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

tagged by: swerve

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### Top Member

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

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

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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%

Cheers,
Brent

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### GMAT/MBA Expert

GMAT Instructor
Joined
08 Dec 2008
Posted:
12127 messages
Followed by:
1237 members
5254
GMAT Score:
770
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

And check out 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

GMAT Instructor
Joined
25 May 2010
Posted:
14738 messages
Followed by:
1849 members
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GMAT Score:
790
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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