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If x and y are positive numbers and z = xy^2, a 50 percent increase

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Bunuel
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If x and y are positive numbers and z = xy^2, a 50 percent increase [#permalink] New post   09 Nov 2015, 00:00
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If x and y are positive numbers and z = xy^2, a 50 percent increase in x and a 20 percent decrease in y would result in which of the following changes in z?

(A) A decrease of 4%
(B) A decrease of 14%
(C) An increase of 4%
(D) An increase of 20%
(E) An increase of 30%
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A
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chetan2u
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Re: If x and y are positive numbers and z = xy^2, a 50 percent increase [#permalink] New post   09 Nov 2015, 03:59
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Bunuel wrote:
If x and y are positive numbers and z = xy^2, a 50 percent increase in x and a 20 percent decrease in y would result in which of the following changes in z?

(A) A decrease of 4%
(B) A decrease of 14%
(C) An increase of 4%
(D) An increase of 20%
(E) An increase of 30%


z=x*y^2
Z=1.5 x*(0.8)^2=.96x*y^2=.96z
so a decrease of 4%
A
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Re: If x and y are positive numbers and z = xy^2, a 50 percent increase [#permalink] New post   10 Nov 2015, 07:57
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z= x*y^2

Now , since x increases by 50 % and y decreases by 20 %
z'=(3/2)x * (8/10)(8/10)y^2
= 192/200 * x*y^2
= 96/100 * x*y^2
= 96/100 * z

a decrease in 4 %

Answer A
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Re: If x and y are positive numbers and z = xy^2, a 50 percent increase [#permalink] New post   17 Apr 2016, 05:19
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Bunuel wrote:
If x and y are positive numbers and z = xy^2, a 50 percent increase in x and a 20 percent decrease in y would result in which of the following changes in z?

(A) A decrease of 4%
(B) A decrease of 14%
(C) An increase of 4%
(D) An increase of 20%
(E) An increase of 30%


Just take smart numbers
x=4 and y=5-----> z=100
a 50 percent increase in x ---->x=6
a 20 percent decrease in y----->y=4
now z=6*4^2---->96
so Z decreased from 100 to 96
Ans A
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Re: If x and y are positive numbers and z = xy^2, a 50 percent increase [#permalink] New post   30 Apr 2016, 14:09
Given fact z = \(xy^2\)
A 50% increase in x = 1.5x
A 20% decrease in y = 0.8y
calculating z = \(xy^2\)
change in z = \(1.5x\) * \(0.8y^2\)
so z = 0.96 times original z
clearly its a 4 % decrease
correct answer - A
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Re: If x and y are positive numbers and z = xy^2, a 50 percent increase [#permalink] New post   18 Jun 2023, 09:08
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Re: If x and y are positive numbers and z = xy^2, a 50 percent increase [#permalink]
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