math & puzzles Online Quiz - 209

Working backwards: "three days after Saturday" = Tuesday. "The day before the day before yesterday" = two days before yesterday. If yesterday was Thursday, then two days before yesterday = Tuesday. So if yesterday = Thursday, today = Friday. This matches the pattern.

The pattern is subtract 4: 10-4=6, so 3-4=-1. This is a linear relationship where each term is 4 less than the corresponding term in the other pair. The analogy follows the form (first number) : (first number - 4) :: (second number) : (second number - 4).

The series increases by successive integers: 1(+2)=3, 3(+3)=6, 6(+4)=10, 10(+5)=15. The next increment is +6, so 15 + 6 = 21.

The code uses the position of letters in the alphabet: P=16, E=5, A=1, C=3, E=5. For 1215225: 12=L, 15=O, 22=V, 5=E. Thus, the word is 'love'.

200% of 14 is 28. The equation is (x/100) * 80 = 28. Solving for x: 0.8x = 28 -> x = 28 / 0.8 = 35.

Simple Interest = P×R×T/100 = 500×5×2/100 = Rs 50. Compound Interest = P×(1+R/100)^T - P = 500×(1.05)^2 - 500 = 500×1.1025 - 500 = 551.25 - 500 = Rs 51.25. The difference is 51.25 - 50 = Rs 1.25.

Total age of 20 students = 20 * 21 = 420. Total age of 21 people (including teacher) = 21 * 22 = 462. Teacher's age = 462 - 420 = 42.

Let the numbers be x-1, x, x+1. Sum: 3x = 15, so x = 5. The middle number is 5, and its square is 25.

This is a standard syllogism: If A ⊂ B and B ⊂ C, then A ⊂ C. Since all snarks are in the category of sneels, and all sneels are in the category of bontos, snarks must be bontos.

This is a logical fallacy. From 'all snarks are sneels' (snarks are a subset of sneels) and 'some sneels are bontos' (there is some overlap between sneels and bontos), we cannot conclude that some snarks are bontos. The snarks could be entirely outside the portion of sneels that overlaps with bontos. This is a classic categorical syllogism error.

This is a reference to the 'Battle of Wits' in The Princess Bride. Logic alone cannot solve the problem if the opponent is unpredictable or has poisoned both/neither; it is a psychological gamble, not a logical certainty.

The sentence is a classic example of center-embedding and complex noun phrases. While difficult to parse, it follows English syntactic rules for relative clauses and verb-object relationships.

This is a classic self-referential paradox similar to the Epimenides paradox. The sentence 'Their are four errors in this sentence' contains at least one grammatical error (using 'their' instead of 'there'). If we count this as one error, the statement becomes false, making the false statement itself an error - creating a logical contradiction.

Let C = x. Then A = x + 4. B = A - 6 = (x + 4) - 6 = x - 2. Total: x + (x + 4) + (x - 2) = 20. 3x + 2 = 20 -> 3x = 18 -> x = 6.

The squirrel needs 24 × 30 = 720 acorns total for September. In the first 6 days, it ate 20 × 6 = 120 acorns. Remaining needed: 720 − 120 = 600 acorns. Over 24 remaining days: 600 ÷ 24 = 25 acorns per day. 24 acorns/day would fall short of the monthly minimum, while 26 or 28 would exceed it.