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# If X is 60 percent more than Y and Y is 40 percent less than Z, then

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Math Expert
Joined: 02 Sep 2009
Posts: 50044
If X is 60 percent more than Y and Y is 40 percent less than Z, then  [#permalink]

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18 Apr 2018, 18:21
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Difficulty:

15% (low)

Question Stats:

75% (01:12) correct 25% (02:09) wrong based on 47 sessions

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If X is 60 percent more than Y and Y is 40 percent less than Z, then what percent of Z is X?

(A) 64%
(B) 80%
(C) 96%
(D) 120%
(E) 124%

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Joined: 22 May 2016
Posts: 2040
If X is 60 percent more than Y and Y is 40 percent less than Z, then  [#permalink]

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18 Apr 2018, 20:20
Bunuel wrote:
If X is 60 percent more than Y and Y is 40 percent less than Z, then what percent of Z is X?

(A) 64%
(B) 80%
(C) 96%
(D) 120%
(E) 124%

$$X = 1.6Y=1\frac{3}{5}Y=\frac{8}{5}Y$$
$$\frac{5}{8}X = Y$$

$$Y =.60Z=\frac{3}{5}Z$$

$$Y = Y$$

$$\frac{5}{8}X=\frac{3}{5}Z$$

$$X = \frac{3}{5}Z*\frac{8}{5}$$

$$\frac{X}{Z}=\frac{24}{25}$$

"what percent of Z is X?"
REWRITE: X = what percent of Z?

$$(\frac{X}{Z}*100)$$ From above, $$\frac{X}{Z}=\frac{24}{25}$$

$$(\frac{24}{25}*\frac{4}{4}*100)=(\frac{96}{100})*100)=96$$
percent

$$X$$ is $$96$$ percent of $$Z$$

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Joined: 22 Feb 2018
Posts: 360
If X is 60 percent more than Y and Y is 40 percent less than Z, then  [#permalink]

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18 Apr 2018, 20:25
Bunuel wrote:
If X is 60 percent more than Y and Y is 40 percent less than Z, then what percent of Z is X?

(A) 64%
(B) 80%
(C) 96%
(D) 120%
(E) 124%

OA:C

X is 60 percent more than Y.
$$X = Y + \frac{60}{100}.Y$$
$$X= \frac{160}{100}.Y$$
$$X= 1.6 Y$$ [1]

Y is 40 percent less than Z
$$Y= Z - \frac{40}{100}.Z$$
$$Y= \frac{60}{100}.Z$$
$$Y= 0.6.Z$$ [2]

What percent of Z is X will be given by $$\frac{X}{Z}.100$$
Putting value of Y from [2] into [1],we get
$$X= 1.6 * 0.6 Z$$
$$\frac{X}{Z}= 1.6 * 0.6$$
$$\frac{X}{Z}*100 =1.6*0.6*100$$
$$\frac{X}{Z}*100=96$$
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Re: If X is 60 percent more than Y and Y is 40 percent less than Z, then  [#permalink]

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18 Apr 2018, 21:57
Let Z= 100,

Y = 40 % less than Z = 60 % of Z= 60

X = 60% more than Y = 160% of Y = 160/100 *60 = 96

Hence X is 96% of Z

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Posts: 36
Re: If X is 60 percent more than Y and Y is 40 percent less than Z, then  [#permalink]

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18 Apr 2018, 22:51
Bunuel wrote:
If X is 60 percent more than Y and Y is 40 percent less than Z, then what percent of Z is X?

(A) 64%
(B) 80%
(C) 96%
(D) 120%
(E) 124%

X=>1.6Y or Y = X/1.6
Y= (1-0.4)Z or 06.Z
x/1.6 = .6Z=> X = .96Z
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Joined: 26 Mar 2013
Posts: 1841
Re: If X is 60 percent more than Y and Y is 40 percent less than Z, then  [#permalink]

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19 Apr 2018, 00:23
Bunuel wrote:
If X is 60 percent more than Y and Y is 40 percent less than Z, then what percent of Z is X?

(A) 64%
(B) 80%
(C) 96%
(D) 120%
(E) 124%

$$x = 1.6 y$$

$$y =0.6 z$$

$$x = 1.6 * 0.6 z$$

$$\frac{x}{z}= 1.6 * 0.6$$

I will check the unit digit of the multiplication. It should be 6

Only one answer choice with unit digit 6

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Posts: 2830
Re: If X is 60 percent more than Y and Y is 40 percent less than Z, then  [#permalink]

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23 Apr 2018, 16:54
Bunuel wrote:
If X is 60 percent more than Y and Y is 40 percent less than Z, then what percent of Z is X?

(A) 64%
(B) 80%
(C) 96%
(D) 120%
(E) 124%

We can create the equations:

X = 1.6Y

X = 8Y/5

And

Y = 0.6Z

Y/0.6 = Z

10Y/6 = Z

5Y/3 = Z

So X/Z x 100 is:

(8Y/5)/(5Y/3) x 100 = 24Y/(25Y) x 100 = 24/25 x 100 = 96

Alternate Solution:

We can create two equations:

X = 1.6Y

X/1.6 = Y

and

Y = 0.6Z

Since we have two equations, each equal to Y, we can set the two equations equal to each other:

X/1.6 = 0.6Z

X = 0.96Z

Thus, X is 0.96 x 100 = 96% of Z.

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Re: If X is 60 percent more than Y and Y is 40 percent less than Z, then &nbs [#permalink] 23 Apr 2018, 16:54
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