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 Post subject: GMAT Percentage
PostPosted: Wed Apr 10, 2013 2:50 am 
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Joined: Tue Apr 13, 2010 8:48 am
Posts: 483
If w is 40 percent less than x, x is 40 percent less than y, and z is 46 percent less than y, then z is greater than w by what percent of w?

A. 4%
B. 18%
C. 36%
D. 40%
E. 50%

(E) In order to answer this question, you need to get the value of all the variables in terms of y: z = 0.54y, x = 0.6y, and w = 0.6x = 0.6(0.6y) = 0.36y.

Now, compare the two. To find a percent difference between two numbers or variables, you take one and subtract it from the second, and then divide by the second. The amount being subtracted is usually the one following "than" in the question. Therefore: (zw) / w = (0.54y – 0.36y) / 0.36y = 0.18y / 0.36y = 0.5.

z is 50% larger than w.
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It would be nice to see the problem worked out with smart values..


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 Post subject: Re: GMAT Percentage
PostPosted: Wed Apr 10, 2013 2:51 am 
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Joined: Fri Apr 09, 2010 2:11 pm
Posts: 459
Suppose the y = 100.

We know that x is 40 percent less than y. So x is 60% of y.
x = 0.6 × y = 0.6 × 100 = 60

w is 40 percent less than x. So w is 60% of x.
w = 0.6 × x = 0.6 × 60 = 36.

z is 46 percent less than y. So z is 54% of y.
x = 0.54 × y = 0.54 × 100 = 54

We need to calculate by what percent z is greater than w. Let us find what percent z makes of w.
z/w = 54 / 36 = (18 × 3) / (18 × 2) = 3/2 = 1.5

So z makes 150% of w. w is 100% of w. Therefore z is by 150% – 100% = 50% greater than w.

**********

The logic of the solution can be seen clearly if we use the following simpler values:

If w is 50 percent less than x, x is 50 percent less than y, and z is 50 percent less than y, then z is greater than w by what percent of w?

x is 50 percent less than y:
x = (1 – 0.5)y = 0.5y

w is 50 percent less than x:
w = (1 – 0.5)x = 0.5 × 0.5y = 0.25y

z is 50 percent less than y:
z = (1 – 0.5)y = 0.5y

(zw)/w = (0.5y – 0.25y) / 0.25y = 1 = 100%

z is by 100% greater than w.


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