Hi,

The following data sufficiency problem was giving me a bit of trouble. I can test numbers and see why solution A does not make sense, but can someone explain to me from a logical perspective why this answer (choice A) doesn't make sense (ie. is there a way I can just tell my looking at the given info that I can eliminate the answer?

In 2003 Acme Computer priced its computers five times higher than its printers. What is the ratio of its gross revenue for computers and printers respectively in the year 2003?

(1) In the first half of 2003 it sold computers and printers in the ratio of 3:2, respectively, and in the second half in the ratio of 2:1.

(2) It sold each computer for $1000.

Thanks,
Rohan

The key problem with statement (1) is that we don't have any comparison between what was sold in the first half and the second half of the year. For example, maybe it sold 100 total units the first half, while selling only selling 6 units the second half. This would result in a different answer than if the store sold 10 units the first half and 300 units the second half.

In a more algebraic approach,
Gross Revenue = Number of Sales * Unit Price

So if we look at the unit price, the price of computers was five times higher than its printers. So in terms of unit price, we can let p = price of printer, 5p = price of computer.

For the first half of the year, the ratio of computers to printers sold is 3:2, so we can say it sold 3x computers and 2x printers. For the second half of the year, the ratio of computers to printers sold is 2:1, so we can say it sold 2y computers and y printers.

During the year, the company sold 3x + 2y computers, so the gross profit for computers is (3x + 2y) * 5p. Likewise, the company sold 2x + y printers, so the gross profit for printers is (2x + y) * p. If you set up the ratio for the gross profits of computers and printers:

5p(3x+2y) / p(2x + y)
= (15x + 10y) / (2x + y)

You'll see that we cannot determine the exact value of the ratio, because we don't know x and y.

_________________
Ben Ku
Instructor
ManhattanGMAT

Ben Ku, I don't understand your explanation. Is there a std rule to ratios that this particular problem violates? I thought if ratios are given and we are able to find percentage with the given ratios.

Manually calculating, it is easy to detect the AC. But is there a rule that this particular problem does not conform to that makes it easy to choose the right answer?

Hmm... I don't think that I understand your question. What does "if ratios are given and we are able to find percentage with the given ratios" mean? Shouldn't there be another clause there?

Perhaps your point is that...

IF we have the ratio of # of computers sold to # of printers sold...

AND we have the ratio of price per computer to price per printer...

THEN we can calculate the ratio, revenue from computers to revenue from printers.

Right so far, but Ben's point is that we can't infer the the ratio of # of computers sold to # of printers sold for the year from the ratios for each half of the year.

Is there a general rule?, you ask. Sure, but I wouldn't call it simple. How about this, "You can't add ratios unless you know that each unit in each term of each ratio stands for the same thing." In this case, you don't know, for instance, that the value represented by a 3 in one ratio is three times as great as the value represented by a 1 in the other ratio. You don't know that the value represented by a 2 in one ratio is the same as the value represented by a 2 in the other.

If that doesn't mean anything to you, I suggest that you read the material on "unknown multipliers" in Chapter 3 of your Word Translations Strategy Guide.

I think I got it now

first I pick A and got wrong

so it should be like ben ku's idea

if 1st half sale 100 unit --> 60 coms and 40 printers
and then
2nd half sales only 6 unit --> 4 coms and 2 printers

let say price of printer is x then price of com will be 5x
then ration might be (64*5x)/(42x) = ~<8 times

if 2nd half sales only 120 unit --> 80 coms and 40 printers
then ration might be (140*5x)/(80x) = ~<9 times

Is it make sense??

perfect