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# A certain company that sells only cars and trucks reported that revenu

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Re: A certain company that sells only cars and trucks reported that revenu [#permalink]
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Well, I cannot say its exactly a short method, but looking at the options one can surmise the ans.
Take 100 as base figure. Now try the options.
You can say that "The drop produced by less revenue by Car sales" MUST BE Surpassed by" The gain from Truck Sales". to achieve the Net Gain Effect.
i.e the proportion of Truck Revenue has to be greater than Car Revenue.

By this you can directly eliminate C,D and E. Now for remaining options,
Say we start from B. Then 4:5 will mean :
Rev 400 for cars and Rev 500 for Trucks
Calculate 11% @ 400 and 7% @500. We just have to ensure that
7% @ Trucks MUST BE > 11% @ Cars. Right !!!
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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

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Re: A certain company that sells only cars and trucks reported that revenu [#permalink]
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Drik wrote:
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 in 1997 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 in1996?
[*]1:2
[*]4:5
[*]1:1
[*]3:2
[*]5:3

Its 1/2
Consider the revenue from cars in 1996 x, which reduced to 0.89x in 1997.

Consider the revenue from trucks in 1996 y, which rose to 1.07y in 1997.

Another piece of information that is given is that the total revenue which was (x+y) in 1996, rose to 1.01(x+y) in 1997.
We are required to find x/y.

So using these information, we get $$0.89x +1.07y=1.01x +1.01y$$.
On solving we get x/y as 1/2.
+1A
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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:

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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Re: A certain company that sells only cars and trucks reported that revenu [#permalink]
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jpr200012 wrote:
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 us say that the revenues from selling cars was $100x and from trucks was$100y in 1996, total revenue: 100x + 100y

Revenue in 1997:
cars: $89x trucks:$ 107y total revenue: 89x + 107y = 101x + 101y

Solving the above total revenue equation we get: 12x = 6y i.e. x/y = 1/2

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Re: A certain company that sells only cars and trucks reported that revenu [#permalink]
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Re: A certain company that sells only cars and trucks reported that revenu [#permalink]
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The company sells only cars and trucks.
Let c = revenue from car sales in 1996
Let t = revenue from truck sales in 1996
Equating the total revenue in 1997 with the individual revenue from selling cars and trucks in 1997,
c(0.89) + t(1.07) = (c+t) (1.01)
Dividing throughout by t,
(c/t) (0.89) + 1.07 = (c/t + 1) (1.01)
=> (c/t) (0.12) = 0.06
=> (c/t) = 1/2

Option (A).
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A certain company that sells only cars and trucks reported that revenu [#permalink]
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getzgetzu wrote:
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 in 1997 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

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 another discussion on the same question, check: https://gmatclub.com/forum/a-certain-com ... ml#p541483

Originally posted by KarishmaB on 12 Mar 2014, 23:07.
Last edited by KarishmaB on 17 Oct 2022, 00:35, edited 1 time in total.
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Re: A certain company that sells only cars and trucks reported that revenu [#permalink]
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This is how my brain processed this one,

Step 1 --> Set up the equations.

In 1996: R = C+T
In 1997: 1.01R = .89C+1.07T

Remember we are looking for C/T.

Step 2 --> Substitute

1.01(C+T) = .89C+1.07T or,
1.01C + 1.01T = .89C+1.07T

Step 3 --> Solve

.12C = .06T
.12C/T = .06
C/T = .06/.12
C/T = 1/2 or 1:2

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Re: A certain company that sells only cars and trucks reported that revenu [#permalink]
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Car-------------------------------Truck
(-11%)-----------------------------(+7%)
-------------------------(+1%)-------- (Wtd Avg)
--------(12%)------------/----(6%)--
Thus ratio of Car Sales/Truck Sales = 6/12= 1/2

FWIW, this is one of the fastest and easiest way to solve such problems
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Re: A certain company that sells only cars and trucks reported that revenu [#permalink]
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Straight forward weighted average approach
Car Total Truck
-11------ 1------ 7
-----12------6----
So Car/ Truck = 6/12 = 1:2
Ans: A
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Re: A certain company that sells only cars and trucks reported that revenu [#permalink]
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This problem can be solved in less than one minutes by drawing a graph.
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File comment: This problem can be solved in less than one minute by drawing a graph.

Revenue.JPG [ 115.44 KiB | Viewed 51519 times ]

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Re: A certain company that sells only cars and trucks reported that revenu [#permalink]
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jpr200012 wrote:
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

We can let the revenue from car sales in 1996 = c and the revenue from truck sales in 1996 = t.

Since revenue from car sales in 1997 was down 11 percent from 1996, revenue from truck sales in 1997 was up 7 percent from 1996, and total revenue from car and trucks sales in 1997 was up 1 percent from 1996, we can create the following equation:

0.89c + 1.07t = 1.01(c + t)

89c + 107t = 101(c + t)

89c + 107t = 101c + 101t

6t = 12c

t = 2c

1/2 = c/t

Thus, the ratio of revenue of car sales to truck sales in 1996 is 1 : 2.

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Re: A certain company that sells only cars and trucks reported [#permalink]
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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 that revenu [#permalink]
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Here is an easy solution
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Re: A certain company that sells only cars and trucks reported that revenu [#permalink]
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Hi All,

We're told that 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 in 1997 were up 7 percent from 1996. If total revenues from car sales and trucks 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?

This prompt does NOT give us any information about the actual revenues for car sales or truck sales in 1996, so we'll end up using a mix of TESTing VALUES and TESTing THE ANSWERS in a moment. Based on the information in the prompt, if those two revenue values from 1996 were EQUAL though, then we can run a quick calculation on what the results would have been in 1997.

IF in 1996....
Car revenue = $100 Truck Revenue =$100
Total Revenue = $200 then the revenue in 1997 would have been... Car revenue = 11% drop =$89
Truck Revenue = 7% gain = $107 Total revenue =$196

This is a 2% DROP from the year before, but the prompt states that it's supposed to be a 1% GAIN. To 'offset' the 11% drop in car revenue, we clearly need there to be a LARGER amount of Truck revenue. So the ratio of car revenue to truck revenue must be SMALLER than 1:1 (e.g. 1:2, 2:3, 2:5 4:7, etc.). Thus, the correct answer is either A or B.

IF in 1996....
Car revenue = $100 Truck Revenue =$200
Total Revenue = $300 then the revenue in 1997 would have been... Car revenue = 11% drop =$89
Truck Revenue = 7% gain = $214 Total revenue =$303

This is a 1% gain from the year before - and this matches what we were told, so this MUST be the answer.

GMAT assassins aren't born, they're made,
Rich
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Re: A certain company that sells only cars and trucks reported [#permalink]
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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:

Responding to a pm:
Quote:
Could help me with my small doubt here? If I'm not wrong then this is the mixture (allegation) method right?

In your solution: 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

Would it make any difference if I were to write w1/w2 = (7 - 1)/( -11 - 1) = 6/-12 The sign of 12 would be negative.
Is it compulsory to subtract the decrease in % from the avg when there's a decrease?

Notice that the formula clearly states (Aavg - A1) in the denominator. So whatever Aavg is, from that you must subtract A1, whatever A1 is - positive or negative. If A1 is negative, you still need to subtract it from Aavg (effectively adding it).
The negative or positive signs of A1, A2 and Aavg do not change the formula.
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