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For any positive x, y and z if x is n% of y and z is m% of y

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For any positive x, y and z if x is n% of y and z is m% of y  [#permalink]

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New post 13 Jun 2014, 00:37
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Question Stats:

62% (01:19) correct 38% (01:21) wrong based on 189 sessions

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For any positive x, y and z if x is n% of y and z is m% of y then what percentage must x be of z?
A. (n/m)%
B. (m × n)%
C. (100 / [m × n]) %
D. (100 × m/n)%
E. (100 × n/m)%
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Re: For any positive x, y and z if x is n% of y and z is m% of y  [#permalink]

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New post 13 Jun 2014, 01:18
hapless12 wrote:
For any positive x, y and z if x is n% of y and z is m% of y then what percentage must x be of z?
A. (n/m)%
B. (m × n)%
C. (100 / [m × n]) %
D. (100 × m/n)%
E. (100 × n/m)%


x is n% of y: \(x=\frac{n}{100}*y\);

z is m% of y: \(z=\frac{m}{100}*y\);

What percentage must x be of z: \(\frac{x}{z}*100=\frac{n}{m}*100\).

Answer: E.
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Re: For any positive x, y and z if x is n% of y and z is m% of y  [#permalink]

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New post 13 Jun 2014, 01:19
1
Bunuel wrote:
hapless12 wrote:
For any positive x, y and z if x is n% of y and z is m% of y then what percentage must x be of z?
A. (n/m)%
B. (m × n)%
C. (100 / [m × n]) %
D. (100 × m/n)%
E. (100 × n/m)%


x is n% of y: \(x=\frac{n}{100}*y\);

z is m% of y: \(z=\frac{m}{100}*y\);

What percentage must x be of z: \(\frac{x}{z}*100=\frac{n}{m}*100\).

Answer: E.


Similar questions to practice: if-25-percent-of-p-is-equal-to-10-percent-of-q-and-pq-0-th-168485.html
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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: For any positive x, y and z if x is n% of y and z is m% of y  [#permalink]

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New post 16 Jun 2014, 04:43
2
hapless12 wrote:
For any positive x, y and z if x is n% of y and z is m% of y then what percentage must x be of z?
A. (n/m)%
B. (m × n)%
C. (100 / [m × n]) %
D. (100 × m/n)%
E. (100 × n/m)%



x is n% of y MEANS x= (n/100 )* y------------------------eq1

z is m% of y MEANS z= (m/100 )* y------------------------eq2

Find equation of x & z
substitute value of y from 2nd equation into Ist equation
so x= (n/100)*(100z/m)
so x= (n/m)z
or x= (100n/m)z/100
so answer is 100n/m %
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Re: For any positive x, y and z if x is n% of y and z is m% of y  [#permalink]

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New post 22 May 2017, 18:44
hapless12 wrote:
For any positive x, y and z if x is n% of y and z is m% of y then what percentage must x be of z?
A. (n/m)%
B. (m × n)%
C. (100 / [m × n]) %
D. (100 × m/n)%
E. (100 × n/m)%


We are given:

x = (n/100)y

x/(n/100) = y

100x/n = y

AND

z = (m/100)y

z/(m/100) = y

100z/m = y

We can equate our two equations and then express x as a percentage of z:

100x/n = 100z/m

100x/100z = not n/m

x/z = n/m

Thus, x/z * 100 = n/m * 100.

Answer: E
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Re: For any positive x, y and z if x is n% of y and z is m% of y  [#permalink]

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New post 01 Jul 2018, 17:19
X=n/100 y
Z=m/100 y
X=n/100*100z/m
X=n/m z
Answer E


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Re: For any positive x, y and z if x is n% of y and z is m% of y &nbs [#permalink] 01 Jul 2018, 17:19
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