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If each of the students in a certain mathematics class is 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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If each of the students in a certain mathematics class is 23 Aug 2010, 09:24
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udaymathapati
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.
Show more

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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If each of the students in a certain mathematics class is 24 Dec 2018, 03:21
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udaymathapati
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.
Show more

Just out of curiosity:

Is the total number 35???
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If each of the students in a certain mathematics class is 14 Aug 2020, 09:33
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gota900
Bunuel
udaymathapati
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???
Show more

Let the no. of seniors = \(s\) and no. of juniors = \(j\). We need to find \(s+j\)

1) \(P(s) = \frac{4}{7}\)
\(\frac{s}{s+j} = \frac{4}{7}\)
\(=> 3s = 4j\) INSUFFICIENT. Strike out A and D. Hold B, C, and E

2) There are 5 more seniors in the class than juniors
\(s = j+5\) INSUFFICIENT. Strike out B. Hold C and E

1) + 2)
\(3s = 4j\)
\(s = j+5\)
Solve the above two equations to get \(s+j = 35\). SUFFICIENT. Strike out E. Choose the correct answer C.
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If each of the students in a certain mathematics class is 15 Apr 2023, 21:01
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