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Probability

by rapper » Thu Oct 18, 2012 2:53 pm
Q3:
If each of the students in a certain mathematics class is either a junior or a senior, how
many students are in the class?
(1) If one student is to be chosen at random from the class to attend a conference,
the probability that the student chosen will be a senior is 4/7.
(2) There are 5 more seniors in the class than juniors.

I think A is sufficient to answer this question.However i got it wrong on some test.
Can anybody please help in solving this
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by Anurag@Gurome » Thu Oct 18, 2012 6:02 pm
rapper wrote:Q3:
If each of the students in a certain mathematics class is either a junior or a senior, how
many students are in the class?
(1) If one student is to be chosen at random from the class to attend a conference,
the probability that the student chosen will be a senior is 4/7.
(2) There are 5 more seniors in the class than juniors.

I think A is sufficient to answer this question.However i got it wrong on some test.
Can anybody please help in solving this
Let us assume that, total number of Students = T
Number of juniors = J
Number of seniors = T - J

We have to find the value of T.

(1) If one student is to be chosen at random from the class to attend a conference, the probability that the student chosen will be a senior is 4/7.
Total number of ways of choosing one student at random from the class = T
Number of ways that the chosen student is a senior = T - J
So, probability that the student is a senior = 4/7 = (T - J)/T, but there is one equation and 2 variables; NOT sufficient.

(2) There are 5 more seniors in the class than juniors implies T - J = J + 5
2J = T - 5
J = (T - 5)/2, which is again one equation, 2 variables; NOT sufficient.

Combining 1 and 2 together:

4/7 = (T - J)/T ...Equation (1)
J = (T - 5)/2 ...Equation (2)
We have 2 equations and 2 variables, so we can find the value of T from here; SUFFICIENT.

The correct answer is C.
Anurag Mairal, Ph.D., MBA
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