In a certain class, the ratio of girls to boys is 5:4. How many girls

In a certain class, the ratio of girls to boys is 5:4. How many girls are there?

(1) If four new boys joined the class, the number of boys would increase by 20%. This implies that 4 boys constitute for 20% of the original #of boys. Thus there are 20 boys in the class --> there are 25 girls in the class. Sufficient.

(2) If the number of girls increases by 50%, then after such an increase, the probability that a randomly chosen student would be a boy would be 8/23:

\(\frac{boys}{(girls*1.5+boys)}=\frac{8}{23}\);

\(\frac{4x}{(5x*1.5+4x)}=\frac{8}{23}\);

\(\frac{4x}{(11.5x)}=\frac{8}{23}\);

x cancels: \(\frac{4}{11.5}=\frac{8}{23}\). Not sufficient.

Answer: A.
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1) G/B = 5/4.
4x + 4 = 1.2 * 4x
You can find x and hence ans.

2) 8/23 = 4x/(9x +2.5x)
x will cancel.

So only A stands.

Given ratio of B/G = 5/4 .

Stmt 1 : B+ 4= 1.2 B ie B = 20 , can find out girls sufficient .

Stmt 2 : Probability boy would be selected after girls increase by 50 % = B / B + 1.5 G = 8/23 .
ie B/G = 4/5 . Not sufficient .

Hence answer is A

Could someone provide a more detailed explanation in regards to why Statement 2 is not sufficient?
First off, I wouldn't know how to approach statement 2.

Thanks!

The stem gives us the ratio: the ratio of girls to boys is 5:4. So, there are 5x girls and 4x boys, for some positive integer x,

The second statement also gives a ratio but in a different way: if the number of girls increases by 50%, then after such an increase, the probability that a randomly chosen student would be a boy would be 8/23.

This is basically the same info as we had from the stem. If the number of girls increases from 5x to 7.5x, then the probability that a randomly chosen student would be a boy would be (boys)/(new total) = 4x/(7.5x+4x) = 4x/11.5x = 8/23.

So, the second statement does not give us any info we did not know ourselves from the stem, which means that it's not sufficient.

Does this make sense?
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Bunuel,

Can we assume the ratio as 10x and 8x and then solve statement 2? That will be the only case where the given probability will hold true. Then the answer will be D.

hi, to find the total number of girls, we must calculate the value of x. in this case also (10x and 8x), value of x gets cancel out when we calculate the probability of selecting a boy from the given set of students.

(2) If the number of girls increases by 50%, then after such an increase, the probability that a randomly chosen student would be a boy would be 8/23 --> boys/(girls*1.5+boys)=8/23 --> 4x/(5x*1.5+4x)=8/23 --> 4x/(11.5x)=8/23 --> x cancels: 4/11.5=8/23. Not sufficient.

Answer: A.[/quote]


Doesn't 8/23 imply that there are 8 boys out of 23 total people? What am I missing?

Forget conventional ways of solving math questions. In DS, Variable approach is the easiest and quickest way to find the answer without actually solving the problem. Remember equal number of variables and independent equations ensures a solution.


Let \(b\) and \(g\) be the numbers of boys and girls, respectively.
\(b:g = 4:5\) or \(5b = 4g\).
There are 2 variables and 1 equation. Thus D is the answer most likely.

Condition 1)

From the condition 1), we have \(4 = \frac{1}{5b}\) or \(b = 20\).
Thus g = 25.
This is sufficient.

Condition 2)
We have \(\frac{b}{{b + 1.5g }} = \frac{8}{23}\) or \(23b = 8b + 12g\).
It is equivalent to \(15b = 12g\) or \(5b = 4g\) which is redundant since it is exactly same as the condition of the original question.
Thus this is not sufficient.

Therefore the answer is A.


-> For cases where we need 1 more equation, such as original conditions with “1 variable”, or “2 variables and 1 equation”, or “3 variables and 2 equations”, we have 1 equation each in both 1) and 2). Therefore, there is 59 % chance that D is the answer, while A or B has 38% chance and C or E has 3% chance. Since D is most likely to be the answer using 1) and 2) separately according to DS definition. Obviously there may be cases where the answer is A, B, C or E.

The probability is a ratio. So, there might be 8 and 23 OR 16 and 46 OR 24 and 69...
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For Statement (2) -

If you set it up as 1.5(5x) = 15/23, you can get a unique value for x and therefore a value for 5x (which is the ratio of girls). Why is that not sufficient?

Thanks very much in advance

What is the logic behind this?

We are told that if the number of girls increases by 50%, then after such an increase, the probability that a randomly chosen student would be a boy would be 8/23. So, it should be as shown in the solution above:

\(\frac{boys}{(girls*1.5+boys)}=\frac{8}{23}\).
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Bunuel - thanks for the response. My logic is as follows. Start with the following statement:

(2) If the number of girls increases by 50%, then after such an increase, the probability that a randomly chosen student would be a boy would be 8/23

If this is the case, then given that the original proportion of Girls to Boys is 5x : 4x, then girls have increased to 1.5*(5x). After this increase, the total probability that is would be a girl is 1 - 8/23, or 15/23.

As a result, I can set up the following equation below and solve for x, which will solve for the total number of girls?

1.5*(5x) = 15/23

You are making the same mistake...

15/23 as well as 8/23 represent probability, which is a ratio. The left hand side should be (girls)/(total) = 1.5*(5x)/(1.5*(5x) + 4x)
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Given: In a certain class, the ratio of girls to boys is 5:4.
Let G = number of girls in the class
Let B = number of boys in the class
We can write: G/B = 5/4
Cross multiply to get: 4G = 5B
Rearrange to get: 4G - 5B = 0

Target question: What is the value of G

Statement 1: If four new boys joined the class, the number of boys would increase by 20%.
Here's a word equation for this statement: (new boy population with 4 extra boys) = (old boy population increased by 20%)
In other words: B + 4 = B + (20% of B)
Or: B + 4 = B + 0.2B
Or: B + 4 = 1.2B
Subtract B from both sides: 4 = 0.2B
Solve: B = 4/(0.2) = 40/2 = 20
Once we know that B = 20, we can take 4G - 5B = 0 and plug in B = 20
We get: 4G - 5(20) = 0
Solve to get G = 25
The answer to the target question is G = 25
Since we can answer the target question with certainty, statement 1 is SUFFICIENT

Statement 2: If the number of girls increases by 50%, then after such an increase, the probability that a randomly chosen student would be a boy would be 8/23
So, 1.5G = the NEW number of girls
B = the number of boys
So, 1.5G + B = the NEW number of children.
So, P(selected child is a boy) = B/(1.5G + B)
We're told the probability is 8/23
So, we can write: B/(1.5G + B) = 8/23
Cross multiply to get: 8(1.5G + B) = 23B
Expand to get: 12G + 8B = 23B
Subtract 23B from both sides to get: 12G - 15B
Divide both sides by 3 to get: 4G - 5B = 0
Hmmm, we ALREADY knew that 4G - 5B = 0
So, statement 2 does NOT add any new information.
As such, statement 2 is NOT SUFFICIENT

Answer: A

Cheers,
Brent

In such a question, no math is required. Instead, realize that there are 2 types of information: ratio vs. value information. And further notice that percentage, fraction, probability, ratio, and information about multiples, are all the same type of information in different formats. The key idea is that, in order to get from a ratio to a value, they need to give us a value.


Gives a ratio, asks for a value. In order for a statement to be sufficient, it must give us a value.


Gives us a value (four), and it relates to the ratio we know about. Sufficient.


Gives us only ratio/percentage information. There is no value here, thus this is NOT sufficient.

Answer A