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A good PS.

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by Night reader » Sun Feb 13, 2011 10:29 am
gmat_perfect wrote:What is the value of X if 3^(2x-2)-5*3^(x-2)-66 =0?

A. 2
B. 3
C. 4
D. 5
E. 6
3^(x-2)(3^x - 5)=66
plug in A) 3^0 *( 3^2 -5)=4; B) 3^1* (3^3 -5)=66

IOM B
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by saurabh_maths » Sun Feb 13, 2011 5:44 pm
IMO it is B.

Simplify the equation. Assume 3^x = a in the equation and write it down again.

It will come into this form (a^2)/9 - (5a)//9 = 66

solve this . a = 27 or -22.

now put 3^x = 27 ... which means x = 3
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by Anurag@Gurome » Sun Feb 13, 2011 7:12 pm
gmat_perfect wrote:What is the value of X if 3^(2x-2)-5*3^(x-2)-66 =0?

A. 2
B. 3
C. 4
D. 5
E. 6
Another approach:
Now 3^(2x-2) = 9^(x-1) = 5 * 3^(x-2) + 66.
Note that 5 * 3^(x-2) always ends in 5 because 3^(x-2) is odd.
Or 5 * 3^(x-2) + 66 ends in last digit of 5 + 6 which is 1.
Or 9^(x-1) ends in 1.
So (x-1) is even.
Or x is odd.
Next, check between x =3 and x = 5.
We will get that x = 3 satisfies the equation.
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by gmat_perfect » Mon Feb 14, 2011 4:25 am
Thanks to all. Every solution is interesting.
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