1) On Highway 4, numbered markers from 1 to 10 are placed 10 miles apart. If Mrs. Hunter starts at marker numbered 1, how many miles will she have traveled when she passes marker 10?
2) Eric had 20 nickels, 16 dimes and 4 quarters. He put the coins into 4 stacks so that all the stacks had the same money value. What is the least number of coins Eric could have in any one stack?
3) The scale on a map reads 1” = 50 miles. On the map city A is 5” from city B and city B is 3” from city C. The actual distance from city A to city C could be anywhere from ______ to _____miles.
4) Bart, Blake, Bill, Ben and Bob are standing side by side. Bart is between 2 boys. Bart is next to Ben but not next to Bill. Bob is in the middle. Blake has no one to his left. Put the names in the correct order.
5) A group of 6 persons, including adults and children, buy tickets to get into a museum. The charge for adults is $2 and for children $0.50. The total charge for all 6 persons is $6. How many children were there?
6) The 3 older children in the Harper family are 16, 14 and 10 years old. Next year when the other child will be 5, the sum of the ages of all 4 children will be _______.
7) Jesse has a box containing between 10 and 20 baseball cards. If he counts them out 2 at a time, he has one left over. If he counts them out 5 at a time, then he has 4 left over. How many baseball cards does Jesse have in the box?
8) There are 17 beans in circle A and none in circle B. You can move exactly 5 beans at a time from circle A to circle b and exactly 3 beans at a time from circle B to circle A. What is the least number of moves to transfer all 17 beans from circle A to circle B?
9) Using silver dollars (SD), half dollars (HD), quarters (Q), dimes (D) and nickels (N), it is possible to give change for a dollar in coins, with the number of coins being any number from 1 to 20. One coin: 1 SD; 2 coins: 2 HD; 3 coins: 1HD, 2Q; 4 coins: 4 Q. What 5 coins would be used to give change for a dollar?
1 2 3 4 5 6
1 2 3
4 5 6
11) Tom and Joanne’s job is to take their dog for 4 walks each day. Each is to take the dog for 2 walks. For the first week Joanne cannot take the dog for any walks on Monday or on Tuesday. On Wednesday she can only take it for one walk. The week starts on Monday. She tells Tom that starting Thursday she will take the dog for 3 walks to his 1 until they have evened out the number of walks. Counting Thursday, how many days will this take?
12) A full propane gas tank weighs 32 pounds. After ¾ of the gas is used up, the tank and the remaining gas weighs 14 lbs. The weight of the tank when empty is ______ lbs.
13) The numbers 1, 2, 3, 4 have been placed in the four squares to be multiplied in pairs. The numbers next to each other, right or left, or up and down, are to be multiplied. In this example 1 x 2 = 2, 3 x 4 = 12, 1 x 3 = 3 and 2 x 4 = 8. The sum of these 4 products is 2 + 12 + 3 + 8 = 25. It is possible to place the numbers 1, 2, 3, 4 in a different order so that the sum of the 4 products will be different than 25. There are two other possible sums. What is the smallest sum possible?
14) In the addition problem: 7A + 8A + 9A = 2B7, find the digit represented by B. (Each time a digit appears it represents the same digit.)
15) Irene went shopping in two different stores and noticed that both stores had packages of ballpoint pens for $0.60. One of the stores had 5 pens in each package and the second store had 6 pens in each package. Each pen in the second store was $______ cheaper than each pen in the first store.
16) There are 4 girls who play ping-pong after school. Each girl played exactly 3 games of ping-pong with each of the other girls. How many games of ping-pong were played altogether?
17) Jill ran around the track 4 times for a total of 1,000 yards. The track distance from A to B is the same as the distance from C to D. The distance from B to C is the same as the distance from D to A. The distance from D to A is 50 yards. The distance from A to B is _____ yards.
18) A meter machine for parking at the airport takes only quarters. Each quarter enables each person parking to stay 20 minutes before a red flag appears. Beverly parks her car at one of these meters at 12:05 P.M. with the red flag showing. Her sister is arriving at 1:45 P.M. and Beverly knows that it will take an additional 25 minutes to pick up the luggage and get back to the car. What is the fewest number of quarters that Beverly can put in the meter at 12:05 P.M. so that, by the time she and her sister get back to the car, no red flag appears?
19) A digital clock shows either 3 digits of 4 digits at a time. What time is it when the digits have their greatest sum?
20) Mrs. Flores is 34 years old. In 6 years she will be 4 times as old as her son. How old is her son now?
21) Janis has 85 marbles and Kathleen has 26 marbles. If Janis gives Kathleen ________ marbles, then she will have exactly twice as many marbles as Kathleen.
22) When Mr. Martin arrived at the airport he noticed he was 1 hour early for his scheduled flight. He then heard an Announcement that the flight was delayed one hour. Later, an additional 2½-hour delay was announced. The plane finally took off at 10 P.M. What time was it when Mr. Martin first arrived at the airport?
23) The swimming pool area at the “Y” has 5 doors. Three doors are only entrances and one door is only an exit. In how many different ways can Lorraine enter and leave the pool area?
24) Miss Teller, the bank clerk, is told to lock the cash vault at 1 P.M. Saturday afternoon. She has to set the timer so that the vault can be reopened at 8 A.M. Tuesday morning. She should set the timer for ______hours.
25) Mr. Albright is 42 years old and his son is 6 years old. Two years ago Mr. Albright was 10 times as old as his son was then. In ____ years he will be 5 times as old as his son will be then.
26) Alice, Betty and Carol are playing a game with 48 marbles in a circle. Alice takes 2 marbles, Betty takes 4 marbles and Carol takes 6 marbles. One of them (not saying which one) now takes as many marbles as she did the first time. Another girl takes twice as many as she had taken before and the remaining girl takes 4 times as many as before. There are now 10 marbles left in the circle. Which girl took the same amount as the first time?
27) Vicky has dozens of apples, oranges, pears and bananas. She lines them up in the following order: first and apple, second an orange, third a pear, fourth a banana, fifth an apple again, sixth an orange and so on. If she continues this pattern the 79th piece of fruit will be a/an _______.
28) Allison has dimes and Kevin has nickels. Allison exchanges with Kevin a dime for a nickel. She continues to do this until Kevin is out of nickels. Kevin now has $0.70 and Allison has $0.75 in nickels and dimes. How many dimes did Allison start with?
29) Two containers of each contain the same amount of juice. If 15 ounces of the first container are poured into the second container, then the second container has twice as much juice as the first container. How many ounces of juice did the first container have originally?
30) If 7 X’s = 2 Y’s and 3 Y’s = 5 Z’s, then 21 X’s = how man Z’s?
31) Mark gave Danielle $2.00 more than she already had. She now has $60.00 how much money did Mark give to Danielle?
32) The manager of a food store is selling 12 apples in a bag for $3.00. She also has bags containing 24 apples and wishes to sell these so that each apple is $0.05 less than those in the bag containing 12 apples. What should she charge for the bag that contains 24 apples?
Bill is going to paint all the faces
(or parts of faces) of the blocks that are not covered. He needs enough paint to paint_______ full
faces of the blocks. (All the blocks
are the same size cubes. Do not paint the bottom because it sits on the
The sum of 5 numbers is odd. Which of the followings
statements must be true?
a) There are an odd number of even numbers.
b) There is an even number of odd numbers.
c) There are an odd number of odd numbers.
d) There are no even numbers.
35) Find 3 consecutive numbers that add to the product of 2 x 3 x 4.
36) Barbara bought a coat for $10 less than half the original price. She saved $80. How much did Barbara pay for the coat?
37) Jeff’s hobby is to collect valuable stamps. All of his U.S. stamps are valuable. One-half of his British stamps are valuable. There are 3 times as many valuable stamps as there are U.S. stamps in his collections. Jeff has 50 British stamps and 40 U.S. stamps. How many valuable stamps does Jeff have that are neither U.S. stamps nor British stamps?
38) Ms. Castle, the coach of the girls basketball team, told the girls they could pick their own two digit number to put on the back of their shirts. No two girls could have the same number and the ten’s digit must be less than the unit’s (one’s) digit. The girls could pick from the digits 4, 5, 6, 7, 8, and 9. If all the possible two-digit combinations were used, how many girls are on the team?
39) There were 9 children at a party. Each boy ate 5 cookies and each girl ate 6 cookies. A total of 50 cookies were eaten. How many girls were at the party?
40) Ken, Larry, Moe and Ned had a race. Ken did not finish last (fourth). Moe finished after Larry but before Ned. Moe did not finish right after Larry. Who came in second in the race?
41) Paul is in a twelve-story building. Paul is on the ______ floor if the walk to the 12th floor is twice as far as the walk down to the 6th floor.
42) Sherry has between 50 and 100 pennies in her piggy bank. She can count them 2 at a time and come out even. She can also count them 3 or 5 at a time and come out even. She cannot count them 4 at a time and come out even. How many pennies does Sherry have in her piggy bank?
43) If 15 X’s = 20 Y’s and 16 Y’s = 10 Z’s, then 6 X’s = how many Z’s?
44) Mr. Newsman, Mr. Salesman and Mr. Teacher work as a newsman, a salesman and a teacher. None of them has a job that is the same as his name. Mr. Salesman’s wife is the teacher’s twin sister. Who is the salesman?
45) An archery target has 4 rings in it with possible scores of 3, 5, 8, and 10. Diane shoots 3 arrows and they all land inside rings. Diane’s total score was 28. What were her 3 scores?
46) At Lion stadium it is 90 feet from home plate to first base and 330 feet from home plate to the foul pole. How many yards is it from first base to the foul pole?
47) The element Hydrogen has one electron. How many Hydrogen atoms are needed to form 3 Hydrogen molecules? (Hint: hydrogen molecule is diatomic)
48) Two cans of ABC dog food are selling for $0.99. One can by itself costs $0.50. Jan has a coupon that says, “If you by 7 cans of ABC then you get one can free.” She also knows that DEF dog food is selling at 2 cans for $0.89. Jan wishes to buy 8 cans of dog food. She will save $______ buying 8 cans of ABC dog food with the coupon instead of 8 cans of DEF dog food.
49) For their first 60 games the Robins had a record of 28 wins and 32 losses. How many of their next 90 games must they win if their total record is to show twice as many wins as losses? (There are no ties.)
50) Julia spun one of 4 spinners, each spinner has 3 symbols: @, #, and $ if she spins one of the spinners 100 times with the following outcome: @ = 25, # = 50, and $ = 25. Does this mean the area of the # on the spinner takes up ½ of the space on the spinner dial?
51) Hank and Joe each what to buy a tennis ball. Hank still needs $0.28 to buy the ball and Joe still needs $1.12 to buy the ball. If they combine their money, they still do not have enough to buy the ball. What is the most the ball could cost?
Pick a number. Add 12. Multiply the answer by 3. Subtract 36
from the new answer. Divide this answer by 6. Multiply this answer by 2. The
final answer is:
a) One-half the number picked.
b) Equal to the number picked.
c) Twice the number picked.
d) Three times the number picked.
53) The distance from A to B to C is 7 kilometers and forms a right angle. The distance from A to B is 3 kilometers and the distance from B to C is 4 kilometers. How far is it from A to C? (Hint: ABC forms a right triangle, use the Pythagorean formula a x a + b x b = c x c)
54) There are 72 students in a bicycle race. There are twice as many girls as boys. Five boys are wearing glasses. How many boys in the race are not wearing glasses?
55) Mrs. George’s car can travel 30 miles on one gallon of gasoline. Mr. Herman’s car can travel 25 miles on one gallon of gasoline. Gasoline costs $2.30 per gallon. For a 150 mile trip Mrs. George spends $______ less than Mr. Herman for gasoline.
56) If you start with 1 and count by 2’s you obtain the following: 1, 3, 5, 7, 9, …, where the first number is 1, the second number is 3, the third number is 5, etc. What is the 60th number?
57) The fastest time for the 1 mile run at Westport High School until yesterday was 5 min. 10 sec. Yesterday Jason broke the record by 24 seconds. He ran the mile in ______min. _______sec.
58) Casey has linked 28 1” paper clips together. If these were shaped into a square, the area of the square region would be _____sq. in.
59) Southern Airlines has two different fares for flights from Chicago to San Francisco and back. The regular fare is $425 round trip for adults and $280 round trip for children under 12. The “Red-Eye” special is $119 each way for adults or children. The Aldrich family (2 adults and 2 young children) flew from Chicago to San Francisco and back paying the regular fare. If they had taken the “red=eye” special both ways, they could have saved a total of $______ for all four of them.
60) The sum of five different positive integers is 100. The largest possible value for one of these integers is_______.
61) Christina has 12 coins. One-half the coins are dimes,1/4 of the coins are quarters and the rest are nickels. How much money does Christina have?
62) A bag of a dozen oranges was selling for $3. The manager of the store decided to add some oranges to the bag, but not change the $3 sticker price on the bag. Now the price of the oranges was actually $2 a dozen. How many oranges were added to the bag?
63) Tammy was in the middle rung of a ladder. She went up 3 rungs, then down 5 rungs and then up 7 rungs where she rested. Later she climbed up the remaining 7 rungs on the ladder. How many rungs did the ladder have?
64) One bell rings every 5 minutes, and another bell rings every 6 minutes. If they ring together, in how many minutes will they next ring together?
65) Paul is born on his grandfather’s 60th birthday. In how many years will his grandfather be 11 times as old as Paul?
66) Theresa has a machine that takes a number fed into it and multiplies it by 10. It then takes that product and adds 10 more. Theresa fed a number into her machine and 70 came out. What number did she feed into the machine?
67) Jason decided to play a game. He put 64 chips in a shoebox. He then began tossing a coin. If the coin came up heads, he would increase the number of chips by ½. If it came up tails, he would decrease the chips in the box by ½. The first toss came up heads, the second tails, the third heads and the fourth tails. There are now ____ fewer chips in the shoebox.
68) Don had 3 quarters, 2 dimes and 3 nickels. Phil had 2 quarters and 1 dime. After Don gave Phil 3 of his coins they both had the same amount of money. What 3 coins did don give to Phil?
69) The middle bead in a string of 17 beads was the largest and most expensive. Starting from each end, the end beads were $1 each and each bead is $1 more than the one before it, up to the middle. If the string of beads is worth $100, what is the middle bead worth?
70) A box full of oranges weighs 9 pounds. After the Hull family ate 2/3 of the oranges, the remaining oranges and the box weighed 4 pounds. The weight of the box when empty is ______pounds.
71) Using two equilateral triangles to form a 6-pointed star, how many triangles can you see?
72) What is the smallest positive number that leaves a remainder of 2 when divided by 3,4, and 5?
73) Four friends received $8.36 for recycling cans and bottles. Of that amount $0.16 was in pennies and the rest was in nickels. They shared the money equally. How many nickels did each receive?
74) Janice spent from 7 pm until 9 pm doing her homework. She spent 3 times as much time on her english project as she did on math. The science homework took twice as long as he math homework. How many minutes did she spend on her science homework?
75) A container full of water weights 15 ½ lbs. If ¼ of the water in the container is poured out, the container with the remaining water weighs 12 ½ lbs. How much does the container weigh when it is empty?
76) Katie asked her grandfather how old he was. He replied, “I am over 50, but younger than 70. Last year my age was a multiple of 9. This year my age is a multiple of 8.” How old is Katie’s grandfather?
77) The movie theater has 450 seats. The 10 rows in the front have 19 seats each; the ______ remaining rows have 20 seats each.
78) From a pile of 100 pennies, 100 nickels and 100 dimes, select 21 coins that have a total value of exactly $1. You must use at least one coin of each type.
79) Ann, Beth and Cora each place their hats on the top shelf of a closet. When they go to get them each one reaches in without looking and grabs a hat. One way they could have picked hats is: Ann (A), Beth (C) and Cora (B). Ann took her own hat and Beth and Cora took each other’s. How many different ways could there be of picking these hats where no one got her own hat?
80) The numbers 1, 2, 3, 4, and 5 have been placed so that the same number does not appear in any horizontal row (-), in any vertical row (|), or in any diagonal row (X). The sum of all the numbers is 25. Using the numbers 1, 2, 3, 4, and 5 (at least one of each) and the same conditions, it is possible to get a sum larger then 25. What is the largest sum that can be attained? Hint: use as many of the larger numbers as possible.
81) Mrs. Black, Mrs. Green and Mrs. Gray are in the library. Mrs. Black noticed that the colors of their 3 hats were the same as their 3 names, but no one was wearing a hat that matched the color of her name. When she told the others this, the woman wearing the green hat told her to be quiet. Which woman was wearing the black hat?
82) A grocer bought 50 dozen grapefruit at $2 a dozen. He found 30 bad grapefruit and threw them away. He sold all the rest of the grapefruit at 3 for $1. What was the grocer’s profit on the grapefruit?
83) Abby, Betty and Carol stand together on a scale and it reads 200 pounds. Abby and Betty know they weigh the same. Betty and Carol know they weigh 140 pounds together. How many pounds does Carol weigh?
84) Kathleen needs $0.85 in stamps to mail a package. She only has $0.32 and $0.23 stamps. She has to put on at least $0.85. She puts on the lowest amount of postage possible. Kathleen put $_____ of postage on the package.
85) What chemical element has 9 electrons? (Hint: this element is in toothpaste and added to drinking water to help your teeth, the concentration is kept below 1 part per million (ppm) otherwise brown spots will form on your teeth.)
86) The 4 “dominoes” 3|3, 3|5, 6|1, and 4|2 are to be arranged into a square with an empty space in the center. All the sides are to add up to the same number. What number would all the sides add up to?
87) A dartboard containing the following numbers in the sectors: 1, 1, 3, 6, 6, and 18. All the sums from 1 to 35 can be attained with no more than 1 dart in any one sector. For example 28 = 18 + 6 +3 +1 and 5 = 3 + 1 + 1. How could you score 31?
88) A box of 140 marbles contains only red, green and blue marbles. There are three times as many green marbles as red marbles. There are six times as many blue marbles as red marbles. How many blue marbles are there in the box?
89) A computer, which can print 80 symbols across a page, is printing out the days of the week as follows: SMTWTFSSMTWTFSS … starting with Sunday. What is the 78th letter on the first line?
90) A military clock has 1-24 numbered around the face of the clock. What is the number directly across from 16?
91) The numbers 10, A, 16, B, C, and 25 are in order. The letters A, B and C represent different numbers. The difference between 10 and A, A and 16, 16 and B, B and C, and C and 25 are all the same. Find the number C represents.
92) Two friends, Bob and Ralph, ate at a restaurant together. Bob paid for himself and Ralph paid for himself. Bob spent $3 more than Ralph. The total bill was $53 for the two of them. How much did Bob pay?
93) In the addition problem: 238 + AA + AB6 = 839, A and B represent two different digits. A + B = _____.
94) There are 3 different keys for 3 different locks. Each key opens only one of the locks. Alan, Bill and Charlie each choose one key. How many different ways are there for all 3 keys not fitting the locks chosen by Alan, Bill, and Charlie?
95) The number of bicycles in the repair shop is 5 times the number of tricycles in the shop. There are a total of 39 wheels. How many bicycles are in the shop?
96) How many rectangles are there in the figure?
97) Steve made a mistake in a math problem. He added 5 instead of multiplying by 5. Steve’s answer was 13. The correct answer to the problem is ______.
98) Ann has $1 in nickels, dimes and quarters with at least one of each. What is the difference between the largest number of coins that she could have and the smallest number of coins that she could have?
99) A newspaper ran a contest in which awards of $3 and $5 could be won. Each person could win only one award. Exactly $20 was given in $5 and $3 awards. At least one $5 and one $3 award was given. How many people were given awards?
100) A cube measuring 4 units on each side is painted only on the outside and cut into 1-unit cubes. How many cubes have paint on 3 sides?
101) Marlene receives some granola bars as a present. She eats one granola bar and puts the remaining granola bars into 5 bags with each bag having the same number of granola bars. She gives one bag to her brother. She now has 12 granola bars left. How many granola bars did she receive as a present?
102) A toy manufacturer is mailing out 87 miniature dolls to a toy store. These dolls can only be mailed in packages of 8 or packages of 3. What is the least number of full packages the toy manufacturer would need to mail the 87 dolls?
103) Grandpa has 8 sons. Each of his sons has as many sons as they have brothers. Grandpa is as old as the number of all his sons and grandsons. How old is grandpa?
104) There are two different ways of giving exact change for a dollar using 11 coins, which must be quarters, dimes and nickels, with at least one of each. What are these two ways?
105) Joan, Dan and Peter each have some pennies. Joan has 4 times as many pennies as Dan. Dan has 7 less than Peter. All together they have between 20 and 30. How many pennies does Peter have?
106) The top 3 prizes in a golf tournament totaled $126,000. The golfer who finished second received twice as much as the golfer who finished third. The winner of the tournament received 3 times as much as the golfer who finished second. The winner received $_____.
107) Rich has 6 large marbles and 14 small marbles. One large marble weighs the same as 3 small marbles. If the weight of all 20 marbles is 80 ounces, then the weight of 2 large marbles plus 4 small marbles is ______ ounces.
108) In the multiplication problem: 736 x ∆ = 5∆∆∆, the symbol ∆ represents the same digit everywhere it appears. Find the digit ∆ represents.
109) Jason took a math test with 150 questions. He received 1 point for each correct answer, no points if he left it blank and lost ½ point for each wrong answer. Jason had 12 wrong answers and left 15 questions blank. What score did Jason receive on his math test?
110) An auditorium with 10 rows of seats has 10 seats in the front row. Each successive row has one more seat than the previous row (2nd row has 11 seats, etc.) Students taking a test are permitted to sit in any row, but not next to another student in that row. What is the maximum number of students that can be seated to take a test?
111) Find the area of the path around a pool if the pool is 50’ x 20’ and the path is 5’ wide.
112) Amy had 4 quarter, 3 dimes and 2 pennies. Betty had 1 dime. Amy gave 3 of her coins to Betty. Amy now had $0.02 more than Betty. What 3 coins did Amy give to Betty?
113) Jo can mow a lawn in 4 hours. Paul takes 3 hours to mow a lawn. One month they decided to work together. During that month they mowed a total of 28 lawns. How many hours did it take them to mow the 28 lawns?
114) Mr. Carter worked many hours overtime last week and his weekly pay tripled. He received an additional $700. Mr. Carter’s usual weekly salary is $______.
115) A fourth of a stick is painted red, 2/3 is painted blue and the remaining 2 feet is unpainted. How long is the entire stick?
116) In the addition problem: ABC + DBC + CBD = _______ find the largest possible sum by substituting the digits 3, 4, 5 and 6 for the four letters. (A letter represents the same digit every time it appears. Different letters represent different digits.)
117) A machine takes any number fed into it, doubles it and then adds 1. If 5 is fed into the machine, 2 x 5 +1 = 11 comes out of the machine. Jason fed 3 into the machine. He then fed the answer into the machine. He continued to do this until he got a number larger than 100. What was the last number Jason got out of the machine?
118) Every counting number larger than 7 can be written as the sum of only threes and fives. 11 = 3 + 3 + 5; 13= 3 + 5 + 5. The number 26 can be written thusly in two ways: 26 = 5 + 3 + 3 + 3 + 3 + 3 + 3 + 3, and 26 = 5 + 5 + 5 + 5 + 3 + 3. The number 29 can be written as the sum of threes and fives in two ways. How many threes and how many fives are used? Give both answers.
119) Martha multiplied her age by 6, added 10, divided by 2 and then subtracted 3 times her age. What number was Martha left with?
120) One-fourth of the Smith family consists of female children. One-half of the Smith family consists of male children. Including Mr. And Mrs. Smith, there are _____ people in the smith family.
121) If a ∆ b = (a x b) + (a ÷ b), express 20 ∆ (4 ∆ 2) in simplest form.
122) Renee, Sally, Tessa and Wilma all sank foul shots in a basketball game. Tessa sank half as many as Renee. Sally sank 3 times as many as Wilma who only sank half as many as Tessa. Renee sank 8 foul shots. How many were sunk by all 4 girls together?
123) What chemical element has 12 electrons? (Hint: it is a metal that is less than 2/3 the density of Aluminum, making it the lightest metal used in construction. It is necessary for plant and animal nutrition and it has an important place in the chlorophyll molecule, which is the molecule that is responsible for photosynthesis in plants.)
124) There are 9 pieces of paper in a bowl numbered 1 through 9. James first removes all pieces of paper that contain a number that divides 36 evenly. He then removes all pieces of paper that contain a prime number. What is the number on the piece of paper that is still in the bowl?
125) At a conference table there were a total of 20 men and women. The first woman shook hands with 5 men, the second woman shook hands with 6 men, the 3rd woman with 7 men and so on in this manner until the last women shook hands with all the men. How many men were at the conference?
126) Counting from either end of the line, Don is 14th in line. How many people are in the line?
127) If the numbers 1, 3, 2, 4, 6, 12 are arranged around a circle and each number is multiplied by a number next to it, then 6 different products are obtained; 3, 6, 8, 12, 24, and 72. If these same numbers are arranged in a different order, then some of the products will be the same and there will be fewer different products. What is the fewest number of different products that can be obtained?
128) On June 1 the swimming pool in the state park held 150,000 gallons of water. On sunny days 500 gallons of water evaporate. On cloudy days 200 gallons of water evaporate. During the 30 days of June, 1/3 of the days were cloudy and the rest were sunny. How many gallons of water must be added on July 1 to fill the pool back to 150,000 gallons?
129) Evan and Paul each counted the amount of money they made shoveling snow. Evan said, “If I give you ten dollars we will have the same amount of money. If you give me ten dollars, I will have three times as much money as you.” How much money did Evan have?
130) Each cheerleader is 5’6” tall. When one cheerleader stands on the shoulders of another cheerleader, their combined height is 10’. How tall are 4 cheerleaders if they stand on each other’s shoulders to form a 4-person tower?
131) There are 120 five-digit numbers that can be made from the digits 1, 2, 3, 4, and 5, if each digit is used once in a number. The smallest is 12,345 and the largest is 54,321. If these 120 numbers are listed in order from smallest to largest, what is the 73rd number in the list?
132) The number of dollars that Tracy had in her pocket is an odd number. Hal gave Tracy $2 more that she already had in her pocket. The number of dollars Tracy now has cannot be _____ a) $60 b) $62 c) $64 d) $68
133) In a dog show there are 3 times as many collies as boxers. There are also 3 poodles for every 5 collies. What is the smallest possible number of poodles that could be in the show?
134) What element has 13 electrons? (Hint: 3rd most abundant metal in the earths crust, used to make soda pop cans. It has ½ the number of electrons as Iron (Fe).)
135) A square picture 3 ½ feet wide is to be hung on a wall. The center of the picture is to be 4 feet from the ceiling. The top of the picture is _____ft. ______in. from the ceiling.
136) In a checker club each member played each of the other members exactly once. Over 25 games of checkers were played. What is the least possible number of members in the club?
137) A piece of wire 88 inches long is cut into 3 pieces. Two squares are formed from 2 of the pieces and the third is formed into an equilateral triangle (a triangle with 3 equal sides). All the sides of the squares and triangle are the same length. The area of the region inside one of the squares is _____sq. in.
138) A rectangle exists with points labeled A, B, C, D, E, and F. A, C, D, and E make up the corners of the square. Point B is in between A and C. Point F is in between points E and A. The area of the triangle formed by connecting A, B, and F is equal to 15 units. The area of the triangle formed by connecting B, C, and D is equal to 12 units. . The area of the triangle formed by connecting D, E, and F is equal to 28 units. Segment A to B is 6 units, segment B to C is 2 units, segment E to F is 7 units, and segment F to A is 5 units. What is the area of the triangle formed by connecting B, D, and F?
139) The offices at the Village hall are numbered 1 to 12. When the Mayor walks in Monday morning he opens all the doors. The attorney for the Village then closes the doors of the even-numbered rooms. The Mayor’s Secretary changes every third door, opening the ones that are closed and closing the ones that are open. How many of the 12 doors are open after the Secretary finishes?
140) A large tour group needed 12 buses, each carrying the same number of passengers. When 2 buses broke down each of the other buses had to take on 6 more passengers. How many passengers were there now in each bus?
141) On the Lucky Seven TV Game Show, money is awarded. The amounts that can be won are $1, $7, $49 (7 x 7) and $343 (7 x 7 x 7). No person can win more that one amount and no more than 6 persons can win the same amount. If exactly $80 was won, then how many people won money?
142) Tim spins a spinner with numbers 1 through 6. What situation would have a probability of 1/6? The arrow stops on A) an even number B) a number less than 6 C) a number greater than 5 or D) a whole number.
143) Alice bought a certain number of tickets (more than 1) and paid $35 for them. Betty also bought these tickets at the same price and paid $77 for them. How many tickets did Alice buy?
144) Today Angela’s cat’s age in months is the same as Angela’s age in years. In one year her cat’s age in months will be 2 times Angela’s age in years. Today Angela is ______ years old.
145) There are 5 locked doors and 3 keys. Each key opens one and only one door, and no two keys open the same door. Tanya chooses a key and tries it on different doors until she opens it. Leaving that door open, she repeats the process with the next key and then the 3rd key until 3 doors are open. What is the largest possible number of attempts, both successful and unsuccessful, to open these doors?
146) A one-foot cube is to be divided completely into 6” cubes. All these 6” cubes are to be placed one on top of another. How many feet high is it from the bottom to the top?
147) A 12-gallon tank is to be filled with water at the rate of ¼ gallon in 5 seconds. It will take ____min. ____sec. to fill 5/6 of the tank.
148) In the addition problem, 2BA + C6D = 8AD find the sum of the digits represented by B + D. (Different letters represent different digits. Each time the same letter appears, it represents the same digit.)
149) Half the people at the party left. One third of those remaining started to dance. There were then 12 people who were not dancing. How many people were originally at the party?
150) Linda had 2 red cards in her hand. What is the fewest number of black cards she would have to mix with these red cards so that no matter how she arranged the cards there would be at least 3 black cards in a row?
151) The town Board awarded 3 prizes totaling $10,000 for the best essays titled “My Home Town.” The second prize was 3 times as large as the 3rd prize. The first prize was 2 times the second prize. The value of the first prize was $______.
152) Circling a number changes it’s value. Example: 1 circled = 5, 6 circled = 48 and 48 circled = 50. Drawing a box around a number also changes it’s value. Example: 1 boxed = 6, 5 boxed = 9. How much larger is 1 boxed then circled versus 1 circled then boxed?
153) Cindy can buy a bracelet and a pair of earrings for $50. She can buy a pair of earrings and a ring for $60 or a ring and bracelet for $70. How much does the ring cost?
154) Find the number that when you multiply it by 100 gives you an answer that is one less than when you add it to 100.
155) A clock is divided into 12 equal parts and each of these into 5 equal smaller parts. Normally the hour hand will move one of the smaller parts while the minute hand moves 12 of them. A clock shows 3pm, from this moment on, the hour had moves correctly, but the minute hand only moves 10 of these smaller parts to each one the hour had moves. In two hours the clock will be _____ minutes behind.
156) If a # (b ∆ c) means (a + b) x (a + c), then how much larger is 3 # (4 ∆ 5) than 2 # (3 ∆ 4)?
By taking the 6 one foot squares piled
on top of one another, as shown, and placing them alongside one another the
perimeter increases by _____ feet?
158) Two lines cross at point E. One line is labeled with points AEFB and the other with points CEGD. The number 7 is placed on point B and the numbers 1, 2, 3, 4, 5, and 6 are to be placed on the other 6 points. The sum of the numbers on the line AB is the same as the sum of line CD. What is the smallest possible sum for each line?
159) Container A is filled with 8 liters of water, container B holds 5 liters, and container C holds 3 liters. Containers B and C are empty. Water is poured from A filling B. Water is then poured from B filling C. The water in C is poured into A. The water in B is poured into C. Water is poured from A filling B. Water is poured from B filling C. The water in C is poured into A. How many liters are there in A?
160) A dog weighs 14 pounds plus 2/3 of its own weight. How many pounds does the dog weigh?
161) In binary 11112 is equal to 15 in decimal (base 10, because we humans have 10 fingers to count on) and we would write it 1510 so that we know the number system we are using is base 10 and not base 2 or binary. Binary is used by computers because computers only understand on and off (1 and 0) therefore the first 1 on the right is the ones place holder, the second 1 is the twos place holder, the third one is the fours place holder, and the 1 furthest to the left is the eights place holder. To understand 11112 = 1510 you can add up all the values for any ones that are written in binary. Thus 8 + 4 + 2 + 1 = 15. What decimal (base 10) value would 10012 have?
162) A man died and part of his will involved dividing $180,000 in cash to his sister, his son and his wife. The will said that for every dollar that his sister was given, the son should receive two dollars and his wife six dollars. Of the $180,000 how much did his wife receive?
163) Find the smallest 4-digit number that is divisible by 2, 3, 4 and 5.
164) Light travels at a speed of approximately 186,000 miles per second (2.998 x 108 m/s) to find how far light travels in a year you would have to multiply 186,000 by: a) 60 x 60 x 24 x 365, b) 60 x 60 x 7 x 30 x 12, c) 60 x 24 x 7 x 30 x 12, or d) 60 x 24 x 7 x 365.
165) On Monday, Rebecca spent ½ her money on a gift for her brother. Tuesday she earned $4 babysitting. Wednesday her aunt gave Rebecca as much money as Rebecca had after Tuesday. Rebecca now has $32. How much money did Rebecca start with Monday morning?
166) If you had a square piece of metal 12 feet on one side and cut 36 square feet off of it what % did you cut off?
167) How many consecutive zeros are at the end of the product 25 x 25 x 25 x 25 x 25 x 25 x 8 x 8 x 8?
168) At a student conference 6 students, Al, Beth, Carl, Dot, Ed and Fay, were asked to form committees with the following conditions: 1) each committee was to contain exactly three students; 2) each student was to belong to exactly two committees; 3) no two committees could have more than one student in common (Al and Beth could not be together on two different committees). How many committees were formed?
169) The average of 5 numbers is 20. A sixth number is added and the new average is 21. What was the sixth number?
170) Six students worked 8 hours a day for 3 days at a hamburger stand. Each made the same amount and the total wages paid was $828. What was each student’s hourly wage?
171) Ken started the day with some money in his pocket. After he took some money out of his bank account, he had $4 more than twice the amount he stared with. He then received a birthday present, which doubled the amount of money he had with him. Ken now had $100 in his pocket. How much did he start the day with?
172) Michelle and Audrey both start walking at noon. Michelle walks from P to Q, back to P and back and forth at a constant speed of 3 miles per hour. (P and Q are 5 miles apart) Audrey walks from Q to P, and back to Q and back and forth at a constant speed of 2 miles per hour. They pass each other for the first time at 1 pm, 3 miles from P and 2 miles from Q. At what time will they pass each other for the second time?
173) How many multiples of 7 are there between 250 and 500?
174) What is the unit’s digit in the number 312 ?
175) A water sample has a mass of 33 grams and occupies 33 milliliters. What is the density of water?
176) If A * B means (A + B) / (B – A), what is the numerical value of A * B when B is 3 times as large as A?
177) A certain bacteria doubles every 5 minutes. At 1pm a small amount of this bacteria is placed in a container. By 5 pm the container is filled with the bacteria. At what time was the container ¼ full?
178) Mr. Cole and Mr. Edwards are neighbors. Mr. Cole is 25 years old and, while they are not the same age, Mr. Edward’s age contains the same 2 digits. The next time that will happen is in ______ years.
179) It takes 4 people 5 hours to build 2 sheds. Ten people could build 20 sheds in ______hours. (You have to assume that each person does the same amount of work and they all work together well. In real life this would never be true, give an example why this would not be true in a real life situation.)
180) A clock is divided into 60 parts. When the hour hand moves to the 1, the minute hand moves 12 times as far. If the time is12:12 pm, what time will it be if the hour hand moves to where the minute hand is now?
181) If you have a rectangle with sides of 8 units by 6 units and a 3 by 3 square is cut out of the rectangle, what is the remaining area of the rectangle?
182) Chuck and Roberta have 120 baseball cards between them two of them. If you double the number Chuck has and halve the number Roberta has, then they would have the same number of cards (but not the same total). How many baseball cards does Chuck have?
183) Some counting numbers can be written as the sum of two or more consecutive numbers and some cannot be. Examples: 15 = 7 + 8; 12 = 3 + 4 + 5; 14 = 2 + 3 + 4 + 5. The number 16 cannot be written as the sum of consecutive numbers. How many numbers between 1 and 12 cannot be written as the sum of consecutive numbers? (Do not count 1.)
184) Bill has a bag of 100 balls numbered from 1 to 100. What is the minimum number of balls that would have to be picked to be sure of having at least one number that is a multiple of another number already picked?
185) Mike gave Danny 4 more marbles than he already had. He now has 100 marbles. How many marbles did Mike give to Danny?
186) There are K thousandth’s in a tenth and L ten’s in a thousand. Which of the following is true? A) L is 10,000 times as large as K. B) K is 10,000 times as large as L. C) L is 4 times as large as K. D) K is 4 times as large as L. E) K = L
187) Rebecca and Kate both leave Sandersville on their bicycles at the same time. Rebecca travels at a constant speed of 12 M.P.H. and Kate at a constant speed of 8 M.P.H. Rebecca arrives at Crescent Hills 2 hours before Kate. How many miles is it from Sandersville to Crescent Hills?
188) Don went shopping for gifts for his family. He spent $2 more than ½ his money for gifts for his parents. He then spent $2 more than ½ his remaining money for a gift for his sister. Finally, he spent $2 more than ½ of what was left of his money for cards and wrapping paper. Don now has $0.50 left. How much more did he spend on his parent’s gifts than on his sister’s gift?
189) Beth’s age in the year 2012 is the same as the sum of the digits of the year she was born. That sum is 5 times the sum of the digits in the year 2012. In what year was Beth born?
190) Assume there are 500 people voting on a bill in the House of Representatives. Some bills need at least a 2/3 majority to pass and other bills need just a simple majority to pass (more than half). The difference between the lowest possible passing with a 2/3 majority and the lowest possible passing with a simple majority is ______ votes.
191) If X ^ Y means (X + (X +1) + (X + 2) + (X + 3) + …), Y times. Express 12 ^ 3 in simplest form.
192) Ken and Stan were involved in a 2-day homerun contest. The results were: 1st day Ken had 2 home runs in 43 tries and Stan had 1 home run in 32 tries. 2nd day Ken had 4 homeruns in 6 tries and Stan had 6 home runs in 15 tries. Who had the better home run average for a) the first day? B) the second day? C) overall for the 2 days?
193) Twenty-four pennies were divided into 3 unequal piles. From the first pile was taken as many pennies as there were in the second pile and added to the second pile. Then, from the second pile was taken as many pennies as there were in the third pile and added to the third pile. All 3 piles now had the same number of pennies. How many pennies were in the first pile in the beginning?
194) Mr. Hayes’ water bill for every 30 days is $16. He then put in plants and grass and an automatic sprinkler system. For the next 30 days his sprinklers were on every day for 15 minutes, 4 times a day. His water bill increased to $184. For the next 30 days he will have his sprinklers on every other day and only once for 15 minutes. His water bill for these 30 days should be _______.
195) Jane is taller than Harriet. Harriet is shorter than Marie. Marie is older than Renee who is Jane’s older sister. The heights of the girls are such that the older they are, the shorter they are. The second tallest girl is ______.
196) In the multiplication problem 3A2 x 7 = 2744, find the digit represented by A.
197) Find the smallest positive whole number that is evenly divisible by every single-digit positive whole number except 5.
198) The mole is the key to many chemical calculations. One mole of anything equals 6.022 x 1023 (= 602,200,000,000,000,000,000,000 also called Avogadro’s number) and this number is the number equal to the number of carbon atoms in exactly 12 grams of pure 12C. A) Would you be able to carry one mole of pennies? (Hint: one penny weighs 2.5 grams). B) Would you be able to carry one mole of water (Hint: water is 18 grams/mole).
199) Houses on the south side of Main Street are numbered with consecutive even integers starting with 1846 and ending with 2092. How many houses are on the south side of Main Street?
200) If the houses on Winnetka Avenue are numbered even on the east side and odd on the west side, starting from 6200 the numbers increase by eight. How many houses are on Winnetka Ave from 62ndAvenue(6200) to 63rd (6300) Avenue? (In this real example the largest house number is 6289 there is no 6296 or 6297 because they would be in the middle of the intersection of 63rd and Winnetka.)
201) Find the fewest number of squares, in each with a perimeter of 8”, that would completely cover a square with a side of 8”.
202) Bill wrote 940 different whole numbers. The difference between the number of even numbers Bill wrote and the number of odd numbers he wrote can equal any of the following except ______. A) 0, B) 395, C) 400, D) 550, E) 940
203) Joan runs twice as fast as Sally. In a 200-yard race, Joan gives Sally a 40-yard head start (Sally will only have to run 160 yards). When Joan crosses the finish line, Sally is ______ yards behind her.
204) A square 6” on a side and a rectangle 2” by 10” are placed so they over lap. What is the total area of the two figures minus the largest possible area that would overlap?
205) Two friends, Bob and Ralph, ate at a restaurant together. Bob paid for himself and Ralph paid for himself. Bob spent $3 more than Ralph. The total bill was $52.24. How much did Bob pay?
206) A car is traveling on a highway at a constant speed of 55 M.P.H. Another car is behind this car and is gaining ½ mile on the first car every 15 minutes. How fast is this car traveling?
207) In a 100-yard dash, one student came in second and another student came in next to last. What is the least possible number of students in the race?
208) The product of 3 whole numbers is 60. The numbers are all different and greater than one. The sum of the three numbers is 13. What are the numbers?
209) Mrs. Sanchez stopped for gasoline when the gas gauge indicated the tank was 1/8 full. After putting in $5 worth of gasoline, her gauge indicated the tank was 3/8 full. Gasoline costs, $1.25 per gallon. How many gallons of gasoline does the tank hold when full?
210) Susie’s clock loses 15 minutes every hour. The clock is set at that correct time at 9am. What is the correct time when Susie’s clock first shows 11am?
211) Three boys, Al, Bill, and Chuck, play a game with the understanding that the loser is to double the number of marbles of each of the other two. After 3 games, each had lost once (Al first, then Bill, then Chuck) and each ends up with 24 marbles. How many marbles did Al start with?
212) What is the simplest form for the fraction 10/16?
213) Mrs. Lopez’s 6th grade class has 29 students. In order to raise funds for a field trip, 17 students in the class formed a group to have a car wash, and 16 students formed a group to have a bake-sale. If 9 students belong to both groups, how many students belong to neither group?
214) What 3-digit palindrome (reads the same from right to left as it does from left to right, like 131) has digits that add to 18 and multiply to 196?
215) In the addition problem: A34 + B1C + 53D = E4F3, find the sum of the 6 digits represented by A, B, C, D, E, and F.
216) If A ^ B = AB and A # B = A – B, express [(3 ^ 6) # 4] # [3 ^ (6 # 4)] in simplest form.
217) “Two days ago Adam was 11 year old. Next year he will be 14 years old.” What is the month and day of the statement and what is the month and day of Adams Birthday?
218) Rudy worked for 1 hour and 20 minutes and was paid $16. The next day he worked for 2 hours at the same hourly rate. Rudy was paid $______ for the 2 hours.
219) A jar is 1/5 full of marbles. When 25 marbles are added to the jar it becomes ¼ full. How many more marbles must be added to the jar to make it ½ full?
220) A single digit number divides the dividend 6952. The quotient is a 4-digit number. There is no remainder. All the digits 1, 2, 3, 4, 5, 6, 7, 8, 9 are used exactly once. The divisor is _______ and the quotient is ______.
221) In an NBA basketball game, Michael Jenkins scored 11 points more than Scot Porter, Scot Porter scored 9 more points than Lou Long. Altogether the three of them scored 80 points. How many points did Michael Jenkins score?
222) Dawn bought $3 worth of pencils priced at $0.04 each and $3 worth of pencils priced at $0.06 each. The average price in cents for one of those pencils is $________. (Give your answer to the a tenth of a cent.)
223) Widgets cost $5 each and Wizzles cost $7 each. Kris spent $31 for her Widgets and Wizzles. Kim spent $43 on her Widgets and Wizzles. How many Wizzles did the two girls buy together?
224) Amy has the same number of dimes and quarters. She has $7. How many coins does she have?
225) A stairway has between 30 and 40 steps. If Alex counts them 2 at a time he has one left over. If he counts them 3 at a time he has 2 left over and if he counts them 4 at a time he has 3 left over. The stairway has ____steps.
226) Juanita has a collection of bicycles and tricycles. She has 36 pedals and 43 wheels. How many tricycles does she have?
227) If the digits 6, 5, 4, 3, 2, 1, 6, 5, 4, 3, 2, 1, 6, 5, 4, 3, 2, 1, …. are written in that pattern over and over again, what will be the 4000 digit?
228) By placing a “4” at the right hand end (unit’s place) of a 3 digit number, the value of the number is increased by 4828. What was the original 3-digit number?
229) Sam noticed that the height of his house is exactly 9” more than 3 times his height. His house is 16’6” high. How many more inches does Sam have to grow in order to be exactly 6’ tall?
230) Two 1” squares are cut from the corners of a large rectangle. Is the perimeter the same, larger or smaller after the cuts?
231) Multiplication of two numbers can give a product that has the same digits that are in the two numbers. 3 x 51 = 153. The digits of 153 (1, 3, and 5) are the digits of 3 and 51. Complete the following ___ x ____ = 126. What single digit times a two digit number equals 126 and contains the digits 1, 2, 6?
232) Visible light has a wavelength from 4000 angstroms (Å) to 7000 angstroms (Å). One angstrom (Å) = 0.0000000001 meter. Can we see a virus that is 50 Å with the naked eye? Can we see a bacterium that is 4500 Å? Can we see a pinhead that is 10,000 Å?
233) Tennis balls come in cans of 3 balls each. Each tennis ball cost $1.50. Loretta, Maria and Carol play tennis together for a month. During that time Loretta bought 6 cans of tennis balls and Maria bought 4 cans. Since Carol did not bring any tennis balls, she figures she owes $15. Of the $15, $_______ should go to Loretta.
234) The digits of our number system are 0, 1, 2, 3, 4, 5, 6, 7, 8, and 9. If a two digit number is written on a piece of paper and held up to the mirror so that the number faces the mirror, then the mirror image will show the number with two changes: the left and the right digits are reversed and each digit is flipped over horizontally. The number 23 would appear, in the mirror, as 32 but each number would look wrong because they would be flipped over horizontally.. There is one two-digit number that will appear in the mirror as a larger two-digit number that would look correct in a mirror. What is this two-digit number?
235) In a list of 100 numbers each number after the first number is 10 more than the number that comes before it. What is the difference between the first number and the last number on the list?
236) The 5 tires of a car (4 + 1 spare) were each used equally on a car that had traveled 60,000 miles. Each tire was used for ______ miles during that time.
237) Woody Woodman heats his house by burning wood. He lights his fire on October 2 and on April 29 he stops. During the months of October, November, March and April he burns ¼ cord of wood every 10 days. From December through February he burns ½ cord of wood every 10 days. It is not a leap year. How many cords of wood does he burn from October 2 through April 29?