Math & Logic Puzzles

All numbers except 72 are perfect squares: 16=4^2, 25=5^2, 36=6^2, 144=12^2, 196=14^2, 225=15^2. The number 72 cannot be expressed as the square of an integer.

All numbers except 81 are prime numbers. 81 = 9 × 9 = 3^4 is a composite number (not prime), making it the odd one out.

The differences are squares: +1, +4, +9, +16, +25. The next difference should be +36. 56 + 36 = 92. Therefore, 91 is the wrong number in the sequence.

The pattern is subtracting increasing amounts: 105-20=85, 85-25=60, 60-30=30, 30-35=-5 (not 0), -5-40=-45, -45-45=-90. The number 0 breaks the pattern - it should be -5.

The differences between consecutive numbers are prime numbers: +2, +3, +5, +7, +11. Following 153, the next difference should be +13, making the final number 166. Therefore, 165 is the wrong number.

The sequence consists of squares of descending integers: 14 squared (196), 13 (169), 12 (144), 11 (121), 10 (100), and 8 (64). The number 80 is incorrect because 9 squared should be 81.

The pattern is (x * 3) - 4. (103)-4=26; (263)-4=74; (743)-4=218; (2183)-4=650. The number 654 is wrong because it should be 650 based on the established mathematical progression.

The word 'forty' (40) is the only number in English whose letters (F-O-R-T-Y) appear in alphabetical order. Other numbers like 30 (thirty) or 90 (ninety) do not follow this rule.

Italy, France, and Spain are all European countries. Paris is a city (the capital of France), making it the odd one out as it represents a different category of geographical entity.

The sequence follows a pattern where 'C' is a repeating separator: A, C, B, C, C, C, D, C. The primary letters are A, B, C, D. Following this alphabetical progression, the next primary letter after D is E.

Tulip, daisy, and crocus are exclusively flowers. Iris is the outlier because it has dual meanings - it's both a flower and a part of the human eye (the colored part). This makes it different from the other three options which only have one meaning in common usage. The word association pattern is the key here.

The sequence represents Roman numerals in ascending order of value: I (1), V (5), X (10), L (50). The next standard Roman numeral in the sequence of values is C (100).

Your sister's uncle is your uncle. His wife is your aunt. Their daughter is your cousin, and her brother is also your cousin. The statement correctly identifies the familial relationship.

For a $100 shirt: 10% then 40% means $100 → $90 (after 10% off) → $54 (after 40% off the $90). The final price is $54, meaning you saved $46 (46% total). A straight 50% off means $100 → $50, saving $50. The 50% single discount is better because you save more ($50 vs $46). Sequential discounts apply to decreasing amounts, so total discount is always less than the sum.

Let son's age be x, mother's be 9x. In 5 years: 9x + 5 = 5(x + 5). Solving gives 9x + 5 = 5x + 25, so 4x = 20 and x = 5. The mother's current age is 9 * 5 = 45.