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# If x is 2/3 of y and y is 3/4 of z, what is the ratio of z:x ?

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Math Expert
Joined: 02 Sep 2009
Posts: 51123
If x is 2/3 of y and y is 3/4 of z, what is the ratio of z:x ?  [#permalink]

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25 Feb 2018, 10:34
00:00

Difficulty:

15% (low)

Question Stats:

93% (00:48) correct 7% (01:18) wrong based on 46 sessions

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If x is 2/3 of y and y is 3/4 of z, what is the ratio of z:x ?

(A) 1:2
(B) 1:1
(C) 2:1
(D) 3:2
(E) 4:3

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If x is 2/3 of y and y is 3/4 of z, what is the ratio of z:x ?  [#permalink]

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25 Feb 2018, 11:00
Bunuel wrote:
If x is 2/3 of y and y is 3/4 of z, what is the ratio of z:x ?

(A) 1:2
(B) 1:1
(C) 2:1
(D) 3:2
(E) 4:3

let y =12

x= 2/3 of y = 2/3 x 12 = 8
y = 3/4 of z i.e z = 4/3 of y = 4/3 x 12 = 16
x:z = 8;16 = 1:2

(C) imo
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If x is 2/3 of y and y is 3/4 of z, what is the ratio of z:x ?  [#permalink]

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25 Feb 2018, 12:32
Bunuel wrote:
If x is 2/3 of y and y is 3/4 of z, what is the ratio of z:x ?

(A) 1:2
(B) 1:1
(C) 2:1
(D) 3:2
(E) 4:3

Assign values

Let $$z = 24$$

$$y =\frac{3}{4}z = \frac{3}{4}(24) = 18$$

$$x=\frac{2}{3}y = \frac{2}{3}(18)= 12$$

$$z : x$$?

$$\frac{24}{12} =\frac{2}{1} = (2:1)$$

Algebra

$$x = \frac{2}{3} y$$

$$y = \frac{3}{4} z$$
$$z = \frac{4}{3} y$$

$$(z : x) = \frac{z}{x}$$

$$\frac{z}{x}=\frac{\frac{4}{3}y}{\frac{2}{3}y} = \frac{4}{3} * \frac{3}{2} = \frac{12}{6} = \frac{2}{1}$$

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Re: If x is 2/3 of y and y is 3/4 of z, what is the ratio of z:x ?  [#permalink]

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25 Feb 2018, 12:51
Bunuel wrote:
If x is 2/3 of y and y is 3/4 of z, what is the ratio of z:x ?

(A) 1:2
(B) 1:1
(C) 2:1
(D) 3:2
(E) 4:3

Those students who have the capability to identify variable will surely get this question easy. perhaps it's true for all the questions. in this question, Z plays the key role. Both Y and x are dependent on Z. Thus assigning value for Z will make this question as simple as water. Now, what value could be assigned for Z. we have to look at the fractions given for X and Y. so, we have to pick up such a no. which will be evenly divisible by Both 3 and 4 , denominators. let the no. be 12.

so, Y= (3/4)*12
Y= 9
now, X= (2/3)*9 ( substitute the value of Y)
X=6
now. we have all the value required to find out the ratio of z to X
12: 6
=2:1(C)
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If x is 2/3 of y and y is 3/4 of z, what is the ratio of z:x ?  [#permalink]

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25 Feb 2018, 17:10
Equation 1) x=(2/3)y solve for y y=(3/2)x
Equation 2) y=(3/4)x

Set equations equal to each other
(3/2)x=(3/4)z

Solve for z/x

z/x=2/1
C is correct
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If x is 2/3 of y and y is 3/4 of z, what is the ratio of z:x ? &nbs [#permalink] 25 Feb 2018, 17:10
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