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

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Math Expert
Joined: 02 Sep 2009
Posts: 51100
If x and y are positive numbers and z = xy^2, a 50 percent increase  [#permalink]

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08 Nov 2015, 23:00
1
2
00:00

Difficulty:

15% (low)

Question Stats:

75% (01:15) correct 25% (01:22) wrong based on 126 sessions

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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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Joined: 02 Aug 2009
Posts: 7099
Re: If x and y are positive numbers and z = xy^2, a 50 percent increase  [#permalink]

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09 Nov 2015, 02:59
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]

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10 Nov 2015, 06:57
1
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 %

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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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17 Apr 2016, 04:19
1
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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Joined: 24 Nov 2015
Posts: 521
Location: United States (LA)
Re: If x and y are positive numbers and z = xy^2, a 50 percent increase  [#permalink]

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30 Apr 2016, 13:09
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
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Posts: 9116
Re: If x and y are positive numbers and z = xy^2, a 50 percent increase  [#permalink]

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07 Oct 2018, 07:30
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

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Re: If x and y are positive numbers and z = xy^2, a 50 percent increase &nbs [#permalink] 07 Oct 2018, 07:30
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