Math and Logic Puzzles Quiz

Average speed for round trip = 2xy/(x+y) where x=90 and y=60. Average = (2×90×60)/(90+60) = 10800/150 = 72 km/hr. The harmonic mean formula applies because distances are equal, not times.

Total of 11 results = 11×30 = 330. First five total = 5×25 = 125. Last five total = 5×28 = 140. Sum of first five + last five = 265. Sixth number = 330 - 265 = 65.

In 40L mixture with 3:1 ratio: milk = 30L, water = 10L. Let water added = x. New ratio = 30/(10+x) = 2/1. Cross-multiply: 30 = 2(10+x) → 30 = 20+2x → 2x = 10 → x = 5L.

Profit is divided in investment ratio 1600:1800:2300 = 16:18:23. Total parts = 57. A's share = (16/57)×399 = 112, B's share = (18/57)×399 = 126, C's share = (23/57)×399 = 161. Verify: 112+126+161 = 399.

Anup's rate = 1/10 work per day, Jagdeesh's rate = 1/15. Combined rate = 1/10 + 1/15 = 3/30 + 2/30 = 5/30 = 1/6. Time = 1/(1/6) = 6 days. This uses the standard work-rate formula.

Let total distance = 2x. Time for first half = x/21, second half = x/24. Total time = x/21 + x/24 = x(8/168 + 7/168) = 15x/168 = 5x/56. Speed = distance/time = 2x/(5x/56) = 112/5 = 22.4 kmph. Distance = speed×time = 22.4×10 = 224 km.

First find A U B = {1,2,3,4,5,6,7}, then intersect with C = {1,3,7,8}. The common elements between these sets are 1, 3, and 7, giving the result {1,3,7}. Union combines all unique elements from sets, intersection keeps only common elements.

A U B combines all unique elements from both sets: {a, b, c, e, g} U {a, d, e} = {a, b, c, d, e, g}. Note that element 'a' appears in both sets but is only listed once in the union - this is a fundamental property of set operations.

First find A U B = {1,2,3,4,6,8}, then intersect with C = {3,4,5,6}. The common elements are 3, 4, and 6, so (A U B) n C = {3,4,6}. Remember: union first (combine all), then intersection (keep only what's in both).

First find A n B = {2,4} (common elements only), then union with C = {3,4,5,6}. Combining all unique elements: {2,4} U {3,4,5,6} = {2,3,4,5,6}. Note: 4 appears in both but is listed once in the result.

The intersection of any set with the empty set is always empty. Set B = { } (empty set), so A n B = { } because there are no common elements. This is a fundamental property of set operations.

8 + 7 equals 15. Evaluating each option: A) 20/5 = 4, B) 8*2 = 16, C) 16-2 = 14, D) 45/3 = 15. Only option D equals 15.

Using order of operations (BODMAS/PEMDAS), multiplication comes before addition. So 7*2=14, then 8+14=22. None of the options A, B, or C equal 22, making D the correct choice.

This is a code-breaking question where letters map to numbers: T=1, G=2, K=3, I=4, N=5, H=6. Option C (3 5 4 2 6 1) translates to K-N-I-G-H-T = 'KNIGHT', which is a valid English word. The other options don't spell recognizable words.

Using the code G=1, A=2, R=3, I=4, T=5, S=6, Option B (1 3 2 5 4 6) translates to G-R-A-T-I-S = 'GRATIS', which means 'free' or 'without payment'. The other options don't form valid words when decoded.

The word MEASUREMENT contains letters M, E, A, S, U, R, N, T, M, E, N, T. 'METER' can be formed using M, E, E, T, E, R from these letters. 'ASSURE' needs two S's but only one is available. 'SUMMIT' needs two M's and two I's but 'I' isn't in MEASUREMENT. 'EARTH' needs 'H' which isn't available.