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

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Manager
Joined: 06 Apr 2010
Posts: 109
If each of the students in a certain mathematics class is  [#permalink]

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23 Aug 2010, 08:54
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Difficulty:

25% (medium)

Question Stats:

73% (01:15) correct 27% (01:15) wrong based on 247 sessions

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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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Joined: 02 Sep 2009
Posts: 57155
Re: If each of the students in a certain mathematics class is  [#permalink]

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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.

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Manager
Joined: 15 Aug 2018
Posts: 51
GMAT 1: 740 Q47 V45
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Re: If each of the students in a certain mathematics class is  [#permalink]

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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.

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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