# 2013 Grade 7 Math Challenge – Elimination Round with answer key – Part II

Below are the 2013 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.) In Teacher Ella’s class, a student receives a final grade of A if the student garners an average of at least 92% in the five long test. After four long test, Jonathan got an average of 91%. At least how much should he get in the last long test to get a final grade of A?

27.) What is the largest prime factor of 2013?

28.) A class of 47 students took examinations in Algebra and in Geometry. If 29 passed Algebra, 26 passed Geometry, and 4 failed in both subjects. How many passed both subjects?

29.) A runner started a course at a steady rate of 8 kph. Five minutes later, a second runner started the same course at 10 kph. How long did it take for the second runner to overtake the first?

30.) A rectangle has sides (2x +3) cm and (4x + 5) cm. How many squares of side x cm can be cut from it?

31.) Let ABCD be a regular pentagon. What is the measure of $\angle CAD$

32.) The average of five numbers is 20. If the sum of two of the numbers is 28, what is the average of the other three numbers?

33.) A long straight steel bar is to be cut in the ratio of 2 : 3 : 5. If the middle piece is 7 m, how long is the steel bar?

34.) Marvin is 10% taller than Homer, and Homer is 10% taller than August. How much (in percent) is Marvin taller than August?

35.) Which is the largest, $a = 2^48, b = 3^36, or c = 5^24$?

36.) What is the least value of x that satisfies the inequality $4(x + 3) - 7(2 - x) \geq 2(2x - 7)$?

37.) When 3n is divided by 7, the remainder is 4. What is the remainder when 2n is divided by 7?

38.) If the sides of the cube are tripled, what percent of the original volume is the new volume?

39.) If $2ax^4 - bx^3 + 4x^2 - dx + 3e = (2x - 3)(x + 1)(x - 2)(3x + 1)$, what is ab + cd + e?

40.) If $-\dfrac{12}{5} \leq x \leq -\dfrac{1}{2}$ and $3 \leq y \leq \dfrac {9}{2}$, what is the largest possible value of $\dfrac {x - y}{x + y}$?

41.) Which is smaller, A = (2015)(2014)(2013)(2012)(2011) or B = $2013^5$?

42.) If $x^2 - 3x + 1 = 0$, find the value of $x^2 + \dfrac{1}{x^2}$?

43.) If (x + 3)(x – 2)(x + 1) = (x + 2)Q(x) + (x + 3)(x – 2), what is Q(x)?

44.) All faces of a 4-inch cube have been painted. If the cube is cut into 1-inch smaller cubes, how many of them have no paint on all their faces?

45.) If x = -1, find the value of $2013x^2013 + 2012x^2012 + 2011x^2011 + 2010x^2010 + ... + 2x^2 + x$.

46.) The sum of two numbers is 20 and their product is 15. Find the sum of their cubes.

47.) How many positive factors does $62 \times (63^3 + 63^2 + 63 + 1) + 1$ have?

48.) If the number 10600 is expressed as the sum of 100 consecutive odd positive integers, what is the largest among the odd integers?

49.) How many positive integers n satisfy $\dfrac{2}{7} < \dfrac {n}{13} < \dfrac {4}{5}$

50.) What is the least number of square pieces into which a cardboard, 13 feet long and 8 fee wide, can be cut?

26.) 96%
27.) 61
28.) 12
29.) $\frac{1}{3} hr or 20 min$
30.) 8
31.) $36^\circ$
32.) 24
33.) $\frac{70}{3}m$
34.) 21% or 21
35.) b or $3^36$
36.) $-\frac{12}{7}$
37.) 5
38.) 2700% or 2700
39.) 75
40.) $-\frac{5}{4}$
41.) A
42.) 7
43.) $\frac{x^3 + x^2 - 6x}{x + 2}$
44.) 8
45.) -1007
46.) 7100
47.) 45
48.) 205
49.) 7
50.) 6

View Part II here: 2013 Grade 7 Math Challenge – Elimination Round with answer key – Part I

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