If y is 20% less than 90% of x and z is 25% more than 130% of y, then

Question

If  y  is 20% less than 90% of  x  and  z  is 25% more than 130% of  y , then  z  is what percent of  x ?

(A)  72 %
(B)  92.5 %
(C)  108.5 %
(D)  117 %
(E)  171 %

GMATGuruNY · Accepted Answer

y is 20% less than 90% of x: 
 y = \frac{4}{5} * \frac{9}{10} * x 
 \frac{y}{x} = \frac{18}{25}

z is 25% more than 130% of y: 
 z = \frac{5}{4} * \frac{13}{10} * y 
 \frac{z}{y} = \frac{13}{8}

z is what percent of x? 
 \frac{z}{x} = \frac{z}{y} * \frac{y}{x} = \frac{13}{8} * \frac{18}{25} = \frac{117}{100} =  117%

D

sujoykrdatta · Answer

We have:

y  is  20 % less than  90 % of  x

=>  y  =  80 % of  90 % of  x

=>  y = 80/100 * 90 % of  x

=> y = 72 % of  x => y = 0.72x

z  is  25 % more than  130 % of  y

=>  z  =  125 % of  130 % of  y

=>  z = 125/100 * 130 % of  y

=> z = 162.5 % of  y => z = 1.625y

=> z = 1.625 * 0.72x

=> z > 1.6 * 0.7x

=> z > 1.12x

=> z > 112 % of  x

Answer D

PS> Where is Option E?

Farina · Answer

"If y is 20 less than 90 of x and z is 25 more than 130 of y, then z is what percent of x?" 
The percent sign is missing in the question throughout and that is why i got confused. However I figured out and my answer is D

ScottTargetTestPrep · Answer

We can create the equations:

y = 0.8 * 0.9x

and

z = 1.25 * 1.3y

From the first equation, we see that y = 0.72x, so we can substitute 0.72x for y in the second equation, obtaining:

z = 1.25 * 1.3(0.72x)

z = (1.25 * 0.72) * 1.3x

z = 0.9 * 1.3x

z = 1.17x

We see that z is 117% of x.

Answer: D

TheUltimateWinner · Answer

Thanks  ScottTargetTestPrep  sir. 
Done.
I've tried to put % when I posted it, but i failed. I tried to  mark  every answer option with percent, but It did not work. Now, I've  marked  every answer option (without marking % sign), and it works. 
Thanks__

ScottTargetTestPrep · Answer

Great. Thanks for the update.

Ravixxx · Answer

Use Smart numbers.  
Suppose X = 100
Y = 90 - 18 = 72

130% of Y = 72+(3/10*72)= 93.6

Z= 93.6 + (1/4*93.6)= 117

Finally we have all numbers that we need
X = 100
Z = 117

Z = 117 % of X

Another Approach: 
If you want avoid multiplication and sum with decimals, the range of answer choice permits you to use  estimation . 
Y=72 
130 of Y = 94 ≈95
Z = 95 + (1/4*95) ≈ 95+ (1/5*95) 
Z = 95 + (19) = 114 ≈ 117

Answer D.

verydisco · Answer

There are two ways to solve this.

1. Solution By Ratios

y/x = 4/5*9/10 = 18/25.
z/y = y*5/4*13/10 = 13/8
z/x = z/y * y/x = 117/100 = 117%.

2. Solution by assuming values

Let x = 100, therefore y becomes 0.8*0.9*100 = 72. 
z = 72*5/4*13/10 = 117.
z/x = 117/100 = 117%

preetamsaha · Answer

y = 0.8 * 0.9x 
z = 1.25 * 1.3y
so,z = 1.25 * 1.3(0.72x)
z = (1.25 * 0.72) * 1.3x
z = 0.9 * 1.3x
z = 1.17x

z is 117% of x.
 correct answer D

Archit3110 · Answer

given info can be written as
y=0.8*0.9*x
y= .72x
z= 1.25*1.3*y
z= 1.625y
z= 1.625*.72*x
z/x = 1.17
option D

bumpbot · Answer

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If y is 20% less than 90% of x and z is 25% more than 130% of y, then

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