[PDF] MOEMS Division E Practice Packet 2016 Contest 3 Problems with Solutions and Answers.pdf | Plain Text

Registered School; Meyfleld Junior School (PASADENA CA) Division I &l4athematica(Otympiaâ Contesi january 12, 2016 ) 3 K for TJmentaiy Z 9vli&Th Scfioo& 3A Time: 4 minutes How many square units bigger is a S x S squarethan a 4 x 4 square? 3B Time: 4 minutes A bicyclist takes 2 minutes, 30 seconds to travel a distance of 1 mile. At this rate, how many miles will the bicyclist travel in 1 hour? 3C Time: 5 minutes In a parking lot are 60 cars, all of which are black or blueand all ofwhich are Fords or Dodges. There are 25 black Dodges. There are 18 blue cars. There are 25 Fords. How many blue Fords are there? 3D Tinie: 7 minutes A, B, C, and D represent thenumbers 2,4, 6, and 8, in some order. A±B — D±C We also know that — _____ C+D B+A Find the value (A x B) + (C x D). 3 E Time: 7 minutes A Super-Brick is formed by arranging nine 1cm x 1cm x 1cm cubes into a 3cm x 3cmlayer, 1cm thick. Two Super-Bricks are glued together into the L-shape shown. All faces of the L-shape are completely painted. What is the area of the painted surface in square centimeters? Copyright t 2015 by Mathematical Olympiads for Elementary and Middle Schools.Inc. All rig/its reserved.

Registered Schooh MsytieId Junior School (PASADENA CA) Division gC- [MatfiematicaCOCympiacfs January 12, 2016 ‘s_ for’Ehmentary c2%lfrliIdThSchoo& SOLUTIONS AND ANSWERS 3A METHOD 1: Strategy: Find the area of each square andfind the difference. The area of the larger square is S x 5 = 25 square units. The area of the smaller square is 4x 4 = 16 square units. The difference of the two areas is 25—16 = 9 square units. METHOD 2: Strategy: Draw the smaller square inside the larger square. Find the number of squares outside the smaller square but inside the larger square. There areS square units not shaded. Fouow-Ups: (1) How ninny square units bigger is a 104 x104 square titan a 103 x103 square? [207] (2) Betty is tiling an 8-foot by 8-foot floor with 12-inch square tiles. She buys some and finds that she needs 15 more tiles to completely cover the floor. How uwny tiles did she initiallybuy? [49] 3B METHOD 1: Strategy: Simplify the time it takes to bike 2 miles. 2 mm 30 sec + 2 mm 30 sec = S minutes 5 minutes —* bike 2 miles 10 minutes —+ bike 4 miles 30 minutes —, bike 12 miles 60 minutes—> bike 24 miles METHOD 2: Strategy: Convert all the times The cyclist traveled 12 miles 0 1 in 30 minutes or 24 miles in miles I 60 minutes which is 1 hour. minutes I METHOD 3: Strategy: Simpflfy the time it takes to bike 2 pitiles. There are 120 seconds in 2 minutes, so the bicyclist takes (120 + 30 = 150) 150 seconds to travel 1 mile. There are 3600 seconds in 1 hour (60 sec/mm x 60 mm = 3600 sec). Let x = the number ofmiles traveled in 3600 seconds so the proportion is X 3600 150 Multiply both sides of the equation by 3600, hence, x = 3600/150 = 24 miles in 1 hour. Fouow- Up: Carytravels 2 miles in 20minutes. Cind leaves 5 minutes later from the sante place and following the same route at a rate of 2 miles in 15 minutes. How long will it take Cindy to catch up to Cwy? [15 minutes] E Coniesi 3 3A 9 3B 24 3C 8 to minutes and use a number line. 234567 I I-H-± I I ——I——— 89 10 11 12 02.55 10 15 20 25 30 3D 40 3E 54 sq cm Copyright 2015 by Mathematical Olympiads for Elementary and MiddleSchools, Inc. All rights reserved.

flegltred School: MaylIeId Junior School (PASADENA CA) Olympiad 3, Continued 3C METHOD 1: Strategy: Use the process of elimination. If there are 60 cars and 18 are blue, 60—18 = 42 are black. Twenty-five of the 42 are Dodges so 42—25 = 17 are blackFords. If 17 of the 25 Fords are black, then 25—17 = 8 must be blue, There are 8 blue Fords. METHOD 2: Strategy: Complete a table. Create a table of the four possible cars: The bold numbers in the table are the given values. The italicized numberswere found in the following order: 35, 10, 8. Black Blue Total Dodge 1 25 1035 Ford 8 2S Total 18 60 Foaow-U: A class of 24 students is treated to ice cream cones. The only flavors available are vanilla and chocolate and the only cones available are sugar and waffle. If JO students choose chocolate in a waffle cone, 7 students choose vanilla and JO choose sugar cones, how many students choose vanilla in a sugar cone? [3] 3D Strategy: Apply the commutative propertyof addition. Recognize that A + B = B +A and C+ D = P + C. Therefore the two equal fractions are reciprocals of each other. Theonly number that equals its reciprocal is 1. Thus A + B = C + D. The only arrangement of the four given numbers is 2 + 8 = 4 + 6 = 10 and therefore 2 x 8 = 16 and 4x 6 = 24 5° (A x B) + (Cx D) = 40. Fouow-Up: Let A, B,C, and D be single digit odd numbers. If A + B + C + D = 20, find the value ofA xB xC xD. [189] 3E Strategy: Find the swface area of a Super-Brick and subtract the areas of the glued sides. The surface area of each Super-Brick is the sum of the areas of the 6 faces. Area of the front = area of the back = 3 x 3 = 9 sq cm Area of the top = area of the bottom = 1 x 3 = 3 sq cm Area of left side = area of right side = 1 x 3 = 3 sq cm The sum of all 6 faces = 2 x (9 ÷ 3 + 3) = 30 sq cm. Since there are 2 bricks the total surfacearea is 60 sq cm. One 1 x 3 face is hidden on each brick, so the visible area is 60— (3 + 3) = 54 sq cm. Fouow-Up: Find the total surface area of a 3 x3x3 cube ([the middle column of] x] x3 is removed. [64] NOTE: Other Follow- U problems related to some of the above can be found iii ourthree contest problem books and in “Creative Problem Solving in School Mathematics.” Visit wwwnoeins.orj,’ for details and to order.