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# How many students in the senior class take both French and Spanish?

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Math Expert
Joined: 02 Sep 2009
Posts: 52296
How many students in the senior class take both French and Spanish?  [#permalink]

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08 Oct 2015, 06:58
00:00

Difficulty:

35% (medium)

Question Stats:

66% (00:57) correct 34% (00:47) wrong based on 147 sessions

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How many students in the senior class take both French and Spanish?

(1) In the senior class, 100 students take French and 125 students take Spanish.
(2) There are 200 students in the senior class.

Kudos for a correct solution.

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Re: How many students in the senior class take both French and Spanish?  [#permalink]

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08 Oct 2015, 08:07
1
1
Bunuel wrote:
How many students in the senior class take both French and Spanish?

(1) In the senior class, 100 students take French and 125 students take Spanish.
(2) There are 200 students in the senior class.

Kudos for a correct solution.

(1) Not sufficient to calculate BOTH
(2) Not sufficient, we don't have values for each language
(1+2) Not Sufficient as there may be some students who tak eneither spanish nor french courses
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Re: How many students in the senior class take both French and Spanish?  [#permalink]

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08 Oct 2015, 08:49
(1) In the senior class, 100 students take French and 125 students take Spanish...Insuffcient
(2) There are 200 students in the senior class....Insuffcient

Taking both 1 & 2, no. of students doing only french will be 200-125=75 and students doing only spanish will be 200-100=100. So students doing both french an spanish will be 25.

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Joined: 30 Sep 2013
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Re: How many students in the senior class take both French and Spanish?  [#permalink]

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08 Oct 2015, 09:30
1
Bunuel wrote:
How many students in the senior class take both French and Spanish?

(1) In the senior class, 100 students take French and 125 students take Spanish.
(2) There are 200 students in the senior class.

Kudos for a correct solution.

Actually,

Total = French + Spanish - Both + None

Question asks for 'Both'. To 'Both' , we need to have the values of Total, French, Spanish and None.

1. This statement gives the value for French and Spanish. We also need the values of Total and None.
Not sufficient

2. This statement gives the value for Total. We also need the values of French, Spanish and None.
Not sufficient.

Combining statement 1 and 2 gives us the values for Total, French and Spanish. Still we need the value of None.
Not sufficient.

Math Expert
Joined: 02 Sep 2009
Posts: 52296
Re: How many students in the senior class take both French and Spanish?  [#permalink]

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11 Oct 2015, 06:37
Bunuel wrote:
How many students in the senior class take both French and Spanish?

(1) In the senior class, 100 students take French and 125 students take Spanish.
(2) There are 200 students in the senior class.

Kudos for a correct solution.

VERITAS PREP OFFICIAL SOLUTION:

Question Type: What Is the Value? This is a Venn Diagram question and the question asks: “How many students take both French and Spanish?”

Given information in the question stem or diagram: In any Venn Diagram problem you should draw out the diagram and remember that Total = Set 1 + Set 2 – Both + Neither. It is important to always consider “Neither” in these types of DS questions and to note the difference between total set information and “only” information (for instance, the difference between people who take “only French” and “French”).

Statement 1: French = 100 and Spanish = 125. This can be written to say that French + Spanish – Both + Neither = Total or 100 + 125 – Both + Neither = Total. This statement is not sufficient alone because you do not know how many total students there are, nor how many students take neither French nor Spanish. Not sufficient. Eliminate choices A and D.

Statement 2: Total students = 200. This is not sufficient alone since there is no way to allocate the 200 students among the categories. Eliminate choice B.

Together: Many students will think that the answer is C because they have forgotten to consider “Neither.” You do not know how many students take neither French nor Spanish, so there is no way to determine “Both.” Without this information you only know that at least 25 students take BOTH (that is if Neither = 0) and as many as 100 might take BOTH if the neither category was 75. This is not sufficient and the correct answer is E. Note: In any choice between C and E such as this you must learn to Play Devil’s Advocate and consider anything you might be missing. In this example (as with many Venn problems) that is making sure you remember to consider the value of “Neither.”
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Re: How many students in the senior class take both French and Spanish?  [#permalink]

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19 Apr 2018, 00:37
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Re: How many students in the senior class take both French and Spanish? &nbs [#permalink] 19 Apr 2018, 00:37
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