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In year Y imported machine tools accounted for 25 percent of total mac

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In year Y imported machine tools accounted for 25 percent of total mac  [#permalink]

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New post 12 Nov 2019, 01:02
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Competition Mode Question



In year Y imported machine tools accounted for 25 percent of total machine-tools sales in the United States, and Japanese imports accounted for 45 percent of the sales of imported machine tools. If the total sales of machine tools imported from Japan that year was x billion dollars, then the total sales of all machine tools in the United States was how many billion dollars?


A. \(\frac{9x}{80}\)

B. \(\frac{13x}{20}\)

C. \(\frac{80}{9x}\)

D. \(\frac{20x}{13}\)

E. \(\frac{80x}{9}\)


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Re: In year Y imported machine tools accounted for 25 percent of total mac  [#permalink]

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New post 12 Nov 2019, 01:33
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In year Y imported machine tools accounted for 25 percent of total machine-tools sales in the United States, and Japanese imports accounted for 45 percent of the sales of imported machine tools. If the total sales of machine tools imported from Japan that year was x billion dollars, then the total sales of all machine tools in the United States was how many billion dollars?

Let total sales of all machine tools in the United States = y
imported machine tool = y/4
Japanese imports = 45/100 * y/4 = 9y/80
As given Japanese imports = x
So, x= 9y/80
hence y = 80x/9

Answer E
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Re: In year Y imported machine tools accounted for 25 percent of total mac  [#permalink]

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New post 12 Nov 2019, 02:13
1
from given info
45% of 25% of total sales = x
45*25/10000 = x
80*x/9
IMO E

In year Y imported machine tools accounted for 25 percent of total machine-tools sales in the United States, and Japanese imports accounted for 45 percent of the sales of imported machine tools. If the total sales of machine tools imported from Japan that year was x billion dollars, then the total sales of all machine tools in the United States was how many billion dollars?


A. 9x/80

B. 13x/20

C. 80/9x

D. 20x/13

E. 80x/9
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Re: In year Y imported machine tools accounted for 25 percent of total mac  [#permalink]

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New post 12 Nov 2019, 02:28
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In year Y imported machine tools accounted for 25 percent of total machine-tools sales in the United States, and Japanese imports accounted for 45 percent of the sales of imported machine tools. If the total sales of machine tools imported from Japan that year was x billion dollars, then the total sales of all machine tools in the United States was how many billion dollars?

A. \(\frac{9x}{80}\)
B. \(\frac{13x}{20}\)
C. \(\frac{80}{9x}\)
D. \(\frac{20x}{13}\)
E. \(\frac{80x}{9}\)

Let total sales = S

Now portion of Imports = 25% of S
Portion of Japanese imports in total imports = 45% of 25% of S
x = 0.45 * 0.25 * S
S = \(\frac{x }{0.45 * 0.25}\)
= \(\frac{80x }{ 9}\)

Answer E.
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Re: In year Y imported machine tools accounted for 25 percent of total mac  [#permalink]

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New post 12 Nov 2019, 03:04
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the total sales of all machine tools in the United States be a

From given we can conclude that, x=45/100(25a/100) = 9a/80
So a=80x/9

OA:E
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Re: In year Y imported machine tools accounted for 25 percent of total mac  [#permalink]

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New post 12 Nov 2019, 03:20
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Quote:
In year Y imported machine tools accounted for 25 percent of total machine-tools sales in the United States, and Japanese imports accounted for 45 percent of the sales of imported machine tools. If the total sales of machine tools imported from Japan that year was x billion dollars, then the total sales of all machine tools in the United States was how many billion dollars?

A. 9x/80
B. 13x/20
C. 80/9x
D. 20x/13
E. 80x/9


imported=0.25total
0.45*imported=x
0.45(0.25total)=x
total=x/0.25*0.45
total=x/(1/4)(9/20)
total=80x/9

Ans (E)
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Re: In year Y imported machine tools accounted for 25 percent of total mac  [#permalink]

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New post 12 Nov 2019, 06:13
1
Let total machine-tools be "TM".
Quote:
Imported machine tools accounted for 25 percent of total machine-tools sales in the United States


25% TM = Imported machine tools

Quote:
Japanese imports accounted for 45 percent of the sales of imported machine tools


45% * 25% TM = Japanese imports

Quote:
the total sales of machine tools imported from Japan that year was x billion dollars


45% * 25% TM = x

Quote:
the total sales of all machine tools in the United States was how many billion dollars?


Basically what is "TM"?
(45/100) * (25/100) TM = x (Cross multiply and cancel the values)
TM = (80*x)/9 Therefore, the answer is option E.

Please correct me if I am wrong.
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Re: In year Y imported machine tools accounted for 25 percent of total mac  [#permalink]

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New post 12 Nov 2019, 12:06
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Let total machine-tools sales in the United States be Z & imported machine tool be Y

\(Y = \frac{1}{4}*Z\)
\(X= \frac{45}{100}*Y\)

Therefore \(X= \frac{45}{100}*\frac{1}{4}*Z\)

i.e Z=\(\frac{80}{9} *x\)

Answer is E
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Re: In year Y imported machine tools accounted for 25 percent of total mac  [#permalink]

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New post 12 Nov 2019, 13:03
1
Let total machine sales be z.
Then we know that 0.25z=total machine imports into US that year.
In addition, we know that 45% of that total imports came from Japan.
Hence Japanese machine tools imports =0.45*0.25z
=9/20 * 1/4 z
= 9z/80
But we know from the question stem that the total Japanese machine tools imports =x
Hence x=9z/80
Implying z = 80x/9

The right answer is option E.

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Re: In year Y imported machine tools accounted for 25 percent of total mac  [#permalink]

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New post 12 Nov 2019, 23:02
1
Let the total sales of machine tools in USA = y

Imported machine tools = 25% of y = y/4

Japanese imports accounted for 45% of imported machine tools = 45% of y/4 = x
—> 45/100*y/4 = x
—> 9y/80 = x
—> y = 80x/9

IMO Option E

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Re: In year Y imported machine tools accounted for 25 percent of total mac  [#permalink]

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New post 17 Nov 2019, 20:20
Bunuel wrote:

Competition Mode Question



In year Y imported machine tools accounted for 25 percent of total machine-tools sales in the United States, and Japanese imports accounted for 45 percent of the sales of imported machine tools. If the total sales of machine tools imported from Japan that year was x billion dollars, then the total sales of all machine tools in the United States was how many billion dollars?


A. \(\frac{9x}{80}\)

B. \(\frac{13x}{20}\)

C. \(\frac{80}{9x}\)

D. \(\frac{20x}{13}\)

E. \(\frac{80x}{9}\)


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Let the total sales of all machine tools in the U.S. = m billion dollars. Then the total sales of the imported machine tools in the U.S. = 0.25m billion dollars. Since Japanese imports of x billion dollars accounted for 45 percent of the total sales of the imported machine tools in the U.S., we can create the equation:

x = 0.45(0.25m)

x = (9/20)(m/4)

x = 9m/80

80x/9 = m

Answer: E
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Re: In year Y imported machine tools accounted for 25 percent of total mac   [#permalink] 17 Nov 2019, 20:20
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