Math & Logic Puzzles

If A takes 12 days, then B's efficiency being 60% more means B works at 1.6x A's rate. So B takes 12/1.6 = 7.5 days. The phrase '60% efficient than that of A' is slightly awkward but mathematically leads to option B.

The coding pattern alternates between adding 3 and subtracting 3 from letter positions: B(+3)E, H(-3)E, O(+3)R, P(-3)M, A(+3)D, L(-3)I. Applying this to POWDER: P(-3)S, O(+3)R, W(-3)T, D(+3)G, E(-3)B, R(+3)U, which gives SRTGBU. However, reversing the alternating pattern gives: P(+3)S, O(-3)L, W(+3)Z, D(-3)A, E(+3)H, R(-3)O, which matches option B 'SLZAHO'.

By comparing the three equations, we can identify individual number-word associations. From 256 and 358, we see that 2 and 3 represent 'you/are' and 'we' respectively, while 5 appears in both representing 'bad' or a negation. From 358 and 637, the number 8 is common to both phrases containing 'and', suggesting 8 represents 'and'. The number 3 represents 'we/bad' and 2 represents 'you/are'. Therefore, 'and' corresponds to 8.

Since the speaker has no siblings, 'my father's son' can only refer to the speaker himself. Therefore, 'that man's father is my father's son' means 'that man's father is me', which implies the person in the photograph is the speaker's son. This is a classic logical reasoning puzzle testing family relationships.

An icosahedron is a regular polyhedron with 20 triangular faces. The name comes from the Greek 'icosa' meaning twenty. Each vertex of a regular icosahedron is where 5 triangular faces meet.

The commutative property in mathematics states that the order of operands doesn't change the result: ab = ba for multiplication and a+b = b+a for addition. Option A shows the associative property, Option C is not a standard property, and Option B is incorrect.

The Pythagorean theorem (a² + b² = c² for right triangles) is named after Pythagoras, the ancient Greek mathematician. While the relationship was known to earlier civilizations like the Babylonians, Pythagoras is credited with its formal proof and popularization in Greek mathematics.

This is Euler's formula for convex polyhedra: V - E + F = 2, where V is vertices, E is edges, and F is faces. This relationship holds true for all convex polyhedra (like cubes, pyramids, etc.).

Every equilateral triangle (all sides equal) is also isosceles (at least two sides equal). An isosceles triangle only requires two equal sides, so an equilateral triangle with three equal sides satisfies this condition. The reverse is not true - an isosceles triangle is not necessarily equilateral.

Using the FOIL method: (x+2)(3x-7) = x(3x) + x(-7) + 2(3x) + 2(-7) = 3x² - 7x + 6x - 14 = 3x² - x - 14. Option A has the wrong middle term (+x instead of -x), Option B has -13x instead of -x, and Option D is missing the x term entirely.

The associative property states that when performing the same operation (like multiplication or addition) on three or more numbers, the grouping doesn't matter: (ab)c = a(bc). Option A describes the commutative property, Option C is not a standard property, and Option D is incorrect.

This asks which statement is NOT true. Options A, B, and C are all true: a dodecahedron has 12 faces, in spherical geometry parallel lines do meet, and a square is a special type of rhombus. Option D is FALSE because there are exactly 5 Platonic solids (tetrahedron, cube, octahedron, dodecahedron, icosahedron), not 6. Therefore D is the correct answer to 'which is not true'.

20,000 mg is equal to 20 g (since 1,000 mg = 1 g). The option states it is 2 g, which is incorrect. Other conversions: 30 cm = 0.0003 km is correct ($30/100,000$), and 3000 tonnes = 3,000,000 kg is correct.

The term 'permutative' is not a standard mathematical property. The property $ab = ba$ is called 'commutative', and $a*(bc) = (ab)*c$ is called 'associative'. Therefore, the statement that it is not a mathematical term is correct.

Prime numbers are defined as numbers greater than 1 that are divisible only by 1 and themselves. The examples given (2, 3, 5, 7, 11) are all prime numbers as they each have exactly two factors.

Raising a number to the power of one-half is equivalent to taking its square root. Only 'square numbers' (like 1, 4, 9, 16) result in whole numbers when their square root is taken.

Irrational numbers are real numbers that cannot be expressed as a simple fraction or ratio of two integers (like $\pi$ or $\sqrt{2}$). Rational numbers, by contrast, can be expressed as ratios.

A perfect number equals the sum of its proper divisors (all positive factors except the number itself). For 6: 1+2+3=6; for 28: 1+2+4+7+14=28; for 496: 1+2+4+8+16+31+62+124+248=496.

Real numbers include rational numbers, irrational numbers, and whole numbers, but NOT imaginary numbers. Imaginary numbers (involving i, where i²=-1) are a separate category from real numbers.