Concept

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goyalsau: Legendary Member; Posts: 866; Joined: Mon Aug 02, 2010 6:46 pm; Location: Gwalior, India; Thanked: 31 times

by goyalsau » Wed Nov 10, 2010 2:14 am

The population of a town is 3,11,250. The ratio of the number of men and women is 1075 : 1000 . There are 24 % literates among men and 8 % literates among women. What is the total number of literate people in the town ? Approximately what percentage of the people is the town are illiterates ?

a. 48,900 72.6 %
b. 4,800 70 %
c. 50,700 83.75 %
d. 5,700 80%
e. None of these.

I don't have a query regarding this question. I have a question. Regarding some Concepts.

Population of town is 3,11,250 Now if i divide it by 2075 , I will 150

then 150 * 1075 : 150 * 1000

Now i know 24% of Men and 8 % of women are literate.

what i did was 24 % of 150 and 24 % of 1075 what i get was 36 * 258 ,
result is 9288

On the other hand 150 * 1075 = 161250
and 24% of 161250 is 38700.

So I want to know why is that so, Can any body please explain...
Please help guys...

Saurabh Goyal
[email protected]
-------------------------

EveryBody Wants to Win But Nobody wants to prepare for Win.

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Source: Beat The GMAT — Problem Solving | Wed Nov 10, 2010 2:14 am

beat_gmat_09: Master | Next Rank: 500 Posts; Posts: 437; Joined: Sat Nov 22, 2008 5:06 amFollowed by: 1 member; Location: India; Thanked: 50 times; GMAT Score:580

by beat_gmat_09 » Wed Nov 10, 2010 2:23 am

goyalsau wrote:The population of a town is 3,11,250. The ratio of the number of men and women is 1075 : 1000 . There are 24 % literates among men and 8 % literates among women. What is the total number of literate people in the town ? Approximately what percentage of the people is the town are illiterates ?

a. 48,900 72.6 %
b. 4,800 70 %
c. 50,700 83.75 %
d. 5,700 80%
e. None of these.

I don't have a query regarding this question. I have a question. Regarding some Concepts.

Population of town is 3,11,250 Now if i divide it by 2075 , I will 150

then 150 * 1075 : 150 * 1000

Now i know 24% of Men and 8 % of women are literate.

what i did was 24 % of 150 and 24 % of 1075 what i get was 36 * 258 ,
result is 9288

On the other hand 150 * 1075 = 161250
and 24% of 161250 is 38700.

So I want to know why is that so, Can any body please explain...
Please help guys...

You are trying to apply the distributive principle(to multiplication), which is true for additions, subtractions.
i.e. A(B+C) = AB + BC
but A (B*C) != A*B * A*C
take a example - A=2, B=1,C=3
This applies to additions.
2(1+3) = 2 *1 + 2*3 = 2 + 6 = 8, or the other way, solve the bracket first i.e. (1+3) = 4 , multiply now, 4*2 = 8

Below is what you are trying -
A(B*C), 2(1*3) = 2*1 * 2 * 3 = 12 ................................... Wrong
Correct-> A(B*C) = A * B * C = 2 * 1 * 3 = 6 .................... Correct.
HTH.

Hope is the dream of a man awake

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goyalsau: Legendary Member; Posts: 866; Joined: Mon Aug 02, 2010 6:46 pm; Location: Gwalior, India; Thanked: 31 times

by goyalsau » Wed Nov 10, 2010 9:24 am

beat_gmat_09 wrote:
goyalsau wrote:The population of a town is 3,11,250. The ratio of the number of men and women is 1075 : 1000 . There are 24 % literates among men and 8 % literates among women. What is the total number of literate people in the town ? Approximately what percentage of the people is the town are illiterates ?

a. 48,900 72.6 %
b. 4,800 70 %
c. 50,700 83.75 %
d. 5,700 80%
e. None of these.

I don't have a query regarding this question. I have a question. Regarding some Concepts.

Population of town is 3,11,250 Now if i divide it by 2075 , I will 150

then 150 * 1075 : 150 * 1000

Now i know 24% of Men and 8 % of women are literate.

what i did was 24 % of 150 and 24 % of 1075 what i get was 36 * 258 ,
result is 9288

On the other hand 150 * 1075 = 161250
and 24% of 161250 is 38700.

So I want to know why is that so, Can any body please explain...
Please help guys...
You are trying to apply the distributive principle(to multiplication), which is true for additions, subtractions.
i.e. A(B+C) = AB + BC
but A (B*C) != A*B * A*C
take a example - A=2, B=1,C=3
This applies to additions.
2(1+3) = 2 *1 + 2*3 = 2 + 6 = 8, or the other way, solve the bracket first i.e. (1+3) = 4 , multiply now, 4*2 = 8

Below is what you are trying -
A(B*C), 2(1*3) = 2*1 * 2 * 3 = 12 ................................... Wrong
Correct-> A(B*C) = A * B * C = 2 * 1 * 3 = 6 .................... Correct.
HTH.

thanks

Saurabh Goyal
[email protected]
-------------------------

EveryBody Wants to Win But Nobody wants to prepare for Win.

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MAAJ: Master | Next Rank: 500 Posts; Posts: 243; Joined: Sun Jul 12, 2009 7:12 amFollowed by: 2 members; Location: Dominican Republic; Thanked: 31 times; GMAT Score:480

by MAAJ » Wed Nov 10, 2010 9:47 am

Im curious about the answer 'cause I got 50,700/311,250 which is aprox 16% and I don't see it on the answer choices. Also, I had to spent a lot of time doing calculations, is there a way to solve it faster?

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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

by Stuart@KaplanGMAT » Wed Nov 10, 2010 2:14 pm

MAAJ wrote:Im curious about the answer 'cause I got 50,700/311,250 which is aprox 16% and I don't see it on the answer choices. Also, I had to spent a lot of time doing calculations, is there a way to solve it faster?

Not even remotely a real GMAT question - you'll never have to do those many calculations on the actual exam.

Stuart Kovinsky | Kaplan GMAT Faculty | Toronto

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MAAJ: Master | Next Rank: 500 Posts; Posts: 243; Joined: Sun Jul 12, 2009 7:12 amFollowed by: 2 members; Location: Dominican Republic; Thanked: 31 times; GMAT Score:480

by MAAJ » Wed Nov 10, 2010 2:36 pm

Stuart Kovinsky wrote:
MAAJ wrote:Im curious about the answer 'cause I got 50,700/311,250 which is aprox 16% and I don't see it on the answer choices. Also, I had to spent a lot of time doing calculations, is there a way to solve it faster?
Not even remotely a real GMAT question - you'll never have to do those many calculations on the actual exam.

Hehe, that's what I thought!!

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Ian Stewart: GMAT Instructor; Posts: 2623; Joined: Mon Jun 02, 2008 3:17 amFollowed by: 355 members; Location: Montreal; Thanked: 1090 times; GMAT Score:780

by Ian Stewart » Wed Nov 10, 2010 3:18 pm

MAAJ wrote:Im curious about the answer 'cause I got 50,700/311,250 which is aprox 16% and I don't see it on the answer choices. Also, I had to spent a lot of time doing calculations, is there a way to solve it faster?

It looks like you've done everything correctly - it's just that the question asks what percentage are *illiterate*, whereas 16% is the approximate percentage who are literate, so you need to subtract your answer from 100.

If this were a real GMAT question (it isn't, clearly), the fifth answer choice would never read 'none of the above', and we could very likely use some kind of estimation approach here. This is just a weighted average question. The ratio of men to women is 1075 to 1000, so we have roughly the same number of men and women. If 24% of men and 8% of women are literate, then the overall literacy rate would be 16% *if* we had exactly the same number of men and women. We have a few more men than women, so the literacy rate is just slightly higher than 16%, and the illiteracy rate is therefore just slightly less than 100-16 = 84%. That's enough to get to answer C or E here, at least, without doing any real calculation.

For online GMAT math tutoring, or to buy my higher-level Quant books and problem sets, contact me at ianstewartgmat at gmail.com

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