# 2017 Grade 6 MTAP Elimination Round – Part 2

This is the 2017 Metrobank-MTAP-NCR Math Challenge Elimination Round for Grade 6 questions 26-50. Questions 1-25 can be found hereIf you see any error, please use the comment box below to inform me.

26.) You are given one hour to complete a contest. What fraction of the hour remains for you to complete the contest after thirty-fie minutes have elapsed?

27.) What is the value of 3/4 + 5/2 × 3/4?

28.) In a class of 30 students, 12 are boys. If 6 more girls join the class, what fraction of the class is now female?

29.) What is the value of the product

$(1 - \frac{1}{2})(1 - \frac{1}{3})(1 - \frac{1}{4})(1 - \frac{1}{5})$

30.) It requires 12 hours to fill 3/5 of a swimming pool. At this rate, how many hours is required to fill the remainder of the pool?

31.) Two equal circles are placed in a rectangle, as shown. The distance between the centers of the circles is 12cm. What is the area of the rectangle?

32.) A star is $4.8 \times 10^8$ light-years away. How many light-years are there in half this distance?

33.) Of the numbers 0.5129, 0.9, 0.89, and 0.289, what is the sum of the smallest and the largest?

34.) What is the value of

$\displaystyle\frac{190 + 192 + 194 + 196 + 198 - 200 - 202 - 204 - 206 - 208}{10}$ ?

35.) Each number in a sequence is obtained by adding the two previous numbers. The 6th, 7th, and 8th numbers of the sequence are 29, 47, 76. What is the third number in the sequence?

36.) A square piece of paper is folded in half to form a rectangle. This rectangle has a perimeter of 18cm. What is the area of the original square?

37.) The sides of a cube are doubled in length to form a larger cube. How many original small cubes will fill this larger cube?

38.) A rectangular box has volume 15cm3. If the length, width, and height are doubled, what is the volume of the resulting box?

39.) If each edge of a cube is increased by 150%, what is the percentage increase in surface area?

40.) A rectangular 4 × 3 × 2 block has its surface painted red, and then is cut into cubes with each edge 1 unit. How many cubes have exactly one of its faces painted red?

41.) The sum of fifty consecutive even integers is 3 250. What is the largest of these integers?

42.) The three digit number 2A4 is added to 329 and gives 5B3. If 5B3 is divisible by 3, what is the largest possible value of A?

43.) What number is obtained when the difference 14.2 and 1.69 is divided by 0.03?

44.) What is the radius of a circle having a circumference of 6n cm?

45.) The arc lengths of three semicircles are as shown. What is the area of the shaded region?

46.) The numbers in the sequence 2, 7, 12, 17, 22, … increased by fives. The numbers in the sequence 3, 10, 17, 24, 31, … increased by sevens. The number 17 occurs in both sequence. What is the next number which occurs in both sequence?

47.) If $\frac {2}{3}x = 0.6$, what is the value of x?

48.) When half a number is increased by 15, the result is 39. What is its original number?

49.) Three cuts are made through a larger cube to make eight identical smaller cubes. The total surface area of the smaller cube is
(a) one-eight of the surface are of the larger cube
(b) one-half of the surface are of the larger cube
(c) double the surface are of the larger cube
(d) eight times the surface are of the larger cube
(e) the same as the surface are of the larger cube

50.) Caloy multiplies a number by 4, adds 8 to the product, then divides the sum by 3. If the final result is 28, what is the original number?

Answers:

26.) 5/12
27.) 2 5/8
28.) 2/3
29.) 1/5
30.) 8
31.) 288
32.) $2.4 \times 10^8$
33.) 1.189
34.) -5
35.) 7
36.) 36 sq m
37.) 8
38.) 90 cubic cm.
39.) 525%
40.) 4
41.) 114
42.) 4
43.) 417
44.) 3
45.) $36 \pi$
46.) 52
47.) 0.9
48.) 48
49.) c
50.) 19

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