A student took five papers in an examination, where the full marks were the same for each paper. His marks in these papers were in the proportion of 6 : 7 : 8 : 9 : 10. In all papers together, the candidate obtained 60% of the total marks. Then the number of papers in which he got more than 50% marks is
Let the marks scored in five subjects be 6x, 7x, 8x, 9x
and 10x (on a scale of 1).
Average score = 60%
(6x + 7x + 8x + 9x +10x)/5 = 60/100
⇒ 8x = 0.5
⇒ x = 0.075
So the marks are 0.45, 0.525, 0.6, 0.675 and 0.75.
Number of times the marks exceed 50% is 4.
A square, whose side is 2 m, has its corners cut away so as to form an octagon with all sides equal. Then the length of each side of the octagon, in metres, is
Let x, y and z be distinct integers. x and y are odd and positive, and z is even and positive. Which one of the following statements cannot be true?
If x > 5 and y < –1, then which of the following statements is true?
A red light flashes three times per minute and a green light flashes five times in 2 min at regular intervals. If both lights start flashing at the same time, how many times do they flash together in each hour?