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# In a group of 60 children, 7/12 are girls, 2/3 are right-handed, and 2

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Joined: 02 Nov 2016
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In a group of 60 children, 7/12 are girls, 2/3 are right-handed, and 2  [#permalink]

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04 Mar 2019, 14:32
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Difficulty:

45% (medium)

Question Stats:

71% (01:52) correct 29% (02:20) wrong based on 38 sessions

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In a group of 60 children, $$\frac{7}{12}$$ are girls, $$\frac{2}{3}$$ are right-handed, and $$\frac{2}{5}$$ are right-handed girls. How many of the children are left-handed boys?

A. 36
B. 24
C. 19
D. 16
E. 9

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Posts: 3074
Re: In a group of 60 children, 7/12 are girls, 2/3 are right-handed, and 2  [#permalink]

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04 Mar 2019, 23:16
1

Solution

Given:
In a group of 60 children,
• $$\frac{7}{12}$$ are girls
• $$\frac{2}{3}$$ are right-handed
• $$\frac{2}{5}$$ are right-handed girls

To find:
• The number of left-handed boys present in the group

Approach and Working:
Individual number of boys and girls:
• Girls = $$60 * \frac{7}{12} = 35$$
• Hence, boys = 60 – 35 = 25

Among the right-handed children,
• Total = $$60 * \frac{2}{3} = 40$$
• Girls = $$60 * \frac{2}{5} = 24$$
• Hence, boys = 40 – 24 = 16

So, the number of left-handed boys = total boys – right-handed boys = 25 – 16 = 9

Hence, the correct answer is option E.

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Joined: 14 May 2018
Posts: 96
Location: India
Concentration: Finance, Entrepreneurship
GMAT 1: 710 Q49 V38
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Re: In a group of 60 children, 7/12 are girls, 2/3 are right-handed, and 2  [#permalink]

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04 Mar 2019, 23:40
7/12 ARE GIRLS ==>35 girls (i.e. 25 are boys)....(i)
2/3 are right handed ==> 40 children (girls+boys) are right handed ...(ii)
2/5 are right handed girls ==>24 right handed children are grils (i.e. 16 right handed children are boys)....(iii)

from (i) and (iii), 9 boys are left handed

Ans:E
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Re: In a group of 60 children, 7/12 are girls, 2/3 are right-handed, and 2  [#permalink]

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04 Mar 2019, 23:52
In a group of 60 children, $$\frac{7}{12}$$ are girls, $$\frac{2}{3}$$ are right-handed, and $$\frac{2}{5}$$ are right-handed girls. How many of the children are left-handed boys?

A. 36
B. 24
C. 19
D. 16
E. 9

From the question we can deduce the following information (info in red can be deduced):

Total number of people = 60

Girls Boys Total
Right 24 16 40
Left 11 9 20
Total 35 25

Hence E is the correct answer.
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Re: In a group of 60 children, 7/12 are girls, 2/3 are right-handed, and 2  [#permalink]

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06 Mar 2019, 02:08
In a group of 60 children, $$\frac{7}{12}$$ are girls, $$\frac{2}{3}$$ are right-handed, and $$\frac{2}{5}$$ are right-handed girls. How many of the children are left-handed boys?

A. 36
B. 24
C. 19
D. 16
E. 9

total = 60
girls = 60*7/12 = 35 and boys = 25
right hand children = 2/3 * 60 = 40
and girls RH = 2*60/5 = 24
Boys RH = 40-24 ; 16
so LH Boys = 25-16 ; 9
IMO E
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Re: In a group of 60 children, 7/12 are girls, 2/3 are right-handed, and 2   [#permalink] 06 Mar 2019, 02:08
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