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In a university club of 200 people, the number of Political Science

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In a university club of 200 people, the number of Political Science  [#permalink]

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New post 28 Feb 2017, 02:18
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In a university club of 200 people, the number of Political Science majors is 50 less than 4 times the number of International Relations majors. If one fifth of the club members are neither Political Science majors nor International Relations majors, and no club member is majoring in both Political Science and International Relations, how many of the club members are International Relations majors?

A. 42

B. 50

C. 71

D. 95

E. 124
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Re: In a university club of 200 people, the number of Political Science  [#permalink]

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New post 28 Feb 2017, 04:08
Total members in university club = 200;
No club member is majoring in both Political Science and International Relations;

Now Suppose,
International Relations majors = x;
Political Science majors = (4x-50);

1/5 of the club members are neither Political Science majors nor International Relations majors;
Therefore,
1/5*(200) = 200 - {x + (4x-50)}
=>200 - 5x + 50 = 40
=>5x = 210
=>x = 42

Answer A.
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Re: In a university club of 200 people, the number of Political Science  [#permalink]

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New post 28 Feb 2017, 09:04
vikasp99 wrote:
In a university club of 200 people, the number of Political Science majors is 50 less than 4 times the number of International Relations majors. If one fifth of the club members are neither Political Science majors nor International Relations majors, and no club member is majoring in both Political Science and International Relations, how many of the club members are International Relations majors?

A. 42

B. 50

C. 71

D. 95

E. 124


Breakdown and solve -

Quote:
If one fifth of the club members are neither Political Science majors nor International Relations majors, and no club member is majoring in both Political Science and International Relations


So, No of students studying Political Science majors & International Relations is \(\frac{4}{5*200} = 160\)

Now, \(i + p = 160\)
Quote:
the number of Political Science majors is 50 less than 4 times the number of International Relations majors.


\(p = 4i - 50\)

Now, \(i + (4i - 50) = 160\)

Or, \(5i = 210\)

Or, \(i = 42\)

Thus, the number of club members are International Relations majors is (A) 42
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Re: In a university club of 200 people, the number of Political Science  [#permalink]

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New post 02 Mar 2017, 17:56
vikasp99 wrote:
In a university club of 200 people, the number of Political Science majors is 50 less than 4 times the number of International Relations majors. If one fifth of the club members are neither Political Science majors nor International Relations majors, and no club member is majoring in both Political Science and International Relations, how many of the club members are International Relations majors?

A. 42

B. 50

C. 71

D. 95

E. 124


We can use the formula:

Total students = # of PS majors + # of IR majors - # of both + # of neither

We are given that total = 200 and that the number of Political Science majors is 50 less than 4 times the number of International Relations majors. If we let x = the number of IR majors, we can create the following equation:

# of PS majors = 4x - 50

We are also given that 1/5 of the students major in neither; thus, neither = (1/5)(200) = 40 and # of both = 0.

We can substitute all the above values into our formula and we have:

200 = 4x - 50 + x - 0 + 40

200 = 5x - 10

210 = 5x

42 = x

Answer: A
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Re: In a university club of 200 people, the number of Political Science &nbs [#permalink] 02 Mar 2017, 17:56
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