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Fractions and Variables

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Fractions and Variables

by vongdn » Sat Oct 02, 2010 10:24 pm
Each of the numbers, w, x, y, z is 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



What is the best way to figure this out?

I simplify it down to the following, but then I get stuck...

8w+4x+2y+z = 11
27w+9x+3y+z = 31

what do I do next?
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Source: — Data Sufficiency |

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by Rahul@gurome » Sat Oct 02, 2010 10:48 pm
Statement (1) implies 8w+4x+2y+z = 11
The only combination possible is w = y = z = 1 and x = 0.
So w+x+y+z = 3.
Or (1) alone is sufficient
Statement (2) implies that 27w+9x+3y+z = 31.
Again the only combination possible is w = y = z = 1 and x = 0.
Or w+x+y+z =3.
So (2) alone is also sufficient.

The correct answer is (D).
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