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If each of the students in a certain mathematics class is

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If each of the students in a certain mathematics class is  [#permalink]

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New post 23 Aug 2010, 08:54
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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.
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Re: If each of the students in a certain mathematics class is  [#permalink]

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New post 23 Aug 2010, 09:24
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udaymathapati wrote:
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.


Let the # of seniors in the class be \(s\) and the # of juniors be \(j\). Question: \(s+j=?\)

(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 --> \(\frac{s}{s+j}=\frac{4}{7}\) --> \(3s=4j\): two variables, hence not sufficient to calculate \(s+j\).

(2) There are 5 more seniors in the class than juniors --> \(s=j+5\). Clearly not sufficient to calculate \(s+j\).

(1)+(2) We have two different linear equations with 2 variables, hence we can find the values of both variables and calculate \(s+j\). Sufficient.

Answer: C.
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Re: If each of the students in a certain mathematics class is  [#permalink]

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New post 24 Dec 2018, 03:21
Bunuel wrote:
udaymathapati wrote:
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.


Let the # of seniors in the class be \(s\) and the # of juniors be \(j\). Question: \(s+j=?\)

(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 --> \(\frac{s}{s+j}=\frac{4}{7}\) --> \(3s=4j\): two variables, hence not sufficient to calculate \(s+j\).

(2) There are 5 more seniors in the class than juniors --> \(s=j+5\). Clearly not sufficient to calculate \(s+j\).

(1)+(2) We have two different linear equations with 2 variables, hence we can find the values of both variables and calculate \(s+j\). Sufficient.

Answer: C.


Just out of curiosity:

Is the total number 35???
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Re: If each of the students in a certain mathematics class is   [#permalink] 24 Dec 2018, 03:21
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