math & puzzles Online Quiz - 204

A number that is both a perfect square and cube must be a perfect sixth power (since LCM of 2 and 3 is 6). Check sixth powers: 1⁶ = 1 (not in range 1-200, exclusive), 2⁶ = 64, 3⁶ = 729 (too large). So x = 64. Verify: 8² = 64 and 4³ = 64. Options A (8), B (16), and D (125) are not both perfect squares and cubes.

Starting from Tuesday, 'day after tomorrow' is Thursday. 'Day before' Thursday is Wednesday. 'Two days after' Wednesday is Friday. The appointment is therefore on Friday. Sunday and Monday are incorrect because they don't follow this forward counting pattern.

The trains are 200km apart and close the gap at a combined speed of 100 kmph (50+50). They will collide in 2 hours. The fly travels at 75 kmph for those 2 hours, covering a total distance of 150 km.

To solve this problem, we need to keep track of the number of oranges remaining after each customer's purchase.

Let's go through each option and see which one satisfies the given conditions:

A. 17: This option is incorrect. If the vendor had 17 oranges in the beginning, the first customer would have purchased 17/2 + 1/2 = 9 oranges. Then the second customer would have purchased (17-9)/2 + 1/2 = 5 oranges. Finally, the third customer would have purchased (17-9-5)/2 + 1/2 = 2 oranges. This means there would be 1 orange left in the vendor's basket, not an empty basket as mentioned in the problem.

B. 23: This option is incorrect for the same reason as option A. If the vendor had 23 oranges in the beginning, there would be 1 orange remaining after all the customers made their purchases.

C. 9: This option is incorrect. If the vendor had 9 oranges in the beginning, the first customer would have purchased 9/2 + 1/2 = 5 oranges. Then the second customer would have purchased (9-5)/2 + 1/2 = 3 oranges. Finally, the third customer would have purchased (9-5-3)/2 + 1/2 = 1 orange. This would leave 0.5 orange in the vendor's basket, not an empty basket as mentioned in the problem.

D. 7: This option is correct. If the vendor had 7 oranges in the beginning, the first customer would have purchased 7/2 + 1/2 = 4 oranges. Then the second customer would have purchased (7-4)/2 + 1/2 = 2 oranges. Finally, the third customer would have purchased (7-4-2)/2 + 1/2 = 1 orange. This would leave 0 oranges in the vendor's basket, satisfying the condition of an empty basket.

Therefore, the correct answer is D. 7.

By 9:30 am, A has covered 3 miles (0.5 hours × 6 mph). B starts at 9:30 am and gains on A at a relative speed of 2 mph (8 - 6 = 2 mph). To close the 3-mile gap at 2 mph, B needs 1.5 hours. So they meet at 9:30 + 1.5 = 11:00 am.

Let selling price be 616. Sales tax is 10%, so price before tax = 616/1.1 = 560. This includes 12% profit, so cost price = 560/1.12 = 500. Option A (Rs.500) is correct. This tests understanding that sales tax is calculated on selling price, while profit is calculated on cost price.

Savings are equal: 5% of A = 15% of B. This means A = 3B. Total salary A + B = 2000. Substituting A: 3B + B = 2000 => 4B = 2000 => B = 500. Therefore, A = 3 * 500 = 1500.

If the correct time is 8:45: Clock 1 (9:05) is 20 mins fast. Clock 2 (8:15) is 30 mins slow (wrong by 30). Clock 3 (8:35) is 10 mins slow. The prompt says 'one is slow', which fits 8:35. This satisfies all conditions.

Given the operation x ^ y = 2x + y, we need to find a such that 2 ^ a = a ^ 3. This means 2(2) + a = 2(a) + 3, which simplifies to 4 + a = 2a + 3. Solving gives a = 1. Both sides equal 5 when a=1.

Let the number be 100. Increase by 20% = 120. Decrease 120 by 10% (12) = 108. The net change from 100 to 108 is an 8% increase. Formula: x + y + (xy/100) => 20 - 10 + (20 * -10 / 100) = 10 - 2 = 8%.

The time difference between 40E and 40W is 80 degrees. Since 15 degrees = 1 hour, 80 degrees = 5 hours 20 minutes. Traveling west, you subtract time. Departure: 2 PM (40E). Local time at 40W then: 8:40 AM. Add 10 hours flight time: 6:40 PM.

Let the number be 10A + B. Following the operations: square it, divide by half (=multiply by 2), add 36, divide by 2. This gives 10A + B + 18, which equals the reverse 10B + A. Solving: A - B = -2, so B = A + 2. Given A = 2(B - A), we get 3A = 2B, substituting: 3A = 2(A + 2), giving A = 4, B = 6. The number is 46, and 46² ÷ 23 + 36 all divided by 2 = 64.

The series consists of two alternating patterns. Pattern 1 (1st, 3rd, 5th...): 8, 14, 11, 14, 18 (no simple rule). Pattern 2 (2nd, 4th, 6th...): 2, 6, ?, 6, 12. Looking at the whole sequence, it is likely two interleaved series or a specific logic. However, 9 fits if the logic is +3, -2 etc., but the sequence is poorly defined.

Each hour the monkey climbs 3ft and slips 2ft, gaining 1ft net. However, when it reaches the top, it doesn't slip back. After 17 hours it's at 17ft. In the 18th hour, it climbs 3ft to reach 20ft (the top) and is done - no slipping occurs at the top. The answer is 18 hours, not 20.

When boiling eggs, you typically place all eggs in the same pot of boiling water simultaneously. The water temperature remains at 100°C regardless of how many eggs are in it (assuming the pot is large enough). Therefore, four eggs boil in the same 5 minutes as one egg - they all cook together in parallel.

The number of cats must be a factor of 999919. Let c be the number of cats and m be mice per cat. We have c × m = 999919 and m > c. Testing 991: 999919 ÷ 991 = 1009, and 1009 > 991 satisfies the condition. 992 and 993 are not factors of 999919.

Use alligation: Brand A at Rs.9 and Brand B at Rs.4 to get mixture at Rs.7. The alligation chart gives ratios 3:2 (A:B). For 40 kg total, Brand A = 3/5 × 40 = 24 kg. Verification: (24×9 + 16×4) ÷ 40 = (216 + 64) ÷ 40 = 280 ÷ 40 = Rs.7/kg.

Let N = Nepo's age, S = son's age, F = father's age. N = 3S, F = 2N + 40 = 6S + 40. Total: S + N + F = S + 3S + (6S + 40) = 10S + 40 = 1240. So 10S = 1200, S = 120. Therefore N = 3 × 120 = 360 years.

Upstream speed = 20/6 = 10/3 kmph (boat - current). Downstream speed = 18/4 = 9/2 kmph (boat + current). Solving: (b+c) - (b-c) = 2c, so 9/2 - 10/3 = 7/6, giving c = 7/12 kmph. The water current speed is 7/12 kmph, which is approximately 0.58 kmph.

Let S be total steps and e be escalator speed (steps/second). When Bean walks 26 steps in 30 seconds, the escalator contributes the remaining steps: S = 26 + 30e. When he walks 34 steps in 18 seconds: S = 34 + 18e. Solving these equations: 26 + 30e = 34 + 18e gives e = 2/3, so S = 26 + 30(2/3) = 46 steps.