A number is first increased by 10% and then decreased by 10%. The net change in the number is:
Answer: C
Let the original number be 100.
After a 10% increase, the number becomes 110.
Now, decrease this new number by 10%. The decrease is 10% of 110, which is 11.
The final number is 110 - 11 = 99.
The net change from the original number (100) is a decrease of 1, which is a 1% decrease.
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What is the value of \(0.2 \times 0.2 \times 0.2\)?
Answer: C
First, multiply the numbers without considering the decimals: 2 × 2 × 2 = 8.
Next, count the total number of decimal places in the original numbers. Each number has one decimal place, so there are 3 decimal places in total.
The result must have 3 decimal places. So, the answer is 0.008.
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The sum of the ages of a father and his son is 60 years. Six years ago, the father's age was five times the age of the son. What will be the son's age after 6 years?
Answer: A
Let the present ages of the father and son be F and S.
F + S = 60.
Six years ago, their ages were F-6 and S-6. So, F-6 = 5(S-6) => F - 6 = 5S - 30 => F = 5S - 24.
Substitute this into the first equation: (5S - 24) + S = 60 => 6S = 84 => S = 14.
The son's current age is 14 years. His age after 6 years will be 14 + 6 = 20 years.
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The product of two numbers is 9375 and the quotient, when the larger one is divided by the smaller, is 15. The sum of the numbers is:
Answer: C
Let the numbers be x and y, with x > y.
Given: xy = 9375 and x/y = 15 => x = 15y.
Substitute x in the first equation: (15y)y = 9375 => 15y² = 9375 => y² = 625 => y = 25.
Now find x: x = 15y = 15 × 25 = 375.
The sum of the numbers is x + y = 375 + 25 = 400.
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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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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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A number is doubled and 9 is added. If the resultant is trebled, it becomes 75. What is the number?
Answer: B
Let the number be x. We work backward from the result.
Before being trebled, the number was 75 / 3 = 25.
This resultant (25) was obtained after doubling the number and adding 9. So, 2x + 9 = 25.
2x = 25 - 9 = 16.
x = 16 / 2 = 8.
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What is 0.04% of 15000?
Answer: A
\[ 0.04\% = \frac{0.04}{100} = 0.0004 \]
\[ 0.0004 \times 15{,}000 = 6 \]
Treating 0.04% as 0.04 would give 600, a hundredfold error.
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Find the value of \(999 \frac{995}{999} \times 999\).
Answer: A
The expression can be rewritten as \((999 + \frac{995}{999}) \times 999\).
Using the distributive property: \(999 \times 999 + \frac{995}{999} \times 999\)
= \(999^2 + 995\)
= \((1000 - 1)^2 + 995\)
= \((1000000 - 2000 + 1) + 995\)
= 998001 + 995 = 998996.
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The sum of all prime numbers from 1 to 20 is:
Answer: B
The primes from 1 to 20 are
\[ 2,\ 3,\ 5,\ 7,\ 11,\ 13,\ 17,\ 19 \]
\[ 2+3+5+7+11+13+17+19 = 77 \]
1 is not prime, having only one divisor rather than two.
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