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

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Source: — Data Sufficiency |

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

by Jay@ManhattanReview » Wed Feb 19, 2020 12:39 am
BTGModeratorVI wrote: ↑
Tue Feb 18, 2020 10:55 am
 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

Source: Princeton Review
Answer: A
So, we have 45% of z = 120% of y => 45z/100 = 120y/100 => z = 8y/3;

Again, we have y = 75% of x => y = 3x/4 => x = 4y/3

So, (z/x)*100% = {(8y/3)/(4y/3)}*100% = 200%

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

by Brent@GMATPrepNow » Wed Feb 19, 2020 6:37 am
BTGModeratorVI wrote: ↑
Tue Feb 18, 2020 10:55 am
 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

Source: Princeton Review
Answer: A
Another approach is to find values that satisfy the given information.

y is 75% of x
So it could it be the case x = 400 and y = 300

45% of z is (equals) 120% of y
120% of y = (1.2)(300) = 360
So, 45% of z = 360
In other words, 0.45z = 360
Divide both sides by 0.45 to get: z = 800

What percent of x is z?
In other words: What percent of 400 is 800?
Another way to phrase this is: 800 is what percent of 400?
Since 800 is TWICE 400, we can also conclude that 800 is 200 percent of 400

Answer: A

Cheers,
Brent
Brent Hanneson - Creator of GMATPrepNow.com
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