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

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New post 18 Apr 2018, 17:21
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Question Stats:

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

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New post 18 Apr 2018, 19:20
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 \(Z\)

Answer C
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If X is 60 percent more than Y and Y is 40 percent less than Z, then  [#permalink]

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New post 18 Apr 2018, 19:25
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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New post 18 Apr 2018, 20:57
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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Re: If X is 60 percent more than Y and Y is 40 percent less than Z, then  [#permalink]

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New post 18 Apr 2018, 21:51
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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Re: If X is 60 percent more than Y and Y is 40 percent less than Z, then  [#permalink]

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New post 18 Apr 2018, 23:23
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

Answer: C
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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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New post 23 Apr 2018, 15:54
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.

Answer: C
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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, 15:54
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