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

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BTGmoderatorLU: Moderator; Posts: 2650; Joined: Sun Oct 15, 2017 1:50 pmFollowed by: 6 members

by BTGmoderatorLU » Fri Apr 27, 2018 2:07 pm

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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.

I get the solution as follows,

Let y = 100
z = 120
x = 120*(100-80)/100 = 24

x : y = 24 : 100
i.e. 24%
The correct answer is E.

Please, can anyone explain another way to solve this PS question? Thanks!

Source: Beat The GMAT — Problem Solving | Fri Apr 27, 2018 2:07 pm

GMATGuruNY: GMAT Instructor; Posts: 15539; Joined: Tue May 25, 2010 12:04 pmFollowed by: 1906 members; Location: New York, NY; Thanked: 13060 times; GMAT Score:790

by GMATGuruNY » Fri Apr 27, 2018 2:26 pm

BTGmoderatorLU 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%

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

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

What percentage of Y is X?
X/Y = X/Z * Z/Y = 1/5 * 6/5 = 6/25 = 24/100.

Thus:
X is 24% of Y.

The correct answer is E.

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by Jeff@TargetTestPrep » Fri May 04, 2018 9:35 am

BTGmoderatorLU 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) = (0.24)

Thus, X is 24% of Y.

Answer: E

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

by Brent@GMATPrepNow » Wed Jan 15, 2020 7:23 am

BTGmoderatorLU wrote: ↑
Fri Apr 27, 2018 2:07 pm
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

Brent Hanneson - Creator of GMATPrepNow.com

GMAT/MBA Expert

Scott@TargetTestPrep: GMAT Instructor; Posts: 8246; Joined: Sat Apr 25, 2015 10:56 amFollowed by: 29 members; Location: Los Angeles, CA; Thanked: 43 times

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

by Scott@TargetTestPrep » Tue Jan 21, 2020 8:53 am

BTGmoderatorLU wrote: ↑
Fri Apr 27, 2018 2:07 pm
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.

I get the solution as follows,

Let y = 100
z = 120
x = 120*(100-80)/100 = 24

x : y = 24 : 100
i.e. 24%
The correct answer is E.

Please, can anyone explain another way to solve this PS question? Thanks!

We can create the equations:

Z = 1.2Y

and

X = 0.2Z

X/0.2 = Z

Thus:

X/0.2 = 1.2Y

X = 0.24Y

X/Y = 0.24

X/Y * 100 = 0.24 * 100 = 24 percent

Answer: E

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