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Math Expert V
Joined: 02 Sep 2009
Posts: 57155
If w is 40 percent less than x, x is 40 percent less than y, and z is  [#permalink]

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Difficulty:   35% (medium)

Question Stats: 74% (02:09) correct 26% (02:49) wrong based on 154 sessions

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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%

Kudos for a correct solution.

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CEO  S
Joined: 20 Mar 2014
Posts: 2620
Concentration: Finance, Strategy
Schools: Kellogg '18 (M)
GMAT 1: 750 Q49 V44 GPA: 3.7
WE: Engineering (Aerospace and Defense)
Re: If w is 40 percent less than x, x is 40 percent less than y, and z is  [#permalink]

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Bunuel wrote:
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%

Kudos for a correct solution.

GIven w= 0.6x, x=0.6y, z=0.54y, substituting, w=2/3 Z----> z= 1.5w and thus z is 50% greater than w. E is the correct answer.
CEO  D
Status: GMATINSIGHT Tutor
Joined: 08 Jul 2010
Posts: 2967
Location: India
GMAT: INSIGHT
Schools: Darden '21
WE: Education (Education)
Re: If w is 40 percent less than x, x is 40 percent less than y, and z is  [#permalink]

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1
Bunuel wrote:
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%

Kudos for a correct solution.

Let, y = 100

z is 46 percent less than y
i.e. z = 100 - (46/100)*100 = 54

x is 40 percent less than y
i.e. x = 100 - (40/100)*100 = 60

w is 40 percent less than x
i.e. w = 60 - (40/100)*60 = 36

then z is greater than w by what percent of w?
Amount by which z is greater than w = z-w = 54-36 = 18
This difference as percentage of w = Difference*100/ w = (18/36)*100 = 50%

Answer: Option E
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Director  P
Joined: 21 May 2013
Posts: 651
Re: If w is 40 percent less than x, x is 40 percent less than y, and z is  [#permalink]

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Bunuel wrote:
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%

Kudos for a correct solution.

Let y=100
x=60
z=54
Therefore, w=36
Reqd%=(54-36/36)*100
=50%
Answer E
Math Expert V
Joined: 02 Sep 2009
Posts: 57155
Re: If w is 40 percent less than x, x is 40 percent less than y, and z is  [#permalink]

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Bunuel wrote:
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%

Kudos for a correct solution.

800score Official Solution:

(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.
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Intern  Joined: 02 Jun 2015
Posts: 1
Re: If w is 40 percent less than x, x is 40 percent less than y, and z is  [#permalink]

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if w=60/100 x(40 percent less than x)
similarly x= 60/100 y
z=(54/100 )*Y
substitute the values
then z=(54/100)*(100/60)*(100/60)*w
solving z=(3/2)w=(1+1/2)w
which is nothing but 50 % greater than w
SVP  B
Joined: 06 Nov 2014
Posts: 1877
Re: If w is 40 percent less than x, x is 40 percent less than y, and z is  [#permalink]

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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?

w = x -.4x = .6x
x = y - .4y = .6y
z = y - .46y = .54y

y = z/.54
x = .6y = .6 (z/.54)

w = .6x = .6 (.6(z/.54)) = (2/3)z => 1.5w = z => z is 50 percent greater

A. 4%
B. 18%
C. 36%
D. 40%
E. 50%
Non-Human User Joined: 09 Sep 2013
Posts: 12053
Re: If w is 40 percent less than x, x is 40 percent less than y, and z is  [#permalink]

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_________________ Re: If w is 40 percent less than x, x is 40 percent less than y, and z is   [#permalink] 21 Dec 2018, 18:01
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