If a child is randomly selected from Columbus elementary sch

Question

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

Bunuel · Accepted Answer

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.

Answer: C.

LinaNY · Answer

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.

Bunuel · Answer

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

Pmar2012 · Answer

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!

Bunuel · Answer

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.

chetan2u · Answer

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

BrentGMATPrepNow · Answer

Target question :    What is the probability that the child will be a boy?  
This is a good candidate for  rephrasing the target question . 
Let G = # of girls in the school
Let B = # of boys in the school
So, G + B = total number of children in the school 
So, P(selected child is a boy) = B/(G + B)
  REPHRASED target question :    What is the value of B/(G + B)?

The video posted below has tips on rephrasing the target question

Statement 1 : If 25 boys are removed from the school, the probability of selecting a boy will be 0.75.  
So, the number of boys = B - 25, and the total number of children = G + (B - 25)
We can write:  (B - 25)/(G + B - 25) = 3/4 
Since we have a linear equation with TWO variables, there's no way to solve this equation for B and G. So, statement 1 is NOT SUFFICIENT

If you're not convinced, consider these two CONFLICTING cases: 
 Case a : B = 28 and G = 1. After 25 boys leave, there are 3 boys and 1 girl. So, P(boy) = 3/4 = 0.75, which satisfies statement 1. In this case, the answer to the REPHRASED target question is  B/(G + B) = 28/(1 + 28) = 28/29 
 Case b : B = 31 and G = 2. After 25 boys leave, there are 6 boys and 2 girls. So, P(boy) = 6/8 = 0.75, which satisfies statement 1. In this case, the answer to the REPHRASED target question is  B/(G + B) = 31/(2 + 31) = 31/33 
Since we cannot answer the  REPHRASED target question  with certainty, statement 1 is NOT SUFFICIENT

Statement 2 : There are 35 more boys than there are girls. 
There are several CONFLICTING cases that satisfy statement 2. Here are two: 
 Case a : B = 36 and G = 1. In this case, the answer to the REPHRASED target question is  B/(G + B) = 36/(1 + 36) = 36/37 
 Case b : B = 37 and G = 2. In this case, the answer to the REPHRASED target question is  B/(G + B) = 37/(2 + 37) = 37/39 
Since we cannot answer the  REPHRASED target question  with certainty, statement 2 is NOT SUFFICIENT

Statements 1 and 2 combined    
From statement 1, we can write:  (B - 25)/(G + B - 25) = 3/4 
Cross multiply to get: 3(G + B - 25) = 4(B - 25) 
Expand: 3G + 3B - 75 = 4B - 100
Rearrange to get:  3G - B = - 25

From statement 2, we can write:  B = G + 35

At this point, we have two different linear equations with two variables. So, we COULD solve the system for B and G, which means we COULD answer the  REPHRASED target question  with certainty. 
So, the combined statements are SUFFICIENT

Answer: C

RELATED VIDEOE
 https://www.youtube.com/watch?v=MyG1K3ee69w

CEdward · Answer

St1 - If 25 boys are removed then the probability that a boy is chosen is 3/4

b - 25 / b + g = 3/4

1 equation, 2 unknowns, insufficient.

St2 - There are 35 more boys than girls.

b = 35 + g

Clearly insufficient.

st1 + st2 
Sufficient

C.

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If a child is randomly selected from Columbus elementary sch

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