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The positive numbers w, x, y, and z are such that x is 20 percent grea

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The positive numbers w, x, y, and z are such that x is 20 percent grea  [#permalink]

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New post Updated on: 24 Aug 2015, 23:24
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The positive numbers w, x, y, and z are such that x is 20 percent greater than y, y is 20 percent greater than z, and w is 20 percent less than x. What percent greater than z is w ?

A. 15.2%
B. 16.0%
C. 20.0%
D. 23.2%
E. 24.8%

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Originally posted by bakfed on 12 May 2010, 22:42.
Last edited by Bunuel on 24 Aug 2015, 23:24, edited 1 time in total.
Renamed the topic, edited the question and added the OA.
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Re: The positive numbers w, x, y, and z are such that x is 20 percent grea  [#permalink]

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New post 12 May 2010, 23:44
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I used the choosing numbers strategy. I started with 1, looking back it would have been easier to start with 100.

y = 100 (start with yy, it makes getting x easier).
x = y*1.2 = 120
z = y/1.2 = 83.33
w = x*0.8 = 96

Then for the answer:

(w-z)/z = (96 - 83.33)/83.33
= 15.2% A

There could be an easier way, to me it just seemed like a "choosing numbers" type of question.
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Re: The positive numbers w, x, y, and z are such that x is 20 percent grea  [#permalink]

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New post 13 May 2010, 03:27
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bakfed wrote:
The positive numbers w, x, y, and z are such that x is 20 percent greater than y, y is 20 percent greater than z, and w is 20 percent less than x. What percent greater than z is w ?

A. 15.2%
B. 16.0%
C. 20.0%
D. 23.2%
E. 24.8%

OA

I tried plugging in numbers but my numbers just never match up with the OA's percentage. please help, thanks.


\(x =1.2*y\)
\(y =1.2 *z = 1.2*1.2*x\)

\(=> z = \frac{y}{1.2}= \frac{x}{1.2*1.2} = \frac{x}{1.44}\)

\(w= 0.8*x\)

Question asks \(z * \frac{n}{100} = w\) ( Where n is the percentage greater with which W is greater than Z )

\(z *\frac{n}{100}= \frac{x*n}{1.44*100}= w= 0.8*x\)

\(=> n = 0.8*1.44 *100 = 115.2\)

Hence Z is 15.2 % greater than W
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Re: The positive numbers w, x, y, and z are such that x is 20 percent grea  [#permalink]

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New post 13 May 2010, 07:12
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Re: The positive numbers w, x, y, and z are such that x is 20 percent grea  [#permalink]

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New post 12 Aug 2010, 04:23
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My strategy is same as the "Doberman" but instead take z=100, which makes life a bit easy. As:
z=100
y=120 (20% greater than z)
z=144(20% greater than y)

Now calculate w 20% less than z = 144*80/100= 115.2
Now by just looking, relation between w and z:
w-z/z*100 = 15.2 - Answer
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Re: The positive numbers w, x, y, and z are such that x is 20 percent grea  [#permalink]

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New post 24 Feb 2018, 15:30
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Re: The positive numbers w, x, y, and z are such that x is 20 percent grea   [#permalink] 24 Feb 2018, 15:30
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