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.
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Find the total number of prime factors in the expression \(4^{11} \times 7^5 \times 11^2\).
Answer: A
First, express all bases as prime numbers.
\(4^{11} = (2^2)^{11} = 2^{22}\).
The expression is \(2^{22} \times 7^5 \times 11^2\).
The total number of prime factors is the sum of the exponents of the prime bases.
Total prime factors = 22 + 5 + 2 = 29.
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Simplify: \(36 \div 2 \times 3 + 4 - 6\)
Answer: B
Using BODMAS, we perform division and multiplication from left to right, then addition and subtraction.
Step 1: \(36 \div 2 = 18\)
Step 2: \(18 \times 3 = 54\)
Step 3: \(54 + 4 = 58\)
Step 4: \(58 - 6 = 52\)
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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 increased by 37.5% gives 99. The number is:
Answer: B
Let the number be x. An increase of 37.5% means the new number is 137.5% of the original.
Note that 37.5% = 3/8.
So, the new number is \(x + \frac{3}{8}x = \frac{11}{8}x\).
\(\frac{11}{8}x = 99\)
\(x = 99 \times \frac{8}{11} = 9 \times 8 = 72\).
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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 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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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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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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What is the difference between the largest 4-digit number and the smallest 3-digit number?
Answer: A
The largest 4-digit number is 9999.
The smallest 3-digit number is 100.
The difference is 9999 - 100 = 9899.
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