Tag: general knowledge

The first two numbers are 4 (average of 3 and 5) and 6 (average of 5 and 7). The next pair of twin primes is 11 and 13, whose average is 12. Option 9 is not the average of any twin prime pair.

The sum of two different cubes 1^3 (1) and 2^3 (8) is 9. 9 is a square number (3^2). This is the smallest square that is a sum of two distinct cubes.

Since a > b, a! = a * (a-1) * ... * (b+1) * b!. Therefore, a! is a multiple of b!, and the remainder of any multiple divided by its factor is always 0.

Numbers that are neither prime nor even are odd composite numbers. The first is 1 (by definition here), the next odd numbers are 3 (prime), 5 (prime), 7 (prime), and 9 (composite). Thus, 9 is the second.

The Fibonacci sequence continues: 21, 34, 55, 89, 144... Of these, 21, 34, 55 are not prime. The number 89 is prime and is the next prime Fibonacci number after 13. 79 is not a Fibonacci number.

The number 11 satisfies all conditions: 11/2 leaves remainder 1, 11/3 leaves remainder 2, and 11/4 leaves remainder 3. It is the smallest such positive integer.

Achluophobia is the specific term for fear of darkness. The prefix 'achluo' comes from Greek meaning darkness or gloom. Acrophobia is fear of heights, Ablutophobia is fear of bathing, and Agateophobia is fear of insanity.

Bathophobia is the specific term for the fear of depths. Batophobia is the fear of heights or being close to high buildings, and Bibliophobia is the fear of books.

Chromophobia is the fear of colors. The prefix 'chromo' comes from Greek meaning color. Chronophobia is fear of time, Chorophobia is fear of dancing, and Chrometophobia is fear of money.

Dystychiphobia is the fear of accidents. The prefix comes from Greek 'dystychia' meaning bad fortune or accident. Dinophobia is fear of whirlpools, Dendrophobia is fear of trees, and Dipsophobia is fear of drinking.