q: The average of 9 observations was 9, that of the 1st of 5 being 10 and that of the last 5 being 8. What was the 5th observation?
Options:
(A) 9
(B) 8
(C) 7
(D) 6
(E) 2
a: Stream of consciousness: 1 to 9 = 9 * 9 = 81
1 to 5 = 5 * 10 = 50
5 to 9 = 5 * 8 = 40
5th = 50 + 40 = 90 81 = 9 The answer is (A).
--
q: The average age of A, B and C is 29 years. If the average age of A and C is 32 years, what is the age of B in years ?
Options:
(A) 19
(B) 35
(C) 20
(D) 32
(E) 23
a: Stream of consciousness: Age of B = Age of (A + B + C) Age of (A + C) = 29 3 32 2 = 87 64 = 23 years The answer is (E).
--
q: A die is thrown. If G is the event 'the number appearing is a multiple of 3' and H be the event
'the number appearing is even' then find whether G and H are independent ?
Options:
(A) G and H are not independent events.
(B) G and H are independent events.
(C) Only G independent event
(D) Only H independent event
(E) None
a:
Stream of consciousness: We know that the sample space is S = {1, 2, 3, 4, 5, 6}
Now G = { 3, 6}, F = { 2, 4, 6} and E n F = {6}
Then P(G) = 2/6 = 1/3
P(H) = 3/6 = 1/2 and P(G H) = 1/6
P(G n H) = P(G). P (H)
G and H are independent events. The answer is (B).
--