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If x and y are positive numbers and z = xy^2, a 50 percent increase 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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GMAT Focus 1: 735 Q90 V89 DI81
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If x and y are positive numbers and z = xy^2, a 50 percent increase 09 Nov 2015, 03:59
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Bunuel
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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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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If x and y are positive numbers and z = xy^2, a 50 percent increase 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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If x and y are positive numbers and z = xy^2, a 50 percent increase 17 Apr 2016, 05:19
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Bunuel
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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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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If x and y are positive numbers and z = xy^2, a 50 percent increase 30 Apr 2016, 14:09
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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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If x and y are positive numbers and z = xy^2, a 50 percent increase 23 Sep 2025, 23:55
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The percentage change problem can be tricky when multiple variables are changing at once. Let me walk you through the core approach that makes this manageable.

Here's how to tackle this systematically:

Let's start by understanding what's happening. When \(x\) increases by 50%, it becomes \(1.5x\) (think of it as 100% + 50% = 150% = 1.5). Similarly, when \(y\) decreases by 20%, it becomes \(0.8y\) (that's 100% - 20% = 80% = 0.8).

Step 1: Express the new value of z
Original: \(z = xy^2\)
After changes: \(z_{new} = (1.5x)(0.8y)^2\)

Step 2: Calculate \((0.8y)^2\) carefully
Here's where you need to be careful - notice how we square the entire term:
\((0.8y)^2 = 0.8^2 \times y^2 = 0.64y^2\)

Step 3: Find the new z value
\(z_{new} = 1.5x \times 0.64y^2 = 0.96xy^2\)

Since the original \(z = xy^2\), we have:
\(z_{new} = 0.96z\)

Step 4: Determine the percent change
If the new value is 96% of the original, that means z has decreased by 4%.

The answer is (A) A decrease of 4%

You can check out the step-by-step solution on Neuron by e-GMAT to discover alternative approaches including the smart numbers method and learn the systematic framework that applies to all percentage change problems with compound variables. You can also explore other GMAT official questions with detailed solutions on Neuron for structured practice here.
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If x and y are positive numbers and z = xy^2, a 50 percent increase 02 Oct 2025, 04:19
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increased value be 3/2 x and decreased value 4/5 y ^2 sqauring of 4/5 results 16/25.Now, 3/4 multiply by 16 /25 =24 /25 .
1/25=4% so 24/25 shows decrement of 4%
Bunuel
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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