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Ratios & Proportions

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Ratios & Proportions

by carllecat » Wed Mar 11, 2009 5:22 am
Ok guys, I need your help to help me with the solution provided in a book. #193 in OG 11

In a certain calculus class, the ratio of the number of math majors to the number of students who are not math majors is 2 to 5. If 2 more math majors were to enter the class, the ratio would be 1 to 2. How many students are in the class?

A) 10
B) 12
C) 21
D) 28
E) 35
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by carllecat » Wed Mar 11, 2009 5:28 am
I want to know if this answer makes sense, because it does to me.

You can get the answer right in 15 seconds. The original ratio is 2 o 5 (ratio has a total of 7 parts). So the total number of students must be a multiple of 7. Cross off A and B. (MAKES SENSE TO ME)

Once we add 2 students, the ratio becomes 2 to 1 (ratio has a total of 3 parts). So if we add 2 to the total, the new number of students must be a multiple of 3. Of the remaining answer choices (21, 28 and 35), only D will get us a multiple of 3 after we add the 2 more students. (DOES NOT MAKE SENSE TO ME... ANSWER C - 21 IS ALSO A MULTIPLE OF 3 ISN'T IT?)
The book GMATfIX - The OG Companion suggests to guees answer D.
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by mjjking » Wed Mar 11, 2009 5:56 am
So, let's call:

M -> math majors
NM -> non math majors

we have that:

M/NM = 2/5 and that if M+2 --> M+2/NM = 1/2

hence 5M = 2NM and 2M+4 = 1NM

for substitution of NM into the first equation we can solve for M and get M=8, which means NM = 20. Total students = 28.

thanks
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by carllecat » Wed Mar 11, 2009 6:00 am
mjjking wrote:So, let's call:

M -> math majors
NM -> non math majors

we have that:

M/NM = 2/5 and that if M+2 --> M+2/NM = 1/2

hence 5M = 2NM and 2M+4 = 1NM

for substitution of NM into the first equation we can solve for M and get M=8, which means NM = 20. Total students = 28.

thanks
Thanks for the help. However, I am looking to verify if the shortcut explanation given ir right. Does that make sense to you?
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by sacx » Wed Mar 11, 2009 7:19 am
only D will get us a multiple of 3 after we add the 2 more students. (DOES NOT MAKE SENSE TO ME... ANSWER C - 21 IS ALSO A MULTIPLE OF 3 ISN'T IT?)

What you are missing here is that you need to add '2' before checking whether it is a multiple of 3

21 + 2 not a multiple of 3
28 + 2 multiple of 3
35 + 2 not a multiple of 3
SACX
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by carllecat » Wed Mar 11, 2009 7:50 am
Thanks Sacx it is not clear to me!

What a nice shortcut it is!

Thanks again.
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by carllecat » Mon Mar 16, 2009 2:02 pm
The current ratio of boys to girls at a certain school is 2to 5. If 12 additional boys were added to the school, the new ratio of boys to girls would be 4 to 9. How many boys currently attend the school?
(A) 27
(B) 48
(C) 54
(D) 72
(E) 108

For as far as I am concerned, no answer choices are multiples of 7. What am I missing here?

P.S.: I know how to solve the problem, just looking if the explained shortcup works good... and it doesn't.
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by carllecat » Mon Mar 16, 2009 2:03 pm
The answer is D) 108, which is not a multiple of 7 (ratio 2 to 5).
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by m&m » Mon Mar 16, 2009 4:44 pm
...I would suggest sticking to the full proof method of solving. It's only 1 formula, shouldn't take longer than 1 mins to solve.

(2x+12)/5x = 4/9 cross multiply and solve for x, x=54. Number of boys is 2*54=108


to solve in the other method, you need to remember we are solving for number of BOYS, not total students. So first clue tells us that boys are a multiple of 2 (ratio of 2/5), so A is out.

Second clue tells us that by adding 12 boys are a multiple of 4. So:
b) 48+12 = 60 (yes)
c) 54+12 = 66 (no)
d) 72+12= 84 (yes)
e) 108+12=120 (yes)

now you are left with 3 potential answers. Using your method there may be infinitely many potential solutions, I would recommend using the first method.
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