Only 5% of People with PhDs Passed This Middle School Math Quiz!

By: Zoe Samuel
Estimated Completion Time
4 min
Only 5% of People with PhDs Passed This Middle School Math Quiz!
Image: shutterstock

About This Quiz

When you study something, the higher you rise, the more you are pushed to specialize. Eventually, certain skills which aren't used in your specialty might start to fall away. Baseball pitchers are almost universally terrible batters and fielders, because they spend all their time practicing their pitching repertoire and working on strategy. Magicians who specialize in mind reading tend to become befuddled by tricks with ropes or coins. The same is true in the sciences.

Sometimes, when one is used to doing something at a high level, one becomes accustomed to a level of complexity that makes one second guess one's decisions on simple subjects. An undergraduate degree is nothing to sniff at, but a master's degree or a doctorate are revered because the level of specialty required for these is so great, it means the doctor or master in question really only works in a narrow field. These academics are the perfect people to test out on some basic, skill-based questions.

You have some homework to do. We have spoken with your middle school math teacher, gone through their favorite quiz questions, and come up with a "simple" and "easy" middle school math quiz, however the more studied you are, the more problematic it will be for you. Put your basic skills to the test!

What does * mean?
Multiply.
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.
Divide.
Add.
Subtract.

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A farmer has seventeen cows. All but nine die. How many cows remain?
8
10
9
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".
7

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What is the minimum number of pitches a starting pitcher can throw in a perfect, complete, nine-inning game if every at-bat ends in a strikeout?
54
100
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.

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What do all multiples of 9 have in common?
If you add up their composite digits until you only have one digit left, you'll always end up with 9.
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?
They're all odd.
They're all irrational.
They're all even.

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How would you simplify 3x+4x?
12x
7x
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.
1x
4x

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How far can a dog run into a forest?
Halfway into the forest.
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.
All the way to the other side.
A quarter of the way through.
It won't go in very far.

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How would you simplify 3x*4x?
12x
10x
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.

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What percentage of a dollar is two quarters?
100%
75%
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.

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Rounded off, what percentage of 510 is 17?
33.3%
3.4%
3.33%
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%.
30%

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There are n boxes in a large bag and m toys in each box. What is not the total number of toys in the bag?
nm
n*m
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".

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How do you calculate the radius of a circle?
Divide the diameter in half.
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.
Divide the circumference by four.
Multiply the diameter by π.
Divide the area of the circle by π.

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What makes a number a rational number?
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.
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.
When it is an even number.
When it is a real number.

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What is 2/3 of 21?
3.33
18
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.

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What is not a real number?
Irrational numbers, like π.
A number that is a whole number that can be expressed without a symbol like the square route symbol.
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.

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Two thirds of students in a class are reading about politics. The remaining eight students are studying art instead of politics. What's the total number of students in this class?
16
32
24
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.
8

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A truck driver is driving at a constant rate of 55 miles per hour. How far does he travel in three hours?
110
165
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.
175
155

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I have a bag of marbles. It has 3 blue marbles, 7 pink marbles, and 5 yellow marbles. What is the ratio of yellow marbles to the total number of marbles?
15:1
1:3
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.
5:14
3:10

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What are the factors of 50?
1 , 2 , 5 , 10 , 25 , 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, 2, 5, 10, 20, 15, 49
1, 2, 3, 5, 10, 25, 50
1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 15, 20, 25, 40, 50

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What is the lowest common multiple of 25 and 15?
3,000
750
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.

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What is the difference between 0 and null?
There isn't one.
Null is less than 0.
Null is a lack of information, not the definition of a value.
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.
Null is a transient state, sometimes represented by 0.

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What is 40% of 1/6, represented as a percentage of the whole?
0.667%
0.0667
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%

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Expressed as a fraction, what is 20% of 50%?
1/20
1/10
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.
2/50
20/50

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What is "a squared + b squared = c squared" also called?
Z* theorem.
Conway–Schneeberger Fifteen Theorem
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.

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The Earth's radius is 20,903,520 feet, and you want to know the distance between your eyes and the horizon. What is the only piece of information you need, if you're using geometry to do the calculation?
The circumference of the Earth.
Your height.
The elevation of your eyes.
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)
The diameter of the Earth.

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In "2 x + 5 = 11", what is x?
4
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".

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What do you need to solve "4/5=a/16"?
A common denominator.
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".
A cross product.
Help!
Google.

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

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A rectangular garden has a length of 100 meters and a width of 50 meters. There are plans for a square pool in the center of the garden. What is the length of one side of the swimming pool if the remaining area is equal to 50% the area of the rectangular garden?
75 meters.
40 feet.
50 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.
25 meters.

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The numbers c, d, e, and p have an average equal to 25. The average of c, d, and e is equal to 27. What is p?
18
19
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!
16
17

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What is the circumference of a circle with an area of 100π square centimeters?
30 π cm
22 π cm
20 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"
21 π cm

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The area of a rectangle is equal to 96 square meters. Its perimeter is 40 meters. What is the length and width of the rectangle?
W=8.5, L=52
W=8, L=12
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"
W=12, L=7
W=12, L=10

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The difference between two numbers is 17 and their sum is 69. What is the larger of the two numbers?
32
26
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.

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If if 2/3 of x is 30, what is x?
33
90
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.

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A car travels from point A to point B at a speed of 60 mph. It returns using the same road, from point B to point A, at a speed of 40 mph. What is the round trip's average speed?
51.5 kph
48 mph
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
65 mph
That depends on how long the distance is between points A and B.

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What is the original definition of "a googolplex"?
A 1 followed by a million 0s.
A 1 followed by 1 thousand 0s.
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.

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