The sum of three consecutive multiples of 3 is 72. What is the largest of the three numbers?
Answer: C
Let the three consecutive multiples of 3 be 3x, 3(x+1), and 3(x+2). A simpler way is to let them be n-3, n, n+3, where n is the middle number. Their sum is 3n = 72, so n=24.
The numbers are 21, 24, and 27.
The largest number is 27.
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The sum of 10 numbers is 550. Find their average number.
Answer: B
Average = Sum of numbers / Count of numbers.
Average = 550 / 10 = 55.
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A number exceeds its two-fifth by 75. The number is:
Answer: A
Let the number be x.
Two-fifth of the number is \(\frac{2}{5}x\).
The equation is \(x = \frac{2}{5}x + 75\).
\(x - \frac{2}{5}x = 75\).
\(\frac{3}{5}x = 75\).
\(x = 75 \times \frac{5}{3} = 25 \times 5 = 125\).
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What is the sum of the first 20 odd natural numbers?
Answer: C
The sum of the first 'n' odd natural numbers is given by the formula \(n^2\).
Here, n = 20.
The sum is \(20^2 = 400\).
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Find the value of \(0.6 + 0.66 + 0.066 + 6.606\)
Answer: A
Align the numbers vertically by their decimal points and add:
0.600
0.660
0.066
+ 6.606
-------
7.932
-------
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If \(1^2 + 2^2 + 3^2 + ... + 10^2 = 385\), then the value of \(2^2 + 4^2 + 6^2 + ... + 20^2\) is:
Answer: C
Let the required sum be S.
\(S = 2^2 + 4^2 + 6^2 + ... + 20^2\).
\(S = (2 \times 1)^2 + (2 \times 2)^2 + (2 \times 3)^2 + ... + (2 \times 10)^2\).
\(S = 2^2(1^2) + 2^2(2^2) + 2^2(3^2) + ... + 2^2(10^2)\).
\(S = 2^2 (1^2 + 2^2 + 3^2 + ... + 10^2)\).
\(S = 4 \times (\text{given sum})\).
\(S = 4 \times 385 = 1540\).
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A number whose fifth part increased by 4 is equal to its fourth part diminished by 10. The number is:
Answer: C
Let the number be x.
The equation is \(\frac{x}{5} + 4 = \frac{x}{4} - 10\).
\(4 + 10 = \frac{x}{4} - \frac{x}{5}\).
\(14 = \frac{5x - 4x}{20}\).
\(14 = \frac{x}{20}\).
\(x = 14 \times 20 = 280\).
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What is the value of the expression \(101 + 102 + 103 + ... + 200\)?
Answer: B
This is an arithmetic progression. Number of terms (n) = (Last Term - First Term) + 1 = (200 - 101) + 1 = 100.
Sum = \(\frac{n}{2}(\text{first term} + \text{last term})\)
Sum = \(\frac{100}{2} \times (101 + 200) = 50 \times 301 = 15050\).
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What is the equivalent of 0.375 as a fraction?
Answer: A
The decimal 0.375 can be written as the fraction \(\frac{375}{1000}\).
To simplify, we can divide the numerator and denominator by their greatest common divisor, which is 125.
375 ÷ 125 = 3.
1000 ÷ 125 = 8.
So, the fraction is \(\frac{3}{8}\).
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Evaluate: \(20 - [10 - \{8 - (6 - 2)\}]\)
Answer: B
Using the order of operations (BODMAS/PEMDAS):
Step 1: Solve the innermost bracket: \((6 - 2) = 4\).
Step 2: Solve the curly bracket: \(\{8 - 4\} = 4\).
Step 3: Solve the square bracket: \([10 - 4] = 6\).
Step 4: Perform the final subtraction: \(20 - 6 = 14\).
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