ratio

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aj5105: Legendary Member; Posts: 1169; Joined: Sun Jul 06, 2008 2:34 amFollowed by: 1 member; Thanked: 25 times

by aj5105 » Mon Jul 20, 2009 8:24 am

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 the number of boys in Class B is one less than the number of boys in Class A, and if the number of girls in Class B is two less than the number of girls in Class A, how many girls are in Class A?

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12

I got answer without using the ratio 17:22.

4y = 3x -1
5y = 4x -2

solve and answer. please validate my method.

Source: Beat The GMAT — Problem Solving | Mon Jul 20, 2009 8:24 am

truplayer256: Master | Next Rank: 500 Posts; Posts: 392; Joined: Thu Jan 15, 2009 12:52 pm; Location: New Jersey; Thanked: 76 times

by truplayer256 » Mon Jul 20, 2009 8:44 am

Class A: B/G=3/4

Class B: b/g=4/5

B+b/G+g=17/22

b=B-1

g=G-2

2B-1/2G-2=17/22

4B=3G

2B=3G/2

3G/2-1/2G-2=17/22

33G-22=34G-34

G=12

E

I don't really understand the method that you used.

shibal: Master | Next Rank: 500 Posts; Posts: 345; Joined: Wed Mar 18, 2009 6:53 pm; Location: Sao Paulo-Brazil; Thanked: 12 times; GMAT Score:660

by shibal » Mon Jul 20, 2009 8:48 am

OA???
IMO 12
I did it in 45 sec. By getting one of the the answers. As 3b=4g, i chose a multiple of 4, so 12 would feet... Backsolve and you get the answer... I think by doing setp-by-step ratio will take at least 1.30 min

raghavsarathy: Master | Next Rank: 500 Posts; Posts: 166; Joined: Sat Apr 18, 2009 10:41 pm; Thanked: 9 times; GMAT Score:770

Re: ratio

by raghavsarathy » Tue Jul 21, 2009 7:45 am

aj5105 wrote: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 the number of boys in Class B is one less than the number of boys in Class A, and if the number of girls in Class B is two less than the number of girls in Class A, how many girls are in Class A?

8
9
10
11
12

I got answer without using the ratio 17:22.

4y = 3x -1
5y = 4x -2

solve and answer. please validate my method.

Your method was awesome.. We really dont need the 17: 22 ratio. We have 2 ratios and we have 2 more conditions given to solve this. It is more than sufficient.

I used the 17/22 ratio and was wondering as to why they gave 2 relations between number of boys and girls of the two classes. I guess your method answers my question.

nitya34: Master | Next Rank: 500 Posts; Posts: 179; Joined: Tue Jan 08, 2008 7:23 pm; Thanked: 11 times; GMAT Score:590

by nitya34 » Tue Jul 21, 2009 8:09 am

Class A--(3k1,4k1) and Class B--(4k2,5k2)

eqn is

(3k1+4k2)/(4k2+5k2) = 17/22--------------(A)

given is 4k2+1=3k1; 5k2+2=4k1

now replace 4k2 and 5k2 into main Eqn (A)

and find 4k1=12(hence E)

Many of the great achievements of the world were accomplished by tired and discouraged men who kept on working.

nitya34: Master | Next Rank: 500 Posts; Posts: 179; Joined: Tue Jan 08, 2008 7:23 pm; Thanked: 11 times; GMAT Score:590

by nitya34 » Tue Jul 21, 2009 8:11 am

is this a GMAT type Q?

Many of the great achievements of the world were accomplished by tired and discouraged men who kept on working.

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