What is the smallest number that must be added to 2203 to make it a perfect square?
Answer: C
We need to find the nearest perfect square greater than 2203.
We know \(40^2 = 1600\) and \(50^2 = 2500\). The number is between 40 and 50.
Let's try numbers ending in 3 or 7. \(47^2 = (50-3)^2 = 2500 - 300 + 9 = 2209\).
\(46^2 = (47-1)^2 = 2209 - 94 + 1 = 2116\).
The next perfect square after 2203 is 2209.
The number to be added is \(2209 - 2203 = 6\).
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What is the place value of 5 in the number 67.058?
Answer: B
The digit 5 is in the second position to the right of the decimal point. This is the hundredths place.
Its value is \(5 \times \frac{1}{100}\) or 0.05.
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Find the value of: \(1 - 2 + 3 - 4 + 5 - 6 + ... + 99 - 100\).
Answer: A
We can group the terms in pairs:
(1 - 2) + (3 - 4) + (5 - 6) + ... + (99 - 100).
Each pair sums to -1.
There are 100 terms in total, so there are 100/2 = 50 such pairs.
The total sum is 50 × (-1) = -50.
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What is the number which when multiplied by 13 is increased by 180?
Answer: B
Let the number be x.
According to the question, 13x = x + 180.
13x - x = 180.
12x = 180.
x = 180 / 12 = 15.
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If one-third of one-fourth of a number is 15, then three-tenth of that number is:
Answer: D
Let the number be x.
One-third of one-fourth of the number is \((\frac{1}{3}) \times (\frac{1}{4}) \times x = 15\).
\(\frac{x}{12} = 15\), so x = 180.
Now, we need to find three-tenth of the number:
\((\frac{3}{10}) \times 180 = 3 \times 18 = 54\).
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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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If the product of three consecutive integers is 120, then the sum of the integers is:
Answer: C
Let the consecutive integers be \(n-1, n, n+1\).
We need to find three consecutive numbers whose product is 120. We can estimate the cube root of 120. \(5^3=125\), so the numbers should be around 5.
Let's try 4, 5, and 6.
\(4 \times 5 \times 6 = 20 \times 6 = 120\). This is correct.
The integers are 4, 5, and 6.
Their sum is \(4 + 5 + 6 = 15\).
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3/4 of a number is 60 more than its 1/3. The number is:
Answer: B
Let the number be x.
The equation is \(\frac{3}{4}x = \frac{1}{3}x + 60\).
\(\frac{3}{4}x - \frac{1}{3}x = 60\).
The LCM of 4 and 3 is 12.
\(\frac{9x - 4x}{12} = 60\).
\(\frac{5x}{12} = 60\).
\(x = 60 \times \frac{12}{5} = 12 \times 12 = 144\).
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The sum of the digits of a 2-digit number is 9. When 27 is added to the number, the digits get reversed. The number is:
Answer: B
Let the ten's digit be x and the unit's digit be y. Number = 10x + y.
Given: x + y = 9.
Given: (10x + y) + 27 = 10y + x (reversed number).
\(9x - 9y = -27\), which simplifies to \(x - y = -3\) or \(y - x = 3\).
We have two equations: x + y = 9 and y - x = 3.
Adding them: 2y = 12, so y = 6.
Substituting y=6 into x+y=9, we get x=3.
The number is 36.
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Simplify: \(1.25 \times 40 - 2.5 \times 10\)
Answer: A
Using BODMAS, perform multiplication first.
Part 1: \(1.25 \times 40 = (\frac{5}{4}) \times 40 = 5 \times 10 = 50\).
Part 2: \(2.5 \times 10 = 25\).
Now perform subtraction: \(50 - 25 = 25\).
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