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Math Expert V
Joined: 02 Sep 2009
Posts: 60687
In year Y imported machine tools accounted for 25 percent of total mac  [#permalink]

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Difficulty:   65% (hard)

Question Stats: 61% (02:32) correct 39% (02:30) wrong based on 82 sessions

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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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Retired Moderator V
Joined: 27 Oct 2017
Posts: 1406
Location: India
GPA: 3.64
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Re: In year Y imported machine tools accounted for 25 percent of total mac  [#permalink]

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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

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GMAT Club Legend  V
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Posts: 5738
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Concentration: Sustainability, Marketing
GPA: 4
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Re: In year Y imported machine tools accounted for 25 percent of total mac  [#permalink]

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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
Director  P
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GMAT 1: 580 Q43 V27
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Re: In year Y imported machine tools accounted for 25 percent of total mac  [#permalink]

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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 = $$\frac{x }{0.45 * 0.25}$$
= $$\frac{80x }{ 9}$$

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

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1
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
VP  P
Joined: 24 Nov 2016
Posts: 1124
Location: United States
Re: In year Y imported machine tools accounted for 25 percent of total mac  [#permalink]

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1
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)
Manager  B
Joined: 09 Jun 2019
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Re: In year Y imported machine tools accounted for 25 percent of total mac  [#permalink]

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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.
Dablu
Manager  G
Joined: 31 Oct 2015
Posts: 95
Re: In year Y imported machine tools accounted for 25 percent of total mac  [#permalink]

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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=$$\frac{80}{9} *x$$

Director  P
Joined: 18 May 2019
Posts: 665
Re: In year Y imported machine tools accounted for 25 percent of total mac  [#permalink]

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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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VP  V
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Posts: 1266
Location: India
Concentration: Entrepreneurship, Marketing
WE: Education (Education)
Re: In year Y imported machine tools accounted for 25 percent of total mac  [#permalink]

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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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Target Test Prep Representative V
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Re: In year Y imported machine tools accounted for 25 percent of total mac  [#permalink]

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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. $$\frac{80x}{9}$$

Are You Up For the Challenge: 700 Level Questions

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

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