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Copyright © 2020 by Mathematical Olympiads for Elementary and Middle Schools, Inc. All rights reserved. Mathematical Olympiads For Elementary & Middle Schools November 1 , 2021 Name: ____________________________________________________ 1A Which whole number is equal to 1000 – 531 – 315 – 153? 1B How many stars ‘ * ’ are there in the pattern shown? 1C The New York Nicks had a streaky season. They began by winning 4 games in a row, and then they lost 12 games in a row. After those 12 losses, they won every game, finishing with 3 wins for every 2 losses overall. How many games did they win after the first 16 games? Directions to Students: After all questions have been read by your PICO, you will have 30 minutes to complete this contest. You may not have a pen or pencil in your hand while the PICO reads the set of questions to the class. Calculators are not permitted. All work is to be done on the pages provided. No additional scrap paper is to be used. Answers must be placed in the corresponding boxes in the answer column.
Name: _________________________________________________________________ 1D The least prime that is the sum of four different prime numbers is 17 because 17 = 2 + 3 + 5 + 7. What is the least prime greater than 17 that is the sum of four different prime numbers? 1E In a video game, Brian collects unbreakable gems, each of which has its own value. He earns 21 points when he collects 2 red gems and 3 yellow gems. He earns 31 points when he collects 2 yellow gems and 3 blue gems. He earns 23 points when he collects 2 blue gems and 3 red gems. When Brian collects 2 red gems, 2 yellow gems, and 2 blue gems, how many points does he earn? Answer Column 1A 1B 1C 1D 1E Do Not Write in this Space. For PICO’s Use Only. SCORE:
Copyright © 2020 by Mathematical Olympiads for Elementary and Middle Schools, Inc. All rights reserved. Mathematical Olympiads For Elementary & Middle Schools December 6 , 20 2 1 Name: ____________________________________________________ 2A Evaluate 1357 + 3571 + 5713 + 7135. 2B In the figure, four squares are placed on a grid whose small squares are each 1 1. What is the perimeter of the shaded figure? 2C On Main Street in Springfield, the first house is numbered 13, and each house number is 4 more than the house right before it. Jenny lives in the last house on the street. Her house number is 221. How many houses are on Main Street? Directions to Students: After all questions have been read by your PICO, you will have 30 minutes to complete this contest. You may not have a pen or pencil in your hand while the PICO reads the set of questions to the class. Calculators are not permitted. All work is to be done on the pages provided. No additional scrap paper is to be used. Answers must be placed in the corresponding boxes in the answer column.
Name: _________________________________________________________________ 2D Exactly seven years ago, Sam was 5 times the age of Janet. Exactly two years ago, Sam was 3 times the age of Janet. What is the sum of their ages today? 2E The counting number ABAB is a multiple of 36. If different letters represent different digits, what is the greatest value ABAB can have? Answer Column 2A 2B 2C 2D 2E Do Not Write in this Space. For PICO’s Use Only. SCORE:
Copyright © 2021 by Mathematical Olympiads for Elementary and Middle Schools, Inc. All rights reserved. Mathematical Olympiads For Elementary & Middle Schools January 1 , 2022 Name: ____________________________________________________ 3A What whole number is equal to 2 3 4 5 7 25? 3B Sarah wrote the whole numbers from 1 to 85 on a sheet of paper. How many times did Sarah write the digit 7? 3C Bert and Ernie are looking at their paper clip collections. Bert has 5 paper clips for every 3 paper clips that Ernie has. If Bert gives Ernie 12 paper clips, they will have the same number of paper clips. How many paper clips does Bert have? Directions to Students: After all questions have been read by your PICO, you will have 30 minutes to complete this contest. You may not have a pen or pencil in your hand while the PICO reads the set of questions to the class. Calculators are not permitted. All work is to be done on the pages provided. No additional scrap paper is to be used. Answers must be placed in the corresponding boxes in the answer column.
Name: _________________________________________________________________ 3D A rectangle that measures 12 inches 18 inches is cut into six identical squares by making three cuts. How many inches is the perimeter of one of those six squares? 3E Suppose that WARM – COLD = 6591 and each letter represents a different digit from 0 through 7. What is the greatest four-digit number WARM? Answer Column 3A 3B 3C 3D 3E Do Not Write in this Space. For PICO’s Use Only. SCORE: WARM – C O L D 6 5 9 1
Copyright © 2021 by Mathematical Olympiads for Elementary and Middle Schools, Inc. All rights reserved. Mathematical Olympiads For Elementary & Middle Schools February , 2022 Name: ____________________________________________________ 4A Evaluate 987 – 876 + 765 – 654 + 543 – 432 + 321 – 210. 4B More than twenty people came to a sticker exchange. Every person brought the same number of stickers. Every person brought more than one sticker. In all, there were 141 stickers at the exchange. How many people came to the exchange? 4C The Fibonacci sequence 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, … is formed by summing two consecutive numbers to get the next number. The number after 55 is 34 + 55 = 89. A Fibonacci game cube has a different Fibonacci number on each face selected from the set {1, 2, 3, 5, 8, 13}. One red and one blue Fibonacci game cube are tossed together. How many of the 36 possible outcomes show a pair of numbers on the tops of the cubes whose sum is also a Fibonacci number? Directions to Students: After all questions have been read by your PICO, you will have 30 minutes to complete this contest. You may not have a pen or pencil in your hand while the PICO reads the set of questions to the class. Calculators are not permitted. All work is to be done on the pages provided. No additional scrap paper is to be used. Answers must be placed in the corresponding boxes in the answer column.
Name: _________________________________________________________________ 4D Jan is making a logo for her company. She begins with a 6-cm-by-12-cm rectangle. Two points along the bottom side divide that side into three equal pieces. A point on the top side divides that side into two equal pieces. The logo itself is the total shaded area, as shown. What is the area of the shaded logo, in square cm? 4E A palindromic number is a number that reads the same forwards as it does backwards (example: 282 or 51715). How many 5-digit palindromic numbers have digits that add up to 14? Answer Column 4A 4B 4C 4D 4E Do Not Write in this Space. For PICO’s Use Only. SCORE:
Copyright © 2021 by Mathematical Olympiads for Elementary and Middle Schools, Inc. All rights reserved. Mathematical Olympiads For Elementary & Middle Schools March , 2022 Name: ____________________________________________________ 5A Evaluate 99 + 11 + 88 + 22 + 77 + 33 + 66 + 44 + 55. 5B How much greater than 21 2 is 22 2 ? 5C In a cryptarithm, each letter is assigned its own unique digit. In the cryptarithm shown (where MATH is 3 times FUN), FUN is a 3-digit number with its digits in consecutive and increasing order. What 3-digit number is FUN? [No leading digit can be 0.] Directions to Students: After all questions have been read by your PICO, you will have 30 minutes to complete this contest. You may not have a pen or pencil in your hand while the PICO reads the set of questions to the class. Calculators are not permitted. All work is to be done on the pages provided. No additional scrap paper is to be used. Answers must be placed in the corresponding boxes in the answer column. F U N F U N + F U N M A T H
Name: _________________________________________________________________ 5D Start with a square as shown, whose perimeter is 800 inches. Penelope folds this in half along the horizontal dotted line. She then folds the result in half along the vertical dotted line shown, and so on, for some number of similar alternating folds (horizontal then vertical). How many folding-in-half steps does Penelope need to do in order to get the perimeter of the resulting quadrilateral to be 100 inches? 5E Express the given fraction below in simplest form. Answer Column 5A 5B 5C 5D 5E Do Not Write in this Space. For PICO’s Use Only. SCORE: