Which of the following is equal to (2^12 - 2^6)/(2^6 - 2^3)

Question

Which of the following is equal to  \frac{2^{12} - 2^6}{2^6 - 2^3} ?

A.  2^6 + 2^3 
B.  2^6 - 2^3 
C.  2^9 
D.  2^3 
E. 2

PareshGmat · Accepted Answer

\frac{(2^{12} - 2^6)}{(2^6 - 2^3)}

=  \frac{(2^6)^2 - (2^3)^2}{(2^6 - 2^3)}

=  \frac{(2^6 + 2^3)(2^6 - 2^3)}{(2^6 - 2^3)}

=  2^6 + 2^3

Answer = A

Abhishek009 · Answer

\frac{2^{12} - 2^6}{2^6 - 2^3}

= \frac{2^6 ( 2^6 - 1 )}{2^3 ( 2^3 - 1 )}

= \frac{2^3( 2^6 - 1 )}{( 2^3 - 1 )}

= \frac{2^3( 2^3 - 1 )( 2^3 + 1 )}{( 2^3 - 1 )}

= 2^3( 2^3 + 1 )

= 2^6 + 2^3

Thus, answer must be (A)  2^6 + 2^3

BrentGMATPrepNow · Answer

If we recognize the numerator is a  difference of squares , we can solve this question quickly...

\frac{2^{12} - 2^6}{2^6 - 2^3}=\frac{(2^6 + 2^3)(2^6 - 2^3)}{2^6 - 2^3}=2^6 + 2^3

Answer: A

neo4897 · Answer

2^12 = 2^6 * 2^6

1. 2^12 - 2^6 = 2^6 * 2^6 - 2^6 = 2^6 (2^6 -1)
 2. 2^6 - 2^3 = 2^3 * 2^3 - 2^3 = 2^3 (2^3 -1)

2^6 / 2^3 = 2^(6-3)=2^3
2^6 -1 = (2^3)^2 – (1)^2 =(2^3 +1) (2^3 – 1)

Dividing 
2^3(2^3 +1) = 2^6 + 2^3

Answer A.

sidhu4u · Answer

(2^12 - 2^6)/(2^6 - 2^3)
= (2^6*(2^6 - 1))/(2^3*(2^3-1))
=2^3 * (2^3+1) * (2^3 - 1) / (2^3 - 1)
=2^3 * (2^3 + 1) = 2^6 + 2^3

Answer is A

mustdoit · Answer

Using the formula a^2 - b^2 = (a+b) (a-b) we can easily get the answer as A

Nadiuska · Answer

I did it a slightly different. and I was unable identify the solution. But the answer is correct.

2^6(2^6-1)/2^3(2^3-1)= 2^3*9= 72. Which is equal ro 2^6+2^3

chetan2u · Answer

it is good that you have done it by a different method..
But the best is to use a^2-b^2 formula whenever you see a Q in that format..

\frac{(2^{12} - 2^6)}{(2^6 - 2^3)} ....

=  \frac{(2^6 + 2^3)(2^6 - 2^3)}{(2^6 - 2^3)} ....

=  2^6 + 2^3

ScottTargetTestPrep · Answer

Notice that the numerator is a difference of two squares, so let’s simplify the given expression:

(2^12 - 2^6)/(2^6 - 2^3)

(2^6 + 2^3)(2^6 - 2^3)/(2^6 - 2^3)

2^6 + 2^3

Answer: A

Esguitar · Answer

Hi,

Could someone tell me! what is wrong with my approach. I did that:

( 2^12 - 2^6 ) / ( 2^6 - 2^3 ) = 
2^6 ( 2^2 - 1 ) / 2^3( 2^2 - 1 ) = 
2^6 / 2^3 = 
2^3 
Answer D

generis · Answer

Esguitar ,when you factored out 2^6 and 2^3 , you divided the exponents instead of subtracting them. Easy mistake to make. \frac{a^{12}}{a^{6}} = a^{12-6} = a^{6} , and \frac{2^{12}}{2^{6}} = 2^{12-6} = 2^{6} So first factoring would be 2^{6}(2^{6} - 1) 2^{12} = 4,096 2^6 = 64 2^2 = 4 64*4= 256, not 4,096 Hope it helps. :-)

Esguitar · Answer

Hi genxer123

Yes, easy mistake to avoid. Thank you for your help. I got it.

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Which of the following is equal to (2^12 - 2^6)/(2^6 - 2^3)

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Which of the following is equal to (2^12 - 2^6)/(2^6 - 2^3)

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