Math Talent Test Practice Questions for Grade 5

Transcription

1 Math Talent Test Practice Questions for Grade 5 1. There are 6 yellow balls, 4 red balls, and 5 blue balls in a bag. How many balls do you need to draw from the bag to guarantee that you have a blue ball? (11) In extreme situation, the first 10 balls drawn from the bag are 6 yellow balls and 4 red balls. In this situation, the next ball drawn must be blue. So, the number of balls you need to draw from the bag to guarantee that you have a blue ball=6+4+1= A snail is climbing up a tree. It climbs 3 cm and takes a break; then it climbs 7 cm and takes another break and so on, each time climbing 4 cm farther than the previous climb before stopping. If the snail reaches the top of the tree on a final climb of 39 cm, how tall is the tree? (Answer in centimeters). (210 cm) Since each time climbing 4 cm father than the previous climb, Climb #1=3 cm Climb #2=7cm=3+1*4 cm Climb #3=11cm=3+2*4cm Climb #4=15cm=3+3*4cm 39-3=36 36/4=9 So, Climb#10=39cm=3+9*4cm The pattern is: Climb #1=3 cm Climb #2=7cm=3+1*4 cm Climb #3=11cm=3+2*4cm Climb #4=15cm=3+3*4cm Climb #5=19cm Climb #6=23cm.. Climb #9=35cm Climb#10=39cm=3+9*4cm If we add climb #1 to climb #10, we get 3+39=42. If we add climb #2 to climb #9, we get 7+35=42 1

2 . If we add climb #5 to climb #6, we get 19+23=42. So, totally, we have five pairs with the sum of 42. So the total sum of all the climbs is 42*5=210cm 3. Mrs. Smith spent half her money plus a dollar at the grocery store and then spent half her remaining money plus a dollar on her lunch. This left Mrs. Smith with $7 to take the bus back home. How much money did Mrs. Smith have at the beginning? ($34) Method 1: The remaining money for bus is $7. If Mrs. Smith did not spend the extra on dollar for lunch, the remaining money after lunch will be $8, which is half of the money after the grocery store. Therefore, the money remained after grocery store is $8*2=$16. If Mrs. Smith did not spend the extra money, she would have $16+$1=$17 after the grocery, which is half of her money. So her money is $17*2=$34. Method 2: Set her money as x, the money spent in grocery store is x/2+1, the remaining money after grocery is x/2-1. The cost for lunch is (x/2-1)/2+1, the remaining money is (x/2-1)/2-1, which is $7. So, we have an equation as (x/2-1)/2-1=7 (x/2-1)/2=8 x/2-1=16 x/2=17 x=34 4. A 20 cm 20 cm 20 cm cubic gift box is packed as shown in the diagram below. The knot at the top requires 40 cm of ribbon. What length of ribbon do you need to pack the box? (200cm) Total length of ribbon=length of perimeter of one face*2+the length of knot =4*side length*2+length of knot =4*20*2+40 =200 cm 5. Two cars departed from the same point in opposite directions. Car A has a speed of 44 km/h and car B has a speed of 46 km/h. When the distance between the two cars 2

3 is 180 km, how far has car A traveled? (88km) For each hour, the distance between the two cars will increase by 44km+46km=90km. So, when the distance is 180km, the time used is 180/90=2 hour. During the two hours car A travelled 44*2=88km. 6. The average of 5 integers is 11. If we change one of these five numbers into a 5, then the average of the five new numbers is 12. What is the value of the number that was changed? (0) Suppose the five numbers are a, b, c,d,and e. The average of 5 integers is 11, so the sum of the 5 integers is 55. a+b+c+d+e=55 (equation #1) Suppose e is changed to 5.After the change, the average is 12, so the sum of the 5 integers is 60. a+b+c+d+5=60 (equation #2) so, a+b+c+d=55 (equation #3) use equation #3 in equation #1, we get 55+e=55, so e=0. 7. Divide a cube with edges of 10 cm into two congruent rectangular prisms. What is the sum of the surface areas of these two rectangular prisms? (800 cm 2 ) Before the dividing, the total surface area of the cube=6*side 2 =6*10 2 =600 cm 2. After the cutting, two faces are formed, so the newly formed surface area=2* side 2 =2*10 2 =200 cm 2 Add them together, the total surface area after the cutting is =800 cm 2 8. David built a fence for his trapezoid-shaped backyard garden, as shown in the diagram below. The total length of fence is 20.5 m and one side is 6.5 m. The side on the left is the wall of his house, which does not need to be fenced. What is the area of the garden? (45.5 m 2 ) 3

4 Area=( )*6.5/2=45.5 m 2 9. If you try to wrap a rope 10 times around a tree, you ll find that the rope is 8 m too short. If you wrap that rope 8 times around the same tree, you ll have 1 m of rope left over. How much rope will you have left over if you wrap it 5 times around the tree? (14.5m) Set the length of rope as r, the perimeter of the tree as p. r=10*p-8 r=8*p+1 Since r is same, 10p-8=8p+1 2p=9 p=4.5 r=4.5*10-8=45-8=37m Rope left after 5 wraps=37-5*4.5= =14.5m Or, Rope left after 5 wraps=3 wraps +1=3*4.5+1=14.5 m 10.Peter has 12 more than twice the number of pencils that Kevin has, or 9 less than three times the number of pencils that Kevin has. How many pencils does Peter have? (54) Number of pencils that Kevin has=12+9=21 Number of pencils that Peter has=2*21+12=54 11.The sum of three positive integers is 23. What is the greatest possible product of these three numbers? (448) 8+8+7=23 8*8*7= Using one penny, one nickel, one dime and one quarter, how many different amounts of money can you make? (16) For each coin, there is a choice to use it or not use it. So, there will be 2*2*2*2=16 different amounts of money to form (including 0). 13.Three cubes with edges of 1 m, 2 m and 3 m are glued together as shown in the diagram below. Find the surface area of the combined solid. (74 m 2 ) 4

5 . If the three cubes are separate, the total surface area=6*1 2 +6*2 2 +6*3 2 = =84 m 2 But the glue hides two 1*1 areas and two 2*2 areas, so the surface area of the combined solid=84-2*1*1-2*2*2=74 m A dying man left three houses to his five sons. To ensure an equal division of value, three of his sons will receive one house each, and they will each pay $800,000 for the other 2 sons to split. How much are the three houses worth altogether? ($6,000,000) For the son who gets the house, the value he gets is house-$800,000 For the son who gets only money, the value he gets is 3*$800,000/2=$1,200,000 The two values are equal, so, House-$800,000=$1,200,000 So house=$2,000,000 The total value of the three houses is $6,000, The price of a plane ticket from Vancouver to London is $980. If we book the ticket through a travel agency, agency A gives a 5% discount but charges a $30 fee, while agency B does not give a discount but also does not charge any fees. Which agency would you purchase the ticket from? (A) If we use agency A, we need to pay $980*95%+$30=$961 If we use agency B, we need to pay $980 So, we will use agency A. 16.The sum of two numbers is 789. If we remove the unit s digit of the larger number (ABC becomes AB), it will be same as the smaller number. What is the value of the larger number? (718) ABC + AB = 789 where A,B,C are digits ; 11 * AB = C which gives C= 8 and AB = 71 Therefore ABC = When Sean worked on a division problem, he mistakenly used 257 as the dividend instead of 227, so his quotient was 5 more than the correct answer but his remainder was correct. What is the remainder? (5) ( )/5=6, so the divisor is /6=37 5 so the remainder is One pencil and two pens cost $1.20; three pencils and two pens cost $2.40. How 5

6 much does one pencil and one pen cost? ($0.9) 1 pencil+2 pen=1.2 3 pencil+2 pen=2.4 The second purchase costs $1.2 than the first purchase, and this is due to the extra purchase of 2 pencils, so each pencil costs $0.6. Since 1 pencil+2 pen=1.2, 2 pens cost $0.6, each pen costs $0.3. So, one pencil and one pen cost $0.6+$0.3=$ Three baskets of apples contain a total of 90 apples. If we transfer 15 apples from basket A to basket B, then transfer 20 from basket B to basket C, and finally transfer 17 from basket C to basket A, the three baskets will contain the same number of apples. How many apples did basket A contain at the beginning? (28) Total number of apples is 90. So after the transfers, basket A must have 30 apples. So, basket A gives out 15 apples and gets 17 apples, which means it totally gets 2 apples, to have 30 apples. Originally, basket A contains 28 apples. 20.Annie s watch stopped, so she asked Bob for the time. Bob told her that after 2014 hours, 2015 minutes and 2016 seconds, it will be 3 PM exactly. What time is it now? (22:51:24) 2014 hours divided by 24 hours, the remainder is 6 hours minutes is 33hours and 35 minutes. Minus 24 hours, the time is 9 hours and 35 minutes seconds is 33 minutes and 36 seconds Add them together: 6 hours + 9 hours and 35 minutes + 33 minutes and 36 seconds = 15 hours and 68 minutes and 36 seconds = 16 hours and 8 minutes and 36 seconds Change 3PM to 15:00:00, since 15<16, add 24 hours to 15, it becomes 39:00:00. For the convenience of minus calculation, we change it to 38:59:60 38 hours 59 minutes 60 seconds - 16 hours 8 minutes 36 seconds = 22 hours 51 minutes 24 seconds So, the current time is 22:51:24 6