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# The ratio of males to females in a particular school is 4:5. How many

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Re: The ratio of males to females in a particular school is 4:5. How many [#permalink]
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Ans- B

(1)INSUFFICIENT when female increases by 20%, male= 40 % of total.
$$\frac{m}{f}= \frac{4}{5}$$
$$\frac{m}{1.2f} = \frac{40}{60}=\frac{2}{3}$$ - of no use. since we need 2 equations to solve

(2) SUFFICIENT. if 10 more male students join , new ratio= \frac{9}{10}
$$\frac{(m+10)}{f} = \frac{9}{10}$$ - eq-1
$$\frac{m}{f}= \frac{4}{5}$$ - eq-2

Solving which we will get m= 80 and f= 100 ( not required to solve actually, but we should always reach to the final answers).

Hence. Solved.
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Re: The ratio of males to females in a particular school is 4:5. How many [#permalink]
from stem m/f = 4/5. Let x be the common multiplier, then

(1) 4x/(1.2*5x+4x) = 40/100 => 20x = 20x. This equation cannot be solved for x. Hence, INSUFFICIENT.

(2) (4x+10) /5x = 9/10. This equation can be solved for x and hence this is SUFFICIENT.

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Re: The ratio of males to females in a particular school is 4:5. How many [#permalink]
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Hi All,

Ratio questions can be solved in variety of ways and in a variety of "formats" (fractions, decimals, percents, etc.). If you're not great with ratios yet, then that's okay - a bit of "brute force" and TESTing VALUES can still get you the correct answer.

In this prompt, we're told that the ratio of males:females is 4:5. This does NOT tell us how many actual people there are. It DOES tell us that for every 4 males there will be 5 females. Furthermore, we know that the number of males MUST be a multiple of 4, the number of females MUST be an equivalent multiple of 5 and the total number of people MUST be an equivalent multiple of 9. The question asks how many males there are.

Fact 1: If the number of girls increased by 20%, then males would constitute 40% of this larger student body.

Let's TEST VALUES....

IF the original number of...
Males = 4
Females = 5
20% more females = +1
Males:Females is now 4:6 which is 4/10 of the total and equals 40%
The answer to the question is 4

IF the original number of...
Males = 8
Females = 10
20% more females = +2
Males:Females is now 8:12 which is 8/20 of the total and equals 40%
The answer to the question is 8

Fact 1 is INSUFFICIENT

Fact 2: If 10 more male students joined the school, the new ratio of males to females would be 9:10.

With the original ratio of males to females, we could have....
4 males and 5 females
8 males and 10 females
12 males and 15 females
Etc.

Adding 10 more males to each of these options would yield DIFFERENT results.....

4 males and 5 females becomes 14 males and 5 females = 14:5
8 males and 10 females becomes 18 males and 10 females = 18:10
12 males and 15 females becomes 22 males and 15 females = 22:15

Recognizing this, we will EVENTUALLY get to the ONE answer that creates a 9:10 ratio. It ends up being....

80 males and 100 females becomes 90 males and 100 females = 9:10
Fact 2 is SUFFICIENT

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Re: The ratio of males to females in a particular school is 4:5. How many [#permalink]
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Bunuel wrote:
The ratio of males to females in a particular school is 4:5. How many male students are there?

(1) If the number of girls increased by 20%, then males would constitute 40% of this larger student body.
(2) If 10 more male students joined the school, the new ratio of males to females would be 9:10.

Kudos for a correct solution.

MAGOOSH OFFICIAL SOLUTION:

We are given “ratio information” and we want actual numbers. To get counts, actual numbers of people, we need something besides more ratio information.

Statement #1 just gives us more “ratio information,” so we can’t solve for counts. This statement, alone and by itself, is not sufficient.

Statement #2 gives us some actual counts. Let M and F represent the current numbers of males and females in the school. We know M/F = 4/5 from the prompt. From this statement, we know (M + 10)/F = 9/10. Together, we have two equations for two unknowns, so we could solve for the values of M & F. This statement, alone and by itself, is sufficient.

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Re: The ratio of males to females in a particular school is 4:5. How many [#permalink]
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The problem gives us ratio of males to females in class; This ratio is 4:5. The problem wants to know the actual number of males.
Since the males to female relationship is given , we can say if females = 5x then males = 4x.
statement #1: - If females go up by 20% the males to students ratio is 40%.
Well let us increase females by 20%. 5x*6/5 = 6x. So males to student ratio is 4x/(6x+4x) = 4/10. At this point we can see that no more information is given on the actual number of students. This is not very helpful since it is true that if the original ratio is 4/5 then if we increase the denominator by 20%, then the ratio of males to total will be 4:10. So we end with a new ratio. Insufficient

statement #2:- gives a number 10
10+4x/5x= 9/10. We can solve for x which then gives us the # of males.
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The ratio of males to females in a particular school is 4:5. How many [#permalink]
Hi all,

This is a very good question to illustrate how GMAT would play with time managment (in terms of advanced candidates). An advanced candidate would solve it in 1.30-2.00 minutes by doing the maths, but an outstanding candidate would realize that the first choice keeps talking about relative terms, when the second does not

Therefore, we would quickly select B without spending much time
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Re: The ratio of males to females in a particular school is 4:5. How many [#permalink]
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