# 2014 Grade 7 Math Challenge – Elimination Round with answer key – Part II

Below are the 2014 Grade 7 Math Challenge – Elimination Round questions and answers – Part II. More reviewers can be found on the Past Tests and All Posts pages.

26.) Subtract $2a^2 + 2ab - ac$ from the product of $a + b$ and $2a - b + c$.

27.) A cylindrical container which with radius 10 cm is filled with water to a height of 2 cm. The water is poured into a second cylindrical container with 4 cm radius. How high will the water be in the second container?

28.) Luis can arrange 6 or 9 stickers to a page without any stickers left over. If he arrange his stickers 10 to a page, there are 2 stickers left over. What is the smallest number of stickers Luis can have?

29.) ABCDEFGH is a regular octagon. What is the measure of $\angle BAD?$

30.) Given a rectangle ABCD, let E be the midpoint of side AB and F be the midpoint of side BC. What part of the rectangle ABCD is triangle DEF?

31.) At a party, married people came with their husbands or wives. If half of the women and $\frac{1}{6}$ of the men in the party were single, what percentage of the people in the room were married?

32.) If the length of a rectangle is $x + 5$, its width is $2x - 1$, and its area is $2x^2 + 5x + 7$, what is x?

33.) How many four-digit numbers are multiples of 12?

34.) Simplify: $(x^2 - 4)(x - 2) - (x + 3)(x^2 - 4x + 4)$

35.) If n and m are positive integers, what is the value of $\left[ (-2)^{n^2} + 2^{m+3} - (-2^n)^n\right] \div 2^m$?

36.) Simplify: $\dfrac{(\sqrt{x} - \sqrt{2})(\sqrt{x} + \sqrt{2})}{x^2 - 4}$.

37.) A rectangle with dimension x by x + 10 has the same area as the square with side x + 3. What is x?

38.) If today is Saturday, what day is $10^{20}$ days from now?

39.) Which is larger $\sqrt{75} + 1$ or $8 + \sqrt{3}$

40.) Which values of x satisfy $|x + 1| = |2x - 4|$?

41.) What is the value of: $\left( 1 - \dfrac{1}{2}\right) \left( 1 - \dfrac{1}{3}\right) \left( 1 - \dfrac{1}{4}\right) ... \left( 1 - \dfrac{1}{2013}\right)$?

42.) The vase of a pyramid is a square and its other faces are equilateral triangles. Draw all possible nets for the pyramid.

43.) A car leaves A at 8 AM and travels to B at a rate of 60 kph. A bus leaves B at 8:30 AM and travels to A at a rate of 75 kph. If the car and the bus pass each other midway between A and B, at what time will the car pass the bus?

44.) Which integer values of x satisfy $3x + 1 < 2x + 11 \leq 4x - 3$?

45.) Find the solution set: $2 < |2x - 3| \leq 5$.

46.) In a class of 30, ten students have computers at home and 15 have cellphones. What are the possible number of students who don’t have a computer nor cellphone?

47.) If n is a positive integer, which of the following is a perfect square: $3^{n^2}, (-3)^{3n}, 3(12)^{n^{2-1}}$?

48.) If 5n leave a remainder of 8 when divided by 11, what is the remainder when 4n is divided by 11?

49.) With what polynomial must $6x^4 - 2x^3 + x^2 + x - 5$ be divided to get a quotient of $2x^2 + 5$ and a remainder of $6x + 30$?

50.) Give the solution set to $|3 - 2x| + |-6 + 1| < 12$.

Answer key:

26.) $2ac + bc - ab + b^2$
27.) 12.5 cm
28.) 72
29.) $45^\circ$
30.) $\frac{3}{8}$
31.) 62.5%
32.) $x = 3$
33.) 750
34.) $-x^2 + 4x - 4$
35.) 8
36.) $\dfrac{1}{x + 2}$
37.) $x = \dfrac{9}{4}$
38.) Monday
39.) $8 + \sqrt{3}$
40.) $x =1$ or 5
41.) $\frac{1}{2013}$
42.)

43.) 10:30 AM
44.) $x = 7, 8, or 9$
45.) $[x | -1 \leq x < \frac{1}{2} or \frac{5}{2} < x \leq 4]$ or $[-1, \frac{1}{2}) \cup (\frac{5}{2}, 4]$
46.) from 5 to 15
47.) If n is even, then all of them are perfect squares. If n is odd, then all of them are not perfect squares.
48.) 2
49.) $3x^2 - x -7$
50.) $[x | -2 < x < 5]$ $or (-2, 5)$

View Part I here: 2014 Grade 7 Math Challenge – Elimination Round with answer key – Part I

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