Aptitude & Reasoning Interview Questions and Answers

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.

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.

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.

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.

No. The premises are:

• All roses are flowers (roses are a subset of flowers).
• Some flowers fade quickly (a non-empty overlap exists between flowers and things that fade quickly).

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".

Two weighings.

Weighing 1: split into 3, 3 and 2. Weigh the two groups of 3.

• If one side is heavier, the heavy ball is in that group of 3.
• If they balance, the heavy ball is in the group of 2.

Weighing 2:

• If in a group of 3: weigh one against another. If one is heavier it is the ball; if they balance, the third one is heavy.
• If in a group of 2: weigh them against each other; the heavier is the answer.

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.