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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, 01:36
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Question Stats:

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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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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, 03:16
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, 06:04
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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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, 09:51
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, 01:53
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.
_________________

New to the Math Forum?
Please read this: Ultimate GMAT Quantitative Megathread | All You Need for Quant | PLEASE READ AND FOLLOW: 12 Rules for Posting!!!

Resources:
GMAT Math Book | Triangles | Polygons | Coordinate Geometry | Factorials | Circles | Number Theory | Remainders; 8. Overlapping Sets | PDF of Math Book; 10. Remainders | GMAT Prep Software Analysis | SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) | Tricky questions from previous years.

Collection of Questions:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


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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, 02:02
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, 04:22
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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