Quiz about Mathematical Food for Thought
Quiz about Mathematical Food for Thought

Mathematical Food for Thought Trivia Quiz


If math isn't your thing, you might not be up to this, but you'll learn something along the way.

A multiple-choice quiz by SJM2015. Estimated time: 4 mins.
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Author
SJM2015
Time
4 mins
Type
Multiple Choice
Quiz #
394,264
Updated
Dec 03 21
# Qns
10
Difficulty
Average
Avg Score
7 / 10
Plays
334
1. Number Theory: All prime numbers greater than 2 are odd, but a prime greater than ten can never end in which digit? Hint

1
7
3
5

2. 3-D Geometry: If the volume of a cube is 27 cubic inches, what is its surface area? Hint

27 square inches
27 cubic inches
54 cubic inches
54 square inches

3. Algebra: There is just one perfect square number (a number that can be arrived at by multiplying a positive integer x by itself) between 30 and 40. What is it? Hint

32
39
38
36

4. Number Theory: Other than 1, the smallest positive number that is both a perfect square and a perfect cube is 64, which is 4 cubed as well as 8 squared. What is the smallest number greater than 64 that is both a perfect square and a perfect cube? Hint

256
729
4096
149

5. Geometry: If a decagon (a ten sided geometric figure) is equi-angular, how many degrees are there in each angle? Hint

144
90
180
60

6. Irrational Numbers: Without a calculator, if possible, determine which is greater: the cube root of 2 or the tenth root of 10. Hint

the cube root of two is greater
they are equal to each other
the tenth root of ten is greater
the answer is indeterminate

7. Binary Math: In binary, which of these numbers represents the Fahrenheit temperature at which water boils (at sea level)? Hint

1100010
1010010
11010100
1011101

8. Algebra: I'm three times as old as my little brother but five years from now I'll only be twice as old as him. How old am I now? Hint

15
12
20
30

9. Clock Mathematics: It is a little after one o'clock and the hour hand and the minute hand are in exactly the same position on my clock. To the naked eye, it is about 1:05, but exactly what time is it? Hint

1:05 5/11
1:05 3/8
1:05 5/12
1:06

10. Geometry: If all the angles of a triangle are less than 90 degrees, the triangle is called what? Hint

the Bermuda triangle
an obtuse triangle
an acute triangle
a right triangle


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Quiz Answer Key and Fun Facts
1. Number Theory: All prime numbers greater than 2 are odd, but a prime greater than ten can never end in which digit?

Answer: 5

All numbers ending in 5 are divisible by, you guessed it, 5. Hence, they are not prime.
2. 3-D Geometry: If the volume of a cube is 27 cubic inches, what is its surface area?

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.
3. Algebra: There is just one perfect square number (a number that can be arrived at by multiplying a positive integer x by itself) between 30 and 40. What is it?

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.
4. Number Theory: Other than 1, the smallest positive number that is both a perfect square and a perfect cube is 64, which is 4 cubed as well as 8 squared. What is the smallest number greater than 64 that is both a perfect square and a perfect cube?

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.
5. Geometry: If a decagon (a ten sided geometric figure) is equi-angular, how many degrees are there in each angle?

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.
6. Irrational Numbers: Without a calculator, if possible, determine which is greater: the cube root of 2 or the tenth root of 10.

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.
7. Binary Math: In binary, which of these numbers represents the Fahrenheit temperature at which water boils (at sea level)?

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
8. Algebra: I'm three times as old as my little brother but five years from now I'll only be twice as old as him. How old am I now?

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.
9. Clock Mathematics: It is a little after one o'clock and the hour hand and the minute hand are in exactly the same position on my clock. To the naked eye, it is about 1:05, but exactly what time is it?

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!
10. Geometry: If all the angles of a triangle are less than 90 degrees, the triangle is called what?

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.
Source: Author SJM2015

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