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Post subject: GMAT Percentage Posted: Tue Nov 16, 2010 4:36 pm 

Joined: Sun May 30, 2010 3:15 am Posts: 424

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: (z – w) / w = (0.54y – 0.36y) / 0.36y = 0.18y / 0.36y = 0.5.
z is 50% larger than w. 
It would be nice to see the problem worked out with smart values..


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Gennadiy

Post subject: Re: math (test 1, question 11): percentages Posted: Tue Nov 16, 2010 4:52 pm 

Joined: Sun May 30, 2010 2:23 am Posts: 498

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
(z – w)/w = (0.5y – 0.25y) / 0.25y = 1 = 100%
z is by 100% greater than w.


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