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

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Intern
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WE: Human Resources (Consulting)
In a certain class, the ratio of girls to boys is 5:4. How many girls [#permalink]

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22 Sep 2013, 13:57
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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
[Reveal] Spoiler: OA
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Re: In a certain class, the ratio of girls to boys is 5:4. How many girls [#permalink]

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22 Sep 2013, 18:50
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Dhairya275 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

Easy one ! but still not able to think any easy way out !

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.
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Re: In a certain class, the ratio of girls to boys is 5:4. How many girls [#permalink]

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22 Sep 2013, 23:37
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Dhairya275 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

Easy one ! but still not able to think any easy way out !

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.

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Re: In a certain class, the ratio of girls to boys is 5:4. How many girls [#permalink]

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01 Nov 2016, 05:08
stmt1. 4x+4 = (1.2) (4x) => 5=x

stmt2. no real numbers are given so it is not sufficient.
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Re: In a certain class, the ratio of girls to boys is 5:4. How many girls [#permalink]

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02 Jul 2017, 14:55
(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.

Doesn't 8/23 imply that there are 8 boys out of 23 total people? What am I missing?
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In a certain class, the ratio of girls to boys is 5:4. How many girls [#permalink]

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03 Jul 2017, 02:49
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azelastine wrote:
Doesn't 8/23 imply that there are 8 boys out of 23 total people? What am I missing?

The probability is a ratio. So, there might be 8 and 23 OR 16 and 46 OR 24 and 69...
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Re: In a certain class, the ratio of girls to boys is 5:4. How many girls [#permalink]

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09 Apr 2018, 21:34
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?

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Re: In a certain class, the ratio of girls to boys is 5:4. How many girls [#permalink]

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09 Apr 2018, 21:41
KNA32 wrote:
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?

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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Re: In a certain class, the ratio of girls to boys is 5:4. How many girls [#permalink]

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11 Apr 2018, 08:26
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
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Re: In a certain class, the ratio of girls to boys is 5:4. How many girls [#permalink]

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11 Apr 2018, 08:32
KNA32 wrote:
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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Re: In a certain class, the ratio of girls to boys is 5:4. How many girls   [#permalink] 11 Apr 2018, 08:32
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