Mathematical Food for Thought Trivia Quiz

Answer: 5

All numbers ending in 5 are divisible by, you guessed it, 5. Hence, they are not prime.

Answer: 54 square inches

The volume of a cube is equal to its side cubed. Hence, for a cube to have a volume of 27, its side must be 3 inches, as 3 inches x 3 inches x 3 inches is 27 cubic inches.

A cube has six faces (if you doubt this, take out your Rubik's cube and count) and each face of the cube is a square with area of 3 inches x 3 inches, which is 9 square inches. If each of the six faces of the cube has an area of 9 square inches, the total surface area of the cube is 54 square inches.

Answer: 36

Algebraically, a perfect square is a positive number that can be computed by multiplying a smaller positive number by itself. If x is 6, then x squared is 36, as 6 x 6 is 36, so it is a perfect square number. Five squared, which is 25, is too small, and seven squared, which is 49, is too big.

Answer: 729

For a positive number to meet both conditions, it must be of the form of x to the sixth power, where x is a positive integer, as the computed number will always be the square of x cubed and the cube of x squared.

As we see in the hint, two to the sixth power is 64, hence 64 meets the conditions.

The next smallest number that works is 3 to the sixth power, which is 729, the square of 27 as well as the cube of 9.

Answer: 144

A decagon's angles add up to 1440, which, as noted in the hint, can be computed as 180 x (10 - 2) = 180 x 8 = 1440.

Hence, if it is equi-angular, each of its ten angles much equal 144 degrees.

Answer: the cube root of two is greater

To make this determination, raise each number to the 30th power. In the case of the cube root of 2, the result is 2 to the tenth power, or 1,024. In the case of the tenth root of ten, you get 10 cubed, or 1,000. Hence, the cube root of two is greater.

Answer: 11010100

Water boils at 212 degrees Fahrenheit.

Sticking to the powers of 2, 212=

128 (2^7) + 64 (2^6) + 16 (2^4) + 4 (2^2)

In binary, that's 11010100

Answer: 15

My age is x and my brother's age is y.

Hence, x = 3y and x + 5 = 2(y + 5)

Solving simultaneously, you can determine that y is equal to 5, so my brother is 5. Hence x, which is equal to 3 times y, is 15, is my age.

Answer: 1:05 5/11

I once asked this question of a ten year old and was shocked that their solution was far simpler than mine! The easiest way to figure this out is to notice that the hour hand and minute hand will coincide eleven times in every twelve hour period. As this phenomenon must necessarily occur at equal intervals, it must happen once every 12/11 hours, or every 1 hour 5 minutes and 5/11. Hence, it is 1:05 5/11.

Now for the difficult way. Starting at twelve o'clock, the minute hand moves 6 degrees every minute and the hour hand moves 30 degrees per hour, and .5 degrees per minute. As it's between 1:00 and 2:00, let's say it's 1:00 and x minutes.

Hour hand position in degrees = 30 + .5x
Minute hand position in degrees = 6x

30 + 1/2 x = 6x
Multiply each side of the equation by 2.
60 + x = 12x, so 60 = 11x
hence, x is 60/11 = 5 5/11

So it's 1:05 5/11. Take a deep bow if you figured this one out the easy way or the hard way!

Answer: an acute triangle

Angles of less than 90 degrees are called acute, so a triangle having three such angles is called an acute triangle. Angles of greater than 90 degrees are called obtuse and a triangle containing an obtuse angle is called an obtuse triangle. A triangle containing a 90 degree angle is called a right triangle. The Bermuda triangle is unrelated to geometry.