What is the value of \(587 \times 999\)?
Answer: A
We can write 999 as (1000 - 1).
So, \(587 \times 999 = 587 \times (1000 - 1)\).
\(= 587 \times 1000 - 587 \times 1\).
\(= 587000 - 587 = 586413\).
Enter details here
Simplify: \(18 - [6 - \{4 - (8 - 6 + 3)\}]\).
Answer: B
Using BODMAS rule:
Step 1: Innermost bracket \((8 - 6 + 3) = (2 + 3) = 5\).
Step 2: Curly bracket \(\{4 - 5\} = -1\).
Step 3: Square bracket \([6 - (-1)] = [6 + 1] = 7\).
Step 4: Final calculation \(18 - 7 = 11\).
Enter details here
A number when divided by 296 gives a remainder of 75. When the same number is divided by 37, the remainder is:
Answer: A
Let the number be N. N = 296k + 75.
We need to find the remainder when N is divided by 37.
First, check if 296 is divisible by 37. \(296 = 37 \times 8\).
Since the first divisor is a multiple of the second divisor, we can simply divide the first remainder by the second divisor.
Remainder = \(75 \div 37\).
\(75 = 2 \times 37 + 1\).
The remainder is 1.
Enter details here
Find the value of \((243)^{0.16} \times (243)^{0.04}\).
Answer: B
When multiplying powers with the same base, we add the exponents.
The expression becomes \((243)^{0.16 + 0.04} = (243)^{0.20}\).
\(0.20\) as a fraction is \(20/100 = 1/5\).
So we need to find \((243)^{1/5}\), which is the fifth root of 243.
We know that \(3^5 = 3 \times 3 \times 3 \times 3 \times 3 = 243\).
Therefore, the value is 3.
Enter details here
\(0.6 + 0.66 + 0.066 + 6.606 = ?\)
Answer: A
Align the numbers vertically by their decimal points and add:
0.600
0.660
0.066
+ 6.606
-------
7.932
-------
Enter details here
What is the result of \(3.5 \times (60 \div 2.5)\)?
Answer: A
Using BODMAS, we solve the bracket first.
\(60 \div 2.5 = 60 \div (\frac{5}{2}) = 60 \times \frac{2}{5} = 12 \times 2 = 24\).
Now, multiply by 3.5: \(3.5 \times 24 = (\frac{7}{2}) \times 24 = 7 \times 12 = 84\).
Enter details here
If a number is decreased by 4 and divided by 6, the result is 8. What would be the result if 2 is subtracted from the number and then it is divided by 5?
Answer: B
Let the number be x.
According to the first condition: \(\frac{x-4}{6} = 8\).
\(x-4 = 48\), so \(x = 52\).
Now, according to the second condition, subtract 2 from the number: \(52 - 2 = 50\).
Then divide by 5: \(50 \div 5 = 10\).
Enter details here
A boy was asked to multiply a number by 25. He instead multiplied the number by 52 and got the answer 324 more than the correct answer. What was the number?
Answer: A
Let the number be x.
Correct multiplication = 25x.
Incorrect multiplication = 52x.
Given, 52x - 25x = 324.
27x = 324.
x = \(324 \div 27 = 12\).
Enter details here
Which of the following numbers is divisible by 9?
Answer: B
A number is divisible by 9 if the sum of its digits is a multiple of 9.
A) 7+5+3+2+0 = 17 (Not divisible by 9)
B) 7+5+3+2+1 = 18 (Divisible by 9, since 18 = 9 × 2)
C) 7+5+3+2+2 = 19 (Not divisible by 9)
D) 7+5+3+2+3 = 20 (Not divisible by 9)
Enter details here
Find the sum of first 30 natural numbers.
Answer: B
The sum of the first n natural numbers is given by the formula \(S_n = \frac{n(n+1)}{2}\).
Here, n = 30.
Sum = \(\frac{30(30+1)}{2} = \frac{30 \times 31}{2} = 15 \times 31 = 465\).
Enter details here