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If w is 40 percent less than x, x is 40 percent less than y, and z is

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If w is 40 percent less than x, x is 40 percent less than y, and z is  [#permalink]

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New post 10 Jul 2015, 02:36
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E

Difficulty:

  35% (medium)

Question Stats:

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

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Re: If w is 40 percent less than x, x is 40 percent less than y, and z is  [#permalink]

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New post 10 Jul 2015, 04:16
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.
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Re: If w is 40 percent less than x, x is 40 percent less than y, and z is  [#permalink]

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New post 10 Jul 2015, 07:04
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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

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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Re: If w is 40 percent less than x, x is 40 percent less than y, and z is  [#permalink]

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New post 11 Jul 2015, 10:51
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
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Re: If w is 40 percent less than x, x is 40 percent less than y, and z is  [#permalink]

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New post 13 Jul 2015, 02:53
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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Re: If w is 40 percent less than x, x is 40 percent less than y, and z is  [#permalink]

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New post 13 Jul 2015, 03:02
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
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Re: If w is 40 percent less than x, x is 40 percent less than y, and z is  [#permalink]

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New post 14 Jul 2015, 05:22
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%
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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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