CAT #5 - Ration Question (Class Act)

[skyjarrett12]

The question stem states "The ratio of boys to girls in Class A is 3 to 4. The ratio of boys to girls in Class B is 4 to 5. If the two classes were combined, the ratio of boys to girls in the combined class would be 17 to 22. If Class A has one more boy and two more girls than class B, how many girls are in Class A?"

I totally understand how to solve for the answer but noticed that the statement included in the question stem "If the two classes were combined, the ratio of boys to girls in the combined class would be 17 to 22" was not needed to solve the problem. I was just curious if this has been added in to complicate things or if there is a solution that involves using this piece of information?

Thanks!

[tim]

well it certainly doesn't complicate things beyond just wasting a few seconds of your time to read the problem. rest assured that this sort of thing rarely happens on the GMAT. most of the time you need to use all the information given in the problem. to answer your question though, i can't think of a good way to solve the problem that requires this information..

[skyjarrett12]

Makes sense. Thanks Tim

[tim]

:)

[griffin.811]

Any reason this problem doesn't work in reverse order, or is my math just off?

In the solution provided, we should start with the ratio given for class A, then subtract the students to arrive at the ratio for B, then set this equal to the ratio for class B which is 4/5.

I tried doing this the opposite way, working from class B's ratio to class A's ratio, setting this equal to A's ratio, and I get X=2.

Class B: B/G --> 4/5. (4x+1)/(5x+2)=(3/4) -->16x+4=15x+6 --> x=2.

where am I going wrong, or why doesn't this work in reverse order? Thanks!

[RonPurewal]

you're not going wrong anywhere.

the original numbers of boys and girls in class B are 4x and 5x. so, 8 and 10.

class A has one more boy and two more girls, so, 9 and 12.

if you're "going wrong" anywhere, i can tell you where: you're not writing down enough labels on your work.

if you'd made a chart--boys and girls on the columns, classes A and B on the rows, or vice versa--then there's no way you would have thought anything was wrong here. you'd have just plugged x = 2 back into the cells when you were done with the math.

ALWAYS write EVERYTHING down.
ALWAYS LABEL EVERYTHING.

[RonPurewal]

and, per the forum rules, we need the answer choices before we can continue discussing the problem.

[griffin.811]

Got it!

...and my apologies, hadn't realized the original post didn't contain the answers. For future discussions, the choice are:

(A)9 (B)10 (C)11 (D)12 (E)13

Thanks

[RonPurewal]

Got it!

...and my apologies, hadn't realized the original post didn't contain the answers. For future discussions, the choice are:

(A)9 (B)10 (C)11 (D)12 (E)13

Thanks

wow. seriously? those are the choices?

in that case, all we need is "The ratio of boys to girls in Class A is 3 to 4". this statement doesn't tell us much--but it tells us that the # of boys must be a multiple of 3, and, more importantly, that the # of girls must be a multiple of 4.

choice D is the only multiple of 4, so ... well, we're done. done!
finished, game over, end of story, go home.

needless to say, those answer choices could use a little editing.

[EricH836]

well it certainly doesn't complicate things beyond just wasting a few seconds of your time to read the problem. rest assured that this sort of thing rarely happens on the GMAT. most of the time you need to use all the information given in the problem. to answer your question though, i can't think of a good way to solve the problem that requires this information..

In response to the OP's question, you could use the new 17:22 ratio if you were to "draw out" the ratios of A and B to try to find combinations of A+B that equaled 17:22, right? For example:

Class A:
3:4
6:8
9:12
12:16

Class B:
4:5
8:10
12:15

Find ratios of A + B that equal 17:22:
Class A: 9:12
Class B: 8:10
These ratios add up to 17:22; thus, number of girls in Class A = 12

Is this logic OK to use, or did I just get lucky?

[RonPurewal]

^^ that sort of "trial and error" approach is perfectly valid -- as long as you still check the other conditions from the problem statement!
i.e., the FIRST "match" that you find won't necessarily be the correct answer to a problem, if there's also other information you have to check as well.

here, once you find a "match" for the 17:22 ratio, you still have to check this condition:
Class A has one more boy and two more girls than class B
here this is true (since 9 = 8 + 1, and 12 = 10 + 1), so, you've indeed found the correct answer. but, if this statement DIDN'T work, then you would have to keep searching for other matches, and testing those in the same way.

it's EXCELLENT to see you using a trial and error approach, though!
far too many users on this forum are singularly obsessed with trying to find algebraic approaches to everything -- all the time -- so, it's refreshing to see that you're trying to find other kinds of solutions. that's the most important key to doing extremely well on this exam.

[shenchun002]

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[Sage Pearce-Higgins]

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