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

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Retired Moderator
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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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Updated on: 24 Aug 2015, 23:24
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Difficulty:

55% (hard)

Question Stats:

68% (02:46) correct 32% (02:38) wrong based on 152 sessions

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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.
Intern
Joined: 23 Feb 2010
Posts: 13
Re: The positive numbers w, x, y, and z are such that x is 20 percent grea  [#permalink]

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12 May 2010, 23:44
2
1
I used the choosing numbers strategy. I started with 1, looking back it would have been easier to start with 100.

x = y*1.2 = 120
z = y/1.2 = 83.33
w = x*0.8 = 96

(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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13 May 2010, 03:27
1
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
Retired Moderator
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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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13 May 2010, 07:12
thanks, guys, got it now
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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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12 Aug 2010, 04:23
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1
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:
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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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24 Feb 2018, 15:30
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

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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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