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Value of X

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Value of X

by sivaelectric » Mon Jun 06, 2011 3:34 am
If 2^X - 2^(X-2) = 3 x 2^17, What is the value of X?

A. 16
B. 17
C. 18
D. 19
E. 20
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by Anurag@Gurome » Mon Jun 06, 2011 3:52 am
sivaelectric wrote:If 2^X - 2^(X-2) = 3 x 2^17, What is the value of X?

A. 16
B. 17
C. 18
D. 19
E. 20
2^x = (2^2)(2^(x-2)) = 4(2^(x-2))
2^(X-2) = 1(2^(x-2))
So, 4(2^(x-2)) - 1(2^(x-2)) = 3(2^(x-2))
Hence, 3(2^(x-2)) = 3(2^17)
Since base is the same so equate the exponents, x - 2 = 17 implies x = 19

The correct answer is D.
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by GMATGuruNY » Mon Jun 06, 2011 3:54 am
sivaelectric wrote:If 2^X - 2^(X-2) = 3 x 2^17, What is the value of X?

A. 16
B. 17
C. 18
D. 19
E. 20
We can plug in the answers, which represent the value of X.

Answer choice C: 18.
2^18 - 2^(18-2) = 3 * 2^17
2^18 - 2^16 = 3 * 2^17
2*16(2^2 - 1) = 3 * 2^17
2^16 * 3 = 3 * 2^17.
Doesn't work. Eliminate C.

To match 2^17 on the right side of the equation, the exponent on the left side of the equation needs to be increased by 1.

The correct answer is D.

Answer choice D: 19.
2^19 - 2^(19-2) = 3 * 2^17
2^19 - 2^17 = 3 * 2^17
2*17(2^2 - 1) = 3 * 2^17
2^17 * 3 = 3 * 2^17.
Last edited by GMATGuruNY on Mon Jun 06, 2011 7:46 am, edited 1 time in total.
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by cans » Mon Jun 06, 2011 6:20 am
If 2^X - 2^(X-2) = 3 x 2^17, What is the value of X?

A. 16
B. 17
C. 18
D. 19
E. 20
lhs = (2^x)(1 - 1/4) = (3/4)2^x = 3 * 2^17
2^x=2^19
x=19
IMO D
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by bajwa2307 » Mon Jun 06, 2011 6:29 am
This question is based on the basic rules of exponents

(x^m)(x^n) = x(m + n)

and, (x^m)/(x^n) = x(m - n)

so if we have 2^(X-2), it can be re-written as

(2^x)(2^-2) = (2^x)/2^2
Verbal is testing my patience
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by sivaelectric » Mon Jun 06, 2011 7:43 am
Great Discussion Guys! OA D
If I am wrong correct me :), If my post helped let me know by clicking the Thanks button ;).

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by aftableo2006 » Mon Jun 06, 2011 8:38 pm
the answer is 19 it is D
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