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# A certain company that sells only cars and trucks reported

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VP
Joined: 18 May 2008
Posts: 1131
A certain company that sells only cars and trucks reported  [#permalink]

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Updated on: 23 Dec 2013, 00:05
1
18
00:00

Difficulty:

35% (medium)

Question Stats:

75% (02:27) correct 25% (02:47) wrong based on 417 sessions

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A certain company that sells only cars and trucks reported that revenues from car sales in 1997 were down 11 percent from 1996 and revenues from truck sales were up 7 percent from 1996. If total revenues from car sales and truck sales in 1997 were up 1 percent from 1996, what is the ratio of revenue from car sales in 1996 to revenue from truck sales in 1996?

(A) 1:2
(B) 4:5
(C) 1:1
(D) 3:2
(E) 5:3

OPEN DISCUSSION OF THIS QUESTION IS HERE: a-certain-company-that-sells-only-cars-and-trucks-reported-97674.html

Originally posted by ritula on 19 Nov 2008, 00:30.
Last edited by Bunuel on 23 Dec 2013, 00:05, edited 2 times in total.
Renamed the topic, edited the question, added the OA and moved to PS forum.
Math Expert
Joined: 02 Sep 2009
Posts: 50042
Re: A certain company that sells only cars and trucks reported  [#permalink]

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23 Dec 2013, 00:06
10
12
A certain company that sells only cars and trucks reported that revenues from car sales in 1997 were down 11 percent from 1996 and revenues from truck sales were up 7 percent from 1996. If total revenues from car sales and truck sales in 1997 were up 1 percent from 1996, what is the ratio of revenue from car sales in 1996 to revenue from truck sales in 1996?
(A) 1:2
(B) 4:5
(C) 1:1
(D) 3:2
(E) 5:3

Let the revenue from cars in 1996 be $$c$$ and revenue from trucks in 1996 be $$t$$.

Total revenue in 1997 would be $$0.89c+1.07t$$.
Also as total revenue in 1997 were up 1 percent from 1996, then total revenue in 1997 would be $$1.01(c+t)$$.

Equate above two: $$0.89c+1.07t=1.01(c+t)$$ --> $$\frac{c}{t}=\frac{1}{2}$$.

OPEN DISCUSSION OF THIS QUESTION IS HERE: a-certain-company-that-sells-only-cars-and-trucks-reported-97674.html
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Intern
Joined: 05 Jul 2011
Posts: 4

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14 Jul 2011, 11:20
5
1
ritula wrote:
A certain company that sells only cars and trucks reported that revenues from car sales in 1997 were down 11% from 1996 and revenues from truck sales in 1997 were up 7 perent from 1996. If total revenues from car sales and truck sales in 1997 were up 1 % from 1996, what is the ratio of revenue from car sales in 1996 to revenue from truck sales in 1996?
1:2
4:5
1:1
3:2
5:3

T+C=R
89C+107T=101R
12C=6T
C/T=6/12=1:2

##### General Discussion
Director
Joined: 14 Aug 2007
Posts: 683

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19 Nov 2008, 00:43
1
ritula wrote:
A certain company that sells only cars and trucks reported that revenues from car sales in 1997 were down from 1996 and revenues from truck sales in 1997 were up 7 perent from 1996. If total revenues from car sales and truck sales in 1997 were up 1 % from 1996, what is the ratio of revenue from car sales in 1996 to revenue from truck sales in 1996?
1:2
4:5
1:1
3:2
5:3

Are you sure the question is correctly typed?

Approach

----- cars---Trucks -Total
1996- x----- y------- x+y
1997- x1---- y1-- x1+y1

x1= a*x .....(P)
y1= 1.07*y...(Q)

x1+y1/x+y = 1.01
solve using P and Q and find x/y
VP
Joined: 18 May 2008
Posts: 1131

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19 Nov 2008, 03:09
sorry I had missed the percent decrease in sales from 1996. I have edited my post.
Manager
Joined: 21 Jul 2009
Posts: 214
Location: New York, NY

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02 Sep 2009, 19:14
3
2
My approach to this is as follows:

The difference between the change in cars and the change in trucks is 7% - (-11%) = 18%.
If cars and trucks were at a 1:1 ratio then the overall change would be evenly spaced between -11% and +7%, which is -2%.
The overall change in this case is +1% which is 6% below trucks, and 12% above cars, which means the increase in truck sales dragged the overall percent twice as far as the car sales did. This means the ratio was 1:2 cars to trucks.
Veritas Prep GMAT Instructor
Joined: 16 Oct 2010
Posts: 8406
Location: Pune, India

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14 Jul 2011, 21:43
11
7
ritula wrote:
A certain company that sells only cars and trucks reported that revenues from car sales in 1997 were down 11% from 1996 and revenues from truck sales in 1997 were up 7 perent from 1996. If total revenues from car sales and truck sales in 1997 were up 1 % from 1996, what is the ratio of revenue from car sales in 1996 to revenue from truck sales in 1996?
1:2
4:5
1:1
3:2
5:3

This is a weighted average question. Average of -11% and +7% is +1%.
Using w1/w2 = (A2 - Aavg)/(Aavg - A1),
we get w1/w2 = (7 - 1)/(1- (-11)) = 6/12
Revenue from Car:Revenue from Trucks = 1:2

For explanation of the formula and other details, go to:
http://www.veritasprep.com/blog/2011/03 ... -averages/
http://www.veritasprep.com/blog/2011/04 ... ge-brutes/
_________________

Karishma
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Veritas Prep GMAT Instructor
Joined: 16 Oct 2010
Posts: 8406
Location: Pune, India

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02 Jan 2014, 22:59
1
VeritasPrepKarishma wrote:
ritula wrote:
A certain company that sells only cars and trucks reported that revenues from car sales in 1997 were down 11% from 1996 and revenues from truck sales in 1997 were up 7 perent from 1996. If total revenues from car sales and truck sales in 1997 were up 1 % from 1996, what is the ratio of revenue from car sales in 1996 to revenue from truck sales in 1996?
1:2
4:5
1:1
3:2
5:3

This is a weighted average question. Average of -11% and +7% is +1%.
Using w1/w2 = (A2 - Aavg)/(Aavg - A1),
we get w1/w2 = (7 - 1)/(1- (-11)) = 6/12
Revenue from Car:Revenue from Trucks = 1:2

For explanation of the formula and other details, go to:
http://www.veritasprep.com/blog/2011/03 ... -averages/
http://www.veritasprep.com/blog/2011/04 ... ge-brutes/

Responding to a pm:
Quote:
Hi, are you sure you set up the equation correctly? Because if we assume that cars are denoted with 1 and trucks with 2, and then we use the w1/w2 formula, does that formula not say to us "the ratio of cars to trucks is w1:w2".

But then, if we use the formula as you put it, we get this: w1/w2 = (A2 - Aavg)/(Aavg - A1) = (-11 - 1) / (1 - 7) = -12/-6 = 2/1 ---> ratio of cars to trucks is 2:1..

I understand the numbers I have put in the numerator and denominator are the polar opposite of those you used, but again: if 1 = cars, then according to your formula A2 = the percentage of trucks, and A1 = percentage of cars. And thus we have -11 - 1 in the numerator and 1 - 7 in the denominator.

Am I missunderstanding, or did you in fact simply just put the numbers for A1 and A2 in the wrong places?

Cars denoted by 1 and trucks by 2

w1/w2 = (A2 - Aavg)/(Aavg - A1)
Revenue of cars/Revenue of trucks = (Revenue change of trucks - Avg)/(Avg - Revenue change of cars)
Revenue of cars/Revenue of trucks = (7 - 1)/(1 - (-11))
Notice the highlighted part above. Revenue of trucks changes by +7% and that of cars by -11%.
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Karishma
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Posts: 8406
Location: Pune, India
Re: A certain company that sells only cars and trucks reported  [#permalink]

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13 Nov 2017, 23:41
1
VeritasPrepKarishma wrote:
A certain company that sells only cars and trucks reported that revenues from car sales in 1997 were down 11% from 1996 and revenues from truck sales in 1997 were up 7 perent from 1996. If total revenues from car sales and truck sales in 1997 were up 1 % from 1996, what is the ratio of revenue from car sales in 1996 to revenue from truck sales in 1996?
1:2
4:5
1:1
3:2
5:3

Responding to a pm:

Quote:
Please let me know why is my method incorrect??
now let the revenue of the car in 1996 be x then in 1997 it is 0.89x
now let the revenue of the truck in 1996 be y then in 1997 it is 1.07y
therefore the total revenue in 1996 = x+y and the total revenue in 1997 = 0.89x+1.07y
Now since there is a 1% rise in the total revenue , therefore 1.01(0.89x+1.07y)

The last step has the error.

New Revenue is 1% more than Old Revenue

0.89x+1.07y = (x + y) + 1% of (x + y)
0.89x+1.07y = 1.01 * (x + y)
0.12x = 0.06y
x/y = 1/2
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Re: A certain company that sells only cars and trucks reported &nbs [#permalink] 13 Nov 2017, 23:41
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