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Z is 120% of Y. X is smaller than Z by 80%. What percentage

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Z is 120% of Y. X is smaller than Z by 80%. What percentage

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Z is 120% of Y. X is smaller than Z by 80%. What percentage is X of Y?

A. 96%
B. 50%
C. 45%
D. 40%
E. 24%

The OA is E.

If Z is 120% of Y, then Z=1.2Y, or Y = Z / 1.2.

If X is smaller than Z by 80%, then X = 0.2Z.

Finally, X / Y = 0.2Z / (Z/1.2) = 0.24 or 24%.

Please, can any expert explain this PS question for me? I need your help. Thanks.

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swerve wrote:
Z is 120% of Y. X is smaller than Z by 80%. What percentage is X of Y?

A. 96%
B. 50%
C. 45%
D. 40%
E. 24%
We can also solve this by assigning values that meet the given conditions.

Z is 120% of Y
So, let Z = 120 and let Y = 100

X is smaller than Z by 80%.
In other words, X is 20% of Z
If Z = 120, then X = 20% of 120
So, X = 24

What percentage is X of Y?
24/100 = 24%

Answer: E

Cheers,
Brent

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swerve wrote:
If Z is 120% of Y, then Z=1.2Y, or Y = Z / 1.2.

If X is smaller than Z by 80%, then X = 0.2Z.

Finally, X / Y = 0.2Z / (Z/1.2) = 0.24 or 24%.

Please, can any expert explain this PS question for me? I need your help. Thanks.
Your algebraic solution is perfect.

Cheers,
Brent

_________________
Brent Hanneson – Creator of GMATPrepNow.com
Use our video course along with Beat The GMAT's free 60-Day Study Guide

Sign up for our free Question of the Day emails
And check out all of our free resources

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GMAT Prep Now's comprehensive video course can be used in conjunction with Beat The GMAT’s FREE 60-Day Study Guide and reach your target score in 2 months!

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swerve wrote:
Z is 120% of Y. X is smaller than Z by 80%. What percentage is X of Y?

A. 96%
B. 50%
C. 45%
D. 40%
E. 24%
Alternate approach:
X/Y = X/Z * Z/Y.

Since X is 80% less than Z, X is 20% of Z:
X/Z = 20/100 = 1/5.

Since Z is 120% of Y, we get:
Z/Y = 120/100 = 6/5.

Substituting X/Z = 1/5 and Z/Y = 6/5 into the blue equation above, we get:
X/Y = 1/5 * 6/5 = 6/25 = 24/100 = 24%.

The correct answer is E.

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