1. Multiply.
   Divide.
2. Add.
   Subtract.

Computing uses mathematical symbols other than the ones one would write by hand. * is for multiplying, / is for dividing, for example. Don't worry though, + and - and = are all still used.

1. 8
   10
2. 9
   7

This is a typical middle school math question, as it simultaneously makes you engage your math brain and it plays on your ability to understand the language around numbers. "All but nine die" means "nine live".

1. 54
   100
2. 72
   81

Many stats in sports can be bettered, but it is essentially impossible to beat this hypothetical one. If a perfect pitcher, capable of striking out an entire team, were to play a full nine innings, this is how it would break down: Each inning involves 3 at-bats (meaning a total of 27 in the game) and each at-bat requires 3 strikes for an out, assuming the ball isn't put in play (we're assuming for this that it isn't). This means to get the minimum number of pitches, you multiply the number of at-bats (27) by the number of strikes per at bat (3). It is possible for a pitcher to win a complete, perfect game in just 27 pitches, if each pitch is contacted by the batter, and put into play for an out.

1. If you add up their composite digits until you only have one digit left, you'll always end up with 9.
   They're all odd.
2. They're all irrational.
   They're all even.

9 has a strange property, which means that if you take any number multiplied by 9 and add up its composite digits until it's just one number, that one number will be nine. Take for example 9*73, which is 657. 6+5+7=18. 1+8=9. Strange, right?

1. 12x
   7x
2. 1x
   4x

Polynomials can be confusing, but in this simple situation, it's jut a matter of adding the Arabic numbers, and not worrying about the variables.

1. Halfway into the forest.
   All the way to the other side.
2. A quarter of the way through.
   It won't go in very far.

A dog, or indeed anyone who runs into a forest, is limited in how far into the forest they can go. Going "into" a forest isn't the same as traveling a distance through a forest. The longest distance traveled through a forest could be a line, or a spiral, depending on geography, but the radius of the forest determines how far "into" it one can go. Thus, going "halfway" into the forest is going into the deepest part of the forest.

1. 12x
   10x
2. 7x
   12x

Using the computerized math symbol for multiplication, the answer is actually very simple. The 3x ( x+x+x) multiplied by the 4x (x+x+x+x) is really just 3*4, which is 12, but the 12 is multiplied by x. Thus, 12x.

1. 100%
   75%
2. 25%
   50%

In the US, we call pennies "cents" because each is 1% of a dollar. A US quarter is 25 cents, and two US quarters is 50 cents. Thus, two quarters are 50% of a dollar.

1. 33.3%
   3.4%
2. 3.33%
   30%

Getting a percentage is a fairly easy thing to do, especially when you don't have to deal with decimals. 17*30 is 510, so it's not hard to work out. Let's call the percentage "x". First, if 510=100%, then 17=x%. Stack these two equations, creating a single equation("100/x=510/17"). Multiply both sides of the equation by X ("(100/x)*x=(510/17)*x"), and simplify what you can, dividing 510 by 17, giving you 30x. No, divide both sides by 30. This means one side of your equation will be x, and the other side will be the percentage. The answer is 3 and a third percent, which rounds off to 3.33%.

1. nm
   n*m
2. n(m)
   n*n+m

The answer to the math question is n times m. This can be expressed as "nm" as putting two variables beside each other means they are multiplying by each other, "n*m" because it expresses the same thing with a multiplication symbol, or (n)(m) since parenthetical beside each other are multiplied. The answer to the math doesn't have addition in it, so the right test answer is the one with the addition, or "n*n+m".

1. Divide the diameter in half.
   Divide the circumference by four.
2. Multiply the diameter by π.
   Divide the area of the circle by π.

The radius of a circle can be measured if you have the diameter. The diameter is the distance from one side of a circle to the other, and the radius is half of that. Thus, a circle with a diameter of ten feet has a radius of five feet.

1. When it doesn't so stupid things like going out in the winter without a coat.
   When it is a real number that can be expressed as the fraction of two integers, the bottom of which isn't zero.
2. When it is an even number.
   When it is a real number.

Rational numbers are real numbers that can be expressed as a fraction, the bottom of which isn't zero. Essentially, if you divide the fraction, 3/4 for example, you get a number, 0.75 in this case. If you don't get a neat decimal that stops, as in the case of π, and the decimal just keeps going without repeating, you have yourself an irrational number.

1. 3.33
   18
2. 12
   14

To determine what one third of 21 is, you could divide 21 by 3. This would give you a result of 7. 7*2=14, so 14 is 2/3 of 21.

1. Irrational numbers, like π.
   A number that is a whole number that can be expressed without a symbol like the square route symbol.
2. A number that isn't imaginary or infinity.
   ∞

A real number can be either rational or irrational; either algebraic or transcendental; and either positive, negative or zero.

1. 16
   32
2. 24
   8

If two thirds of the class are doing something, and the remaining 8 are doing something else, then those 8 students are a third of the class. If you multiply 1/3 by 3, you get the total of the whole group. In this case, this works out to 8*3=24, so there are 24 students in the class.

1. 110
   165
2. 175
   155

A trucker who manages a constant speed of 55 mph will cover, as the measurement suggests, 55 miles in an hour. In three hours at that speed, he or she would travel 165 miles.

1. 15:1
   1:3
2. 5:14
   3:10

If you add up all the marbles, you get 15 total marbles. 5 marbles (the number of yellow marbles) makes up a third of 15, so the ratio is 1:3.

1. 1 , 2 , 5 , 10 , 25 , 50
   1, 2, 5, 10, 20, 15, 49
2. 1, 2, 3, 5, 10, 25, 50
   1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 15, 20, 25, 40, 50

A factor of a number is really only a factor of that number when it can cleanly divide the number in question. 50 is divisible by 1 and 50, obviously. It's also divisible by 2, 5, 10, and 25. Thus, its factors are 1, 2, 5, 10, 25, 50.

1. 3,000
   750
2. 375
   75

While all of these numbers are multiples of 15 and 25, 75 is the lowest. The first few multiples of 25 are: 25, 50, 75, 100, 125, etc. The first few multiples of 15 are: 15, 30, 45, 60, 75, 90, etc. The lowest common number is 75.

1. There isn't one.
   Null is less than 0.
2. Null is a lack of information, not the definition of a value.
   Null is a transient state, sometimes represented by 0.

Null doesn't mean 0, but sometimes it is represented that way. Null means "there isn't a value", which can sometimes be taken to mean 0, but actually means... nothing. If for example, you take photos and do not give them a geotag, and then you post them on a site like Google Earth, it will likely place them at 0 latitude and 0 longitude, a location in the South Atlantic known colloquially as "Null Island", since it is the place so many "null" value photos go. There is no island there.

1. 0.667%
   0.0667
2. 1/12
   6.667%

To compute 40% of a sixth, divide 1 by 6, and then multiply that by .4. Remember that when it comes to expressing decimals as a percentage, the "whole number" or "100%" in question is just "1.0" so if you get a value of 0.0667, it's really 6.66.7%

1. 1/20
   1/10
2. 2/50
   20/50

To computer 20% of 50%, convert to decimals: .5 and .2, and then multiply the two. The result is .1, which is 1 10th, represented as 1/10.

1. Z* theorem.
   Conway–Schneeberger Fifteen Theorem
2. Gödel's incompleteness theorems
   Pythagorean Theorem.

The Pythagorean Theorem is the manner in which one can computer the lengths of the three sides of a triangle, a useful basic building block of mathematics.

1. The circumference of the Earth.
   Your height.
2. The elevation of your eyes.
   The diameter of the Earth.

Like the Pythagorean Theorem, this is deceptively simple. If the answer is "c", then "a" is the radius of the Earth (20,903,520 feet), and "b" is 20,903,520 feet plus the height of your eyes and the elevation you are standing on (sea level=0 feet, Denver=5,280 feet)

1. 4
   2
2. 3.2
   3

First, subtract 5 from both sides of the equation. This gives you "2x = 6". Divide both sides by 2 to get rid of the 2 on the left side, and you get "x=3".

1. A common denominator.
   A cross product.
2. Help!
   Google.

To solve this, first you need to multiply both sides by "5*16", which is the common denominator, giving you "(5*16)(4/5)=(a/16)(5*16)"Next, you sort out the cross product, by simplification, producing "16*4=5*a", which is "64=5a". Now divide both sides by 5, resulting in "64/5=a".

1. A number that is a 1 with 100 zeros after it.
   A second rate search engine.
2. It's a made up thing from Back To The Future.
   It's the largest named number.

A googol isn't an important number in mathematics, as it is an arbitrarily named number, named by a nine year old in the 1920s. Its use is mostly in comparing different kinds of huge numbers, and it sounds cool. Also, it was the inspiration for the name of the company known as Google.

1. 75 meters.
   40 feet.
2. 50 meters.
   25 meters.

If x is the side of the square pool, then we just have to work out the area of the garden, divide it by two, and then determine the dimensions of the pool if it has that amount of area. What we get is "x squared=(1/2)100*50=2500". Solving this will mean doing the square route of 2500, which is 50.

1. 18
   19
2. 16
   17

If "(c+d+e+p)/4=25" and "(c+d+e)/3=27", then "(p+(3*27))/4=25", "81+p=100", and "p=19". Easy!

1. 30 π cm
   22 π cm
2. 20 π cm
   21 π cm

A in this case is Area. Area=100π. R is for Radius. Thus, "A=π(R squared)=100π". This gives us the equation "π(R squared)=100π" and you have to solve for R. "(R squared)=100", so R=10 cm. The circumference C is given by "C=2πR=20π cm"

1. W=8.5, L=52
   W=8, L=12
2. W=12, L=7
   W=12, L=10

If the area is 96, then "L*W=96". The perimeter is 40, so "2(L+W)=40". Substitute L by 20 - W in equation "L*W=96": "(20-W)*W=96". Expand and group like terms: "20W-(W squared)=96", "20W-(W squared)-96=0" "(W squared)-20W+96=0". Factor and solve "(W-8)(W-12)=0". Solutions are thus W = 8, W = 12. Find L for each W: "W=8, L=20-W=20-8=12" "W=12 , L=20 - W=20-12=8"

1. 32
   26
2. 40
   43

"69=2x+17", so "2x=52". If you divide both sides by 2, you get x=26, thus the larger of the two numbers is "26+17", which is 43.

1. 33
   90
2. 60
   45

If 30 is 2/3rds of x, then by dividing 30 by 2, you get exactly one third of x. That means 15 is 1/3 of x. Multiply 15 by 3 and you get x, which is therefore 45.

1. 51.5 kph
   48 mph
2. 65 mph
   That depends on how long the distance is between points A and B.

To determine this, you need to divide the total distance traveled by the total time. If x is the distance from A to B, then the total distance is equal to 2x (away and return). Total time spent on the journey is "t1=x/40 from A to B" plus "t2=x/60 from B to A". As a result, "T=x/40+x/60=100x/2400=x/24". The formula and answer for the average speed is thus 2x/(x/24)=48 mph

1. A 1 followed by a million 0s.
   A 1 followed by 1 thousand 0s.
2. A 1 followed by a number of 0s equal to 10 to the power of 100.
   A 1, followed by 0s until you get tired from writing them.

When Edward Kasner's 9 year old nephew first suggested the concept of a googol, he also suggested an even larger number, a googolplex. The child's definition was simply "a 1 followed by 0s until you tired", which could be seen as meaning "tired of writing" or just generally exhausted, or "until bedtime". Either way, Kasner codified the definition we use today: 1 followed by a googol 0s.