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

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

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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%.

(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

OA A

Source: Magoosh

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BTGmoderatorDC wrote:
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%.

(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
g:b = 5:4 = 10:8 = 15:12 = 20:16 = 25:20...

Statement 1:
In other words, 4 boys are equal to 20% of the current number of boys, implying the blue ratio above, since 20% of 20 boys = 4 boys.
In the blue ratio above, the number of girls = 25.
SUFFICIENT.

Statement 2:
Test the smaller red case above: 10 girls and 8 boys
Here, if the number of girls increases by 5, the total number of students increases from 18 to 23, with the result that P(boy) = 8/23.

Test the larger red case above: 20 girls and 16 boys
Here, if the number of girls increases by 10, the total number of students increases from 36 to 46, with the result that P(boy) = 16/46 = 8/23.

Since the number of girls can be different values -- 10 in the first case, 20 in the second case -- INSUFFICIENT.

The correct answer is A.

This problem is flawed.
Statement 1 indicates that g = 25.
If this number is increased by 50% -- as required by Statement 2 -- the result will be a noninteger value.
Thus, it is not possible in Statement 2 that g = 25.
As a result, there is no combination of values satisfies both statements.
In an official DS problem, there will always be at least one case that satisfies both statements.

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BTGmoderatorDC wrote:
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%.
(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
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

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