Thirty-six vehicles are parked in a parking lot in a single row. After the first car, there is one scooter. After the second car, there are two scooters. After the third car, there are three scooters and so on. Work out the number of scooters in the second half row.
In a reality show, two judges independently provided marks based on the performance of the participants. If the marks provided by the second judge are given by y= 1+ x, where x is the marks provided by the first judge. Then for a participant
On Monday, Akash ran 4 km less than the distance he ran on Tuesday. Sanjay, who ran the same distance on Monday and Tuesday, ran 5 km more on Tuesday than the distance Akash ran on Monday. Find the difference between the distances covered by Akash and Sanjay over the two days.
A university is offering elective courses in Mathematics, Economics and Sociology. Each of its 100 undergraduate students has to opt for at least one of these electives. Course enrollment data showed that 47 students enrolled for Mathematics, 47 students enrolled for Economics and 57 students enrolled for Sociology. If 7 students enrolled for all three courses, how many students enrolled for exactly one course?
Venn Diagram Problem: Students in Elective Courses
Given:
Total students = 100
Math (M) = 47
Economics (E) = 47
Sociology (S) = 57
All three (M ∩ E ∩ S) = 7
Objective:
Find the number of students who enrolled in exactly one course.
Step-by-step:
Let’s use the formula for total union of 3 sets:
Total = M + E + S − (M∩E) − (E∩S) − (S∩M) + (M∩E∩S)
Let the number of students who enrolled in exactly 2 courses = x
So those who enrolled in all 3 = 7
Let the number of students who enrolled in exactly one course = y
Then, the total number of course enrollments = 1 × y + 2 × x + 3 × 7 = M + E + S = 47 + 47 + 57 = 151
⇒ y + 2x + 21 = 151
⇒ y + 2x = 130 — (1)
Also, total students = 100 = y + x + 7
⇒ y + x = 93 — (2)
Subtracting (2) from (1):
(y + 2x) − (y + x) = 130 − 93
⇒ x = 37
Now, from (2): y + 37 = 93 ⇒ y = 56
✅ Final Answer:
56 students enrolled in exactly one course.
3
A cat climbs a 21- meter pole. In the
first minute it climbs 3 meter and in the second minute it descends one meter.
In how minutes the cat would reach the top of the pole?
In a recent survey of 500 employees in
a company, it was found that 60% of the employees prefer coffee over tea, 25%
prefer tea over coffee, and the remaining 15% have no preference. If 20% of the
employees who prefer coffee are also tea drinkers, how many employees prefer
only tea?
