Set problem

[BTGmoderatorRO]

There are 70 students in Math or English or German. Exactly 40 are in Math, 30 in German, 35 in English and 15 in all three courses. How many students are enrolled in exactly two of the courses? Math, English and German.

a. 5
b. 10
c. 50
d. 75
e. 40

correct option is A

How does Exactly influenced your answer in this context. kindly present a mathematically analogy to this and defend your choice of answer. option B seem so close and may be the correct option

[Jay@ManhattanReview]

There are 70 students in Math or English or German. Exactly 40 are in Math, 30 in German, 35 in English and 15 in all three courses. How many students are enrolled in exactly two of the courses? Math, English and German.

a. 5
b. 10
c. 50
d. 75
e. 40

correct option is A

How does Exactly influenced your answer in this context. kindly present a mathematically analogy to this and defend your choice of answer. option B seem so close and may be the correct option

Total number of students = 70
Number of students enrolled in one course = 40 + 30 + 35 = 105
Number of students enrolled in all the three courses = 15

We know that

Total = # of students enrolled in one course - # of students enrolled in two courses + # of students enrolled in all the three courses

70 = 105 - Number of students enrolled in two courses + 15

=> Number of students enrolled in two courses = 120 - 70 = 50

However, this is not the answer to the question.

'50' is the number of students enrolled in two courses including the number of students enrolled in all the three courses

Thus, the number of students enrolled in EXACTLY two courses = 50 - 15 - 15 -15 = 5.

We deducted '15' thrice for each for the three courses.

The correct answer: A

Hope this helps!

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-Jay
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[Scott@TargetTestPrep]

There are 70 students in Math or English or German. Exactly 40 are in Math, 30 in German, 35 in English and 15 in all three courses. How many students are enrolled in exactly two of the courses? Math, English and German.

a. 5
b. 10
c. 50
d. 75
e. 40

correct option is A

How does Exactly influenced your answer in this context. kindly present a mathematically analogy to this and defend your choice of answer. option B seem so close and may be the correct option

Letting M = math, E = English, and G = German, we can use the formula for a 3-category scenario:

Total = n(M) + n(E) + n(G) - n(M and E) - n(M and G) - n(E and G) + n(all 3) - n(none)

70 = 40 + 35 + 30 - n(M and E) - n(M and G) - n(E and G) + 15 - 0

70 = 120 - n(M and E) - n(M and G) - n(E and G)

50 = n(M and E) + n(M and G) + n(E and G)

Note that the term n(M and E) includes those taking M and E, but it also includes the 15 who are taking all three. Similarly, the term n(M and G) includes those taking M and G, but it also includes the 15 who are taking all three. And, finally, the term n(E and G) includes those taking E and G, but it also includes the 15 who are taking all three.

Thus, we have added an extra 15 individuals three times. The total taking exactly 2 courses is not 50. Rather, it is

50 - 15 x 3 = 50 - 45 = 5.

Answer: A