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

tagged by: BTGmoderatorLU

### Top Member

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

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

The OA is A.

If x increase by 50% then, x = 1.5x

If y decrease by 20% then, y = 0.8y

Finally, z = (1.5x)(0.8y)^2 = 0.96xy^2, that's represent a decrease of 4% in z, right?

Experts, any suggestion? Thanks in advance.

### GMAT/MBA Expert

GMAT Instructor
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LUANDATO wrote:
If x and y are positive numbers and z = xy^2, a 50 percent increase in x and 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%
Since x increases by 50% = 1/2, plug in an EVEN NUMBER for x:
x=4.
Since y decreases by 20% = 1/5, plug in a MULTIPLE OF 5 for y:
y=5.

Original z:
z = xy² = (4)(5²) = 4*25 = 100.

New z:
x increased by 1/2 = 4 + (1/2)(4) = 4 + 2 = 6.
y decreased by 1/5 = 5 - (1/5)(5) = 5 - 1 = 4.
z = xy² = (6)(4²) = 6*16 = 96.

Result:
z decreases from 100 to 96, a decrease of 4%.

Quote:
If x increase by 50% then, x = 1.5x

If y decrease by 20% then, y = 0.8y

Finally, z = (1.5x)(0.8y)^2 = 0.96xy^2, that's represent a decrease of 4% in z, right
Perfect!

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### GMAT/MBA Expert

GMAT Instructor
Joined
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Posted:
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Followed by:
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LUANDATO wrote:
If x and y are positive numbers and z = xy^2, a 50 percent increase in x and 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%
Since x increases by 50% and y decreases by 20% we have:

z = (1.5x)(0.8y)^2

z = (1.5x)0.64y^2

z = 0.96xy^2

So we see that z is decreased by 4%.

Alternate Solution:

If we let x = 1 and y = 1, then the initial value of z is also 1.

After we increase x by 50% and decrease y by 20%, we have:

z = 1.5*(0.8)^2

z = 0.96

We use the percent change formula (new - old)/old x 100% to get:

(0.96 - 1)/1 x 100% = -0.04 x 100% = 4% decrease.

_________________
Jeffrey Miller Head of GMAT Instruction

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