Average - Study Mode

[#341] The mean of the first ten even natural number is-
Correct Answer

(C) 11

Explanation

Solution: Required mean $$eqalign{
& = left( {frac{{2 + 4 + 6 + ..... + 20}}{{10}}}
ight) cr
& = frac{{2left( {1 + 2 + ..... + 10}
ight)}}{{10}} cr} $$ $$ = left( {frac{1}{5} imes frac{{10 imes 11}}{2}}
ight)$$ xa0 xa0 $$left[ {x08ecause 1 + 2 + 3 + ... + n = frac{{nleft( {n + 1}
ight)}}{2}}
ight]$$ $$ = 11$$

[#342] The average of the first nine prime numbers is-
Correct Answer

(C) $$11frac{1}{9}$$

Explanation

Solution: Average $$ = left( {frac{{2 + 3 + 5 + 7 + 11 + 13 + 17 + 19 + 23}}{9}}
ight)$$ $$eqalign{
& = frac{{100}}{9} cr
& = 11frac{1}{9} cr} $$

[#343] The arithmetic mean of first 11 natural numbers is
Correct Answer

(C) 6.0

Explanation

Solution: Required mean $$eqalign{
& = left( {frac{{1 + 2 + ..... + 11}}{{11}}}
ight) cr
& = left( {frac{1}{{11}} imes frac{{11 imes 12}}{2}}
ight) cr
& = 6 cr} $$ $$left[ {x08ecause 1 + 2 + ..... + n = frac{{nleft( {n + 1}
ight)}}{2}}
ight]$$

[#344] The average age of seven boys sitting in a row facing North is 26 years. If the average age of the first three boys is 19 years and the average age of the last three boys is 32 years, what is the age of the boy who is sitting in the middle of the row?
Correct Answer

(C) 29 years

Explanation

Solution: Age of the boy sitting in the middle = [26 × 7 - (19 × 3 + 32 × 3)] = (180 + 153) years = 29 years

[#345] The average weight of A, B and C is 45 kg. If the average weight of A and B be 40 kg and that of B and C be 43 kg, then the weight of B is:
Correct Answer

(D) 31 kg
(H) 31 kg.

Explanation

Solution: Let A, B, C represent their respective weights. Then, we have : A + B + C = (45 × 3) = 135.....(i) A + B = (40 × 2) = 80.....(ii) B + C = (43 × 2) = 86.....(iii) Adding (ii) and (iii), we get: A + 2B + C = 166.....(iv) Subtracting (i) from (iv), we get: B = 31 ∴ B's weight = 31 kg