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

tagged by: swerve

This topic has 3 expert replies and 0 member replies

### Top Member

swerve Master | Next Rank: 500 Posts
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#### Z is 120% of Y. X is smaller than Z by 80%. What percentage

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.

### GMAT/MBA Expert

Brent@GMATPrepNow GMAT Instructor
Joined
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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%

Cheers,
Brent

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### GMAT/MBA Expert

Brent@GMATPrepNow GMAT Instructor
Joined
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Posted:
11778 messages
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1232 members
5254
GMAT Score:
770
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.

Cheers,
Brent

_________________
Brent Hanneson – Creator of GMATPrepNow.com
Use our video course along with

Check out the online reviews of our course
Come see all of our free resources

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!

### GMAT/MBA Expert

GMATGuruNY GMAT Instructor
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Posted:
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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%.

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