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

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Carcass
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If 45% of z is 120% of y and y is 75% of x, what percent of x is z? A [#permalink] New post   15 Jan 2021, 05:56
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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

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A
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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? A [#permalink] New post   15 Jan 2021, 06:33
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Carcass wrote:
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

Kudos for the right answer and explanation


One 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

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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? A [#permalink] New post   23 Feb 2021, 08:19
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i) 1.2 y = 0.45 z [45% of z is 120% of y]
ii) y = 0.75 x [y is 75% of x]

Putting y's value in (i)

1.2 * 0.75 x = 0.45 z
(1.2 * 0.75) / 0.45 x = z
2 x = z

So, x is 200% of z. Ans is A.
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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? A [#permalink] New post   27 Oct 2023, 19:26
Hello from the GRE Prep Club BumpBot!

Thanks to another GRE Prep Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

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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? A [#permalink]
27 Oct 2023, 19:26
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