Ratio Question.

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carllecat: Master | Next Rank: 500 Posts; Posts: 131; Joined: Thu Feb 21, 2008 7:13 pm; Location: Canada; Thanked: 3 times; GMAT Score:590

by carllecat » Wed Feb 11, 2009 12:12 pm

The current ratio of boys to girls at a certain school is 2 to 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

I do not exactly know where to start. Any shortcuts?

Thanks,

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Source: Beat The GMAT — Problem Solving | Wed Feb 11, 2009 12:12 pm

carllecat: Master | Next Rank: 500 Posts; Posts: 131; Joined: Thu Feb 21, 2008 7:13 pm; Location: Canada; Thanked: 3 times; GMAT Score:590

by carllecat » Wed Feb 11, 2009 12:13 pm

The correct answer id E) 108

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Stuart@KaplanGMAT: GMAT Instructor; Posts: 3225; Joined: Tue Jan 08, 2008 2:40 pmFollowed by: 614 members; Location: Toronto; Thanked: 1710 times; GMAT Score:800

Re: Ratio Question.

by Stuart@KaplanGMAT » Wed Feb 11, 2009 12:20 pm

carllecat wrote:The current ratio of boys to girls at a certain school is 2 to 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

I do not exactly know where to start. Any shortcuts?

Thanks,

Let's set up our ratios:

B/G = 2/5

and

(B+12)/G = 4/9

we have 2 equations and 2 unknowns, we can solve.

Cross multiplying the first equation, we get:

5B = 2G
5B/2 = G

Cross multiplying the second equation, we get:

9B + 108 = 4G

Subbing the value for G into the second equation:

9B + 108 = 4(5B/2)
9B + 108 = 10B
108 = 10B - 9B
108 = B

done!

Quick (and of course accurate) manipulation of equations is an incredibly important skill for the GMAT. Setting up the equations is the "thinking" part of the question, but the mechanical manipulation is something you need to be able to get through very quickly so you have more thinking time on future questions.

Note that we could have also approached this question by backsolving (working backward from the answer choices), but because of the multiple ratios it would likely have been more time consuming than the algebraic approach.

Also note that even if we're completely stumped we can eliminate (a); boys make up 2 parts of the ratio and, since people are indivisible (i.e. there will always be an integer number of boys and girls), we need an even number of boys to ensure an integer number of girls.

Stuart Kovinsky | Kaplan GMAT Faculty | Toronto

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x2suresh: Master | Next Rank: 500 Posts; Posts: 258; Joined: Thu Aug 07, 2008 5:32 am; Thanked: 16 times

Re: Ratio Question.

by x2suresh » Wed Feb 11, 2009 12:59 pm

carllecat wrote:The current ratio of boys to girls at a certain school is 2 to 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

I do not exactly know where to start. Any shortcuts?

Thanks,

Before
2:5 = 18k:45k
After
4:9 = 20k:45k

20-18 =2k --> 12 -->k=6

total boys= 18*k=6*18 = 108

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carllecat: Master | Next Rank: 500 Posts; Posts: 131; Joined: Thu Feb 21, 2008 7:13 pm; Location: Canada; Thanked: 3 times; GMAT Score:590

Re: Ratio Question.

by carllecat » Wed Feb 11, 2009 1:18 pm

Stuart Kovinsky wrote:
carllecat wrote:The current ratio of boys to girls at a certain school is 2 to 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

I do not exactly know where to start. Any shortcuts?

Thanks,
Let's set up our ratios:

B/G = 2/5

and

(B+12)/G = 4/9

we have 2 equations and 2 unknowns, we can solve.

Cross multiplying the first equation, we get:

5B = 2G
5B/2 = G

Cross multiplying the second equation, we get:

9B + 108 = 4G

Subbing the value for G into the second equation:

9B + 108 = 4(5B/2)
9B + 108 = 10B
108 = 10B - 9B
108 = B

done!

Quick (and of course accurate) manipulation of equations is an incredibly important skill for the GMAT. Setting up the equations is the "thinking" part of the question, but the mechanical manipulation is something you need to be able to get through very quickly so you have more thinking time on future questions.

Note that we could have also approached this question by backsolving (working backward from the answer choices), but because of the multiple ratios it would likely have been more time consuming than the algebraic approach.

Also note that even if we're completely stumped we can eliminate (a); boys make up 2 parts of the ratio and, since people are indivisible (i.e. there will always be an integer number of boys and girls), we need an even number of boys to ensure an integer number of girls.

Setting up the equations IS my problem.
If I have the equation already setup in front of me, I will solve the problem with my eyes closed (almost). I really need to learn how to translate problems into equations. Any suggestion / advice?

Thanks for your help Stuart!.

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