This is the 2016 MTAP Grade 7 Math Challenge questions 26 to 50 with answer key. More reviewers can be found on the **Past Tests** and **All Posts** pages.

26.) The sum of the square roots of two positive integers is . If the two integers differ by , what are the integers?

27.) A worm crawls 7.5 inches in 80 seconds. What is its speed in feet per hour?

28.) By how much is greater than ?

29.) A game consists of drawing a number from 1 – 20. A player wins if the number drawn is either a prime number or a perfect square. What is the probability of winning in this game?

30.) The number of boys in a class is equal to the number of girls. Nine boys are absent today, and this leaves twice as many girls as boys in the classroom. How many students belong to the class?

31.) A square region is removed from a rectangular region. Which of the following can be true?

(a) The perimeter is decreased.

(b) The perimeter is not changed.

(c) The perimeter is increased.

32.) A bag contains 5 black, 5 red, 6 blue, 6 green, 7 white, 8 yellow, and 10 orange beads. At least how many beads must be drawn from the bag to ensure that at least 3 beads of the same color are chosen?

33.) How many positive numbers less than are divisible by but not by ?

34.) A 4cm × 5cm × 7cm rectangular prism is painted on all faces. If the prism is cut into 1cm × 1 cm × 1 cm cubes, how many cubes do not have paint on any of its sides?

35.) Andrew is 5 years old and Charlie is 26. In how many years will Charlie be 21 times as old as 2 Andrew?

36.) A car is driving along a highway at 55 kph. The driver notices a bus, 1 km behind. The bus 2 passes the car one minute later. What was the speed of the bus?

37.) With what polynomial must be divided to get a quotient of and a remainder of ?

38.) The volume of a sphere is equal to its surface area. What is the diameter of the sphere?

39.) If is divisible by , what are the values of and ?

40.) Find the solution set: .

41.) If is equal to the square of , find the digit .

42.) Consider the sequence 1, 2, 2, 3, 3, 3, 4, 4, 4, 4, 5, 5, 5, 5, 5, …. How many numbers in the sequence are needed so that the sum of the reciprocals is 100?

43.) If is a positive odd integer, which of the following is a perfect square: , , ?

44.) The sum of the first odd integers is . What is the sum of the next odd integers?

45.) Felix has an average of in five tests, each test with points. What is the lowest possible score Felix could have gotten in a test?

46.) In square , is the midpoint of and is the midpoint of . What percent of the area of is the area of △PQD?

47.) If ,which is bigger, or ?

48.) Find the least positive integer that leaves remainder of 1, 2, and 3 when divided by 3, 5, and 7, respectively.

49.) Find all points on the real number line such that the sum of the distances from to and from to is .

50.) If leaves a remainder of when divided by , what is the remainder when is divided by ?

Answer key:

26.) 4 and 9

27.)

28.)

29.)

30.) 36

31.) (b) and (c)

32.) 15

33.) 133

34.) 30

35.) 9

36.) 85 kph

37.)

38.) 6

39.) A = 0 and B = 8

40.) (-7, 12) or (x | -7 < x < 12)

41.) 8

42.) 5050

43.)

44.) 7500

45.) 45

46.) 37.5%

47.)

48.) 52

49.) 6 and -6

50.) 4

View Part 1 here: 2016 Grade 7 Math Challenge Elimination Questions with answers – Part 1