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# If a child is randomly selected from Columbus elementary sch

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Intern
Joined: 06 Feb 2013
Posts: 22
If a child is randomly selected from Columbus elementary sch [#permalink]

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12 Oct 2013, 12:30
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45% (medium)

Question Stats:

64% (01:21) correct 36% (01:22) wrong based on 236 sessions

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If a child is randomly selected from Columbus elementary school, what is the probability that the child will be a boy?

(1) If 25 boys are removed from the school, the probability of selecting a boy will be 0.75

(2) There are 35 more boys than there are girls
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Joined: 02 Sep 2009
Posts: 45367
Re: If a child is randomly selected from Columbus elementary sch [#permalink]

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12 Oct 2013, 12:41
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If a child is randomly selected from Columbus elementary school, what is the probability that the child will be a boy?

$$P(b)=\frac{b}{b+g}=?$$

(1) If 25 boys are removed from the school, the probability of selecting a boy will be 0.75 --> $$\frac{b-25}{(b-25)+g}=\frac{3}{4}$$ --> $$b-3g=25$$. Not sufficient.

(2) There are 35 more boys than there are girls --> $$g=b-35$$. Not sufficient.

(1)+(2) We have two linear equation with two unknowns ($$b-3g=25$$ and $$g=b-35$$), thus we can solve for both and get the value of $$\frac{b}{b+g}$$. Sufficient.

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Re: If a child is randomly selected from Columbus elementary sch [#permalink]

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12 Oct 2013, 12:49
Bunuel wrote:

$$P(b)=\frac{b}{b+g}=?$$

Thanks, Bunuel.
Could you please clarify how the statement 1 "...the probability of selecting a boy will be 0.75" is different from the question itself "what is the probability that the child will be a boy". I'm stuck here because to me it looks like they provide the same information.
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Re: If a child is randomly selected from Columbus elementary sch [#permalink]

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12 Oct 2013, 12:51
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LinaNY wrote:
Bunuel wrote:

$$P(b)=\frac{b}{b+g}=?$$

Thanks, Bunuel.
Could you please clarify how the statement 1 "...the probability of selecting a boy will be 0.75" is different from the question itself "what is the probability that the child will be a boy". I'm stuck here because to me it looks like they provide the same information.

(1) says that "IF 25 boys are removed from the school, the probability of selecting a boy will be 0.75"
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Re: If a child is randomly selected from Columbus elementary sch [#permalink]

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12 Oct 2013, 12:56
Bunuel wrote:

(1) says that "IF 25 boys are removed from the school, the probability of selecting a boy will be 0.75"

Thanks Bunuel! I totally overlooked it.
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Joined: 23 Jan 2013
Posts: 6
Re: If a child is randomly selected from Columbus elementary sch [#permalink]

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08 Nov 2013, 05:33
Bunuel wrote:
If a child is randomly selected from Columbus elementary school, what is the probability that the child will be a boy?

$$P(b)=\frac{b}{b+g}=?$$

(1) If 25 boys are removed from the school, the probability of selecting a boy will be 0.75 --> $$\frac{b-25}{(b-25)+g}=\frac{3}{4}$$ --> $$b-3g=25$$. Not sufficient.

(2) There are 35 more boys than there are girls --> $$g=b-35$$. Not sufficient.

(1)+(2) We have two linear equation with two unknowns ($$b-3g=25$$ and $$g=b-35$$), thus we can solve for both and get the value of $$\frac{b}{b+g}$$. Sufficient.

Hi Bunuel,

Can you please shed some light on why it would not be correct to state the following:

For the statement 1, p(girl)=(g/(b-25+g))=0.25.

Assuming this inference is correct, we can find the number of boys using a two equation,two unknowns approach.

Thank you!
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Posts: 45367
Re: If a child is randomly selected from Columbus elementary sch [#permalink]

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08 Nov 2013, 05:48
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Pmar2012 wrote:
Bunuel wrote:
If a child is randomly selected from Columbus elementary school, what is the probability that the child will be a boy?

$$P(b)=\frac{b}{b+g}=?$$

(1) If 25 boys are removed from the school, the probability of selecting a boy will be 0.75 --> $$\frac{b-25}{(b-25)+g}=\frac{3}{4}$$ --> $$b-3g=25$$. Not sufficient.

(2) There are 35 more boys than there are girls --> $$g=b-35$$. Not sufficient.

(1)+(2) We have two linear equation with two unknowns ($$b-3g=25$$ and $$g=b-35$$), thus we can solve for both and get the value of $$\frac{b}{b+g}$$. Sufficient.

Hi Bunuel,

Can you please shed some light on why it would not be correct to state the following:

For the statement 1, p(girl)=(g/(b-25+g))=0.25.

Assuming this inference is correct, we can find the number of boys using a two equation,two unknowns approach.

Thank you!

Yes, it's correct but if you simplify it you'd still get the same equation: $$b-3g=25$$. Thus you'd still have only one equation with two unknowns.

Hope it's clear.
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child is randomly selected from Columbus elementary school [#permalink]

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10 Aug 2017, 12:30
If a child is randomly selected from Columbus elementary school, what is the probability that the child will be a boy?

(1) If 25 boys are removed from the school, the probability of selecting a boy will be 0.75

(2) There are 35 more boys than there are girls
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Re: child is randomly selected from Columbus elementary school [#permalink]

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10 Aug 2017, 19:33
fitzpratik wrote:
If a child is randomly selected from Columbus elementary school, what is the probability that the child will be a boy?

(1) If 25 boys are removed from the school, the probability of selecting a boy will be 0.75

(2) There are 35 more boys than there are girls

Hi..
For getting a ratio here, you require all terms with variable.
But here by first look, you have a term without variable so none can be sufficient individually but let's see

1) $$\frac{b-25}{b+g-25}=0.75=\frac{3}{4}...... 4b-100=3b+3g-75....b=25+3g$$
Ratio can't be found
Insufficient
2) b=g+35
Again ratio cannot be found
Insuff

Combined..
You can find values of b and g and thus get ratio or PROBABILITY
35+g=3g+25.....2g=10...G=5
b=35+5=40..
Probability of picking boy is b/t=40/40+5=8/9..
Suff
C
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Re: If a child is randomly selected from Columbus elementary sch [#permalink]

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10 Aug 2017, 22:08
fitzpratik wrote:
If a child is randomly selected from Columbus elementary school, what is the probability that the child will be a boy?

(1) If 25 boys are removed from the school, the probability of selecting a boy will be 0.75

(2) There are 35 more boys than there are girls

Merging topics. Please search before posting. Thank you.
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Re: If a child is randomly selected from Columbus elementary sch   [#permalink] 10 Aug 2017, 22:08
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