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A class consists of 12 girls and 20 boys. One quarter of the

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A class consists of 12 girls and 20 boys. One quarter of the

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Manhattan Prep

A class consists of 12 girls and 20 boys. One-quarter of the girls in the class have blue eyes. If a child is selected at random from the class, what is the probability that the child is a girl who does not have blue eyes?

A. 3/32
B. 9/32
C. 3/8
D. 23/32
E. 29/32

OA B

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AAPL wrote:
Manhattan Prep

A class consists of 12 girls and 20 boys. One-quarter of the girls in the class have blue eyes. If a child is selected at random from the class, what is the probability that the child is a girl who does not have blue eyes?

A. 3/32
B. 9/32
C. 3/8
D. 23/32
E. 29/32
$$? = P\left( {{\rm{girl}}\,{\rm{and}}\,\,{\rm{not}}\,\,{\rm{blue}}} \right)$$
$$20\,{\rm{boys}}\,\,\,{\rm{and}}\,\,\,12\,\,{\rm{girls}}\,\,\,\left\{ \matrix{
\,{1 \over 4}\left( {12} \right) = 3\,\,{\rm{girls}}\,\,{\rm{blue}} \hfill \cr
\,9\,\,\,{\rm{girls}}\,\,{\rm{not}}\,\,{\rm{blue}} \hfill \cr} \right.$$
$$? = {9 \over {12 + 20}} = {9 \over {32}}$$

This solution follows the notations and rationale taught in the GMATH method.

Regards,
Fabio.

_________________
Fabio Skilnik :: GMATH method creator ( Math for the GMAT)
English-speakers :: https://www.gmath.net
Portuguese-speakers :: https://www.gmath.com.br

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Hi All,

We're told that a class consists of 12 girls and 20 boys. One-quarter of the girls in the class have blue eyes. We're asked for the probability that a randomly selected child is a girl who does NOT have blue eyes. This question comes down to some basic organization and Arithmetic.

From the first sentence, we know that there are 12 girls and 20 boys.

With the second sentence, we can break the 12 girls down into 2 groups: those with blue eyes and those that don't have blue eyes:
(1/4)(12) = 3 with blue eyes
12 - 3 = 9 that don't have blue eyes

The number of girls who DON'T have blue eyes.... out of the total number of students in the class... is 9/32

Final Answer: B

GMAT assassins aren't born, they're made,
Rich

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Contact Rich at Rich.C@empowergmat.com

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