100 Math Trivia Questions and Answers
Numbers, geometry and the problems that are more fun than they sound.
Every question below is shown with its answer, so you can scan the whole set, pick the ones you want, and run a round without clicking through. They are free to use for quiz nights, classrooms and pub quizzes. Where a question has extra background, it links to the full explanation.
1.What is the sum of angles in a triangle?
Answer: 180 degrees
Read the full explanation2.What is the square root of 144?
Answer: 12
Read the full explanation3.a. What was the last year which read the same right side up as upside down? b. What will be the next year?
Answer: a. 1961 b. 6009
Read the full explanation4.If a square has the same area as a circle whose radius is one unit in length, exactly how long is each side of the square?
Answer: SQUARE ROOT OF PI
Read the full explanation5.What is the highest possible score you could get in a game of bowling without throwing even one strike?
Answer: 190 is incorrect. The highest without a strike: spare every frame (10 frames) gives 10 pins + next ball's pins. If you spare every frame and get 9 on the 11th ball (in 10th frame), total = 191.
Read the full explanation6.If a 10 mile taxi ride costs $12 and a 15 mile ride costs $18, then at the same rate how much would a 24 mile ride cost?
Answer: $28.80
Read the full explanation7.If there is a 40% chance that you will get a red light at a certain traffic intersection, what is the probability of you passing through the intersection with green lights three times in a row?
Answer: .6*.6*.6 = .216 OR 21.6 %
Read the full explanation8.There are 8 people on the winning Trivia team, and each person shakes hands with each other person once. How many handshakes take place?
Answer: 28 7+6+5+4+3+2+1
Read the full explanation9.39,370 inches is equivalent to what unit of distance?
Answer: one KILOMETER
Read the full explanation10.If you add the numerical value of all seven Roman numerals, what is the sum?
Answer: 1666
Read the full explanation11.A restaurant is owned by three partners. Partner "A" owns 3/5 of it, and partner "B" owns twice as much as partner "C". What percentage of the restaurant belongs to partner B?
Answer: 26.67% (or 26.7%) — A owns 3/5 = 60%; remaining 40% is split with B twice C, so B = 2/3 of 40% = 26.67%
Read the full explanation12.How many numbers between 0 and 100 are divisible by both 6 and 8?
Answer: 4 ... they are 24, 48, 72, 96
Read the full explanation13.If the temperature is 100 degrees Fahrenheit, what is the temperature to the nearest degree, Centigrade?
Answer: 38 C = 5/9 F-32
Read the full explanation14.How many total degrees are there among all the angles of a hexagon?
Answer: 720 degrees
Read the full explanation15.If the difference between two numbers is 6, and the difference of their squares is 180, what is the sum of the numbers?
Answer: 30 18 AND 12
Read the full explanation16.A driver embarks on a 60 mile drive. He drives half the time at 60 miles per hour and half the time at 30 miles per hour. How much time will this trip take?
Answer: 80 MINUTES or 1:20
Read the full explanation17.If tourists in Switzerland pay $1.00 to get 1.5 Swiss Francs, then they pay the equivalent of how many dollars for a meal that costs 80 Francs?
Answer: ($53.33)
Read the full explanation18.If an airplane flies 100 miles due north, then turns and flies 100 miles directly northeast, how far is it then from the original starting point, to the nearest mile? margin 3 miles for calculation errors.
Answer: 185 MILES ... ok 182-188
Read the full explanation19.What is the sum of the square root of 4/9 and the square root of 9/16? Express your answer as a mixed number.
Answer: 2/3 + 3/4 = 17/12 = 1 5/12
Read the full explanation20.You buy a car, and wish to pay the car seller $12,000, divided into 24 payments, so that each payment is $20 more than the previous payment. How much will you pay in the first payment?
Answer: 270.5
Read the full explanation21.60% of the people at a party are males, and 60% of the females are there with their husbands. What percentage of the people are males who are not married to any of these women?
Answer: 36% is the percentage of people who are married males, not unmarried males. The correct answer is 24%
Read the full explanation22.A 19th century mathematician once stated that he was x years old in the year x2. In what year was he born?
Answer: 1806 /// X=43, x2=1849
Read the full explanation23.There are 17 hours difference in time zones between San Francisco and Tokyo. If an airplane leaves Tokyo at 3 p.m. on Friday, and flies 10 hours to San Francisco, what day and time does it arrive in SF? (don't forget to write am or pm and the day)
Answer: 8 AM FRIDAY
Read the full explanation24.If a bicyclist rides at 10 miles per hour for 10 minutes, and then speeds up to 20 miles per hour for the next 20 minutes, what is her average speed for this ride?
Answer: 16 + 2/3 MILES / HOUR TOTAL DISTANCE / TOTAL TIME = {10/6 + 20/3 =50/6 } /1/2
Read the full explanation25.What is the value of pi rounded to two decimal places?
Answer: 3.14
Read the full explanation26.If there are 16 telephone poles in a straight line, each pole 80 meters apart, how far is it from the first pole to the last?
Answer: 1200 METERS
Read the full explanation27.If four interior angles of a five-sided figure pentagon measure 100 degrees each, what will the fifth angle measure?
Answer: 140 DEGREES - because the sum of the five angle is 540 degrees.
Read the full explanation28.A normal stop sign has the shape of what geometrical figure?
Answer: OCTAGON
Read the full explanation29.What simple fraction has a decimal value of .0625?
Answer: 1/16
Read the full explanation30.A jogger can run down a hill five times as fast as she can run up the hill. If a round-trip jog up and down a hill takes one and one-half hours, how long does it take her to descend the hill?
Answer: 15 MINUTES
Read the full explanation31.What will be the units digit of the number represented by 3 to the 24th power?
Answer: 1 ... last digit goes in cycle 3, 9, 7, 1...
Read the full explanation32.Three kids put up their own money to make a lemonade stand: the first kid puts up $6, second $3, and the last $1. If they take in $100 and share the profits equally, how much of the $100 will go to the first kid?
Answer: Approximately $33.33 (profits split equally, then each gets their original investment back: first gets $6 + $30 = $36, second gets $3 + $30 = $33, third gets $1 + $30 = $31)
Read the full explanation33.If a rubber band weighs 40 milligrams, how many of them will weigh one kilogram?
Answer: 25,000
Read the full explanation34.The numbers game: if I said, 24 = h. in a d., you would say "hours in a day." See if you can figure out this one: 206 = b. in the h.b.
Answer: BONES IN THE HUMAN BODY
Read the full explanation35.To the nearest whole number, what is the area of a triangle each of whose sides is 10 inches?
Answer: 43 SQUARE INCHES
Read the full explanation36.Drivers in the Indianapolis 500 motor race cover 200 laps of the course. If a race car driver maintained a speed of 200 miles per hour for an entire lap, how long would it take him to negotiate that lap?
Answer: 45 SECONDS
Read the full explanation37.One bicyclist can ride around a circular track in four minutes, a second in five minutes, and a third in six minutes. If all three riders begin at the same time, how long will it be until they coincide the next time?
Answer: 60 MINUTES
Read the full explanation38.If the length, width, and height of a rectangular solid box were each increased by 50%, by what percentage would the volume be increased?
Answer: 237.5%
Read the full explanation39.Let's say a slot machine contains three independent spinning reels; each reel has 10 symbols and 3 of them are winners. What's the probability that all three reels will turn up a winner? (write answer as a percent).
Answer: .3^3 = .027 = 2.7%
Read the full explanation40.If, beginning at 10:30 AM, the minute hand of a clock rotates 960 degrees, what time will it then be?
Answer: 1:10 PM
Read the full explanation41.How many numbers between 0 and 200 are divisible by both 6 and 8?
Answer: 8 ... they are 24, 48, 72, 96, 120, 144, 168, 192
Read the full explanation42.If the sales tax on a product rises by 1/4 %, and this tax increase causes you to pay an extra $10 on a purchase, what was the original price of the item?
Answer: $4,000
Read the full explanation43.In how many different ways can a poker player form a straight flush from a normal deck of 52 cards, no wild cards?
Answer: 36 - ace through nine as the lowest card, four suits
Read the full explanation44.Let's say a pizzeria charges for their pies proportional to the size of the pie. If a 10" pizza costs $10, then what should a 12" pizza cost?
Answer: $14.40 since area is 1.44 times as large
Read the full explanation45.How many of the whole numbers from 1 to 100 are either divisible by 7 or include a 7 in their digits?
Answer: 30 of them: 7,14,17,21,27,28,35,37,42,47,49,56,57,63,67,70,71,72,73,74,75,76,77,78,79,84,87,91,97,98
Read the full explanation46.How many prime numbers are there between 50 and 70?
Answer: THERE ARE 4 - they are 53, 59, 61, 67
Read the full explanation47.Can you find a pair of numbers whose sum is 100 and whose product is 2356?
Answer: 38*62
Read the full explanation48.If a rocket could fly from the earth to the sun at a speed of 1,000 km per hour, about how many years would the trip take?
Answer: 17.2 YEARS
Read the full explanation49.What is the next number is this sequence? 1, 4, 10, 20, 35, 56, ?
Answer: 84
Read the full explanation50.If you roll three dice at the same time, what's the probability of rolling a sum of 3 or 4?
Answer: 3/216 = 1/72
Read the full explanation51.How many numbers between 1 and 100 can be written using only the digits {1,2,3,4, and 5}? repeating digits o.k.
Answer: 30 one digit numbers: 5 two digit numbers: 5*5 = 25 TOTAL = 30
Read the full explanation52.If 40% are of the people at an event are women and 20% of the people at the event are left-handed, then at most what percentage are right-handed men?
Answer: 48%
Read the full explanation53.What number lies halfway between 1/3 and 1/5?
Answer: 4/15
Read the full explanation54.In how many different ways could a basketball player score exactly 8 points in a game? (Combinations of foul shots, 2-pointers, and 3-pointers).
Answer: 10 WAYS /// foul, 2-pointer, 3-pointer = 8,0,0 , 6,1,0 , 4,2,0 , 2,3,0 , 0,4,0 , 5,0,1 , 3,1,1 , 1,2,1 , 2,0,2 , 0,2,2
Read the full explanation55.Can you describe in words the set of all numbers, if any, that are larger than their squares?
Answer: ALL NUMBERS BETWEEN 0 AND 1
Read the full explanation56.In how many different ways can the opening pair of moves be made in a game of chess - one white move followed by one black move.
Answer: 400 - white can make any of 20, black also
Read the full explanation57.From February 29, 1896, through February 29, 1996 inclusive, how many February 29th's were there?
Answer: 25 One every four years, but none on Feb. 29, 1900
Read the full explanation58.If 5 workers can pack 5 boxes of flowers in 5 minutes, at the same rate, how many boxes can 10 workers pack in 10 minutes?
Answer: 20 is correct. (Each worker packs 1 box in 5 minutes, so in 10 minutes each packs 2 boxes; 10 workers × 2 boxes = 20 boxes.)
Read the full explanation59.Three sisters have a total of $91. The first sister has 20% more than the second and the second sister has 20% more than the third. How much does the first sister have?
Answer: $36 ... 2nd has $30, 3rd has $25
Read the full explanation60.How many prime numbers are there between 50 and 100?
Answer: (THERE ARE 10) - they are 53, 59, 61, 67, 71, 73, 79, 83, 89, and 97
Read the full explanation61.If a clock started ticking on January 1, by which date would it reach one million seconds? By January 12 or February 12?
Answer: 12-Jan
Read the full explanation62.An airplane departs at exactly 8:08:08 a.m. and arrives at its destination at exactly 3:03:03 p.m. What was the plane's exact travel time?
Answer: 6:54:55 (the given answer '14:62:63-' is nonsensical)
Read the full explanation63.If, the first number of an arithmetic sequence is 200, and the 100th number is 2, what is the 40th number of this sequence?
Answer: 122 2nd term is 200 - 2x1, 3rd term is 200 - 2x2, so 40th term is 200 - 2x39
Read the full explanation64.In a single-elimination sports tournament beginning with 64 teams, how many games are played altogether until only one team, the champion, remains?
Answer: 63 - one game for each losing team
Read the full explanation65.If you looked at a clock in the mirror and the time on the clock face appeared to read 8:20, what time would it be in reality?
Answer: 3:40 non-digital
Read the full explanation66.As you sit in your stopped car at a railroad crossing, a train travelling at 60 miles per hour takes twenty seconds to pass you. How many feet long is the train?
Answer: 1760 FEET 1 mile per minute, 1/3 mile per 20 seconds, 5280/3 = 1760
Read the full explanation67.If 20 people are drinking beer, 16 are eating fish, and 12 are doing both, what fraction of the people are eating fish and drinking beer?
Answer: 1/2 12 out of 24
Read the full explanation68.Evaluate the given trigonometric expression: The sine of a 420 degree angle, in non-decimal form (exact answer)
Answer: √3/2 (sine 420° = sine 60° = √3/2; spelling 'SQR.3' is nonstandard)
Read the full explanation69.To the nearest square inch, what is the surface area of a balloon which is 20 inches in diameter?
Answer: 1257 SQUARE INCHES 4 pi * r^2
Read the full explanation70.How many degrees are there between boiling and freezing point of water in degrees fahrenheit?
Answer: 180 DEGREES BETWEEN BOILING POINT 212 degrees AND FREEZING POINT 32
Read the full explanation71.In a non-leap year, what month and date can be called the exact "middle day" of the year?
Answer: JULY 2 - 182 days before it, 182 days after it.
Read the full explanation72.How many liters of water would fill a container which is one cubic meter in volume?
Answer: 1000
Read the full explanation73.You begin writing down the letters of the alphabet in this pattern: You write A one time, B two times, C three times, D four times, and so on. What letter is 100th on the list?
Answer: N
Read the full explanation74.If you flip a coin three times, what's the probability of getting at least one "tail"?
Answer: 1/8 for all heads, so probability of at least one tail is 7/8. The answer is correct. Actually, wait: 2^3 = 8 outcomes, only HHH has no tail, so 7/8 is correct. So OK.
Read the full explanation75.A person is rowing a boat 2 miles from shore, at 5 miles per hour. Immediately on arrival at the shore he takes a taxi 5 miles down the shore, averaging 20 miles per hour. How long will this trip take?
Answer: 2/5 HR. + 5/20 HR. = 24 MIN.+ 15 MIN.= 39 MINUTES
Read the full explanation76.A bicycle wheel whose tire radius is 14 inches is rotating at 120 revolutions per minute. How fast is the bicycle moving in feet per second (to the nearest whole number)?
Answer: 14.66 FEET PER SECOND o.k. 14-15
Read the full explanation77.A three digit number contains the digits 9, 5, and another digit. When this three digit number is reversed and subtracted from the original number, the result contains the same three digits as in the original number. What is the third digit?
Answer: 4
Read the full explanation78.In a scale model drawing of a car, the linear scale is 1:20. If it would take 1/4 liter of paint to cover the outside of the model of the car, how much paint would it take to cover the real car?
Answer: 100 liters
Read the full explanation79.If a 6'8" foot long piece of wood is cut so that one piece is one-fourth the size of the other, how long will the longer piece be, in feet and inches?
Answer: 5 FEET 4 INCHES 80/5 *4 = 64 "
Read the full explanation80.The Parthenon was built around 440 B.C. a. To which goddess was the temple dedicated? B. On which hill is it located?
Answer: A. Athena B. Acropolis
Read the full explanation81.If you give me $100, then I will have half as much money as you, but if I give you $100, then you'll have five times as much money as I do. How much does each of us have now?
Answer: You have $100, I have $300
Read the full explanation82.Joe drank 1/3 of a glass of milk in one swallow, then drank 4/5 of the remaining milk in another swallow. What fraction of the original milk was left?
Answer: 2/15
Read the full explanation83.What is the area, to nearest whole number, of an equilateral triangle whose perimeter is 300 meters?
Answer: 4330 SQ. METERS
Read the full explanation84.A nine-meter long piece of wood is cut so that one piece is 50% longer than the other. Exactly how long is the longer piece?
Answer: 5 METERS 40 CENTIMETERS or 5.4 METERS
Read the full explanation85.What is the reciprocal of the sum of the reciprocals of 2 and 3?
Answer: 6/5 OR 1 1/5 OR 1.2
Read the full explanation86.Last year a dinner cost $32 and a bottle of wine cost $18. This year the cost of the dinner increased by 5% and the cost of the wine increased by 10%. What was the percent increase in the combined cost of the dinner and wine?
Answer: .068 = 6.8 %
Read the full explanation87.A perfect number is one whose proper factors add up to the number. For example, 6 = 1+2+3. What's the next "perfect number"?
Answer: 28 = 1+2+4+7+14
Read the full explanation88.To the nearest whole number, what is the area of a circle whose circumference is 100 cm.?
Answer: 2500 / pi = 796 sq. cm
Read the full explanation89.The classes in a school run from 8:15 a.m. until 3:06 P.M. . There are 8 class periods with 5 minutes passing time between classes. How long is each class period?
Answer: 47 minutes
Read the full explanation90.If you go out to eat at a restaurant in a foreign country, and you must pay a 15% service fee, followed by a 12% tax on everything, even the service fee, what actual exact percentage did you pay above the base price?
Answer: 28.8% (not 28.80%, but the calculation is correct: 15% + 12% of 115% = 15% + 13.8% = 28.8%)
Read the full explanation91.Can you think of two numbers for which the sum of their squares is 628 and the difference of their squares is 340?
Answer: X=22, Y=12
Read the full explanation92.This region was a kingdom of Czechoslovakia until the 15th century, when it passed to Hungary and then to the Hapsburgs. It became the core of the new state of Czechoslovakia in 1918. Today the name can refer to certain artistic intellectuals. Which regio
Answer: BOHEMIA
Read the full explanation93.A "perfect number" is one in which the sum of the divisors of the number add up to the number. The first "perfect number" is 6, because its divisors are 1,2,3. What is the second perfect number?
Answer: 28
Read the full explanation94.If a sports team has won 30 games and lost 20 so far this season, what percentage of their remaining 20 games must they win in order to have a 50% winning season?
Answer: 25% (5 wins out of 20 remaining games)
Read the full explanation95.Alan and Brigitte are beginning a bike race. Alan begins riding at 12 miles per hour, and ten minutes later Brigitte begins riding at 15 miles per hour. How many minutes will it take her to catch up to Alan?
Answer: 40 MINUTES
Read the full explanation96.If you draw one card from a normal deck of cards, what is the probability of drawing a jack, queen, or king? answer as a simple fraction.
Answer: 3/13th
Read the full explanation97.In order to estimate the population of fish in a lake, a biologist catches 75 fish, marks them, releases them. Next month she catches 75 fish and finds that 5 are tagged. Use this to estimate the fish population in the lake.
Answer: 1125 = 1/5 of fist were caught: 75 * 15
Read the full explanation98.The number 222, written in base three number system, would be equal to what number in base 10?
Answer: 26 = 2*9 + 2*3 + 2*1
Read the full explanation99.If you roll a pair of dice once, which is a more likely outcome? An odd sum or an even sum, or are they both equally likely?
Answer: EQUALLY LIKELY
Read the full explanation100.If, after receiving a 20% discount when buying a television set, and after paying 7% tax, you paid $642, what was the original marked price of the TV set?
Answer: $750
Read the full explanation