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

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Math Expert
Joined: 02 Sep 2009
Posts: 60778
The positive numbers w, x, y, and z are such that x is 20 percent grea  [#permalink]

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07 Nov 2019, 01:48
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Difficulty:

25% (medium)

Question Stats:

86% (02:25) correct 14% (02:43) wrong based on 22 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%

Are You Up For the Challenge: 700 Level Questions

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Joined: 19 Oct 2018
Posts: 1297
Location: India
Re: The positive numbers w, x, y, and z are such that x is 20 percent grea  [#permalink]

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07 Nov 2019, 07:15
x:y=6:5
y:z=6:5
w:x=4:5

x:y:z:w= 5*6*6 : 5*5*6 : 5*5*5 : 4*6*6= 180:150:125:144

$$\frac{w-z}{z}*100$$= $$\frac{144-125}{125}*100$$= 15.2%

Bunuel 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%

Are You Up For the Challenge: 700 Level Questions
GMAT Club Legend
Joined: 12 Sep 2015
Posts: 4235
Re: The positive numbers w, x, y, and z are such that x is 20 percent grea  [#permalink]

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07 Nov 2019, 08:20
Top Contributor
Bunuel 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%

Let's test values that satisfy the given information.

y is 20 percent greater than z
Let's say y = 120 and z = 100

x is 20 percent greater than y
So, x is 20 percent greater than 120
In other words, x = (1.2)(120) = 144

w is 20 percent less than x
So, w is 20 percent less than 144
20% of 144 = 28.8
So, w = 144 - 28.8 = 115.2

What percent greater than z is w ?
In other words, 115.2 is what percent greater than 100 ?

Cheers,
Brent
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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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07 Nov 2019, 08:39
Bunuel 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%

Are You Up For the Challenge: 700 Level Questions

Given: 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.

Asked: What percent greater than z is w ?

x = 1.2y
y = 1.2z
w = .8x

w = .8x = .8 * 1.2 * 1.2z
w = 1.152z

w is 15.2% greater than z.

IMO A
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Posts: 5751
Location: India
Concentration: Sustainability, Marketing
GPA: 4
WE: Marketing (Energy and Utilities)
Re: The positive numbers w, x, y, and z are such that x is 20 percent grea  [#permalink]

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07 Nov 2019, 09:44
Bunuel 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%

Are You Up For the Challenge: 700 Level Questions

x=1.2y
y=1.2z
w=.8x
w=.96y
z=y/1.2
w/z = .96*1.2 ; 1.152 = 15.2 %
IMO A
Re: The positive numbers w, x, y, and z are such that x is 20 percent grea   [#permalink] 07 Nov 2019, 09:44
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