# 2016 Grade 7 Math Challenge Elimination Questions

This is the 2016 MTAP Grade 7 Math Challenge questions 26 to 30. Solutions and answer will be posted later. More reviewers can be found on the Past Tests and All Posts pages.

1.) Simplify: $6(2)^2 - (4 - 5)^3$.

2.) By how much is $3 - \frac{1}{3}$ greater than $1 - \frac{1}{2}$?

3.)  Write $\frac{11}{250000}$ in scientific notation.

4.)  The product of two prime numbers is $3024$. What is the sum of the two numbers?

5.)  A shirt is marked P 315 after a discount of 10% and value added tax of 12%. What was the price of the shirt before tax and the discount?

6.)  How many different lengths of diagonals does a regular octagon have?

7.)  What number is midway between $3 + \frac{1}{3}$ and $2 - \frac{1}{3}$.

8.)  Simplify: $\left ( \dfrac{7}{2} + \dfrac{5}{6} \right )^2 -\left ( \dfrac{7}{2} - \dfrac{5}{6} \right )$

10.)  The sum of the measures of the interior angles of a polygon is $1980^\circ$. How many sides has the polygon?

11.) The average of three numbers is 20. Two numbers are added to the set and the average of the five numbers becomes 42. If one of the added numbers is twice the other, what are the two numbers added to the data set?

12.) Compute:

$24 \div \dfrac{1 + \frac{1}{5}}{2 - \frac{1}{3}}$

13.)  Subtract $5a - 2b + c$ from the sum of $3a + b - 2c$ and $a - b + 3c$.

14.)  Alex, Beth and Carla play a game in which the losing player in each round gives each of the other players as much money as the player has at that time. In Round 1, Alex loses and gives Beth and Carla as much money as they each have. In Round 2, Beth loses and in Round 3, Carla loses. After 3 rounds, they find that they each have P 40. How much money did Alex have at the start of the game?

15.)  Three two-digit numbers have consecutive tens digits and have units digit all equal to $5$. If the tens digit of the smallest number is $n$, what is the sum of three numbers?

16.)  The length of a rectangle is 8 cm more than its width. If the length is decreased by 9 and the width is tripled, the area is increased by 50%. What was the area of the original rectangle?

17.)  Evaluate:

$236 \times 542 + 458 \times 764 + 542 \times 764 + 236 \times 458$.

18.)  TRUE OR FALSE: If $n$ is a real number, then $n^2$ is positive.

19.) If $n$ kilos costs $p$ pesos, how much will $x$ kilos of rice cost?

20.) If the letters of the word MATHEMATICS are repeatedly and consecutively written, what is the 2016th letter?

21.)  Simplify:

$\dfrac{(x - \sqrt{2})(x + \sqrt{2})}{x^3 - 2x}$.

22.) If $x$ is three times as far from $-5$ as it is from $15$, what are the possible values of x?

23.) If three children eat 4 kilos of rice in 5 days, how long will 12 children eat 48 kilos of rice?

24.) A conical tank full of water is emptied into an empty cylindrical tank of the same height. If the base radius of the cylinder is twice that of the cone, what fraction of cylinder will be filled with water?

25.) Find the minimum integer $n$ for which $\frac{18}{n + 1}$ is an integer.

26.) The sum of the square roots of two positive integers is $54$. If the two integers differ by $54$, 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 $(3x - 5)(x + 2)$ greater than $(x + 4)(2x - 1)$?

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 $1000$ are divisible by $6$ but not by $5$?

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 $8x^5 - 10x^3 + 2x + 5$ be divided to get a quotient of $4x^2 - 3$ and a remainder of $5 - x$?

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

39.) If $3A54B10$ is divisible by $3304$, what are the values of $A$ and $B$?

40.) Find the solution set: $|5 - 2x| < 194$.

41.) If $47A29694$ is equal to the square of $3(721 + A)$, find the digit $A$.

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 $n$ is a positive odd integer, which of the following is a perfect square: $2^{n^2}$, $25^{(3n+2)}$, $7^{n(n+1)}$?

44.) The sum of the first $50$ odd integers is $2500$. What is the sum of the next $50$ odd integers?

45.) Felix has an average of $90$ in five tests, each test with $100$ points. What is the lowest possible score Felix could have gotten in a test?

46.) In square $ABCD$, $P$ is the midpoint of $AB$ and $Q$ is the midpoint of $BC$. What percent of the area of $ABCD$ is the area of △PQD?

47.) If $1 < x < \frac{9}{8}$,which is bigger, $\sqrt[3]{3x}$ or $\sqrt{2x}$?

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 $x$ on the real number line such that the sum of the distances from $x$ to $4$ and from $x$ to $-4$ is $12$.

50.) If $11n$ leaves a remainder of $6$ when divided by $7$, what is the remainder when $5n$ is divided by $7$?