2016 WMI Grade 7 Questions Part 1 [PDF]

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2016 WMI Competition Grade 7 Part 1 Logical Reasoning Test Problems (1) – (10). Six Points Each. Total 60 Points. Choose the best answer from (A) – (D). 1.



Which one of the following expressions yields a different result as (A) –(63 + 47 – 56)



2.



(B) 56 + (–63) – 47



–63 – 47 + 56?



(C) –(63 – 47) + 56



(D) (–47) – (–56) – 63



Four sets of machines can do the same amount of work as 5 workers. If it takes 30 workers 60 days to complete one project, how many sets of machines need to be added to the work force of these 30 workers so that the project can be completed in 20 days? (A) 36



3.



(D) 54



(C) π : 4 is simplified to



(B) 5



(D) π : 2



m < x < n, what is m+n?



(C) –3



(D) 3



Follow the figure below, the number on top is the sum of two numbers below it.



(A) –1



6.



(B) 2 : 3



If the inequality –13 < 4x+3 < –1 (A) –5



5.



(C) 48



If the perimeter of a square has the same length as the circumference of a circle, then what is the ratio of the area of the square to the area of the circle? ( (A) 1 : 4



4.



(B) 44



Given the equation (A)



11 16



(B) –3½



x 2



(C) 0



x x 4 8



x＝1– ＋ – ＋ (B)



– 11 16



x. 16



Find a.



(D) 4½



Solve for x. (C) 16 21



(D) – 16 21



7.



8.



Suppose a is the largest prime number and b is the smallest prime number between 31 and 61 exclusively. If c = a – b, which one of the following statements is true? (A) c has 5 positive factors



(B) c has 6 positive factors



(C) c is a multiple of 11



(D) c is a prime number



Eighty oranges and 82 apples are passed to a number of students where each student gets the same number of oranges and the same number of apples. If, at the end, there are 8 oranges left and we are 8 apples short, what is a possible number of students among the answers below? (A) 6



9.



(B) 8



(C) 16



(D) 18



Suppose |m| = –m and |m+n| = m+n where m ≠ 0 and n ≠ 0. Which of the points on the right figure possibly represents the 𝑚



point ( , m–n). 𝑛



(A) A



(B)



(C) C



𝐵



(D) D



10. James, Curry, Lowry, and Wade shot, respectively, 25, 26, 27, and 28 times in a basketball game. Among these shots, they had made, respectively, 22, 23, 24, and 25 baskets. Which one of them has the highest shooting percentage? (A) James



(B)



Curry



(C) Lowry



(D) Wade



Problems (11) – (15). Eight Points Each. Total 40 Points. Choose the best answer from (A) – (D). 11. In the beginning of the month, Warren had bought 1000 shares of Stock A at $27 a share, 2000 shares of Stock B at $9 a share, and 2000 shares of Stock C at $16 a share. He sold all those stocks at the end of the month selling them at $33 a share for A, $10 a share for B, and $13 a share for C. Which of the following represents Warren's profit or loss? (A) $4000 loss



(B) $4000 profit



(C) $2000 loss



(D) $2000 profit



12. As shown in the figure on the right, rectangle ABCD is composed with one square and three identical sized small rectangles. Suppose this rectangle's length is three times its width. What fraction is the shaded area to the entire area of rectangle ABCD? (A)



1 7



(B)



7 127



(C)



2 5



(D)



11 36



13. Each small cube



has 6 surfaces. The solid shown on the right is composed with 9 small identical cubes. How many small cube surfaces are shown on outside of this solid? (Include the top, bottom, and all sides of this solid) (A) 3 (B) 6 (C) 7 (D) 9



14. Suppose an equilateral triangle has side lengths of 2x+3y, 10–y, and 4x+18. What is the perimeter of this triangle? (A) 12



(B) 15



(C) 18



(D) 21



15. If |2x+2y–2| + (3x–y+9)2 = 0, then the point (x, y) is on which quadrant of the plane coordinate system? (A) I



(B) II



(C) III



(D) IV