6th Grade Misc.
A submarine is 2,733 ft. below the surface of the ocean. The submarine must rise ________ ft. to be 1889 ft. below the surface.
(844)
2733 - 1889 = 844. If the submarine rises 844 ft, it will be 1889 ft below the surface.
If 6 × 7 = 26 + ____ , find the number that belongs in the space.
(16)
6 × 7 = 42; 42 - 26 = 16.
Find the 3 two-digit numbers that are factors of 114.
(19, 38, 57)
Louise walks to her friend’s house. One day when she had walked 1⁄4 of the way to her friend’s house she looked at her watch and it was 10:30 A.M. When she had walked a of the way to her friend’s house she noticed it was 10:34 A.M. She continued walking at the same rate. Louise arrived at her friend’s house that day at _______ A.M.
(11:06)
From 10:30 A.M. to 10:34 A.M. she walked of the way to her friend’s house (a - 1⁄4 = ). If of the way took 4 minutes, then the entire trip took 48 minutes. At 10:30 she had already walked 1⁄4 of the way and had 3⁄4 of the way to go. 3⁄4 of 48 minutes is 36 minutes. 36 minutes from 10:30 is 11:06 A.M.
The perimeter of a rectangle is 38", (L > W). The area of the rectangle is 48 sq. in. If the length is doubled and the width is halved, the perimeter of this new rectangle is ________".
(67)
For the original rectangle, to find the length and width is like asking: “Find two numbers whose product is 48 and add to 19 ( )”. 16 × 3 = 48; 16 + 3 = 19. The length of the new rectangle is 32" and the width is ". P = 32 + 32 + + = 67".
In the number 602, the value of the digit 6 is _________ times the value of the 2.
(300)
A digit gets its value in a number by its placement in the number as well as its inherent value. Because 6 is in the hundred’s place, it is worth 100 times as much. Since 6 = 3 × 2, it is worth 3 times as much. In the number 602, the value of the 6 is 100 × 3 = 300 times the value of the 2.
When a positive number n is divided by 5, the remainder is 1. When 3n is divided by 5, the remainder is _________.
(3)
The number n has a unit’s digit of 1 or 6. 3n will have a unit’s digit of 3 or 8. When 3n is divided by 5, the remainder will be 3.
Maryann has some fish in her fish tank. When she buys k fish, she will have 3 times as many fish as she has now. In terms of k, how many fish does Maryann have now?
x+k = 3x. x =2/k
A hose can fill a 50-gallon drum with water at the rate of a gallon in 5 seconds. It will take _________ minutes to fill the empty drum with water.
(12 1⁄2)
One-third gallon in 5 seconds or 12 × a = 4 gallons in 12 × 5 = 60 seconds or 1 minute. Then 48 gallons in 12 minutes and the remaining 2 gallons in 1⁄2 minute. (Accept 12 min. 30 sec. as correct.)
The perimeter of a rectangle is 38", (L > W). The area of the rectangle is 48 sq. in. If the length is doubled and the width is halved, the perimeter of this new rectangle is ________".
(67)
For the original rectangle, to find the length and width is like asking: “Find two numbers whose product is 48 and add to 19 ( )". 16 × 3 = 48; 16 + 3 = 19. The length of the new rectangle is 32" and the width is ". P = 32 + 32 + + = 67".
Eight (8) people required 20 days to complete 1⁄4 of a job. If two additional people were hired, then they could complete the job in _______ days. (Assume everyone works at the same rate.)
(48)
People, Job, Days
8, 1⁄4, 20
1, 1⁄4, 160 (÷ people, × days)
10, 1⁄4, 16 (× people, ÷ days)
10, 3⁄4, 48 (× job, × days).
Four adults took their five children to a movie. The price for the 9 people was $160. The 5 children received a 20% discount on their tickets. The cost for a child ticket was $_____ less than the cost of an adult ticket.
(4)
With the 20% discount, 5 children can see the movie for the same price as 4 adults. So, 10 children can see the movie for the same price as 5 children and 4 adults. $160 ÷ 10 = $16 for a child ticket. $16 × 5 = $80. $160 - $80 = $80 for 4 adult tickets. $80 ÷ 4 = $20 for an adult ticket. $20 - $16 = $4.
If A is 66% of 56 and B is 77% of 64, then A is _____% of B.
(75)
(.66)(56)/(.77)(64) = 6/7 x 7/8 = 3/4
An escalator moves down at the rate of 58 steps per minute. Zach can walk fast up ordinary steps at the rate of 70 steps per minute. There are 45 steps from one level to another. Zach decides to walk fast up the down escalator. It will take him ______ min. ______ sec. to go up one level.
(3 min. 45 sec.)
70 - 58 = 12. He goes up at the rate of 12 steps per minute. To go up 45 steps will take 45 ÷ 12 = 3 3⁄4 min. = 3 min. 45 sec.
An altitude of 12 inches is drawn to the base of an isosceles triangle. The triangle is folded along its only line of symmetry. The perimeter of the folded right triangle is 38 inches. The perimeter of the original isosceles triangle is __________ inches.
(52)
Sides a + b = 38" - 12" = 26". That would be 1⁄2 the perimeter of the isosceles triangle. P = 52".
What one number can be placed on both lines so that the sentence becomes a true statement?
17 + ___= 4 × ___- 7.
(8)
17 + 8 = 25; 4 × 8 - 7 = 25.
The final score of a soccer game between Northport and Southport was 3 to 1 with Northport winning. How many possible scores could there have been at half time?
(8)
0 - 0, 2 - 1, 1 - 1, 2 - 0, 1 - 0, 3 - 0, 3 - 1 and 0-1.
If you add the square of Susan’s age to Ted’s age, the sum is 76. If you add the square of Ted’s age to Susan’s age, the sum is 152. How old is Susan?
(8)
S^2 + T = 76. Susan is less than 9 years old (9^2 = 81). T^2 + S = 152. Ted is less than 13 (13^2 = 169). Since Susan is less than 9 years old, Ted must be 12. Susan would then be 8. 12^2 + 8 = 152.
Allan is 30 yards behind Bob and Bob is 90 yards behind Carl. All 3 boys run at constant speeds. It takes 11 minutes for Alan to overtake Bob and another 11 minutes to overtake Carl. From this position as shown, how many minutes will it take Bob to overtake Carl?
(33)
In 11 minutes Allan is even with Bob and halfway to Carl or 60 yards from Carl. So Bob gained 30 yards on Carl in 11 minutes. It will take him 33 minutes to gain 90 yards.
x @ y means find the product of x and y and then reverse the digits. For example, 4 @ 6 = 4 × 6 = 24 ÿ 42. Thus 4 @ 6 = 42. If both x and y are greater than 1, find x + y if x @ y = 51.
(8)
If x @ y = 51, x times y = 15. Since both x and y are greater than 1, x and y must be 3 and 5. 3 + 5 = 8.
Jason forms a sequence of 7 consecutive numbers. The sum of the first, fourth and sixth numbers is 122. Find the sum of the 4 remaining numbers.
(165)
The 3 given numbers must start in the 30's and end in the 40's with the 3 unit digits adding to 12. The unit’s digit of the 4th number must have a unit’s digit 3 more
than that of the 1st number and the unit’s digit of the 6th number must have a unit’s digit 2 more than that of the 4th number. Start with 36 __ __ 39 __41__ (No); 37 __ __ 40 __42 __ (No); 38 __ __41__ 43 __ (Yes). 38 + 41 + 43 = 122.The remaining 4 numbers, 39, 40, 42, 44, add to 165.
One-fourth of the marbles in an urn are green and one-fifth are red. Seven times the difference between the number of green and the number of red marbles is the number of yellow marbles. The remaining marbles in the urn are blue. When Jorge chooses a marble from the urn, the probability he chooses a blue marble is __________.
(4/5 or 1/5)
1/4 + 1/5 = 9/20. 7(1/4 -1/5) = 7/20. 9/20 + 7/20 = 16/20. The remaining marbles in the urn represent 4/20 of the total number of marbles in the urn. If there were 20 marbles in the urn; P(B) = 4/20 = 1/5