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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) [#permalink]

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New post 15 Mar 2010, 12:12
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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
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Re: Exponents [#permalink]

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New post 15 Mar 2010, 12:41
1
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) [Hint a^2 - b^2]

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

Answer A.
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Re: Exponents [#permalink]

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New post 15 Mar 2010, 13:04
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abhi758 wrote:
Which of the following is equal to \(\frac{2^1^2 - 2^6}{2^6 - 2^3}\)?

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

Kindly show your working. OA to be posted soon..


(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
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Re: Exponents [#permalink]

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New post 19 Mar 2010, 01:30
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abhi758 wrote:
Which of the following is equal to \(\frac{2^1^2 - 2^6}{2^6 - 2^3}\)?

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

Kindly show your working. OA to be posted soon..


Using the formula a^2 - b^2 = (a+b) (a-b) we can easily get the answer as A
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Re: Which of the following is equal to (2^12 - 2^6)/(2^6 - 2^3) [#permalink]

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New post 25 Mar 2014, 19:28
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\(\frac{(2^{12} - 2^6)}{(2^6 - 2^3)}\)

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

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

= \(2^6 + 2^3\)

Answer = A
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Re: Which of the following is equal to (2^12 - 2^6)/(2^6 - 2^3) [#permalink]

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New post 23 Feb 2016, 05:13
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
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Re: Which of the following is equal to (2^12 - 2^6)/(2^6 - 2^3) [#permalink]

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New post 23 Feb 2016, 05:41
Nadiuska wrote:
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


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..

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

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

= \(2^6 + 2^3\)
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Re: Which of the following is equal to (2^12 - 2^6)/(2^6 - 2^3) [#permalink]

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New post 02 Mar 2017, 07:37
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abhi758 wrote:
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


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

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

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

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

\(= 2^3( 2^3 + 1 )\)

\(= 2^6 + 2^3\)

Thus, answer must be (A) \(2^6 + 2^3\)
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Re: Which of the following is equal to (2^12 - 2^6)/(2^6 - 2^3) [#permalink]

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New post 06 Mar 2017, 18:03
abhi758 wrote:
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


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
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Re: Which of the following is equal to (2^12 - 2^6)/(2^6 - 2^3) [#permalink]

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New post 02 Aug 2017, 14:11
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
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Which of the following is equal to (2^12 - 2^6)/(2^6 - 2^3) [#permalink]

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New post 03 Aug 2017, 09:10
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Esguitar wrote:
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

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. :-)
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Re: Which of the following is equal to (2^12 - 2^6)/(2^6 - 2^3) [#permalink]

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New post 03 Aug 2017, 12:36
Hi genxer123

Yes, easy mistake to avoid. Thank you for your help. I got it.
Re: Which of the following is equal to (2^12 - 2^6)/(2^6 - 2^3)   [#permalink] 03 Aug 2017, 12:36
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