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Potpourri – 5th Grade 1. 2 points: George, a 4th grader, has yet to learn about the “order of operations”, so he “solves” the mathematical expression 2 + 3 × 20 − 16 ÷ 4 strictly from left to right. Georgina, however, is a 6th grader who knows the order of operations inside and out. As a result, she accurately evaluates the mathematical expression using the order of operations. What is the positive difference in their two answers? 2. 2 points: If the first four terms of a sequence are 3, 6, 12, 21, and 33, what is the sum of the next three terms of the sequence? 3. 2 points: In a “hundreds chart”, the numbers from 1 to 100 inclusively are written in increasing order from left to right and top to bottom, ten numbers per row. If the second column of numbers is accidentally covered in pie during the math club’s annual pie catapult contest, how many multiples of 3 in the chart are not covered with pie? C A and , are created, such that A, B, C, and D are all unique B D digits between 1 and 9, inclusively. What is the greatest possible positive difference between C A and ? Express your answer as a simplified mixed number. B D 5. 3 points: How many positive three-digit integers are there such that they will remain a positive three-digit integer when divided by 2? 4. 3 points: Two fractions, 6. 3 points: The distance around Earth is approximately 24902 miles. Suppose that The Flash was traveling 2017 feet per second. To the nearest hour, how long would it take for The Flash to travel around Earth twice? 7. 3 points: Consider the mathematical expression 4 4 4 4 4, where each blank represents an operation: addition, subtraction, multiplication, or division. What is the greatest possible value of this expression if you must use each of the four operations exactly once? 8. 4 points: Given that x is a positive four-digit integer and z is a positive two-digit integer, x and = z, what is the largest possible integral value of y? y 9. 4 points: At home with the flu all day, Paul decided to painstakingly watch his 12-hour digital clock for twelve straight hours starting at the moment the clock switched to 8:00 am. Assuming his clock only shows the hours and minutes, for how many minutes will the digit ‘5’ be displayed during those 12 hours? 10. 4 points: What is the ones digit in the sum 12017 + 22017 + 32017 + . . . + 82017 + 92017 ?