What is the value of the expression 101 + 102 + 103 + ... + 200?
Answer: B
The sum of an arithmetic progression is given by the formula \(S_n = \frac{n}{2}(a_1 + a_n)\), where \(n\) is the number of terms, \(a_1\) is the first term, and \(a_n\) is the last term.
Number of terms (n) = (Last Term - First Term) + 1 = (200 - 101) + 1 = 100.
First term (\(a_1\)) = 101.
Last term (\(a_n\)) = 200.
Sum = \(\frac{100}{2} \times (101 + 200) = 50 \times 301 = 15050\).
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If you subtract -1 from +1, what is the result?
Answer: C
The operation is \((+1) - (-1)\).
Subtracting a negative number is equivalent to adding its positive counterpart.
So, \((+1) - (-1) = 1 + 1 = 2\).
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The sum of three consecutive even numbers is 144. What is the largest of these numbers?
Answer: C
Let the three consecutive even numbers be \(x\), \(x+2\), and \(x+4\).
Their sum is \(x + (x+2) + (x+4) = 144\).
\(3x + 6 = 144\).
\(3x = 138\).
\(x = 46\).
The numbers are 46, 48, and 50. The largest number is 50.
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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.
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What is the value of \(\sqrt{0.000441}\)?
Answer: B
We can write \(0.000441\) as \(\frac{441}{1000000}\).
\(\sqrt{\frac{441}{1000000}} = \frac{\sqrt{441}}{\sqrt{1000000}} = \frac{21}{1000} = 0.021\).
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Simplify: \(1 \div [1 \div \{1 \div (1 \div 1)\}]\).
Answer: A
Working from the innermost bracket outwards:
Step 1: \((1 \div 1) = 1\).
Step 2: \(\{1 \div 1\} = 1\).
Step 3: \([1 \div 1] = 1\).
Step 4: \(1 \div 1 = 1\).
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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 = \(\frac{30(30+1)}{2} = \frac{30 \times 31}{2} = 15 \times 31 = 465\).
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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)
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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 = \(324 \div 27 = 12\).
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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: \(50 \div 5 = 10\).
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