







Four multiples of 10 
20170923 

From Laudacir: Four multiples of 10 are added together.the total is a 3 digit number with three consecutive digits. What could the four number be? Answered by Penny Nom. 





3 consecutive multiples of 11 
20170722 

From nisha: using the multiples formula shown at ypur site how can we solve finding 3 consecutive multiples of 11 whose sum is 363 Answered by Penny Nom. 





Two boys on the same route 
20161206 

From Abbey: Starting from the same spot, one boy completed a route in 9 minutes and another boy completed it in 15 minutes. When will both boys be at the same starting point at the same time again? Answered by Penny Nom. 





An airplane schedule 
20161014 

From Stephanie: Starting at 8:00a.m., a passenger plane leaves from an airport every 6 minutes and a cargo plane leaves every 7 minutes. When is the next time these kinds of planes will leave at the same time? Answered by Penny Nom. 





The difference between the ares of two rectangles 
20160609 

From Ingrid: I am trying to help my son with an area question.
I have the answer, from the solutions, but I cannot figure out how to teach him.
Question:
Two rectangles have lengths 13cm and 19cm respectively.
Their total area is 376cm squared.
If both their widths are whole numbers, what is the difference in their areas?
I know that this is solvable once I determine the widths of the rectangles ,
but how do I go about finding that?
Thanks for your help Answered by Chris Fisher and Harley Weston. 





n^2 is a multiple of 100 
20150330 

From Rahul: I have to prove that n^2 is a multiple of 100 is necessary or
Sufficient condition (or both) for n being multiple of 10 Answered by Penny Nom. 





Multiples 
20120528 

From Kenneth: If I understand correctly , a multiple is a product of two numbers. For example some of the multiples of 6 are 6, 12, 18, 24, 30, etc. I just multiplied 6 by 1, 2, 3, 4, 5, etc.
Are the multiples of a fraction, for example, 2/3, determined in the same way? Are they 2/3, 4/3, 6/3, 8/3, 10/3, etc., or are they instead, 2/3, 4/6, 6/9, 8/12, 10/15, etc.?
Or do fractions have no multiples? Answered by Penny Nom. 





I started with Euler's identity and manipulated it 
20111114 

From anonymous: I started with Euler's identity and manipulated it
e^i*pi=1
e^i*pi=(1)^1
e^i*pi=1
e^i*i*pi=(1)^i
e^pi=(1)^i
e^pi=(1)^i
type it in in a calculator and you get e^pi=23.1406926... and
(1)^i=0.0432139183... What did I do wrong? Answered by Robert Dawson. 





Prove sin x = sin (pi  x) 
20110215 

From Janet: Prove sin x = sin (pi  x) Answered by Penny Nom. 





x/200+x/400+x/600+x/800 
20101008 

From Ashishthombre: step by step LCM of x/200+x/400+x/600+x/800 Answered by Penny Nom. 





Three cars 
20100830 

From Anil: 3 cars are moving at speed of 4 kmph,5.5 kmph and 8 kmph in a circular track.The circular track has
a distance of 11 km. What is the time taken for all the 3 cars to meet at the starting point ? Answered by Stephen La Rocque. 





Two problems 
20100527 

From debbie:
Question from debbie, a parent:
hi, i have a daughter and she asked me a maths question I cannot solve. I was just wondering if you can give me the answers plus the working out so I could explain to my daughter,
1. The leftmost digit of a sixdigit number N is 1. If this digit is removed and then written as a rightmost digit, the number thus obtained is three times N .Find N.
2. Four friends are racing together down a flight of stairs. A goes 2 steps at a time, B 3 steps at a time. C 4 steps at a time and D 5 steps at a time. The only steps which all four tread on are the top one and the bottom one. How many stairs in the flight were stepped on exactly once? Answered by Penny Nom. 





cos(x) = sin(x  1) 
20100428 

From alex: In the equation cos x = sin x1 for pi/2
A: solve for x graphically
B: solve algebraically and prove the solution is correct.
Alex Answered by Penny Nom. 





Two bus routes 
20100203 

From kiyah: from 4:30 pm to 6:30 pm the route 1 bus stops every 12 min at the gym's bus stop. the route 2 bus stops there every 15 min. if both buses are now at the stop and schedule is kept, how long will it be before both buses will be at the stop again? Answered by Penny Nom. 





Dividing seashells among girls 
20100106 

From Eileen: A group of girls collected some seashells from the beach. They tried to divided these seashells equally among them. If each girl received 8 seashells, they would need 5 more seashells. If each girl received 7 seashells, they would have 3 seashells extra. How many seashells did they collect from the beach altogether? Answered by Robert Dawson and Penny Nom. 





Common multiples of 36 and 48 
20090915 

From Kamaldeep: Find the first 2 common multiples of 36 and 48. Answered by Penny Nom. 





Jogging and swimming 
20090911 

From Brandon: Trevor swims jogs 3 days and swims every 4 days. How often does he jog and swim on the same day Answered by Leeanne Boehm. 





Investing in multiple accounts 
20090626 

From Kenneth: Hello:
If an investor has $1000.00 to invest in multiple accounts, and he
wants a total return of 4%, is there one calculation that can be used
to determine what these amounts could be even though there may be
numerous amounts used as answers for most of the following examples?
For example,
Invest $1000.00 @ 2% and 5% for total return of 4%.
Invest $1000.00 @ 2%, 3% and 5% for total return of 4%.
Invest $1000.00 @ 2%, 3%, and 5% for total return of 4%.
Invest $1000.00 @ 2%, 3%, 4% and 5% for total return of 4%.
etc. Answered by Robert Dawson. 





Common multiples of 2 and 5 
20090423 

From pat: what are the common multiples of 2 and 5, through 30, because i been working on it for hours Answered by Robert Dawson and Stephen La Rocque. 





2sinB=3tanA 
20090410 

From Xanathax: ABC is a rightangled triangle. 2sinB=3tanA.
Calculate the measure of angle A. Answered by Penny Nom. 





A rectangular open box 
20090321 

From tina: An open box is to be made from a rectangular piece of tin by cutting two inches squares out of the corners and folding up the sides. The volume of the box will be 100 cubic inches. Find the dimensions of the rectangular piece of tin. Answered by Stephen La Rocque. 





Confusion in a multiple choice question 
20081114 

From BJ: My son got this math problem which he could mostly solve. Here it is:
The highest location in a certain country is 4525 m above sea level. The lowest point in the same country is 192 m below sea level.
a) Find the difference of the two elevations. His answer: a(b)= a+b or 4525(192)= 4525+192=4717 m. No problem.
b) A city is 2221 m above sea level. Is this elevation closer to the highest point or the lowest point?
His answer: highest point because: 45252221= 2304 m (closest to the highest point) and 2221(192)=2221+192= 2413 m. (farthest to the lowest point). OK so far.
But then he was given 4 choices for this question with no other information:
a) 4717 m; lowest b) 4333 m; lowest c) 4333 m; highest d) 4717 m; highest
What does it mean? What's the connection with the rest of the problem? Answered by Harley Weston. 





A multiple choice exam 
20080913 

From Phalange: A multiple choice exam consists of 12 questions, each having 5 possible answers. To pass, you must answer at least 9 out of 12 questions correctly. What is the probability of passing if:
a. You go into the exam without knowing a thing, and have to resort to pure guessing?
b. You have studied enough so that on each question, 3 choices can be eliminated. But then you have to make a pure guess between the remaining 2 choices.
c. You have studied enough so that you know for sure the correct answer on 2 questions. For the remaining 10 questions you have to resort to pure guessing. Answered by Harley Weston. 





sin(2x)/sin(3x) 
20080619 

From matt: how does sin2x break down (not with identities) and how would sin3x be created. My
prob. is sin 2x/ sin 3x and I want to know how the double(or triple angle) would break
down. I want to be able to cancel out sins. Thanks! Answered by Harley Weston. 





How do you reduce an equation with multiple variables? 
20080430 

From Jonathon: How do you reduce an equation with multiple variables?
For example, if 3x + y = k(x3), what would x be equal to? Answered by Penny Nom. 





LCM over 100 
20071209 

From Aris: A teacher has more than 100 sweets. She thinks that if she give 6, 8 or 9
sweets to her students she will have no remaining in the case. What is the
smallest number of sweets in the bag? Answered by Stephen La Rocque. 





6 consecutive multiples of 6 
20071111 

From jeff: find 6 consecutive multiples of 6 whose sum is the least common multiple of 13 and 18 Answered by Penny Nom. 





13 year and 17 year locusts 
20071012 

From stefan: how many years pass between the years when both 13 year and 17 year locusts are out at the same time? Answered by Penny Nom. 





Least Common Multiples 
20070920 

From Aiyanna: What is The Lcm Of 3,7,and 8 Because my Teacher gave me That and he didnt even know the answer....
I Worked and worked but I Couldnt Find It..... Answered by Penny Nom and Victoria West. 





Guessing multiple choice answers 
20070724 

From carla: You are taking a multiple choice quiz that consist in 3 questions, each question has
3 possible answers only one is correct. To complete the quiz you randomly guess the answer
to each question . Find the probability of guessing exactly 2 answer correctly. b) at least to answer correctly . c)less than two answer correctly Answered by Stephen La Rocque. 





The lcm of polynomials 
20070531 

From devin: x^38 , x^34, x^2+4x+4 Answered by Penny Nom. 





Triple angle tangent formula 
20070315 

From sam: Hi I am trying to derive a triple angle formulae for tan. I know i need to use compound and double angle formulae but am finding it difficult to "clean" up my fraction to get the triple angle formulae can you show me a worked derivation?! thanks Answered by Penny Nom. 





Least common multiple 
20061108 

From Melenie: I have a daughter in 5th grade she can't seem to grasp the concept of finding LCM's does anyone have a quick easy way for her to learn????? Answered by Stephen La Rocque. 





Least common multiple 
20060925 

From A student: What is the LCM of 10,45 and 38? Answered by Stephen La Rocque. 





How many people are in the race? 
20060407 

From Marty: You're in a race with 1/5 of the racers ahead of you and 5/6 of them behind you. How many people are in the race? Answered by Penny Nom. 





cos(3X) 
20060329 

From Joshua: I'm having trouble proving that cos(3X)=cos^{3}X (cosX)(sin^{2} X) Answered by Penny Nom. 





The Least Common Multiple of two primes 
20060221 

From Kristine: Is the Least Common Multiple to two prime numbers always their product? Why or Why not? Answered by Stephen La Rocque. 





GCF, LCM, primes and the ladder method 
20060107 

From Linda: How would I teach both finding the GCF and LCM with prime factors...I recall the ladder method vaguely.??? Answered by Penny Nom. 





LCM 
20051212 

From Alex: what is the LCM of 210 and 54 and the LCM of 42 and 126 Answered by Penny Nom. 





Least common multiple 
20051022 

From Dayna: I'm stumped! I can't seem to come up with a least common multiple of 22 and 25. Is there one? Answered by Penny Nom. 





The lcm of 5, 3, 4, 7 and 2 
20041105 

From Christine: what is the lcm of 5,3,4,7,2 Answered by Penny Nom. 





The lcm of 1 and 1 
20041103 

From Nayiyan: I would like to know what is the LCM of (1) and (+1) is. Answered by Penny Nom. 





GCD and LCM 
20041031 

From Cartalina: how do you calculate the "positive difference between the GCF and LCM of two numbers"? Answered by Penny Nom. 





sin(3A) 
20041020 

From A student: Express sin3A in terms of sinA and cosA. Answered by Penny Nom. 





The Parliament of the land of Achronia 
20040529 

From Christine: The Parliament of the land of Achronia consists of two houses. The parliament was elected in 2003 for a period of six years beginning on Thursday, the 1st of January 2004, when the two houses had their first sessions. According to the rules, the meetings of the first house must occur every twelve days for the duration of the term, and the meetings of the second house must occur every eighteen days. For example, the second meetings of the first and the second houses were held on the 13th and 19th of January respectively. A new law can be passed on any day when both houses meet, except on a Thursday. On how many days can the parliament members pass new laws during this six year term? Answered by Penny Nom. 





Sin(3x), cos(3x) and tan(3x) 
20040128 

From Jon: What is the identity for cos3x, sin3x, and tan3x? In class, we learned double angel identities and were asked to find out the identity to these three trig functions. If you can help, please do. Also, i know that the cos^{4}x sin^{4}x is the same as cos2x. Is cos^{8}xsin^{8}x = cos2x also true? Thank you.s Answered by Chris Fisher. 





Multiples of all four of the numbers 2, 3, 4, and 5 
20030211 

From Stephanie: How many of the first 1000 positive integers are multiples of all four of the numbers 2, 3, 4, and 5? Answered by Penny Nom. 





Why is 5 divided by 1/7 greater than 5 divided by 2/3? 
20021119 

From Elizabeth:
 Without performing the division, explain why 5 divided by 1/7 is a number greater than 5 divided by 2/3.
 Is the least common multiple of two prime numbers always their product? Why or why not?
Answered by Diane Hanson and Penny Nom. 





sin 2x = cos 3x 
20020225 

From Allan: solve: sin 2x = cos 3x Primary question: how do you handle the cos 3x? Answered by Paul Betts and Chris Fisher. 





Manufactures golf balls 
20011106 

From Kevin: A company manufactures golf balls. Golf balls are each numbered consecutively 0 to 4, and then the numbering starts over with zero again. Every 12th golf ball is yellow. Every 8th golf ball is tested for defects. The company produces 120,000 golf balls in an eighthour shift. A. How many yellow golf balls are tested for defects during the day? Explain your reasoning. B. How many of these yellow balls that are tested are imprinted with the numeral 2? Explain your reasoning. Answered by Penny Nom. 





Locusts 
20011008 

From A parent: JOHN CONJECTURED THAT BOTH 13YR.&17YR. LOCUSTS CAME OUT THE SAME YEAR. ASSUME IT IS CORRECT. HOW MANY YEARS PASS BETWEEN THE YRS. WHEN BOTH 13 YR. & 17YR. LOCUSTS ARE OUT AT THE SAME TIME? EXPLAIN. NEXT, SUPPOSE THERE WERE 12YR.,14 YR.,& 16YR. LO CUSTS,& THEY ALL COME OUT THIS YR. HOW MANY YRS. WILL IT BE BEFORE THEY ALL COME OUT TOGETHER AGAIN? Answered by Leeanne Boehm. 





GCD and LCM 
20010924 

From David: Find the GCD adn LCM of the following numbers. Assume p 2 to the power p, 3 to power q, 5 to power r and 2 to power q, 3 to power r, 7 to power p Answered by Penny Nom. 





A four digit number 
20010217 

From Dean: Need to find a 4 digit number that can be divided by 2, 3, 4, 5, 6, 7, 8, 9, and will always have a remainder of 1 in the answer. Answered by Penny Nom. 





Two number theory questions 
20010130 

From Richie: i have two questions and they are:  the product of three consecutive prime numbers is 7429. Find the product of the smallest and largest of these three integers.
 the least common multiple of two relatively prime positive integers, a and b, is 144. if a (a>or=2) is as small as possible, compute the value of b.
Answered by Penny Nom. 





Is n^2  2 a multiple of n  4? 
20010110 

From John: Find all positive integers n so that n^{2}  2 is a multiple of n  4. Answered by Sukanta Pati. 





Why does division start from the left? 
20000524 

From Salil Dave: Addition, subtraction and multiplications start with right most digit and proceed left, but division starts from leftmost digits and goes right ... why? Answered by Harley Weston. 





Factoring, primes, GCF and LCM 
20000227 

From Ruth Kroek: My son is in grade seven, he has to do a Factoring Booklet the areas covered are:  Prime #'s
 Composite #'s
 Rainbow Factoring
 Finding Multiples (consecutive multiples)
 Finding GCF of 23 numbers uning Rainbow factoring
 Finding LCM of 2 numbers using consecutive multiples
 prime factor trees
 prime factor ladders
 finding GCF of 2 numbers using Prime number Method
Although his text 'Math Power' gives some information, we are at a loss .. Answered by Penny Nom. 





Triple angle formula 
20000223 

From Sara: Can one derive a triple angle formula for sine and cosine? If so, how? Answered by Chris Fisher. 





Least Common Multiple 
20000216 

From Kathy Heath: The way I understand it is for 2,3,9 the least common multiple is 18. Am I right? If so, I guess the least common multiple for 3,4,7 is 105. Please let me know if I'm right so I can tell my daughter. Answered by Denis Hanson. 





Climbing stairs 
19991222 

From Harman Chaudhry: Paul, Michelle and Michael all climb up 54 steps. Paul climbs the steps one at a time i.e. 1, 2, 3, etc. Michelle Climbs the stairs 2 at a time i.e. 2, 4, 6, etc. Michael climbs the stairs 3 at a time i.e. 3, 6, 9, etc. How many steps are used by exactly two people? Answered by Penny Nom. 





Jose and Arthur 
19990926 

From Joel Hammer: Jose can run around the track in 40 seconds. Arthur runs with Jose but in the opposite direction. They meet every 15 second. How long will it take Arthur to make one trip around the track? Answered by Denis Hanson. 





A Multiple Choice Test 
19990831 

From Cintra Ramnarine: I have ten questions. There are two multiple choice answers to each question. What are the chances of answering all questions correctly. Answered by Harley Weston. 





Sin 4A 
19990622 

From Ryan Cochrane: If sinA = 4/5, and A is a first quadrant angle, find sin4A Answered by Harley Weston. 





Where three sequences meet. 
19990306 

From Ali: My name is Ali and I am in the 5th grade. I have a math question: What is the least positive integer meeting each of the following conditions:  Dividing by 7 gives a remainder of 4
 Dividing by 8 gives a remainder of 5
 Dividing by 9 gives a remainder of 6
Help! Answered by Denis Hanson. 





The Board Problem 
19990215 

From Avery: Mr. Avery has 3foot boards and 4foot boards. If he puts the 3foot boards in a line, they have the same length as the 4foot boards put in a line. Altogether he has between 16 and 25 boards. How many 3foot boards does he have? Answered by Jack LeSage and Penny Nom. 





Greatest Common Factor. 
19980109 

From Percy Stribling: how do you figure out what the greater common factor is? Answered by Penny Nom. 





Two Questions 
19970828 

From Faye Tan: I am a trainee teacher. I would appreciate it very much if you could help me solve the following two problems which I think are meant for students at middle grade. 1. If a hen and a half lays an egg and a half in a day and a half, how many hens are needed to lay a dozen eggs in one day? 2. There are fewer than 200 passengers on a train. If they get off in pairs, one passenger will be without a partner. If they get off in groups of 3 or 4, there will still be one passenger left by himself. However, if they get off in groups of 5, no one will be left by themselves. How many passengers are there on the train? Answered by Penny Nom. 





How many digits are there in 2^2520? 
19961007 

From Rita Leung: A)The number 64 is a sq., a cube, and a sixth power because 64=8*8, 4*4*4, 2*2*2*2*2*2. Find the smallest integer greater than 1 that is a sq., a cube, a 4th, 5th, 6th, 7th, 8th, 9th and 10th power. I have found that the answer is 2 to the power 2520th. B) How many digits are in the correct answer to part A? The answer is uncertain. It is either 758 or 759. Can you give me any ideas? Answered by Penny Nom. 

