MOL # 1
1. Make a table of the days of the week & # the days starting with 1 day from today
in the problem. Now expand that out. You do not have to # everything out to
100….. Think of counting by…..
2. Make a chart. Include all the choices for one of the coins then add to each all the
choices for the other coin. Can you have a zero option for both coins? One?
3. This one is much easier if you think about rules for beverages, otherwise you can
make the adding easier by making a table listing the #’s with each row having 5
#’s. Then add each column down and row across. Then add the totals.
4. Which item is the most expensive? How much would 5 pens and 5 pencils be?
Can you use that to then find what 1 of each would cost together? Then 2? Now
your close to one of the problems….
5. Figure out how many days each of the 3 people work. How many total days are
worked? Now how does that fit when there are 4 workers?
MOL# 2
1. Find the total amount for what she paid and what she sold. Find the difference.
2. Make a table listing the # of nickels, # of quarters, and the total. Then keep track
of you attempts on the table.
3. Convert ft. to inches. Then how many fit across? Down? Use mult. to find the
total.
4. Using what we know about averages, the problem tells us what the average is and
how many scores there are. So find out the other score by finding the total of the
scores. Then use that to find the answer.
5. How many times will 1 show up in the ones place, tens place, hundreds place for
the numbers 1-99, 100-199, 200-299, 300-399, 400-499. Except for the second
grouping you should see a pattern.
MOL #3
1. Find the least common multiple (LCM) of all the numbers. Since 2 and 3 are
factors of 6 you only need to find the LCM of 4, 5, and 6.
2. The average speed for any trip is the total distance divided by the total time spent
traveling. So first find out how long it took the driver each way.
3. If the number is divisible by 9 then using the rules of divisibility, the sum of the
digits 3+A+A+1 must be divisible by 9. So try a number to represent A.
4. If you know that one over 9x10 or 1/9x10=(1/9-1/10) then you can convert each
of those fractions and simplify (eliminate the doubles). Remember if you have the
same number on top and bottom, the fraction then equals 1.
5. Make a table with three rows, the 1st telling what number in the sequence it is, the
2nd using the sequence they had starting at 1, and the 3rd counting by 3 but
starting at 3. Now compare the 2nd and 3rd rows. What is the difference?
MOL #4
1. What is the decimal equivalent of 1 and ¼?
2. A + AB=114 Find the combinations of #’s that have a 4 in the 1’s place.
3. As you add a new line you must try to make it across as many lines as possible.
4. The numbers must be larger than 3 and can be a 2 digit number. Don’t forget that
when you add fractions they must have the same denominator. Don’t forget to
simplify the fractions.
5. The order of operations states that you must do parantheses first so do (6*8)first.
This changes to 6 +8 divided by 2 as in the example.
MOL #5
1. This is an average problem. The average of the numbers will always be the
middle number.
2. 1 sq. yard =9 sq. feet so how many times larger is 600 sq. yards than 600 sq. feet?
Also convert hours to minutes.
3. This one is tough. Work from the bottom up. Start by converting the mixed
number 2 ½ to a fraction. Then remember if you have a one in the top
(numerator)of a fraction and a fraction in the bottom (denominator)you can
convert it to a simple fraction by removing the 1 and inverting the bottom
fraction. 1 over 3/2 becomes 2/3. Then continue converting the mixed number and
so on.
4. As with any problem with a remainder subtract the remainder from the dividend
(109) and then use this new number to look at what 2 digit #’s divide into it.
Notice that this new dividend ends in a 5….
5. Make a chart to track your attempts. Try packaging some marbles in the larger
boxes and see what is left over.
MOL #6
1. Make X + Y as large as possible and X – Y as small as possible.
2. Place the numbers in a row 1-6 and then place 12-7 in reverse order underneath.
Now look at the vertical pairs.
3. What is the total weight of the first 5 then go on from there.
4. What # of pennies must you have? Can you have15? 10? Can you have a large
amount of dimes? Make a table to keep track.
5. Make a venn diagram (overlapping circles) showing the relationship between the
languages.
MOL # 7
1. Read and follow directions carefully.
2. Make an organized list starting with the possible options if the smallest coin was
the first coin pulled out. Then continue with each coin. Find the sums of the
combinations and remove the doubles.
3. Divide the numbers in column A by 7. What do you observe? Use division to find
answer.
4. How many days rations do they have to begin with? Now change the number of
travelers and divide to see how long the initial supply will last.
5. What is the area of each small square? What is the length of a side of a small
square? Remember Area= L x W and perimeter is the sum of all sides.
MOL # 8
1. If I pick 5 beads, can I be sure of having 2 of one color? If I pick a 6th bead, can I
be sure of having 2 of one color? Remember this is a probability problem not real
life.
2. How many thirds are there in 2? Another method is to use Algebra to write out the
problem, this one is not a hard algebra problem…
3. Count the squares in an orderly fashion. Start with squares that are 1 by 1, then 2
by 2, then 3 by 3.
4. Work backward. 4 is one third of what number?
5. Start out with a table that shows the answers for the first 5. When is a zero added?
When will the next one be added?
MOL # 9
1. Start with the row that is complete and find what the total must be. Then work
with that total to find the others with two parts given.
2. This is a division problem. If it starts at 2 and is counting by 3’s then if you
subtract the starting point from the final number this will be divisible by 3.
3. Make a table to list all the possible number of pairs for the length of the sides that
equal 22 when added. Remember that perimeter is all the sides added together
and area is length times width.
4. Change miles per hour to miles per minute. Then reduce the fractions so that you
can use this to see how long it would take the car to go 20 miles at that speed.
5. Work backwards. What must be above 432? What # in the 50’s divides evenly
into 432? Next, now that you know the divisor, what times that # has a 6 in the
tens digit.
MOL # 10
1. Answer to the addition problem must be a two digit number. What are the
possible numbers for H? What is the smallest number that H can be? What is the
largest number that H can be?
2. Remember a product is the answer of a mult. problem. Find all the combinations
whose product is 144. Then remember the 2nd condition that must be met is that
the combination when subtracted from each other the answer must be 10.
3. Remember that before you can add two fractions the denominator(the bottom
number) must be equivalent. When you do this the rule is that you must also mult.
the numerator(top number) by the same number you use with the denominator.
4. Remember that to get 121 you will need to be mult. two numbers, the amount by
the # of members. Since 121 is an odd # then the two #s being mult. must be also
odd. So find the odd #ed combinations whose product is 121.
5. Start off by finding out how much the student would have gained if he passed 7
and failed 1 and then continue with combinations that keep this condition.
MOL # 11
1. Reread and follow the directions carefully.
2. Find what combinations of numbers multiplied by 7 that have an answer with 2 in
the ones place. Then continue with the next to find the combinations of numbers
multiplied by 7 and adding the carryover that have an answer of 8 in the ones
place.
3. Make a table with sports on one axis (side) and the names on the other. Use the
information in the problem to mark off on the table yes and no.
4. Label the endpoints so that you can keep track of the combinations you have used.
5. Using the first condition, replace the pear with 4 plums and 1 apple. Then you can
cross off what they have in common.
MOL#12
1. Work backward on this problem. Make 6 underlined dashes for each digit and
follow directions carefully and then double check.
2. Make a 2 week calendar of days. Start with 1st Wed. and follow the directions to
find out which day today is. Then solve.
3. You have 2 choices to keep the choices straight. Either draw out each option
showing the path on a box or label each intersection and write out the path to C
telling the intersections you cross.
4. Make a table with the headings: N, D, Total coins, and $. Then start with nickels
and fill out the chart each new time reducing the nickels and adding another dime.
5. Find out what you would add to the number being divided so that each remainder
would be zero? (N+?)Now plug in the number being divided as N so you get 3
numbers. Finally what common multiple do all have in common?
MOL #13
1. Look for the squares by the size 1 by 1, 2 by 2, 3 by 3.
2. Since C times C ends with C what options can C be? Since the answer is a 3 digit
number, what does A have to be?
3. Think about the rule about averages. (The average is always the middle number).
Consider if the sum was 4, what would be the 1st and 3rd number have to be. And
the 2nd?
4. This is an algebra one. Try writing each part using a letter for each person.
Compare the 1st and the 2nd condition. We will work on understanding this better
using algebra for now try guess and check!
5. Try making the piles as large as possible. Remember you cannot repeat!
MOL #14
1. Make a table. Remember perimeter is the sum of all sides. Also a square is a
rectangle.
2. Make a table to keep track of the correct, incorrect and total. Notice the total
scored to guide your guess.
3. This is a division problem. Find out what row it will appear on. Then examine the
pattern to use the remainder to find out the column. To see how to use the
remainder try using the #6.
4. Use fractions and compare. What fraction for each size of pipe represents the
amount of water it will give in one hour? Remember how do you compare unlike
fractions?
5. Use the diagonal to find out what each should have as a total. Then solve those
rows that will help you get the final answer.
MOL #15
1. This is a problem to solve using a table. Remember the train starts with 0
passengers, then extend the table.
2. Imagine removing all the outer cubes. Draw a picture to help you. What is left?
3. Find the smallest purchase that both bills can get evenly. Then find the difference
between how many bills are needed. What will be the next amount that they can
purchase evenly?
4. Find out what one fourth of the total is.
5. Extend the pattern 8 rows. Do you see a pattern in the end digits? How many rows
before the pattern repeats? Use division to find out how many of these repetions
there are in 35.
MOL #16
1. Thinking about calendars what day of the month would the Friday before the 25th
be? What would 2 Fridays before be?
2. If the letters AB represent the man’s age what represents the wife’s? Find the
average of the total of the two ages. This will give you a starting point. What
number near this average also has a reverse nearby?
3. Using the initial #’s you can find out how many buggies there were. Now fill the
same number of buggies with 4 for the return trip.
4. This is one that making a die would be helpful. Now find out what letters can not
be opposite of H?
5. How many numbers are in the D sum? Is there a pattern when you look at what
the differences as you extend the problems……95+97+99 & 94+96+98 on top of
each other?
MOL # 17
1. Make a table with the various coin choices at the top. Then using the starting
point given in the problem guess & check your attempts. Double check by finding
a $ total and making sure you use 10 coins.
2. Divide all parts of the second part of the problem in 2. Compare this new problem
with the 1st given problem. Use the difference to find out the cost of 4 rolls, then
use this to find out the cost of bread.
3. Find out the total # of outside faces in figure A. Divide this number into the total
perimeter to find the size of each side. Then find our the # of faces on figure B &
multiply this by the size of each side.
4. Begin by finding the starting number for each that satisfies the conditions then
find each next # until you have one in common.
5. What is the sum of A + C?
MOL # 18
1. This is an average problem. Find out what the midpoint is then take away or add
from there.
2. First look at the # as 1800. could the two facing pages be in the 40’s? 50’s?
3. How many possible for each cube? # ea. Cube on the picture telling how many
faces could get painted.
4. What divides into 1.69 evenly? This will give you what they contributed. Then
find out the combination of coins that will give that.
5. This is another average problem. Remember in a string of numbers the average
will always be the middle number. In this problem you do the same thing twice.
MOL # 19
1. Be careful this is easy but make sure your costs for the camera and case meet both
conditions. When added they equal 100 & when subtracted equal 90.
2. Find the answer to B in the 2nd problem. Use this to solve the others.
3. If K + L = 19 then how much more than K is M?
4. Work backwards.
5. You need to know about divisibility rules for this, see appendix 4, section 1 & 4
in the What every Mathlete Should Know handout. If the # is divisible by 72 then
it is also by 8 & 9.
MOL # 20
1. Extend the pattern to see where it becomes an even time, and then count by that #.
Or you could convert from minutes to seconds and then solve.
2. Since there is no remainder with 7 it must be a multiple of 7. Extend out the
multiples of 7 until a # meets the conditions.
3. Which of the train lengths works the easiest? Does 29 work?
4. Extend out multiples of each until they all end in zero again.
5. Make a table of costs of the ruler beginning with 22 cents. Figure out the amount
that B & A each have and then B + A. Continue until the conditions are met.
MOL # 21
1. Make a table with the # of Nickels, Dimes, and total to keep track of your
attempts and make better ones.
2. List out the 7 facts. Use this information to decide which will fit in the problem.
3. What is 1 ¾ as a decimal? Then solve the problem.
4. Make a picture and label each block with the # of exposed sides.
5. Make a table of the 4 brothers and the total. Then use this to keep track of your
attempts.
MOL # 22
1. Find out what today is, then using division find out when the 365th day is. You
will have to use the remainder.
2. Work backward. Remember that you do the opposite of what was done going
forward.
3. Convert ft. to inches. How many fit across? Down? Use mult.
4. Use the following to eliminate choices. What is the largest possible score?
Smallest? What king of a # do you get whenever a even # or odd #’s are added
together?
5. Make a table listing the divisor and the remainder for 17 & 30. Then keep track of
your attempts on the chart.
MOL # 23
1. This is an average problem. Using this find out what the original total of the
numbers was to get an average of 18. Then go from there to adjust for the new
numbers. Do you need to know each of the 5 numbers?
2. Use the picture to figure out how many cubes are on each layer.
3. Which easy squares (tens) (x a number times itself) comes closest to the lower
range and upper? The you have to try more specific #’s between.
4. Make a table with the headings bicycle, tricycle, and # of wheels. Remember the
conditions needed and record your trials.
5. You need to find out how much ½ of the water weighs the use that to find the jar.
MOL # 24
1. How old is person A when person b was born. Make a table to show the year and
ages of each until you meet the conditions.
2. Find combinations of side measurements that add up to 18. Remember perimeter
is the distance around the object. If the original is a square each side must be
equal, so in the square divided in two the short side must be half of the long side.
3. Looking at the second half of the problem AB times A equals something that ends
in a 1. Find what two numbers when multiplied end in a 1. These are you’re A
and B.
4. If you can’t multiply a number with zeros, think of what products make those.
10=2x5, 10x10=100= (2x5)x(2x5)=(2x2)x(5x5)=4x5
5. How many train lengths did the train travel from the time it entered to the time it
cleared the tunnel. If it travels at 30 mph how far is this distance if it takes 2 min.
to go this distance.
MOL # 25
1. List the multiples of 7, now add 1 to each to find which is a multiple of 5.
2. This is a problem to use an organized list strategy. Set up who each person would
play for one game, remove the doubles and then adjust it so that everyone plays
each other three times.
3. Which ten when multiplied by itself three times comes closest to 15,600? Then
when you find which ten it is between try the numbers in-between to find the
correct one.
4. If the average of all three is one, What must the sum be?
5. If a number is divisible by 36 if is also divisible by 9 & 4. What digits can B be?
MOL #26
1. This is a problem where you can divide the total # of days by the pattern and use
the remainder to find the answer.
2. How many total x’s would there be total without the holes? Now subtract the
holes.
3. Count (1x1x24) as one of the triples. How many others are there that equal 24? Be
careful that you don’t use the same one twice.
4. Find out the total number of rations brought, then go from there to see how far it
will last with the new amount of campers.
5. Subtract the remainder from the total. Now what numbers will divide in exactly?
MOL #27
1. What # of ¢13 must you buy?
2. What is the length of a side? Remember all sides of a square are the same.
3. Look at the ones column. If A+B+C=C then A+B must equal? Since B is the
answer in the 100’s column that means B must be?
4. Narrow down your possibilities by looking at what possible two combinations of
10’s would work.
5. What combinations of #’s will give you 4 and 5 when added?
MOL #28
1. Make A x B as lg. as possible and A – B as small as possible.
2. If the clock loses 60 min. will it be the correct time? Home many min. must it lose
to have the correct hour and minute?
3. What # must you count by that is divisible by 3 & 5?
4. Place a dot on the cubes that have exactly 3 faces.
5. What part of the job is done by Alice in 1 min.? Betty? Together?
MOL #29
1. Find the smallest and largest multiples of 3 between 10 and 226. Express each in
the form 3 x N. Or How many multiples of 3 are there in 226? You still need to do
something else...
2. Divide the rectangle into triangles which are congruent to triangle BEF.
3. Express 85 as the product of two factors neither of which is 1. Which factor
represents the sum of two numbers? Think (A + B) x (A – B)= 85
4. Remember that 25 is equal to 5 x 5. Don't separate prime completely first. List the
multiples of 5 1st and then factor those #'s into prime factors, then count 5's. Ex.
5(5x1)......20(5 x 2 x 2)
5. How many pages require 1 piece of type for each page? 2 pieces of type for each
page? 3 pieces of type for each page?
MOL #30
1. Remember the units place is the same as the ones place. Count how many 2’s and
7’s there are in groups, then use that to find the total.
2. The problem asks for how many different sums not combinations. Organize them
so that you get each combination and eliminate the doubles.
3. Find the total turns for front and back wheels, then find the difference.
4. What is the two numbers that will work for C? Now find which numbers will
work for B x C and so on.
5. This is a more complicated work backwards problem. If they both end up with 12
then the total must always be?
MOL #31
1. This is a good algebra problem try to write it out using numbers and the letter B.
1/3B + 4 =B. Now solve for B.
2. This is a twist on the average problems. The problem gives us the average so we
know that this # is the ? in the series of 7 numbers.
3. First find out how many #’s there are between 100-199, then use that to find the
total.
4. First you must convert inches to feet in the circumference. Then find out how
many times the when must turn in a mile.
5. Notice that in adding a 2 digit # to a 3 digit # you get a 4 digit answer. What does
this mean about the R and the D? Now you have fewer #’s to solve.
MOL # 32
1. Think about decimal equivalents for #’s. Remember the rule for dividing #’s by
decimal #’s. You can move the decimal to the right on the divisor as long as you
also move an equal # of places over to the right in the quotient.
2. Think about the first 2 digits you are shooting for 19. What numbers times
themselves come closest to 19. Now it is 1985 so what do you need to change to
increase the answer by two places. Now in between those two numbers is your
answer. Guess and check to see.
3. This is an algebra problem! Represent each name with a letter, making 3
problems. Now add together all 3 problems using parenthesis. Then combine the
problems where you can to simplify the problem. This result can be simplified
further by isolating letters on one side, do this by doing the opposite to both sides.
(Think 5A=5 * A) Ex. 5A = 45 (dividing both sides by 5 you remove the 5 on the
left side and find your answer).
4. What combinations of paired #’s add up to 16. Know that 3 of the sm. rectangle
sides add up to the long rectangle side. Remember perimeter is when you add up
each side!
5. Make a table or tree diagram to keep possible amounts straight using the
possibility of only using one of the coins, two of the coins, three and so on.
MOL # 33
1. What is the weight of the marbles that was added to the bowl and original set of
marbles?
2. Find the smallest number which when divided by 5 or 7 has a remainder of 1.
3. Find the cubes in the tallest column.
4. When the correct clock advances 60 minutes, how many minutes will the slow
clock advance?
5. Work backward.
MOL # 34
1. What is the average of the 1st 25 #’s ? Add this to the average of the 2nd set and
multiply your answer by the # of #’s.
2. This is a trial and error. Which coin has the fewest? What is the fewest it could
be? Try to find what the rest is with that in mind.
3. Find out what the length of a side in the square ABCD is. Then use what you
know about midpoints and rectangles.
4. What does a/b times b/c equal?
5. Don’t know how to help you with this…Trial and error has too much error… The
book suggests using the #’s 5 and 8 instead. Now see how your answer is related
to the given numbers….
MOL # 35
1. This is a division prob. What is the largest # of schools that can enter 4 teams?
2. Find the total of one row, and then use multiplication.
3. Look in appendix 2 of your “What every Mathlete should know. See parts 1-3.
Basically solve the denominator part, then use the rules about reciprocals of a #.
4. Remember to start 1st week with original member. Make a table to keep track of
the # of weeks and new members.
5. Find the period of time after which they will flash together. Now extend time out
from noon by that time period to find your answer.