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11 Dec 2010, 20:03
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C
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Difficulty:
5%
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Question Stats:
86% (00:40) correct
14%
(01:09)
wrong
based on 98
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What percent of x is 3/4?
(1) x = .5y
(2) y = 10
(1) x = .5y
(2) y = 10
I know the answer is C. But my moment of stupity is not allowing me to see through something... How is 15% of 5 = .75 AND essentially 3.75/5 = .75 as well? Im thinking about this incorrectly. Can someone help?
11 Dec 2010, 21:10
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jscott319
Hi,
what % of x is 3/4 means that x is the whole and 3/4 is the part. So:
% = part/whole * 100% = (3/4)/x * 100% = (3/4)*100/x % = (75/x)%
Now, we didn't actually need to do all that to determine that we need x to answer the question.
(1) don't know anything about y - insufficient
(2) no info about x - insufficient
Together: subbing (2) into (1) we get:
x = .5(10) = 5
We have x, so we can answer the question.
It sounds like you're caught up in the actual calculation at the end. One of the nicest things about DS is that we don't actually care what the answer is, we just care whether we have enough info to find it. However, just this one time let's actually do the math:
% = (75/x)% = (75/5)% = 15%
So, back to your original issue:
Quote:
First equation:
.15(5) = .75
Second equation:
3.75/5 = .75
How can these both be true? Well, in one we're multiplying by 5 and in the other we're dividing by 5. Since they're two completely different operations, there's no problem at all.
Here's a simpler example:
10(5) = 50
250/5 = 50
Is there any reason both of those can't equal 50? Of course not!
Here's another way to look at it - since the right side of both equations are equal, so must be the left sides:
.15(5) = (3.75/5)
which is certainly true.
11 Dec 2010, 21:18
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Quote:
Thanks Stuart, This opened my mind back up. My test is in a week and I think I am overworking myself and causing a few short circuits.
As you said, yes we definitely did not need to work out the full calculation. I think when I was doing the problem and ultimately rephrased the question to y = 75/x I somehow brought those two concepts together and confused myself out of the right answer.
Thanks for clearing it up !
