First Name _____________________________________Last Name _____________________________________ Grade __________________________________________ School __________________________________________ City ___________________________________________ RSM Branch____________________________________ 1 2 4 A square is divided into 64 square cells as shown in the diagram. How many of these cells share an even number of sides with other cells? A teacher wrote a 3-digit number on a board. Three RSM students, Rachel, Samantha, and Malvina, each correctly multiplied two of this number’s three digits, and got three different results. Rachel got 24, and Samantha got 36. What did Malvina get? Each price tag shows the cost of the toys inside the bag. Figure out the missing number on the last price tag. Note that all balls cost the same as each other, and all cars cost the same as each other. $3 5 6 $5 The numbers 1, 2, 3, 4, 5, and 6 are covered by the six circles shown (each circle covers only one number). Each arrow in the diagram, except one, points from a smaller number to a larger number. Compute the sum of the numbers covered by circles R, S, and M. $? G R O S ! Five girls, Anna, Beth, Cindy, Dora, and Emily, chose five different digits, one digit each. Only one of the digits chosen by Anna, Beth, Cindy, and Dora was odd. Only one of the digits chosen by Anna, Cindy, and Emily was even. How many even digits were chosen by the five girls? M Please fold over on line. Write answers on back. 3 Harry, Larry and Mary went cherry-picking. Harry picked 10 more cherries than Mary and 2 more than Larry. Harry and Larry gave some of their cherries to Mary so that all three of them have the same number of cherries. How many cherries did Harry give to Mary? Grades 4-5 2015 Grades 4-5 2015 1 2 3 4 5 6 . Sam cut one of Ron’s rectangles into two rectangles each having perimeter 12. and one is off by 35 minutes. one sixth of the remaining time solving problem 5. They all should show the same (correct) time. one fourth of the remaining time solving problem 3. one fifth of the remaining time solving problem 4. All the girls and one third of the boys participated in Math Kangaroo. How many students participated in only one of the two competitions? Ron cut out three identical paper rectangles. the same ending point S. She spent half of the total time solving problem 1. How many minutes had Lily spent altogether doing her math homework? Please fold over on line.First Name _____________________________________ Last Name _____________________________________ Grade __________________________________________ School __________________________________________ City ___________________________________________ ____________________________________________ RSM Branch____________________________________ 7 8 10 11 12 Look at these five clocks. Each route cannot go over any part of itself (points or lines) more than once. S M R O Lily had to solve 5 problems for her math homework. or both. and may or may not share any other points or lines with other routes. 9 An archer shot a total of 20 arrows at several targets. The number of targets that he hit once was 8 more than the number of targets that he hit twice. one third of the remaining time solving problem 2. doing the RSM Olympiad. All the boys and one third of the girls participated in the RSM Olympiad. hitting each target once or twice (each arrow was shot once and hit exactly one target). 0 9 0 0 0 9 1 0 0 9 2 0 0 9 4 5 1 0 0 0 Clock 1 Clock 2 Clock 3 Clock 4 Clock 5 999 RSM students took part in math contests. How many routes are there from R to S using only the lines shown in the diagram? All routes have the same starting point R. How many targets were there altogether? Grades 4-5 2015 . one is off by 20 minutes. Compute the perimeter of Ron’s remaining rectangle. one is off by 15 minutes. Math Kangaroo. and no jumping is allowed. Mike cut another of Ron’s rectangles into two rectangles each having perimeter 21. but one of them is off by 5 minutes. By how many minutes is the remaining clock off? Be sure the answer is between 0 and 100. and finally she spent the last 5 minutes doublechecking the answers. Write answers on back. Grades 4-5 2015 7 8 9 10 11 12 .