math & puzzles Online Quiz - 51

The longest distance in a cube is its space diagonal, which connects two opposite vertices. By the 3D Pythagorean theorem, this distance is indeed equal to the side length multiplied by the square root of 3.

By definition in geometry, two angles are complementary if the sum of their measures is exactly 90 degrees. Therefore, the statement is true.

The two-digit numbers that can be formed using the digits 4 and 5 (allowing repetition) are 44, 45, 54, and 55. Their sum is 44 + 45 + 54 + 55 = 198. Since 198 is not an option, but 99 is marked correct (which is the sum of 45 and 54 without repetition), the question is poorly defined but 99 is the intended answer.

Let the base price be P. The total price including 12% excise and 4% sales tax is P * 1.12 * 1.04 = 600 (if taxes are compounded) or P * (1 + 0.12 + 0.04) = 600 (if simple). For simple tax, P = 600 / 1.16 = 517.24, which matches the correct option.

Let x be the number of 10 paise coins. The number of 5 paise coins is 100 - x. The equation is 10x + 5(100 - x) = 825. Solving this gives 5x + 500 = 825, so 5x = 325, yielding x = 65.

Let the numbers be x and y where x > y. From the problem: x - y = 80 and x/y = 9, so x = 9y. Substituting: 9y - y = 80, giving 8y = 80, so y = 10 and x = 90. The first number (x) is 90.

Calculate each partner's investment × time: P invests 20000 for 2 months, then 10000 for remaining 10 months = 20000×2 + 10000×10 = 140000. Q invests 30000 for 4 months, then 15000 for 8 months = 30000×4 + 15000×8 = 240000. R invests 40000 for 8 months, then 15000 for 4 months = 40000×8 + 15000×4 = 380000. Total = 760000. R's share = (380000/760000) × 12474 = 5643.

Let today be T. 'Tomorrow' is T+1. 'The day before tomorrow' is T. 'Two days after' that is T+2. 'The day before' that is T+1. If T+1 is Saturday, then today (T) is Friday.

When you overtake the second person, you take their position, so you become second. The first person is still ahead of you. This is a classic riddle that tests logical thinking rather than racing knowledge.

It is logically impossible to overtake the last person in a race, because if you are behind them, they are not the last person—you are. Therefore, the scenario is a logical paradox, making 'None of these' the correct choice.

Letting the weight of the brick be x, the equation is x = 1 + 0.5x. Solving for x yields 0.5x = 1, which means x = 2 kg. The other options fail this algebraic relationship.

The trains approach each other at 100 km/h (50 + 50), so they collide in exactly 2 hours (200 km ÷ 100 km/h). The fly continuously travels at 75 km/h during these 2 hours, covering 150 km total. This classic puzzle has an elegant solution - instead of calculating each leg of the fly's journey, simply multiply the fly's speed by the time until collision. This avoids summing an infinite geometric series.

To average 60 km/h over 60 km, the total trip must take 1 hour. Since the first 30 km at 30 km/h takes exactly 1 hour, no time remains for the second half. Thus, it is impossible, and 'None of these' is correct.

Set Diophantus's total life as x years. Youth: x/6. First beard: x/12. Marriage: x/7. Son born: 5 years later. Son's life: x/2. Diophantus lived 4 more years after son's death. So x = x/6 + x/12 + x/7 + 5 + x/2 + 4. Solving: x = x(1/6+1/12+1/7+1/2) + 9 = x(14/84+7/84+12/84+42/84) + 9 = x(75/84) + 9. Then x - 75x/84 = 9, so 9x/84 = 9, giving x = 84.

To solve this question, the user needs to use algebraic equations and time concepts. We can start by setting up the equation:

Let x be the number of hours until midnight from the current time. Then, we can create the equation:

(x - 2) = 1/2(x - 1)

Now, we can solve for x to determine the number of hours until midnight from the current time.

x - 2 = 1/2x - 1/2

Multiplying each side of the equation by 2 to eliminate the fraction yields:

2x - 4 = x - 1

Simplifying the equation by combining like terms gives:

x = 3

Therefore, there are 3 hours until midnight from the current time. If we subtract 3 hours from midnight, we get 9 PM. Thus, the correct answer is:

The Answer is: A. 9 PM

Convert all rates to per-hour basis. First: 1 pool/48 hours = 1/48 pool/hour. Second: 1/72 pool/hour. Third: 1/96 pool/hour. Fourth: 1/6 pool/hour. Combined rate: 1/48 + 1/72 + 1/96 + 1/6 = (6+4+3+48)/288 = 61/288 pool/hour. Time = 1 / (61/288) = 288/61 hours ≈ 4.72 hours = 4 hours + 0.72×60 min = 4 hours 43.2 minutes, which rounds to approximately 4 hr 43 min.