Noetic Math Set 1
Problem #1
Natalie bough 3 cupcakes and 2 donuts for $5.00. James bought 1 cupcake and 2 donuts for $2.40 in the same store. If all cupcakes cost the same and all donuts cost the same, how much does each donut cost?
Problem #2
How many different meal choices are there if you choose 1 appetizer, 1 main course, and 1 dessert from the dinner menu below?
Problem #3
A dartboard has three regions, as shown to the left. Darts that land in the same region give the same number of points. Abby, Bob, and Cory each threw two darts and the positions of their darts are shown to the left. If Abby scores 24 points and Bob scores 21 points, how many points does Cory score?
Problem #4
Shown to the left are three cups. One is filled with milk, one is filled with juice, and one is filled with water. Milk is not in Cup A or Cup B. Juice is either Cup A or Cup C. Which cup has water?
Problem #5
How many four-digit numbers have a digit sum of 3? An example of a four-digit number with a digit sum of 3 is 1002 because 1 + 0 + 0 + 2 = 3.
Problem #6
Letters A, B, and C represent three numbers. A line is drawn between any two numbers and the sum of the two numbers is written next to the line. What number does letter B represent?
Problem #7
Peter is picking a number for his jersey. He wants to have a 2-digit number with an odd digit in the tens-place and an even ndigit in the ones-place. How many different choices does Peter have?
Problem #8
A square with an area of 100 square inches is cut into one smaller square and 2 identical trapezoids as shown below. The area of the smaller square is 24 square inches. What is the are of the shaded trapezoid?
Problem #9
The following sketch shows a grey square rug is on top of a tile floor that is made of equal-sized square tiles. If the dimensions of the tile floor are 10 ft x 10 ft, what is the area of the rug?
Problem #10
Put the digits 1, 2, 3, 4 and 5 in the following 5 circles so that three numbers in a row or in a column have a sum of 9. Use each number once. What number should be in the circle with a question mark?
Problem #11
In each of the following 5 juice boxes, there are some letter cards. Joseph takes exactly one letter card out of each box and spells the word 'QUEST'. Which letter card did he take out from Box 4?
Problem #12
Annie and Jamie are playing a card game. If Jamie gives Annie one of her cards, then Annie will have twice as many cards as Jamie. If Annie gives Jamie one of her cards, then Annie will have the same number of cards as Jamie. How many cards does Annie have?
Problem #13
Jane asked about her grandma's age. Her grandma answered, "Well, I am six years younger than your grandpa. Your dad's age is half of your grandpa's age. And we both know that your age is one-quarter of your dad's age." Jane is nine years old. How old is Jane's grandma?
Problem #14
The following 5 keys are for the following 5 locked padlocks. Each key opens one and only one padlock. Different keys open different padlocks. What is the least number of trials needed to guarantee that you will open all 5 padlocks?
Problem #15
There are as many red marbles as blue marbles in a pouch. If 6 red marbles are removed from the pouch, the number of red marbles will be half of the number of blue marbles. How many blue marbles are in the pouch?
Problem #16
Carla, Ethan, Frank and Mary live on the same straight road. The distance between Carla's house and Mary's house is 470 yards. Ethan's house is in between Carla's house and Mary's house. The distance between Ethan's house and Mary's house is 350 yards. Frank's house is in between Ethan's house and Mary's house. The distance between Carla's house and Frank's house is 270 yards. What is the difference between Ethan's house and Frank's house?
Problem #17
Mother and Maria worked out a deal. For every day Maria walks the family dog, she gets $1.00. For every day Maria doesn’t walk the dog she gives $1.00 back to her mom. Maria made a total of $19.00 during the month of May. How many days did Maria walk the dog in May?
Problem #18
Aiken makes trapezoids using small white and gray triangles. The first 3 trapezoids are shown below. If he keeps the same pattern, how many more white triangles than gray triangles will he need to make the tenth trapezoid?
Problem #19
In the subtraction problem to the left, the same letters represent the same digits, and different letters represent different digits. If D = 0, C = 1 and E = 7, what digit does the letter A represent?
Problem #20
Three boys and three girls went to see a movie together. There are 6 adjacent empty seats left in the auditorium. How many possible ways are there for them to sit in the 6 adjacent seats if no two boys sit next to each other and no two girls sit next to each other?
Problem #21
Luke is arranging cubes with edges 2 inches long inside a cubical shipping box that has edges 8 inches long. At most, how many cubes can Luke put inside the shipping box?
Problem #22
Chloe multiplied a certain number by 3 instead of dividing it by 3. As a result she got 45. What would the result have been if she hadn’t made that mistake?
Problem #23
In a game show, Michelle scored 11 points in the 2nd round, doubled her point total in the 3rd round and earned 34 points in the 4th round. If she had 100 points total at the end of the 4th round, how many points did she score in the 1st round?
Problem #24
Anna has 7 pairs of yellow socks, 8 pairs of red socks and 2 pairs of blue socks mixed together in a drawer. All pairs of socks are identical except for their colors. What is the smallest number of socks she has to take out blindly to make sure of having 2 matching pairs of socks?
Problem #25
The following diagram shows the first three figures that made of squares in a sequence. How many squares are there in the 50th figure?
Problem #26
ABCD is a square with 8-inch sides. Point E is the midpoint of side AB and point F is the midpoint of side BC. What is the area of triangle DEF?
Problem #27
Six poles are equally spaced along one side of a straight road. The distance from the first pole to the third pole is 24 feet. What is the distance in feet between the first pole and the sixth pole?
Problem #28
Jessie wrote down a 3-digit natural number. She said her number consists of three consecutive digits in descending order from left to right with the sum of its digits equal to 24. What number did Jessie write down?
Problem #29
Mrs. Wong bought 3 medals: one gold medal, one silver medal and one bronze medal for the upcoming math contest. One gold medal is twice as expensive as one silver medal and one silver medal is 3 times as expensive as one bronze medal. She spent $35.00 altogether. How much was the gold medal?
Problem #30
Today is November 13th. Logans birthday is on February 15th. How many more days until Logans birthday?
Problem #31
Some of Peter’s darts landed on the dartboard below. He scored a total of 17 points. How many darts landed in the 4-point section?
Problem #32
Place the numbers 1, 2, 3, 4, 5, 6, and 7 in the following seven circles so that any three numbers in a straight line have a sum of 14. Use each number once. What number should be placed in the circle with the question mark?
Problem #33
There are a total of 26 chocolates in five boxes, as shown above. The first two boxes contain a total of 7 chocolates. The second and third boxes contain a total of 10 chocolates. The third and fourth boxes contain a total of 14 chocolates. The fourth and fifth boxes contain a total of 12 chocolates. How many chocolates are in the first box?
Problem #34
Roger went to a store to buy baseball cards. If he buys 5 packages of baseball cards, he will have $2 left. If he buys 7 packages of baseball cards, he will need $8 more. How much money did Roger have?
Problem #35
Hong places the digit 7 to the end of a 3-digit number ABC to make a 4-digit number ABC7. Then, Hong subtracts the original 3-digit number ABC from the 4-digit number ABC7, and he gets 2347. What is the 3-digit number ABC?
Problem #36
The length of rectangle A is 3 times the length of rectangle B. The width of rectangle A is twice the width of rectangle B. If the area of rectangle A is 108 in. , what is the area of rectangle B? Note: The figure is not drawn to scale.
Problem #37
Chris, Dale, and Jon shared a pizza. Chris and Jon ate a total of 210 grams of pizza. Dale and Jon ate a total of 280 grams of pizza. If Jon ate 90 grams of pizza, how many grams of pizza did Chris and Dale eat altogether? Note: The chart is not drawn to scale?
Problem #38
Penny played two games of her favorite game, Bam-Boo. The points she scored in her second game was 3/4 of the points she scored in her first game. She scored a total of 280 points from the two games. How many points did she score in her first game?
Problem #39
Sean built a rectangular vegetable garden that is 16 feet long and 8 feet wide. For him to take care of the vegetables better, he also built two perpendicular brick paths that are 2 feet wide in the middle of the garden as shown in the picture. How many square feet of garden remaining can Sean plant vegetables?
Problem #40
In the following pyramid, every block, except blocks in the bottom row, contains the sum of the two numbers directly below it. For example, 72 = 43 + 29. What number should be on the top block of the pyramid?
Problem #41
From the following 9 numbers, how many different ways can you pick 3 different numbers so that their sum is 22?
Problem #42
Jennifer and Sarah took a walk on the shore and collected a total of 120 seashells. After Jennifer gave 1/3 of her seashells to her younger brother, she had the same number of seashells as Sarah. How many seashells did Jennifer give to her younger brother?
Problem # 43
Some of Peter’s darts landed on the dartboard below. He scored a total of 17 points. How many darts landed in the 4-point section?