math & puzzles Online Quiz - 186

222,222,222 × 222,222 = 49,382,666,617,284. This can be verified by recognizing patterns in multiplying numbers with repeated digits or using algebraic manipulation with the formula for (10^n - 1) type numbers.

444,444,444 × 444,444 = 197,530,666,469,136. This follows from (10^9 - 1)^2 / 9 pattern for numbers of all 4s, where the middle section consists of 6s and the result follows a predictable digit structure.

The product of 555,555,555 and 555,555 is 308,641,666,358,025. This calculation follows the standard multiplication of large integers, where the repeating digits create a specific symmetric pattern in the resulting product.

Multiplying 666,666,666 by 666,666 results in 444,443,999,555,556. This can be verified by long multiplication or observing the pattern of digits produced by repeating numbers in such products.

Mean, median, and mode are the three primary measures used in statistics to identify the center of a data set. While 'average' is often used as a synonym for mean, the collective term for all three is 'Measures of Central Tendency'.

The probability that at least one is alive is 1 minus the probability that both are dead. The probability the husband dies is 0.2 (1-0.8) and the wife dies is 0.1 (1-0.9). 1 - (0.2 * 0.1) = 1 - 0.02 = 0.98.

If x and y are prime, their difference can be 1 (3-2) or 3 (5-2). It can be 15 (17-2) or 9 (11-2). However, for a difference to be 23, one number must be even (2) and the other 25, which is not prime. If both are odd, the difference must be even.

If k is divisible by 2, 3, and 15, it must be a multiple of their LCM, which is 30. For (k + x) to be divisible by 30, x must also be a multiple of 30. Only k+30 satisfies this condition.

From (x+2)²=9, we get x=1 or x=-5. From (y+3)²=25, we get y=2 or y=-8. For maximum x/y: use largest positive x (1) and smallest positive y (2), giving 1/2. Wait - check negative combinations: (-5)/(-8)=5/8 is the maximum.

The total weight increase is 15 persons * 2 kg = 30 kg. Since the new person replaced a 70 kg person and increased the total by 30 kg, the new person's weight is 70 + 30 = 100 kg.

Let the four consecutive numbers be x, x+1, x+2, x+3. Their sum is 4x + 6 = 154, so 4x = 148 and x = 37. Checking: 37 + 38 + 39 + 40 = 154. This confirms 37 is the smallest number.

Total parts = 10 + 15 + 6 = 31. The value of one part is 1581 / 31 = 51. B's share is 15 parts, so 15 * 51 = 765. The other options represent incorrect calculations or shares for A or C.

At 8:30, the hour hand is halfway between 8 and 9 (at 255° from 12, or 8.5 × 30 = 255°). The minute hand points at 6 (180° from 12). The angle between them is 255 - 180 = 75°. This is the smaller angle between the hands.

Calculate each term: 20% of 5 = 0.2 × 5 = 1. And 5% of 20 = 0.05 × 20 = 1. So 1 + 1 = 2. This demonstrates that both expressions give the same result, making the calculation straightforward.

To solve this problem, the user needs to know how to convert a percentage to a decimal and how to solve basic algebraic expressions.

Let x be the unknown number. The problem states that this number is equal to 20 plus 20% of its value.

Thus, we can write the following equation:

x = 20 + 0.2x

Simplifying this expression by subtracting 0.2x from both sides:

0.8x = 20

Dividing both sides by 0.8:

x = 25

Therefore, the correct answer is:

The Answer is: C. 25

The pattern alternates between multiplying by 2 and multiplying by 1.5 (or adding the previous term): 32=6, 61.5=9, 92=18, 181.5=27, 272=54. The next step is 541.5 = 81. Other options do not follow this geometric progression.

Use the Pythagorean theorem to find the missing height: sqrt(10^2 - 8^2) = sqrt(100-64) = 6 cm. Then area = 1/2 × base × height = 1/2 × 8 × 6 = 24 cm².

Let the original number be x. The student mistakenly calculated x + 10 - 16 = 14, which means x - 6 = 14, so x = 20. The question asks for the correct answer to the original instruction of adding 16 and subtracting 10, which is x + 16 - 10 = 20 + 16 - 10 = 26.