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Question Detail
Find the sum of first 30 natural numbers
- 470
- 468
- 465
- 463
Answer: Option C
Explanation:
Sum of n natural numbers
\begin{aligned}
= \frac{n(n+1)}{2}
\end{aligned}
\begin{aligned}
= \frac{30(30+1)}{2} = \frac{30(31)}{2} = 465
\end{aligned}
1. Find the average of first 10 multiples of 7
- 35.5
- 37.5
- 38.5
- 40.5
Answer: Option C
Explanation:
\begin{aligned}
= \frac {7(1+2+3+...+10)}{10}
\end{aligned}
\begin{aligned}
= \frac {7(10(10+1))}{10 \times 2}
\end{aligned}
\begin{aligned}
= \frac {7(110)}{10 \times 2} = 38.5
\end{aligned}
2. Average of five numbers is 27. If one number is excluded the average becomes 25. The excluded number is
- 35
- 45
- 55
- 65
Answer: Option A
Explanation:
Number is (5*27) - (4*25) = 135-100 = 35
3. Find the average of all numbers between 6 and 34 which are divisible by 5
- 15
- 20
- 25
- 30
Answer: Option B
Explanation:
\begin{aligned}
Average = (\frac{10+15+20+25+30}{5}) = \frac{100}{5} =20
\end{aligned}
4. The average of four consecutive odd numbers is 24. Find the largest number.
- 25
- 27
- 29
- 31
Answer: Option B
Explanation:
Let the numbers are x, x+2, x+4, x+6, then
\begin{aligned}
=> \frac{x+(x+2)+(x+4)+(x+6)}{4} = 24
\end{aligned}
\begin{aligned}
=> \frac{4x+12)}{4} = 24
\end{aligned}
\begin{aligned}
=> x+3 = 24 => x = 21
\end{aligned}
So largest number is 21 + 6 = 27
5. If the average marks of three batches of 55, 60 and 45 students respectively is 50, 55, 60, then the average marks of all the students is
- 54.48
- 54.68
- 54.60
- 54.58
Answer: Option B
Explanation:
\begin{aligned}
\frac{(55 \times 50) +(60 \times 55) +(45 \times 60) }{55 + 60 + 45}
\end{aligned}
\begin{aligned}
\frac{8750}{160} = 54.68
\end{aligned}
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