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Generate a random set of questions, reveal answers as you go and score yourself honestly.
Average speed is total distance divided by total time, not the average of the two speeds.
Total distance = 300 + 200 = 500 km.
Total time = 3 + 2.5 = 5.5 hours.
Average speed = 500 / 5.5 ≈ 90.91 km/h.
Common trap: averaging 100 km/h and 80 km/h gives 90, which is wrong because the time spent at each speed differs.
No. The premises are:
The flowers that fade quickly may or may not include roses, so no valid conclusion about roses follows. This is the classic syllogism trap called the fallacy of the undistributed middle.
To conclude "some roses fade quickly", we would need an additional premise such as "all flowers fade quickly" or "no flower except roses fades quickly".
The word LEVEL has 5 letters with repeats: L appears 2 times, E appears 2 times, V appears once.
Total arrangements = 5! / (2! x 2!) = 120 / 4 = 30.
Approach: start with the factorial of the total length, then divide by the factorial of each repeated letter count to remove duplicate permutations. If all letters were distinct it would be 120.
Two weighings.
Weighing 1: split into 3, 3 and 2. Weigh the two groups of 3.
Weighing 2:
General principle: with a balance scale each weighing has three outcomes, so b weighings distinguish up to 3^b cases. For 8 balls, 3^2 = 9 >= 8, so two weighings suffice.
Look at the differences: 4, 6, 8, 10, which increase by 2 each time. The next difference is 12, so the next term is 30 + 12 = 42.
Alternative view: the terms are n(n+1) for n = 1, 2, 3, 4, 5, 6 -> 2, 6, 12, 20, 30, 42.
Both patterns are valid; identifying either leads to 42. When solving number series always check first and second differences, ratios and known formulas.
Successive discounts multiply, they do not add.
Price 100 -> after 20% = 80. After an additional 10% on 80 -> 80 x 0.9 = 72.
Effective discount = 100 - 72 = 28%.
Formula for successive discounts a% and b%: net = a + b - (a x b)/100 = 20 + 10 - 200/100 = 28%. The naive answer 30% is wrong.
Why it matters: the second discount applies to the already reduced price, so the base is smaller and the effective saving is less than the sum of the two rates. This compounding also appears in successive percentage increases, where the multiplier for two changes is (1 + a)(1 + b) rather than 1 + a + b.