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Bunuel
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According to the admissions and records office of a major university, 26 Nov 2014, 07:51
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Tough and Tricky questions: Overlapping Sets.



According to the admissions and records office of a major university, the schedules of X first-year college students were inspected and it was found that S number of students were taking a Spanish course, F number of students were taking a French course, and B number of students were taking both a Spanish and a French Course. Which of the following expressions gives the percentage of students whose schedules were inspected who were taking neither a Spanish course nor a French course?

A. 100*X/(B + F +S)

B. 100*(B + F + S)/X

C. 100*(X - F - S)/X

D. 100*(X + B - F - S)/X

E. 100*(X - B - F - S)/X

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D
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intheend14
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According to the admissions and records office of a major university, 26 Nov 2014, 10:38
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This is a classic overlapping question with variables instead of numbers. We know the total is X, Spanish is S, French is F, taking both is B and let's make neither be N. From the premise, we can make the expression: Total = Group 1 + Group 2 - overlap + neither or Total - Neither = Sum of groups minus overlap. Substitute that with Variables and a Percentage: T = F + S - B + N and % Neither is 100*(X+B-F-S)/X

Choose D
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According to the admissions and records office of a major university, 26 Nov 2014, 21:44
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Neither =X - (S + F - B) , subtracting B since B (both) is counted twice, once in Spanish and once in French).

Neither % = 100 * (X + B - S -F)/X

Answer is D.
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According to the admissions and records office of a major university, 27 Nov 2014, 00:17
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Answer = D. 100*(X + B - F - S)/X

Refer diagram below. We require to find the pink colour region percentage of total x

Attachment:
venn.png
venn.png [ 4.8 KiB | Viewed 5409 times ]

Total x = s + f-b + {Neither}

{Neither} = x - s - f + b

Percentage \(= \frac{100}{x} * (x - s - f + b)\)
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According to the admissions and records office of a major university, 27 Nov 2014, 02:50
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If using equations is difficult then take sample numbers.

Lets say X = 300, S = 100, F=200 and B = 50.
Neither will come as 50. (which is nothing but X+B -F-S).

Substitute these values in the equations. Only D will give the value as 50/300 *100 (as its percent).


PareshGmat
Answer = D. 100*(X + B - F - S)/X

Refer diagram below. We require to find the pink colour region percentage of total x

Attachment:
venn.png

Total x = s + f-b + {Neither}

{Neither} = x - s - f + b

Percentage \(= \frac{100}{x} * (x - s - f + b)\)
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According to the admissions and records office of a major university, 10 Jan 2015, 06:23
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I created this table:
S:Spanish
F:French
B:Both
NS:Not Spanish
NF:Not French

_________F_______NF_______ALL
S________B______S-B________S
NS______F-B___X-F-S+B______
ALL______F_______X-F________X

I started by adding X, S, B, F, which are the variables we have. Then:
NF= S-B (from the table) [1]
NS= F-B (from the table)
NF/ALL- X-F (from the table) [2]

From [1] and [2] we have: NS-NF= X-F-(S-B)= X-F-S+B, which leads to answer D.
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According to the admissions and records office of a major university, 24 Jan 2018, 10:32
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Bunuel

Tough and Tricky questions: Overlapping Sets.



According to the admissions and records office of a major university, the schedules of X first-year college students were inspected and it was found that S number of students were taking a Spanish course, F number of students were taking a French course, and B number of students were taking both a Spanish and a French Course. Which of the following expressions gives the percentage of students whose schedules were inspected who were taking neither a Spanish course nor a French course?

A. 100*X/(B + F +S)

B. 100*(B + F + S)/X

C. 100*(X - F - S)/X

D. 100*(X + B - F - S)/X

E. 100*(X - B - F - S)/X
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We can use the formula:

Total students = # spanish + # french - # both + # neither

X = S + F - B + N

X - S - F + B = N

The fraction of those students taking neither language is (X - S - F + B)/X. We convert this fraction to a percentage by multiplying the fraction by 100:

(X - S - F + B)/X * 100

Answer: D
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According to the admissions and records office of a major university, 25 Mar 2024, 07:49
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