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.
Z is 120% of Y. X is smaller than Z by 80%. What percentage
This topic has expert replies
GMAT/MBA Expert
- Brent@GMATPrepNow
- GMAT Instructor
- Posts: 16207
- Joined: Mon Dec 08, 2008 6:26 pm
- Location: Vancouver, BC
- Thanked: 5254 times
- Followed by:1268 members
- GMAT Score:770
We can also solve this by assigning values that meet the given conditions.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%
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
GMAT/MBA Expert
- Brent@GMATPrepNow
- GMAT Instructor
- Posts: 16207
- Joined: Mon Dec 08, 2008 6:26 pm
- Location: Vancouver, BC
- Thanked: 5254 times
- Followed by:1268 members
- GMAT Score:770
Your algebraic solution is perfect.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
- GMATGuruNY
- GMAT Instructor
- Posts: 15539
- Joined: Tue May 25, 2010 12:04 pm
- Location: New York, NY
- Thanked: 13060 times
- Followed by:1906 members
- GMAT Score:790
Alternate approach: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%
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.
Private tutor exclusively for the GMAT and GRE, with over 20 years of experience.
Followed here and elsewhere by over 1900 test-takers.
I have worked with students based in the US, Australia, Taiwan, China, Tajikistan, Kuwait, Saudi Arabia -- a long list of countries.
My students have been admitted to HBS, CBS, Tuck, Yale, Stern, Fuqua -- a long list of top programs.
As a tutor, I don't simply teach you how I would approach problems.
I unlock the best way for YOU to solve problems.
For more information, please email me (Mitch Hunt) at [email protected].
Student Review #1
Student Review #2
Student Review #3
Followed here and elsewhere by over 1900 test-takers.
I have worked with students based in the US, Australia, Taiwan, China, Tajikistan, Kuwait, Saudi Arabia -- a long list of countries.
My students have been admitted to HBS, CBS, Tuck, Yale, Stern, Fuqua -- a long list of top programs.
As a tutor, I don't simply teach you how I would approach problems.
I unlock the best way for YOU to solve problems.
For more information, please email me (Mitch Hunt) at [email protected].
Student Review #1
Student Review #2
Student Review #3
GMAT/MBA Expert
- Scott@TargetTestPrep
- GMAT Instructor
- Posts: 7266
- Joined: Sat Apr 25, 2015 10:56 am
- Location: Los Angeles, CA
- Thanked: 43 times
- Followed by:29 members
We can create the equations: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%
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
Scott Woodbury-Stewart
Founder and CEO
[email protected]
See why Target Test Prep is rated 5 out of 5 stars on BEAT the GMAT. Read our reviews