Average - Study Mode
[#336] The average of two numbers is 6.5 and square root of their product is 6. What are the numbers?
Correct Answer
(C) 9 and 4
Explanation
Solution: Let the two numbers be x and y Then, x + y = 6.5 × 2 = 13 and $$sqrt {{ ext{xy}}} $$xa0 = 6 or xy = 36 ⇒ (x - y) 2 = (x + y) 2 - 4xy ⇒ (x - y) 2 = (13) 2 - 4 × 36 ⇒ (x - y) 2 = 169 - 144 ⇒ (x - y) 2 = 25 ⇒ (x - y) = 5 Solving x + y = 13 and x - y = 5 We get : x = 9 , y = 4
[#337] A, B, C and D are four consecutive even numbers respectively and their average is 65. What is the product of A and D?
Correct Answer
(C) 4216
Explanation
Solution: Let x, x + 2, x + 4 and x + 6 represent numbers A, B, C and D respectively. Then, $$eqalign{
& Rightarrow frac{{x + left( {x + 2}
ight) + left( {x + 4}
ight) + left( {x + 6}
ight)}}{4} = 65 cr
& Rightarrow 4x + 12 = 260 cr
& Rightarrow 4x = 248 cr
& Rightarrow x = 62 cr} $$ So, A = 62, B = 64, C = 66, D = 68 ∴ A × D = 62 × 68 = 4216
[#338] The arithmetic mean of the series 1, 2, 4, 8, 16, . . . . . . , 2 n is -
Correct Answer
(D) $$frac{{{2^{n + 1}} - 1}}{{n + 1}}$$
Explanation
Solution: The given series is a G.P. with first term, a = 1 and common ratio, r = 2, It has (n + 1) terms. ∴ Sum of the terms of the series = $$frac{{{2^{n + 1}} - 1}}{{2 - 1}}$$ = 2 n + 1 $$ - $$ 1 Arithmetic mean = $$frac{{{2^{n + 1}} - 1}}{{n + 1}}$$
[#339] The following table shows the number of working hours and the number of employees employed in a small scale industry No. of working hours No. of employees 3 - 5 7 5 - 7 10 7 - 9 18 9 - 11 57 11 - 13 14 13 - 15 8 The average number of working hours of an employee is
Correct Answer
(B) 9.5
Explanation
Solution: We have : Mean working hours 4 6 8 10 12 14 No. of employees 7 10 18 57 14 8 Sum of working hours of all the employees = (4 × 7 + 6 × 10 + 8 × 18 + 10 × 57 + 12 × 14 + 14 × 8) = (28 + 60 + 144 + 570 + 168 + 112) = 1082 Total number of employees = (7 + 10 + 18 + 57 + 14 + 8) = 114 ∴ Average number of working hours = $$left( {frac{{1082}}{{114}}}
ight)$$ = 9.49 $$ approx $$ 9.5
[#340] In Arun’s opinion, his weight is greater than 65 kg but less than 72 kg. His brother does not agree with Arun and he thinks that Arun’s weight is greater is that 60 kg but less than 70 kg. His mother’s view is that his weight cannot be greater than 68 kg. If all of them are correct in their estimation, what is the average of different probable weights of Arun?
Correct Answer
(A) 67 kg
Explanation
Solution: Let Arun's weight be X kg. According to Arun, 65 < X < 72 According to Arun's brother, 60 < X < 70 According to Arun's mother, X ≯ 68 i.e. X $$ leqslant $$68 The values satisfying all the above conditions are 66, 67 and 68 ∴ Required average $$eqalign{
& = left( {frac{{66 + 67 + 68}}{3}}
ight){ ext{ kg}} cr
& = left( {frac{{201}}{3}}
ight){ ext{ kg}} cr
& = 67{ ext{ kg}} cr} $$