Category A: Grades 4 5 SOLUTIONS Round 6 Thursday, February 12, 2015

Transcription

1 Category A: Grades 4 5 SOLUTIONS Round 6 Thursday, February 12, 2015 Question #1 A grocery store parking lot has space for 1000 cars. 2/5 of the spaces are for compact cars. On Monday, there were 200 compact cars and some standard size cars in the parking lot. The parking lot was 3/4 full. How many standard size cars were in the parking lot? Solution #1 If the parking lot was 3 full there were = 750 cars there. Of these 750 cars 200 cars 4 4 were compact, which means = 550 cars were standard size. 2 5 of the 1000 parking spaces is for compact cars, which is 400 parking spaces. The remainder 600 parking spaces are for standard cars, therefore the both 550 standard cars and the 200 compact cars had enough of their own kind of parking space. ANSWER #1: 550

2 Question #2 Students at Monty High with a class size under 30 took a math test. One third of the class got a B, one-sixth a C and one eighth failed. The remainder of the students got as A. How many students got an A? Solution #2 Let XX be the number of students and AA the number of students who got A in the class. Therefore, In order for the one-third of the class to be a whole number, the class size must be a multiple of 3. In order for the one-sixth of the class to be a whole number, the class size must be a multiple of 6. Similarly, one-eighth of the class must also be a whole number, therefore the class size is also a multiple of 8. Multiples of 3: Multiples of 6: Multiples of 8: The only common multiple below 30 is 24, therefore 24 students were in the class. One-third of them (8 students) got a B, one-sixth of them (4 students) got a C, and one-eighth of them (3 students) failed = 9 Thus, 9 students got an A. ANSWER #2: 9

3 Question #3 The numbers in the middle column are related in some way to the numbers in the right and left columns. Find out how they are related and find the missing number in the table. Solution #3 The numbers in the 1 st and 3 rd column are multiplied. The product is then written backwards in the middle column. Therefore, 6 times 2 is 12, which is then written backwards as 21. ANSWER #3: 2 Question #4 A large box contains 18 small boxes and each box contains 25 chocolate bars. How many chocolate bars are in the large box? Solution #4 18 small boxes multiplied by 25 chocolate bars in each is = 450 chocolate bars in total. ANSWER #4: 450

4 Question #5 A painter charges $225 for materials and $35 per hour for labor. The total cost of painting an office is $330. How many hours did it take the painter to paint the office? Solution #5 Of the $330 we subtract the cost of the materials, $225, to get $330 $225 = $105, which is 3 times $35. Therefore the painter spent 3 hours on painting the office. ANSWER #5: 3 hours Question #6 50 meters 30 meters POOL grass 15 meters 35 meters In Tim s house, a rectangular pool with length 30 meters and width 15 meters is surrounded by grass. The pool with grassy area makes a large rectangle with length 50 meters and width 35 meters, as shown. What area does the grass occupy? Solution #6 In order to find out the area of the grassy area only, we need to find the total area and subtract the area of the pool. The total area (of pool and grass combined) is 50 mmmmmmmmmmmm 35 mmmmmmmmmmmm = 1750 ssss. mmmmmmmmrrss. The area of the pool is 30 mmmmmmmmmmmm 15 mmmmmmmmmmmm = 450 ssss. mmmmmmmmmmmm Subtracting the two we get = 1300 ssss. mmmmmmmmmmmm. ANSWER #6: 1300 sq.meters

5 Question #7 Find the third number in the following sequence: 1, 8, 3, 10, 5, 12, 7, 14, 9,,, X Solution #7 The rule is add 7 and subtract 5, alternating. Therefore, the next three numbers in the sequence are 16, 11, and the third number being 18. ANSWER #7: 18 Question #8 Write each decimal as a fraction in simplest form. A: D: 0.7 B: 0.08 E: C: F: Which of these fractions (in their simplest form) have the largest denominator? Write A or B or C or D or E or F as your final answer. Solution #8 A: = 1 8 B: 0.08 = 2 25 C: = 3 8 D: 0.7 = 7 10 E: = 1 40 F: = 7 8 Of these six fractions, E has the largest denominator. ANSWER #8: E

6 Question #9 If 20 % of a number is 30, what is 50% of the number? Solution #9 If 20% of a number is 30 then the number is 5 30 = 150. Thus, 50% of 150 is 75. ANSWER #9: 75 Question #10 A number of children are standing in a circle. They are evenly spaced and the 6th child is directly opposite the 20th child. How many children are in the circle altogether? Solution #10 If the 6 th child is opposite of the 20 th child there are 14 children is the semicircle, this can be seen by knowing that 6 th child is opposite the 20 th child 5 th child is opposite the 19 th child 4 th child is opposite the 18 th child 3 rd child is opposite the 17 th child 2 nd child is opposite the 16 th child 1 st child is opposite the 15 th child As there are 14 children in the semicircle, there are 28 children in the full circle. ANSWER #10: 28

7 Question #11 Jeff is putting a fence around his rectangular yard. It is 50 feet long and 30 feet wide. The fence posts must be 10 feet part. How many posts does he need? Solution #11 As shown on the diagram, there will be 16 posts needed for the fence. ANSWER #11: 16 Question #12 You draw one card at random from a regular deck of 52 playing cards (no jokers, an ace = 1). What is the chance of drawing a card with a prime number on it? Give your answer in simplest fraction form. Solution #12 A standard deck of 52 cards has 4 suits: spades, hearts, diamonds, and clubs. Of these the only prime numbers are 2, 3, 5 and 7. The probability of having a prime number of a card in a deck of 52 is then or ANSWER #12: 4/13

8 Question #13 The sale price of CD player is $120, which is 60% of its list price. How much change will you receive back if you buy the CD at its list price and you give the cashier $250? Solution #13 The original price of the CD player must be $ = $200. If you gave the cashier $250 then you will receive $50 change back. ANSWER #13: 50 dollars Question #14 Write billion in standard form. Solution #14 One billion means one thousand million, which is a single 1 followed by 9 zeros. Thus, billion in standard form is 14,050,000,000. ANSWER #14: 14,050,000,000 Question #15 Which is faster? Solution #15 a spider crawling at 2 km per hour or an insect moving at 1,000 meter per hour. The spider s speed is 2km/h. The insect s speed is 1km/h (as 1,000 meters is 1 km). Therefore the spider goes a longer distance in the same amount of time (per hour), so the spider is faster. ANSWER #15: spider

9 Question #16 Shanghai train moves at 600 km per hour for 30 km. What is the approximate amount of time the train moved? Give your answer in seconds. Solution #16 As the speed of the train is 600 km/h it would travel the 30 km in 1 of an hour, which is 3 20 minutes. 3 minutes in seconds is 3 60 = 180 seconds. ANSWER #16: 180 seconds Question #17 In a 60 kg adult, about 39 kg of weight is water. What percent of the weight is water, rounded to nearest whole percent? Solution #17 We are to find the value of in decimal form, or in another words solve for X in = XX. To find the decimal form we may do the following: Therefore, 65% of the weight is water. ANSWER #17: 65% = 0.65

10 Question #18 There are 100 people applying for a job that requires both Science and Business background. 12 have no experience in either field. 64 have a Science background and 80 of the applicants have the business background. How many of the applicants have background in both Science and Business? Solution #18 Using the Venn diagram shown above we have the following equation to solve: (64 XX) + XX + (80 XX) + 12 = 100 Simplifying this equation we have 156 XX = 100, which results in XX = 56, therefore there are 56 applicants with both Science and Business background. ANSWER #18: 56

11 Question #19 There are seven sisters standing around the kitchen table. Each one has seven backpacks. In each backpack, there are seven large cats. For every large cat, there are seven small cats. How many legs are there in the room? Solution #19 Sisters: As the sisters have 2 legs each, the seven sisters have 14 legs altogether. Large cats: The seven sisters have seven backpacks each, which is 7 7 = 49 backpacks. In each backpack there are 7 large cats, which then is 49 7 = 343 large cats. Each of these large cats has 4 legs so the 343 large cats have = 1372 legs altogether. Small cats: As for every large cat there are seven small cats, there are = 2401 small cats. Each of these small cats has 4 legs so the 2401 small cats have = 9604 legs altogether. Therefore, the total number of legs in the room is = legs. ANSWER #19: 10,990 Question #20 If a baseball and bat cost $110, and the bat costs $100 more than the ball, how much does the ball cost? Solution #20 If the bat costs $100 more than the baseball, then the price of the bat must be $105 and the price of the baseball must be $5. ANSWER #20: 5