To find: w+x+y+z
Statement 1:
w/2+x/4+y/8+z/16=11/16
(8w + 4x + 2y + z) = 11
This is possible when:
w = 1, x = 0, y = 1, z = 1
SUFFICIENT
Statement 2:
w/3+x/9+y/27+z/81=31/81
(27w + 9x + 3y + z ) = 31
This is possible when:
w = 1, x = 0, y = 1, z = 1
SUFFICIENT
Answer [spoiler]{D}[/spoiler]?
Number properties
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Source: Beat The GMAT — Data Sufficiency |
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Hi abhasjha,
Rahul has correctly answered this question. I'm going to add a few more details to the explanation.
We're told that each of the variables is either 0 or 1, which really limits the possibilities. We're asked for the value of W+X+Y+Z.
Fact 1: W/2 + X/4 + Y/8 + Z/16 = 11/16
A little algebra gives us:
8W/16 + 4X/16 + 2Y/16 + Z/16 = 11/16
Then....
8W + 4X + 2Y + Z = 11
With the limitation that each variable is either 0 or 1, we'd have these possibilities:
8W = 0 or 8
4X = 0 or 4
2Y = 0 or 2
Z = 0 or 1
With these options, the ONLY way to get to 11 is 8+0+2+1
So W = 1, X = 0, Y = 1 and Z = 1
With just one possibility, Fact 1 is SUFFICIENT (the answer to the prompt is 1+0+1+1 = 3, but you don't need to do THAT math).
Fact 2: Involves math that is similar to Fact 1, but the fractions and common-denominator are different.
We'd end up with:
27W + 9X + 3Y = Z = 31
27W = 0 or 27
9X = 0 or 9
3Y = 0 or 3
Z = 0 or 1
Here, the ONLY way to get to 31 is 27+0+3+1.
Fact 2 is also SUFFICIENT.
Final Answer: D
GMAT assassins aren't born, they're made,
Rich
Rahul has correctly answered this question. I'm going to add a few more details to the explanation.
We're told that each of the variables is either 0 or 1, which really limits the possibilities. We're asked for the value of W+X+Y+Z.
Fact 1: W/2 + X/4 + Y/8 + Z/16 = 11/16
A little algebra gives us:
8W/16 + 4X/16 + 2Y/16 + Z/16 = 11/16
Then....
8W + 4X + 2Y + Z = 11
With the limitation that each variable is either 0 or 1, we'd have these possibilities:
8W = 0 or 8
4X = 0 or 4
2Y = 0 or 2
Z = 0 or 1
With these options, the ONLY way to get to 11 is 8+0+2+1
So W = 1, X = 0, Y = 1 and Z = 1
With just one possibility, Fact 1 is SUFFICIENT (the answer to the prompt is 1+0+1+1 = 3, but you don't need to do THAT math).
Fact 2: Involves math that is similar to Fact 1, but the fractions and common-denominator are different.
We'd end up with:
27W + 9X + 3Y = Z = 31
27W = 0 or 27
9X = 0 or 9
3Y = 0 or 3
Z = 0 or 1
Here, the ONLY way to get to 31 is 27+0+3+1.
Fact 2 is also SUFFICIENT.
Final Answer: D
GMAT assassins aren't born, they're made,
Rich
