64 
 (b+4)^2=8^2 ,  b+4=|8|  give us b+4=8  b=4  or b+4=-8  b=-12 . Two values
Not sufficient

A

nt2010 · Answer

Answer is A

Stmt 1 :

Manipulating b(b-8) = -16 results in (b-4)^2 = 0 and b = 4.  Sufficient.

Stmt 2 :

Manipulating (b+4)^2 = 64 results in b+4 = +-8 and b = 4 or -12.  Not Sufficient

marcovg4 · Answer

According to GMAT square root of a number is always positive, so SqRt of 25 is ONLY 5, SqRt of 81 is ONLY 9.

Then, why in this case SqRt of 64 yields +-8?

Zarrolou · Answer

You're right, but the question here is different. 
We are not applying the root to 64 only, but to the left term as well. Consider the following case:

If I say b= \sqrt{64}  then  b=8 .
But if I say  b^2=64  (for example) then b can have two values: 8 and -8. Here the root is applyed to both terms  \sqrt{b^2}=\sqrt{64}  and the solutions are +-8 =>  (-8)^2=64  and  8^2=64 .

Whenever you have an expression in the form  \sqrt{x^2}  you translate it into  |x| . So from the upper example you get  |b|=|8|  or b=+-8.

So, with the same method, from  (b+4)^2 = 64  you obtain  |b+4| = |8|  => b+4=+-8 or if you prefer +-(b+4)=8.

Hope it's clear

Bunuel · Answer

When the GMAT provides the square root sign for an even root, such as  \sqrt{x}  or  \sqrt {x} , then the  only accepted answer is the positive root . That is,  \sqrt{25}=5 , NOT +5 or -5.  Even roots have only non-negative value on the GMAT.

In contrast , the equation  x^2=25  has TWO solutions,  \sqrt{25}=+5  and  -\sqrt{25}=-5 .

Hope it helps.

nt2010 · Answer

I was applying the pattern \sqrt{(x*2)} = |x| and in this problem x is 8. The pattern does not apply here for 64 but to b-4 on the LHS :oops:

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What is the value of b?

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