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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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Joined: 26 Nov 2014
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If 45% of z is 120% of y and y is 75% of x, what percent of x is z?  [#permalink]

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04 Aug 2015, 22:44
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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
CEO
Status: GMATINSIGHT Tutor
Joined: 08 Jul 2010
Posts: 3394
Location: India
GMAT: QUANT EXPERT
Schools: IIM (A)
GMAT 1: 750 Q51 V41
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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?  [#permalink]

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05 Aug 2015, 05:53
shyind 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

(45/100)z = (120/100)y

and y = (75/100)x i.e. y = (3/4)x

i.e. (45/100)z = (120/100)*(3/4)x

i.e. z = (120*3)x/(45*4)

i.e. z = (2)x = (200/100)x

i.e. z is 200% of x

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If 45% of z is 120% of y and y is 75% of x, what percent of x is z?  [#permalink]

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08 Feb 2020, 06:56
Top Contributor
1
shyind 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

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

Cheers,
Brent
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If 45% of z is 120% of y and y is 75% of x, what percent of x is z?   [#permalink] 08 Feb 2020, 06:56
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