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Power Prep Question - Help.

by romeroil » Mon Dec 07, 2009 12:52 am
Hello,

Can someone assist me on this power prep DS question:
Each of the numbers w, x, y, and z is equal to either 0 or 1. What is the value of w + x + y + z?

(1) w/2 + x/4 + y/8 + z/16 = 11/16
(2) w/3 + x/9 + y/27 + z/81 = 31/81

The answer is each statement alone is sufficient, but I just don't see it. What obvious thing am I missing?

Thanks
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by papgust » Mon Dec 07, 2009 1:39 am
Instead of breaking your head to solve algebraically, the easiest way to solve this is by plugging-in method,

Assume all w,x,y,z are 1 each. Substitute in 1st stmt.
1/2 + 1/4 + 1/8 + 1/16 = (8+4+2+1)/16 = 15/16. Wrong!

To get a value of 11 in the numerator, at least one of the four values must be 0.

Try putting a zero for y, 8+4+0+1 = 13 (Again Wrong! We need a values of 11)
Try putting a zero for x, 8+0+2+1 = 11 (Right!)

You can have only 1 set of values to get 11 in the numerator. So it is sufficient to find w+x+y+z.

Same method applies for stmt 2.
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by Testluv » Mon Dec 07, 2009 1:53 am
We need to find w + x + y + z. We also know that each value is either 0 or 1.


(1) w/2 + x/4 + y/8 + z/16 = 11/16

8w/16 + 4x/16 + 2y/16 + z/16 = 11/16

8w + 4x + 2y + z = 11

Because 11 is odd, we need at least one odd number participating in the summing. But if any of w, x, or y were 1, then 8w, 4x, and 2y are just 8, 4, and 2, which are all even. Therefore, we know z's value is 1. And, we need a sum of 10 from w, x, and y. Again, we know that they are each either 0 or 1. The only way we can get a sum of 10, then, is if w is 1, y is 1, and x is 0. Then, you would have: 8(1) + 4(0) + 2(1) = 10.

Therefore, z is 1, w is 1, y is 1, x is 0, and their sum is 3.

The analysis of statement (2) is verisimilar but the common denominator is 81.

Each statement is sufficient by itself.

Choose D.
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