1. If the average of the numbers 6, 7, x, 8, y, and 16 is 9, then—?
(a) x + y = 21 (b) x + y = 17 (c) x - y = 21 (d) x - y = 19
2. If the average of the numbers 6, 7, x, 8, y, 14 is 9,
(a) x+y=21 (b) x+y=19 (c) x-y=21 (d) x-y=19
3. If the average of the numbers 6, 7, \(x\), 8, \(y\), 14 is 9, then –
(a) x+y=21 (b) x+y=29 (c) x-y=21 (d) x+y=19
4. If the combined average of the data set 7, 5, 2, 10, x, 6, 4, y, 8, 1 is 5, then what is the value of \(x + y\)?
5. If 16, 15, 17, 16, 15, x, 19, 17, 14 have a mode of 15, then the value of x is-
(a) 15 (b) 16 (c) 17 (d) 19
6. If the mode of the data set 16, 15, 17, 16, 15, x, 19, 17, 14 is 15, then the value of x is—
7. If the combined average of 5, 15, 22, x, y, 25, and z is 14, then which of the following is correct?
(a) x+y+z=42 (b) x+y+z=31 (c) x+y=z (d) x+y=2z
8. If the mode of the data 16, 15, 16, 16, 15, x, 19, 17, 14 is 16, then the value of x must be 16.
9. If the mode of the data set 16, 15, 17, 16, 15, x, 19, 17, 14 is 15, then the value of x is—
10. In a game, scores of 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, and 15 were obtained; the average score was 10.
11. If the mode of the data set 16, 15, 17, 16, 15, x, 19, 17, 14 is 15, then the value of x will be 15.
12. Here’s the English translation of your math problem: If the ascending data set is \[ 27,\ 31,\ 46,\ 52,\ x,\ y + 2,\ 71,\ 79,\ 85,\ 90 \] and the median of the set is \(64\), then what is the value of \(x + y\)?
(a) 125 (b) 126 (c) 127 (d) 128
13. If the data arranged in ascending order is 6, 9, 11, 12, x+2, x+3, 17, 20, 21, 24 and the median is 21, then the value of x will be —
(a) 13.5 (b) 15.5 (c) 18.5 (d) 21.5
14. If the average of the first four numbers out of five is 26, and the average of the last four numbers is 25, then find the difference between the first and the last number.
15. If the combined average of the numbers 7, \(x - 3\), 10, \(x + 3\), and \(x - 5\) is 15, then the median is _____.
(a) 16 (b) 10 (c) 18 (d) 24
16. If the ages of several students are 10, 11, 9, 7, 13, 8, and 14 years, then their median _____.
17. Translate the following and find the mode of the data: 15, 11, 10, 8, 15, 18, 17, 15, 10, 19, 10, 11, 10, 8, 19, 15, 10, 18, 15, 3, 16, 14, 17, 2 Mode = 15 (since it appears most frequently)
18. If the data arranged in ascending order is 8, 9, 12, 17, x+2, x+4, 30, 31, 34, 39 and the median is 24, then the value of x is—
(a) 22 (b) 21 (c) 20 (d) 24
19. If the data arranged in ascending order is 8, 9, 12, 17, x+2, x+4, 30, 34, 39 and the median is 24, then the value of x is _____.
20. The median of the data set 6,7,8,8,9,15,10,15,20,19,25,24,216,7,8,8,9,15,10,15,20,19,25,24,21 is:
(a) 10 (b) 15 (c) 9 (d) 19
21. If 35 is not present in the data set 30, 34, 35, 36, 37, 38, 39, 40, then the median increases by
(a) 2 (b) 1.5 (c) 1 (d) 0.5
22. If the mode of the numbers 64, 60, 48, x, 43, 48, 43, 34 is 43. Then the value of \((x+3)\) is.
(a) 44 (b) 45 (c) 46 (d) 48
23. The median of the series 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 16, 18 will be –
(a) 10 (b) 11 (c) 10.5 (d) 11.5
24. If 7, x, y, 189 are in continued proportion, then the values of x and y respectively will be:
(a) 63,21 (b) 21,23 (c) 21,63 (d) 23,21
25. What is the median of 3, 9, 7, 4, 8, and 6?
(a) 5 (b) 5.5 (c) 6 (d) 6.5
26. If a cuboid has number of faces = x, number of edges = y, number of vertices = z, and number of diagonals = p, then what is the value of (x − y + z + p)?
27. The numbers 11, 12, 14, \(x - 2\), \(x + 4\), \(x + 9\), 32, 38, 47 are arranged in ascending order, and their median is 24. Find the value of \(x\).
28. A, B, and C started a business together with capital investments of ₹6,000, ₹8,000, and ₹9,000 respectively. After a few months, A invested an additional ₹3,000 into the business. At the end of the year, the total profit was ₹30,000, and C received ₹10,800 as his share of the profit. When did A invest the additional ₹3,000?
29. The ages (in years) of some students are: 10, 11, 9, 7, 13, 8, 14; the median of their ages is _____ years.
30. If 8, 14, \(7x + 2\), and 28 are in continued proportion, then what is the value of \(x\)?
(a) 1 (b) 3 (c) 2 (d) 4
