Problem Solving

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

Yes, there's an algebraic way to do this, but here's my "common sense" approach:

First, since cars went down 11% and trucks went up 7%, but overall the two together went up 1%, we know that we must have sold more trucks. So, only choices A and B might work since C, D, and E make the ratio either equal or more cars.

Now that we've narrowed it down, plugging in the answer choices is easy. Let's plug in any two numbers with a ratio of 1:2 and see what happens.

I picked 100 (cars) and 200 (trucks), for a total of 300, since they are easy to work with.

If cars decrease 11%, we're down to 89. If trucks increase 7%, we're up to 214, for a total of 303. Since 303 is 1% higher than our old total of 300, (A) must be the right answer since it "fits" with the conditions in the problem.

Finding multiple, creative ways to solve problems is the key to the GMAT quant section.

Hope this helps!

imo A

Let the revenue from car sales in 1996 = X
Revenue from truck sales in 1996 = Y
Total Revenue in 1996 = Z = X+Y

Now, in 1997
Revenue from car sales in 1997 = 0.89X (11% less than revenue from cars in 1996)
Revenue from truck sales in 1997 = 1.07Y (7% more than revenue from trucks in 1996)
Total Revenue in 1997 = 1.01Z (as this is 1% greater than the total revenue in 1996)..................equation 1

Total revenue in 1997 also equals 0.89X + 1.07Y.........equation 2

Equating 1 and 2

we get:

0.89X + 1.07Y = 1.01Z (As Z = X + Y.. from above)

0.89X + 1.07Y =1.01(X + Y)
0.89X + 1.07Y = 1.01X + 1.01Y
1.07Y - 1.01Y = 1.01X - 0.89X
0.06Y = 0.12X
X/Y = 0.06/0.12
X/Y = 1/2

imo A

Let the revenue from car sales in 1996 = X
Revenue from truck sales in 1996 = Y
Total Revenue in 1996 = Z = X+Y

Now, in 1997
Revenue from car sales in 1997 = 0.89X (11% less than revenue from cars in 1996)
Revenue from truck sales in 1997 = 1.07Y (7% more than revenue from trucks in 1996)
Total Revenue in 1997 = 1.01Z (as this is 1% greater than the total revenue in 1996)..................equation 1

Total revenue in 1997 also equals 0.89X + 1.07Y.........equation 2

Equating 1 and 2

we get:

0.89X + 1.07Y = 1.01Z (As Z = X + Y.. from above)

0.89X + 1.07Y =1.01(X + Y)
0.89X + 1.07Y = 1.01X + 1.01Y
1.07Y - 1.01Y = 1.01X - 0.89X
0.06Y = 0.12X
X/Y = 0.06/0.12
X/Y = 1/2

i solved d same way...
but it takes more ten 2 mins..

Thanks Guys!

A

you have -11% cars and +7% trucs and both +1

so the distance between -11 to +1 is 12
and the distance between +1 to +7 is 6
the ratio between both is 6 to 12 (you cross the numbers) and that is the same to say 1:2
and just a few seconds to resolve.
I hope that the method help you.