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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

by swerve » Wed Feb 21, 2018 4:31 am
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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by Brent@GMATPrepNow » Wed Feb 21, 2018 7:39 am
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

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by Brent@GMATPrepNow » Wed Feb 21, 2018 7:40 am
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.

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by GMATGuruNY » Wed Feb 21, 2018 9:39 am
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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by Scott@TargetTestPrep » Sun Jun 23, 2019 10:20 am
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 create the equations:

Z = 1.2Y

and

X = 0.2Z


Z = X/0.2

Since Z is equal to both 1.2Y and X/0.2, let's set these two quantities equal to each other:

X/0.2 = 1.2Y

X = 1.2Y(0.2)

X/Y = (1.2)(0.2)

X/Y = 0.24

X = 0.24Y

Thus, X is 24% of Y.

Answer: E

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