I do not get this problem solving question! I need help

Hi Setarehrrr,

To start, when posting GMAT questions, you should post the full prompt - with the answer choices. Certain GMAT questions can be solved in Tactical ways by using the answer choices to your advantages (and this question IS one of them).

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?

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

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 TESTing VALUES 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.

Let's TEST Answer A:

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.

Final Answer: A

GMAT assassins aren't born, they're made,
Rich

Setarehrrr 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 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?

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

Say car sales in 1996 is $x, thus car sales in 1997 = x - 11% of x = x - 0.11x = 0.89x

Say truck sales in 1996 is $y, thus truck sales in 1997 = y + 7% of x = y + 0.07y = 1.07y

Thus, the total sales in 1996 = x + y, and the total sales in 1997 = 0.89x + 1.07y

It is given that the total sales in 1997 = Total sales in 1996 + 1% of Total sales in 1996

=> 0.89x + 1.07y = (x + y) + 1% of (x + y)

=> 0.89x + 1.07y = 1.01(x + y)

=> 89x + 107y = 101x + 101y; multyplying both the sides by 100

=> 6y = 12x

=> [spoiler]x/y = 1/2[/spoiler]

The correct answer: A

Hope this helps!

Relevant book: Manhattan Review GMAT Word Problems Guide

-Jay
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