In 2003 Acme Computer priced its computers

[rohansingal]

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 the price for each of Acme Computer’s computers was five times the price for each of its printers. What was the ratio of its gross revenue from computers to its gross revenue from printers in 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

[Ben Ku]

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.

[acethegmat]

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?

[mschwrtz]

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.

[prapruet.w]

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??

[mschwrtz]

perfect

[gmatwork]

Although I do understand the explanation given here, I do have a slightly different question not directly related to this problem -

Stat 1 gives ratios of comps and printers in the two halves of the same year. Can we just take average of these two ratios to have an overall ratio (representative of the whole year)? Why will that be wrong?

For calculating weighted average ratio of the two given ratios in statement what weights will we need?

[jnelson0612]

Although I do understand the explanation given here, I do have a slightly different question not directly related to this problem -

Stat 1 gives ratios of comps and printers in the two halves of the same year. Can we just take average of these two ratios to have an overall ratio (representative of the whole year)? Why will that be wrong?

For calculating weighted average ratio of the two given ratios in statement what weights will we need?

No, that is what the GMAT test writers are hoping you will think! Let's review statement 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."

Let's assume that they actually sold 3 computers and 2 printers in the first half of the year, and 2 computers and 1 printer in the second half of the year. That would be a ratio of 5 computers to 3 printers for the year.

Now, let's assume that they actually sold 3000 computers and 2000 printers (3:2 ratio) in the first half and 2 computers and 1 printer in the second half (2:1 ratio). That would be 3002:2001 or about 3:2, which is not the same as 5:3 from the first example.

This is why averaging two ratios is so very dangerous!

[griffin.811]

Im trying to relate this question to the statement in the FDP strategy guide that states: When asked for the relative value of two pieces of a ratio, any statement that give relative values of any two pieces of the ratio will be sufficient.

We're looking for Rc/Rp --> (Pc*Qc)/(Pp*Qp) --> (5P*Qc)/(P*Qp)?



Because we already have the relative values of the prices (5:1) would a statement that gave us the relative values of the Quantities of each sold for the full year be sufficient here?

Thanks

[RonPurewal]

too abstract for me.
(i tried to read that and understand it ... really, i tried. couldn't make heads or tails of the statement after the colon.)

can you make that a little more specific, please?
numbers?

or, if there are examples of this particular principle anywhere in the strategy guides, could you please indicate where they are?

thank you.

[griffin.811]

Thanks for trying, and I apologize for being unclear.

On pg. 93 in the FDP strategy guide, there is a bold caption that says "If a data sufficiency question asks for the relative value of two pieces of a ratio, ANY statement that gives the relative value of ANY two pieces of the ratio will be sufficient."

The book uses a very simple example:

A Company sells only two kinds of pie: apple and cherry pie. What fraction of the total pies sold last month were apple pies?
(1)The company sold 460 pies last month
(2)The Company sold 30% more cherry pies than apple pies last month.

In the book example, statement (2) is sufficient because we are asked about the quantity of apple pies sold relative to the total amount sold (ratio: Apple/(Apple+Cherry)) and statement 2 provides a relationship between the quantities sold for both of the ratios components.

Im really just trying to figure out how the above example applies to this question, if at all.

This question asks for the ratio of computer revenues to printer revenues. I broke this down to the product of computer price and quantity of computers sold "over" the product of printer price and quantity of printers sold.

In the stem, however, we are given the relative values for prices (5:1). So it seems that if we had a statement that provided us with the relative values of the quantities of each, printers and computers sold for the entire year, we'd have enough information to answer the original question about the ratio of comp revenue to printer revenue, since we would then have a ratio of two components of the ratio, as mentioned on P.93 in the FDP guide.

Just wondering if this is the correct application of the caption on pg. 93.

Thanks

[RonPurewal]

ah. ok.

basically, here's the deal with that statement: there are lots of mathematical ways to express what we're calling "relative value" here.
e.g.,
fractions
percents
% increase/decrease from one to the other
ratios
one thing as a constant multiple of another thing
etc.

the point is that these things are all equivalent; if you have one of them, then you have all of them.

for instance, for an elementary-school class of boys and girls, all of the following are equivalent:
• girls make up 40% of the class
• boys make up 60% of the class
• there are 50% more boys than girls
• there are 33 1/3 % fewer girls than boys
• 2/5 of the class consists of girls
• 3/5 of the class consists of boys
• the ratio of girls to boys is 2 to 3
• the number of boys is 1.5 times the number of girls
you get the point. if you know one of these, then you know them all.

[RonPurewal]

so, in response to your question, yes: if you had two ratios for the entire year--one for the numbers of units sold, the other for prices--then, sure, you'd have the revenue ratio.

(this is also just a simple algebraic substitution. if the price of item #1 is K times the price of item #2, then the prices are Kp and p, respectively; if the number of units of #1 sold was L times the number of units of #2 sold, then those numbers are Lq and q, respectively. thus, the revenues are KLpq and pq, respectively; you're just multiplying the constant ratios together.
...which makes perfect sense, since revenue is just the product of those two parameters.)

[griffin.811]

Thanks!

[RonPurewal]

you're welcome.