Number Puzzles and Prime Numbers

Indigo is one of the seven traditional colors of the visible spectrum (ROYGBIV). While lime, purple, and cyan are colors, they are not part of Newton's classic seven-color rainbow sequence, which consists of red, orange, yellow, green, blue, indigo, and violet.

The ratio of consecutive Fibonacci numbers (e.g., 8/5, 13/8) converges to the Golden Ratio, approximately 1.618. Pi and the square root of 2 are also irrational numbers, but they relate to circles and squares respectively, not the Fibonacci sequence.

Prime numbers between 30 and 50 are: 31, 37, 41, 43, 47. That's 5 prime numbers total. Option A (4) is too few, Option C (3) is even fewer, Option D (8) is too many. Option B correctly states there are 5 prime numbers in this range.

A prime number is only divisible by 1 and itself. 91 (7x13), 93 (3x31), and 99 (9x11) are composite. 97 has no divisors other than 1 and 97, making it the only prime number in the 90-100 range.

14 is the odd number because all other numbers (3, 5, 11, 17, 21) are odd numbers, while 14 is an even number. In odd man out questions, you look for the one element that doesn't follow the pattern of the others.

In all numbers except 427, the sum of the first and third digits equals the middle digit (e.g., 3+6=9, 4+2=6, 5+2=7). For 427, 4+7=11, which does not equal 2.

All numbers in the set except 20 are perfect squares: 1 (1^2), 4 (2^2), 9 (3^2), 16 (4^2), 36 (6^2), and 49 (7^2). 20 does not fit this mathematical pattern.