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If 45% of z is 120% of y and y is 75% of x, what percent of x is z?

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Re: If 45% of z is 120% of y and y is 75% of x, what percent of x is z?

by Jay@ManhattanReview » Tue Apr 14, 2020 11:32 pm
BTGmoderatorDC wrote: ↑
Tue Apr 14, 2020 4:38 pm
 If 45% of z is 120% of y and y is 75% of x, what percent of x is z?

A. 200
B. 160
C. 100
D. 65
E. 50

OA A

Source: Princeton Review
So, we have

45% of z = 120% of y => 45z/100 = 120y/100 => y = 3z/8 ---(1)

y = 75% of x => y = 75x/100 => y = 3x/4 ---(2)

From (1) and (2), we have

3z/8 = 3x/4

z = 2x

Thus, z is 200% of x.

The correct answer: A

Hope this helps!

-Jay
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Re: If 45% of z is 120% of y and y is 75% of x, what percent of x is z?

by Scott@TargetTestPrep » Fri Apr 17, 2020 3:33 am
BTGmoderatorDC wrote: ↑
Tue Apr 14, 2020 4:38 pm
 If 45% of z is 120% of y and y is 75% of x, what percent of x is z?

A. 200
B. 160
C. 100
D. 65
E. 50


OA A

Source: Princeton Review
We can create the equations:

0.45z = 1.2y

and

y = 0.75x

We need to determine the value of z/x * 100.

Solving the first equation, we have:

y = 0.45z/1.2 = 4.5z/12 = 9z/24 = 3z/8

Substituting y = 3z/8 into the second equation, we have:

3z/8 = 0.75x

3z/8 = 3x/4

z/x = 3/4 * 8/3

z/x = 2

Therefore, z/x * 100 = 2 * 100 = 200.

Answer: A

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GMAT/MBA Expert

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Joined: Sat Apr 25, 2015 10:56 am
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Re: If 45% of z is 120% of y and y is 75% of x, what percent of x is z?

by Scott@TargetTestPrep » Fri Apr 17, 2020 3:34 am
BTGmoderatorDC wrote: ↑
Tue Apr 14, 2020 4:38 pm
 If 45% of z is 120% of y and y is 75% of x, what percent of x is z?

A. 200
B. 160
C. 100
D. 65
E. 50


OA A

Source: Princeton Review
We can create the equations:

0.45z = 1.2y

and

y = 0.75x

We need to determine the value of z/x * 100.

Solving the first equation, we have:

y = 0.45z/1.2 = 4.5z/12 = 9z/24 = 3z/8

Substituting y = 3z/8 into the second equation, we have:

3z/8 = 0.75x

3z/8 = 3x/4

z/x = 3/4 * 8/3

z/x = 2

Therefore, z/x * 100 = 2 * 100 = 200.

Answer: A

Scott Woodbury-Stewart
Founder and CEO
[email protected]

Image

See why Target Test Prep is rated 5 out of 5 stars on BEAT the GMAT. Read our reviews

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