math & puzzles Online Quiz - 58

If 1.5 is a root, substitute x = 1.5 into x² + mx + 24 = 0: (1.5)² + m(1.5) + 24 = 0, giving 2.25 + 1.5m + 24 = 0, so 1.5m = -26.25, therefore m = -26.25/1.5 = -17.5. Verification: x² - 17.5x + 24 = 0 has roots 1.5 and 16 (product = 24, sum = 17.5).

The triangle with sides 5, 12, 13 is a right triangle since 5² + 12² = 13². For any triangle, the inradius r = A/s where A is the area and s is the semi-perimeter. Here, s = (5+12+13)/2 = 15 and A = (5×12)/2 = 30, so r = 30/15 = 2 units. Options A (6.5) and D (6) are not the inradius; B (12) is the longest side, not the inradius.

The number of diagonals in an n-sided convex polygon is given by n(n-3)/2. For n = 63, we get 63×60/2 = 1890 diagonals. Each vertex connects to n-3 other vertices via diagonals, and we divide by 2 to avoid double-counting. Option A (1953) and C (3720) are incorrect calculations; B (8906) is far too large.

The original area is L × W. After changes, new area = 1.1L × 0.9W = 0.99LW. This is a 1% decrease overall. The 10% increase and 10% decrease don't cancel out exactly - they multiply to 0.99, giving a net loss.

Solve 15x - 2 > x - 16. Move terms: 15x - x > -16 + 2, so 14x > -14. Divide by 14: x > -1. Any number greater than -1 satisfies this inequality.

The equation of a circle is (x-h)^2 + (y-k)^2 = r^2. For center (3,2) and radius 6, this is (x-3)^2 + (y-2)^2 = 36. Expanding gives x^2 - 6x + 9 + y^2 - 4y + 4 = 36, which simplifies to x^2 + y^2 - 6x - 4y = 23.

Ram takes 24 days alone. If Ram is half as efficient as Krish, Krish is twice as efficient, so Krish takes 12 days alone. Together: 1/24 + 1/12 = 3/24 = 1/8, so they take 8 days.

Let c = chickens, p = pigs. c + p = 200 (heads). 2c + 4p = 540 (legs). Solve: from first, c = 200 - p. Substitute: 2(200 - p) + 4p = 540, so 400 - 2p + 4p = 540, giving 2p = 140, so p = 70. Then c = 130.

This is a trick question - Mount Everest was always the highest mountain even before it was discovered. Discovery doesn't change physical reality. Kufri is a hill station, Ojos del Salado is in Chile, Huascaran is in Peru.

This is a pattern-breaking riddle. If Larry's father has five sons and four are named Ten, Twenty, Thirty, Forty - the fifth is Larry himself (not Fifty, which continues the pattern).

This is a trick question - you can subtract 5 from 25 only once, because after one subtraction you have 20, not 25. The question specifically asks about subtracting from 25.

Racecar is a palindrome - it reads the same forwards and backwards. MadaM is a palindrome but not a vehicle. Jaquer and Liril are not palindromes.

This is a mental math trick question. 1000+40+1000+30+1000+20+1000+10 = 4100. The riddle relies on people mistakenly grouping as thousands and getting 5000.

This is a classic riddle - if you say the word 'silence', the silence itself disappears. Cloud, wind, and poverty don't disappear when you name them.

This is a classic lateral thinking riddle. When the hunter shoots two birds, the loud gunshot scares the remaining birds away, so none remain on the wire. The answer tests whether you simply do arithmetic (5-2=3) or consider the real-world consequence of the scenario. Options A (1) and D (3) are incorrect because they ignore the birds flying away. Option B (2) incorrectly assumes only the shot birds are gone.

This question tests knowledge of animal biology and attention to detail. Peacocks are male peafowl, and only females (peahens) lay eggs. The trick is catching that the question says 'peacock' not 'peahen'. Options A and C are incorrect because they accept the false premise. Option B is incorrect because ownership depends on the bird's identity, not location.