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# In a history class that consisted of 30 students, the number

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In a history class that consisted of 30 students, the number [#permalink]  09 May 2018, 10:00
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Question Stats:

63% (00:48) correct 36% (01:44) wrong based on 44 sessions
In a history class that consisted of 30 students, the number of seniors was 3 more than twice the number of juniors, and $$\frac{3}{10}$$ of the students were neither juniors nor seniors.

 Quantity A Quantity B The number of juniors in the class 6

A)The quantity in Column A is greater.
B)The quantity in Column B is greater.
C)The two quantities are equal.
D)The relationship cannot be determined from the information given.
[Reveal] Spoiler: OA

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Manager
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Re: In a history class that consisted of 30 students, the number [#permalink]  11 May 2018, 11:05
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more than twice the 3 number makes the question confusing. looks like there is a typo.
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Re: In a history class that consisted of 30 students, the number [#permalink]  11 May 2018, 20:02
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Quote:
more than twice the 3 number makes the question confusing. looks like there is a typo.
yes 3 was at a wrong place. it is fixed now

total number of students =$$30$$
total number of students that are not juniors or seniors = $$3/10 * 30 = 9$$
no of juniors + no of seniors = $$21$$
Let j = no of juniors
Let s = no of seniors
we have $$j+s = 21$$.........(i)
from question we get, $$2*j + 3 = s$$......(ii)

replace the value of s from eqn (ii) in (i)
$$j+ 2j +3 = 21$$
solve for $$j; j=6$$
option c
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Re: In a history class that consisted of 30 students, the number [#permalink]  17 Feb 2020, 13:23
Expert's post
Let J = number of juniors in the class
Let S = number of seniors in the class

3/10 of the 30 students were neither juniors nor seniors
So, 7/10 were either juniors or seniors
7/10 of 30 = 21.
We can write: J + S = 21

...the number of seniors was 3 more than twice the number of juniors
We can write: S = 2J + 3

We now have the following system of equations:
J + S = 21
S = 2J + 3

Take the top equation and replace S with 2J + 3 to get; J + (2J + 3) = 21
Simplify: 3J + 3 = 21
Solve: J = 6

So, we get:
Quantity A: 6
Quantity B: 6

Answer: C

Cheers,
Brent
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Re: In a history class that consisted of 30 students, the number [#permalink]  17 Feb 2020, 13:25
correct: C
Total_number_of_students: 30
seniors = 3 + 2* juniors
not_junior_and_not_senior = 3/10 * total_number_of_students = 3/10 * 30 = 9 so 30 - 9 = 21 students are seniors or juniors:
21 = seniors + juniors =3 + 2* juniors + juniors = 3 + 3*juniors -> juniors = 6
So there are 6 juniors in the history class. and A and B are equal.

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Re: In a history class that consisted of 30 students, the number   [#permalink] 17 Feb 2020, 13:25
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# In a history class that consisted of 30 students, the number

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