Population Ratio

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mytentoryours: Newbie | Next Rank: 10 Posts; Posts: 3; Joined: Thu Mar 07, 2013 4:00 am

by mytentoryours » Thu Mar 07, 2013 9:13 am

Hi there I remember coming across a question in my recent GMAT test which went as follows;

Population - 6,754,000
Ratio M:F - 14:9

The question was how many males are there and what percentage of the population are females?

Thank you so much.

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Source: Beat The GMAT — Data Sufficiency | Thu Mar 07, 2013 9:13 am

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Anurag@Gurome: GMAT Instructor; Posts: 3835; Joined: Fri Apr 02, 2010 10:00 pmFollowed by: 523 members; Location: Milpitas, CA; Thanked: 1854 times; GMAT Score:770

by Anurag@Gurome » Thu Mar 07, 2013 9:33 am

mytentoryours wrote:Hi there I remember coming across a question in my recent GMAT test which went as follows;

Population - 6,754,000
Ratio M:F - 14:9

The question was how many males are there and what percentage of the population are females?

Thank you so much.

I'm afraid you don't remember the numbers properly.
Because the total population (6,754,000) is not a multiple of (14 + 9) = 23.
Hence, the number of males and females will not be integer which is impossible.

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mytentoryours: Newbie | Next Rank: 10 Posts; Posts: 3; Joined: Thu Mar 07, 2013 4:00 am

by mytentoryours » Thu Mar 07, 2013 9:41 am

Apologies sir,

Would you be able to give me an example of how to solve the problem with a valid data set?

That would be greatly appreciated.

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GMAT/MBA Expert

Anurag@Gurome: GMAT Instructor; Posts: 3835; Joined: Fri Apr 02, 2010 10:00 pmFollowed by: 523 members; Location: Milpitas, CA; Thanked: 1854 times; GMAT Score:770

by Anurag@Gurome » Thu Mar 07, 2013 10:25 am

mytentoryours wrote:Would you be able to give me an example of how to solve the problem with a valid data set?

Let us take an example question like "The population of a town is 6,250,000. If the ratio of number of males to number of females in the town is 14:11, how many male are there in the town? Also, what percentage of the population are female?"

Ratio of male to female is 14:11
Hence, in each (14 + 11) = 25 people, there are 14 males and 11 females.
Hence, in 6,250,000 people, there are 6,250,000*14/25 males = 250,000*14 males = 3,500,000 males

Hence, number of males in the town is 3,500,000.

Finding the percentage of female in the town mean finding how many female are there in each 100 people in the town.

In each 25 people there are 11 females
Hence, in each 100 people, there are 100*11/25 females = 4*11 females = 44 females.

Hence, 44% of the population are female.

Hope that helps.

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mytentoryours: Newbie | Next Rank: 10 Posts; Posts: 3; Joined: Thu Mar 07, 2013 4:00 am

by mytentoryours » Thu Mar 07, 2013 11:14 am

Thank you sir, you're marvelous.

I couldn't have asked for a better reply, everything is much clearer now.

Have a good day!

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