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Percent

by madimo11 » Tue Jun 18, 2013 11:50 pm
Hi, I hope to reach a good help in this question

In a certain class, 1/5 of the boys are shorter than the shortest girl in the class and 1/3 of the girls are taller than the tallest boy in the class. If there are 16 students in the class and no two people have the same height, what percent of the students are taller than the shortest girl and shorter than the tallest boy?

the answers are

A) 25%
B) 50%
C) 62.5%
D) 66.7%
E) 75%

The right answer is C

I tried to solve it many times but unfortunately I never reached the right answer.....

My approach was this:

There are obviously 10 boys and 6 girls, hence the fractions are clear, since 1/5 of the boys are shorter than the shortest girl, then 4/5 of the boys are taller than the shortest girl so 8 of the boys are taller than the shortest girl + 5 of the girls are certainly taller than the shortest girl so we have 13/16 the ratio of the students who are taller than the shortest girl in the class. Now we want to know the number of the students who are shorter than the tallest boy, clearly 9 other boys are shorter than the tallest boy and 2/3 of the girls are shorter than the tallest boy so this give us again 13/16 students, what I did is that I multiplied 13/16 by 13/16 and I got 169/256 which is arround 66% and my answer was close to D, but this is not the exact answer of D either, so how do you solve such question?

I should be grateful for your help and thanks in advance
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by vivekchandrams » Wed Jun 19, 2013 2:34 am
Hi madimo11,

Looks like you are fine with Boys (b) = 10 and Girls (g) = 6.

So, let's start from here.

1/5 of the boys are shorter than the shortest girl = 10/5 = 2

1/3 of the girls are taller than the tallest boy = 6/3 = 2

Hence, the class structure would look something like this

b1 b2 g1 _ _ _ _ _ _ _ _ _ _ b10 g5 g6

Now, there are 10 students who are taller than g1 and shorter than b10 (the 'underscores' represent them).

Hence, the percentage would be

10/16 * 100 = 62.5%.

Hence, C.



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Last edited by vivekchandrams on Wed Jun 19, 2013 3:36 am, edited 1 time in total.
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by dhiren8182 » Wed Jun 19, 2013 3:34 am
HI ,
how did you figured out about 10 b and 6g?
Thanks
Dhiren
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by vivekchandrams » Wed Jun 19, 2013 3:43 am
The question says 1/5 of boys and 1/3 of girls.

The number of boys has to be only whole numbers and not decimals.

Hence the number of boys must be a multiple of 5 and girls a multiple of 3.

And b + g = 16

So the values of b and g satisfying all the conditions are b = 10 and g = 6.


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by GMATGuruNY » Wed Jun 19, 2013 3:44 am
madimo11 wrote:Hi, I hope to reach a good help in this question

In a certain class, 1/5 of the boys are shorter than the shortest girl in the class and 1/3 of the girls are taller than the tallest boy in the class. If there are 16 students in the class and no two people have the same height, what percent of the students are taller than the shortest girl and shorter than the tallest boy?

the answers are

A) 25%
B) 50%
C) 62.5%
D) 66.7%
E) 75%
Total students = 16.
1/5 of the boys implies that the number of boys must be a multiple of 5:
5 boys, 10 boys, or 15 boys.
1/3 of the girls implies that the number of girls must be a multiple of 3:
3 girls, 6 girls, 9 girls, 12 girls, or 15 girls.
Only one combination works:
10 boys + 6 girls = 16 students.

FAVORABLE students are taller than the shortest girl and shorter than the tallest boy.

Favorable boys:
In ascending order of height, let the 10 boys be A, B, C, D, E, F, G, H, I, J.
1/5 of the boys are shorter than the shortest girl.
Since (1/5)10 = 2, the 2 shortest boys -- A and B -- are shorter than the shortest girl.
Thus, the remaining 8 boys are TALLER than the shortest girl.
Of these 8 boys, the following are shorter than the tallest boy J:
C, D, E, F, G, H, I.
Total favorable boys = 7.

Favorable girls:
In ascending order of height, let the 6 girls be R, S, T, U, V, W.
1/3 of the girls are taller than the tallest boy.
Since (1/3)6 = 2, the 2 tallest girls -- V and W -- are taller than the tallest boy.
Thus, the remaining 4 girls are SHORTER than the tallest boy.
Of these 4 girls, 3 are taller than the shortest girl R:
S, T, U.
Total favorable girls = 3.

Thus:
(total favorable students)/(total students) * 100 = (7+3)/16 * 100 = 62.5%.

The correct answer is C.
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by sy323 » Thu Jun 20, 2013 7:52 am
OP: You are really close. In your solutions when you found the ratio of all students taller than the shortest girl to be 13/16. You then just need to take out the 3 people shorter than then tallest boy which are 2 girls and the tallest boy himself. 13-10. Which gives you 10/16 = 62.5%
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