Five Points Each. Total 150 Points. Choose the best answer from (A) – (D). 1. Which one of the following expressions is incorrect ? (A) 168 – (125 – 25) = (168 (16 8 – 125) + 25 (B) (6000 ÷ 10) ÷ 5 = 6000 ÷ (10 ÷ 5) (C) 988 + (115 + 12) = (988 + 115) + 12 (D) 36 × (20 × 5) = (36 (3 6 × 20) × 5 2. A 4–digit number has the form □92□, where the two □ symbols represent the same digit.
If this 4-digit number number is a multiple multiple of 3, how much larger larger is the
largest possible value for □ than the smallest possible value value for □? (A) 3
(B) 4
(C) 5
(D) 6
3. What number must be subtracted from the numerator of fraction (A) 2
3 8
23 56
in order to yield the
?
(B) 3
(C) 4
(D) 5
4. If a 12×6×2 rectangular solid has the same surface area as a cube, what is the edge length of this cube? (A) 5
(B) 6
(C) 7
(D) 8
5. When a clock shows 10:36, what is the included angle formed by this clock's clo ck's hour and minute hands? (A) 102°
(B) 84°
(C) 66°
(D) 46°
6. Eight years ago, Herbert's age was
3
of his mother's age. If Herbert 's age was x
7 eight years ago, which expression represents his mother’s age now? 3 3 3 3 (A) ( x + 8) ÷ (B) x × + 8 (C) x ÷ + 8 (D) ( x + 8) × 7 7 7 7
7. This year, Christina's mother is three years more than 4 times the age of Christina. If Christina is 6 years old now, now, how much younger than her mother was Christina three years ago? (A) 14
(B) 15
(C) 18
(D) 21 2015 Final
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8. In 6th grade, there are 91 boys and 112 girls. If we place all these students in different groups so that each group has the same number of boys and each group also has the same number of girls, how many groups are there? (A) 2
(B) 4
(C) 7 (D) 13 41 3 larger than number b. Number c is 6 larger than number 9. The number a is 5 8 b. What is the difference between a and c? 3 33 3 7 (A) 1 (B) 1 (C) 2 (D) 2 4 40 10 30 10. There is a large container of size 550 cm × 340 cm × 200 cm and many small cubic boxes of edge length 100 cm. What is the largest number of these small boxes that can be fit inside that large container? (A) 30
(B) 35
(C) 37
(D) 48
11. If the edge length of a large square is 3 times longer than the edge length of another smaller square, how many times larger is the area of the large square over the area of the small square? (A) 3
(B) 6
(C) 9
(D) 12
12. Suppose the price for 9 bottles of juice is the same as the price for 6 cups of coffee. Mother asks Jason to go buy 3 bottles of juice and 5 cups of coffee. However, since Jason does not like juice, he uses all the money his mother gave him to buy coffee. How many cups of coffee can Jason buy? (A) 7
(B) 8
(C) 9
(D) 10
13. If any 6 consecutive integers are multiplied together, what is the units digit of their product? (A) 0
(B) 2
(C) 16
(D) 20
14. Suppose a rectangle has a perimeter of 72 cm. If the ratio between the length of 5 this rectangle and its perimeter is , what is the width of this rectangle? 18 (A) 12
(B) 15
(C) 16
(D) 20
15. Suppose a and b are two three decimal numbers and they become 2.89 and 0.43, respectively, after rounding. What is the difference between the largest possible and smallest possible b? (A) 2.451 2
2015 Final
(B) 2.465
(C) 2.469
(D) 2.471
a
16. After a rock of volume 320 cubic centimeters is placed in a water tank of inside dimensions of 20 cm long and 16 cm wide, the water level of that tank is 17 cm high. What is the height of water level before placing the rock in the tank? (A) 14
(B) 15
(C) 16
(D) 17
17. The angle measurements of three of the interior angles of a 6–sided convex figure are 130°, 150°, and 160° and two other angles are right angles. What is the angle measurement of the sixth angle? (A) 90°
(B) 100°
(C) 110°
(D) 120°
18. A given number is divided by 3, the quotient is then added to 4, and the resulting sum is then multiplied by 5.
When 6 is then subtracted from this product, the
final result is 49. What is the original number?
19.
(A) 36 (B) 21 3 + 6 + 9 + L + 54 4 + 8 + 12 + L + 72 3 (A) 1 (B) 4
(C) 18 =
(D) 12
? 2
(C)
3
(D)
1 2
20. Place three identical size metal balls inside a tank (completely submerged under water) of dimensions 25 cm long, 18 cm wide and 20 cm deep of water. After the placement of these three metal balls, the water level increased to 26 cm. What is the volume of each metal ball? (A) 800
(B) 850
(C) 900
(D) 950
21. How many 3–digit numbers are there whose digits sum to 25? (A) 2
(B) 4
(C) 5
(D) 6
22. How many 3–digit numbers are divisible both by 3 and 7? (A) 47
(B) 45
(C) 43
(D) 42
23. Given four straws of lengths 4 cm, 5 cm, 6 cm, and 9 cm, how many different triangles can be formed by arranging these 4 straws without bending or cutting? (A) 2
(B) 3
(C) 4
(D) 5
24. Suppose it takes 6 minutes and 30 seconds to fry a piece of chicken. If the cook fries one piece at a time without pausing in between pieces and starts the first piece at 5 o'clock in the afternoon, how many pieces of chicken can he fry or start frying before 6 o'clock in the afternoon? (A) 7
(B) 8
(C) 9
(D) 10 2015 Final
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25. A certain calculator has only two operation keys, a [+1] key and a [×2] key. Pressing one of these two keys will perform that operation on the number appearing on the screen. If the number appearing on the screen in the beginning is 1, what is the minimum number of times these keys must be pressed to get the number 200 to appear? (A) 8
(B) 9
(C) 27
(D) 199
26. How many factors of 3 appear in the product (A) 16
(B) 17
(C) 21
1×2×3×4×5×…×49×50?
(D) 22 4
27. After converting the fraction
into a decimal number, what is the 2015th
37 digit appearing to the right of the decimal point? (A) 0
(B) 1
(C) 2
(D) 8
28. The combined volume of the rectangular solid and the cube shown on the right is 13608 cubic centimeters.
What is the
length of the rectangular solid? (A) 26 cm
(B) 27 cm
(C) 28 cm
(D) 30 cm
29. As shown in the figure on the right, there is a rectangle that is large enough to exactly fit 6 small circles each of diameter 3 cm and two larger circles. What is the area of this rectangle? (A) 864
(B) 648
(C) 162
(D) 216
30. A certain ball game allows only two people to play at a time. Five people play the game, taking turns. If each of these five people played exactly the same number of minutes during a 90 minute period, how many minutes did each person play? (A) 18
4
2015 Final
(B) 36
(C) 45
(D) 225
