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# The ratio of the number of students in an auditorium who are seniors..

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Director
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The ratio of the number of students in an auditorium who are seniors..  [#permalink]

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23 Jul 2018, 09:25
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Difficulty:

45% (medium)

Question Stats:

68% (02:09) correct 32% (02:04) wrong based on 179 sessions

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The ratio of the number of students in an auditorium who are seniors to the number of students in the auditorium who are not seniors is 7:5. How many students are there in the auditorium?

1. The ratio of the number of students who are seniors who are taking history to the number of students who are not seniors who are taking history is 21:5.

2. Of the students in the auditorium who are seniors, $$\frac{3}{5}$$ are taking history; of the students in the auditorium who are not seniors, $$\frac{1}{5}$$ are taking history; and the number of seniors in the auditorium who are taking history is 208 greater than the number of students in the auditorium who are not seniors and taking history.

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Manish

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The ratio of the number of students in an auditorium who are seniors..  [#permalink]

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23 Jul 2018, 10:27
1
The ratio of the number of students in an auditorium who are seniors to the number of students in the auditorium who are not seniors is 7:5. How many students are there in the auditorium?

1. The ratio of the number of students who are seniors who are taking history to the number of students who are not seniors who are taking history is 21:5.

Two ratios will not give any numeric value...
Insufficient

2. Of the students in the auditorium who are seniors, $$\frac{3}{5}$$ are taking history; of the students in the auditorium who are not seniors, $$\frac{1}{5}$$ are taking history; and the number of seniors in the auditorium who are taking history is 208 greater than the number of students in the auditorium who are not seniors and taking history.

Let the number $$s:ns = 7x:5x$$
So$$7x*\frac{3}{5}=5x*\frac{1}{5}+208...........\frac{21x}{5}-x=208......\frac{16x}{5}=208.....X=208*\frac{5}{16}=13*5=65$$
Total students =$$7x+5x=12x=12*65=780$$
Sufficient

B
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Re: The ratio of the number of students in an auditorium who are seniors..  [#permalink]

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23 Jul 2018, 12:27
CAMANISHPARMAR wrote:
The ratio of the number of students in an auditorium who are seniors to the number of students in the auditorium who are not seniors is 7:5. How many students are there in the auditorium?

1. The ratio of the number of students who are seniors who are taking history to the number of students who are not seniors who are taking history is 21:5.

2. Of the students in the auditorium who are seniors, $$\frac{3}{5}$$ are taking history; of the students in the auditorium who are not seniors, $$\frac{1}{5}$$ are taking history; and the number of seniors in the auditorium who are taking history is 208 greater than the number of students in the auditorium who are not seniors and taking history.

Let the # of students who are Seniors who are taking History = a

# of students who are Not Seniors who are taking History = b

# of students who are Seniors who have not taken History = c

# of students who are not Seniors & not taken History = d

Hence we have, # of Seniors = a + c & # of Non Seniors = b + d

We are asked to find a + b + c + d

Statement 1: a/b = 21/ 5, clearly not Sufficient.

Statement 2: a = 3/5*(a+c) & b = 1/5*(b+d).......(i)
Also a = b + 208...............................................(ii)

We get a/b = 21/5 from (i), & further using (ii), we can find value of a, hence value of b, c & d.

Statement 2 is Sufficient.

Thanks,
GyM
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Re: The ratio of the number of students in an auditorium who are seniors..  [#permalink]

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07 Feb 2019, 21:44
CAMANISHPARMAR wrote:
The ratio of the number of students in an auditorium who are seniors to the number of students in the auditorium who are not seniors is 7:5. How many students are there in the auditorium?

1. The ratio of the number of students who are seniors who are taking history to the number of students who are not seniors who are taking history is 21:5.

2. Of the students in the auditorium who are seniors, $$\frac{3}{5}$$ are taking history; of the students in the auditorium who are not seniors, $$\frac{1}{5}$$ are taking history; and the number of seniors in the auditorium who are taking history is 208 greater than the number of students in the auditorium who are not seniors and taking history.

S = Seniors, NS = Not Seniors.
Seniors Taking history = S TH, Seniors Not Taking History = NS TH

From 1, you can get multiple values for number of students, said that

Since it is a ratio, S/NS = 7:5, can take different values, which when used in S TH: NS TH = 21:5, can change the final value of number of students in the auditorium.

From 2 Of the students in the auditorium who are seniors, $$\frac{3}{5}$$ are taking history; of the students in the auditorium who are not seniors, $$\frac{1}{5}$$ are taking history; and the number of seniors in the auditorium who are taking history is 208 greater than the number of students in the auditorium who are not seniors and taking history.

We get a lot of information here
Seniors who are students, 3/5 TH.
Not seniors = 1/5 TH
S TH = 208 + NS TH

Now when we plot these in a 2*2 matrix, we definitely will get a unique value for number of students.

B
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Re: The ratio of the number of students in an auditorium who are seniors..   [#permalink] 07 Feb 2019, 21:44
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