How many more passengers visited only Lumbini than only Janakpur?
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25
Working: 70 − 45
Q2 · Sets · 6 marks · SEE Q1 Sets, in 7 of 7 recent papers (an unknown x in the set sizes)
A group of 120 tourists in Kathmandu was asked about two activities. x + 40 like trekking (T), 2x + 10 like rafting (R), 15 like both and 25 like neither.
(a)
Which relation connects all the groups?
n(U) = n(T) + n(R) + n(T ∩ R)
n(U) = n(T) + n(R) − n(T ∩ R) + n(T ∪ R)
n(U) = n(T) + n(R)
n(U) = n(T ∪ R) − n(T ∪ R)
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(b) n(U) = n(T) + n(R) − n(T ∩ R) + n(T ∪ R)
Add the two sets, take away the overlap once, then add the people outside both circles.
(b)
Find n(T ∪ R), the number who like at least one activity.
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95
Working: 120 − 25
(c)
Find the value of x.
Show answer
20
Working: 95 = 3x + 35, so 3x = 60
(d)
How many tourists like only rafting?
Show answer
35
Working: 50 − 15
Q3 · Sets · 5 marks · SEE Q1 Sets, in 7 of 7 recent papers (survey given in percentages)
In a school, 60% of students like maths, 50% like science and 25% like neither subject.
(a)
What percentage of students like at least one subject?
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75
Working: 100 − 25
(b)
What percentage like both subjects?
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35
Working: 60 + 50 − 75
(c)
If 70 students like both subjects, how many students are in the school?
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200
Working: 70 ÷ 0.35
Q4 · Sets · 2 marks · SEE Q1 Sets, in 7 of 7 recent papers (part c: “only one” count)
Of 90 people at a Dashain gathering, 50 ate sel roti, 55 ate goat curry and every person ate at least one. How many ate only one of the two?
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75
Working: Only one = (50 − 15) + (55 − 15) = 35 + 40
Q5 · Sets · 2 marks
In a survey of 120 students, 70 like football, 50 like cricket and 20 like both. How many like neither?