This is the 2016 MTAP Grade 6 Math Challenge questions. Solutions and answer will be posted later. More reviewers can be found on the Past Tests and All Posts pages. The pdf file can be downloaded here.
1.) Write 3 780 as a product of its prime factors using exponents.
2.) What is the GCF of 36, 108 and 126?
3.) The LCM of n and 20 is 60 and the GCF is 5. What is n?
4.) What digits can you place in the blank in 2 67_ to make it divisible by 6?
5.) What is the highest exponent in the prime factorization of 1 008?
6.) What is the largest prime number in the prime factorization of 1 071?
7.) What is the smallest number with 2, 3, 4, 5 and 6 as factors?
8.) What is the largest whole number divisor of 2016 that is less than 2016?
9.) Write 124/7 as a mixed number.
10.) Which fraction is the smallest? 15/75, 9/72, 11/66, 13/39
11.) What number is half-way between 3/7 and 3/5?
12.) If b – a = 7, and a × b = 12, what is 1/a – 1/b?
13.) Two-thirds of a number is 12. If the same number is subtracted from 38, what is the difference?
14.) How many 1 2/3 dm pieces of ribbon can be cut from a spool of ribbon 12 m long?
15.) A tank is 4/5 full of water. After taking out 8 liters, it became 2/3 full. How many liters of water does the tank contain when full?
16.) If 32.5 × 5.07 = 164.775, what is 3.25 × 0.507?
17.) The number 75__37, when rounded to the nearest thousands, results to 76 000. What is the smallest digit that can be put in the blank?
18.) A group of children arranged themselves into a circle. From Remy and counting clockwise, Nita is the 8th child. From Remy and counting counter clockwise, Nita is the 15th child. How many children are there in all?
19.) Tess jogs every 3 days. If she jogged on Sunday and then on Wednesday, what are the next two days when she will jog?
20.) Four numbers on a calendar are enclosed by a square. What is the difference between the sum of the two numbers on the right and the sum of the two numbers on the left?
21.) The natural numbers 1 to 49 are written next to each other. The first 15 digits are 123456789101112. How many digits are there in all when natural numbers 1 to 49 are written next to each other?
22.) How many three-digit whole numbers have digits whose product is 12?
23.) What is the largest whole number that should be placed in the blank to make this statement true? 65 ÷ ____ > 23
24.) The sum of 6 consecutive odd numbers is 132. What is the sum of all the ones digits of these numbers?
25.) Observe the pattern: 2, 5, 8, 11, … What is the difference between the 12th and 7th numbers in the pattern?
26.) In Joy’s garden, she has one-eighth as many white roses as red roses and twice as many red ones as pink ones. There are also 36 roses that are either yellow or pink. Twenty roses are yellow. How many roses are there in Joy’s garden?
27.) Lloyd, Cesar and Joel went camping. For their lunch, Lloyd paid Php 300 and Joel paid Php 570 but Cesar did not pay any. They have agreed to divide the total amount equally among the 3 of them. How much should Cesar pay?
28.) When a two-digit number is divided by 9, the remainder is 4. When it is divided by 6, the remainder is 4 also. What is the smallest possible value of the number?
29.) Cora multiplied a number by 2 instead of squaring it. Then she subtracted 9 from the result instead of dividing the result by 9. If the result of the wrong calculations is 3, what is the result of the correct calculation?
30.) In a basket factory, Raymond finished 5 baskets in 3 hours while Angie finished 7 baskets in 4 hours. If they work at the same rate, how many baskets can they finish together in 12 hours?
31.) A crate of mangoes weighed 9.4 kg. If each mango weighs 0.22 kg and the crate weighs 0.6 kg, how many mangoes are in the crate?
32.) Mike runs 1.5 km every morning and 1.3 km every evening. How many kilometers does he run in 7 days?
33.) Six dozen eggs cost Php 396. How much is the cost of 30 eggs?
34.) What is the sum of 35 hundredths and 9 tenths?
35.) Express the answer in decimal. 7 2/100 + 3 2/100 – 2 7/10
36.) The identical trapezoids are put together to form a parallelogram. The bases of each trapezoid are 10 cm and 15 cm. Its height is 4 cm. What is the area of the parallelogram?
37.) The sides of a triangle have measures in the ratio of 3:5:8. If the perimeter of a triangle is 64 cm. What is the length of the shortest side?
38.) Five equilateral triangles were placed together to form a pentagon. A square is placed on one side of the pentagon so that a heptagon is formed. If the perimeter of the heptagon is 56 cm, what is the perimeter of one of the equilateral triangle?
39.) A 4 cm by 5 cm rectangle was cut along its diagonal. The resulting triangles were placed together to form bigger triangle. What is the area off the bigger triangle?
40.) A cube has a total surface area of 150 sq cm. What is the length of its edge?
41.) How many 1.5 cm × 1.5 cm × 1.5 cm cubes can fill in the 3 cm × 5 cm × 7 cm box?
42.) A rectangular field court has a perimeter of 210 meters. The length of the field is twice its width. What is the length of the field court?
43.) On 6 December 2015, Risa bought a load worth Php 300 for her cellphone. If the load is valid for 60 days, until when is the load available if December 6 is included in the 60 days?
44.) Find the answer: 60 – 24 ÷ 2 × 3 = ?
45.) The ratio of boys to girls in Teacher Len’s class is 5:4. If there are 45 students altogether, how many girls are in the class?
46.) The ratio of Nena’s stickers to Karen’s stickers was 4:3. Nena gave half of her stickers to Karen. She counted her remaining stickers and found that she has now 30 fewer stickers than Karen. How many stickers did Nena have at first?
47.) Four-fifths of the boys in my school have played basketball. One-third of the boys who played basketball have also played football. What fraction of all the boys have played both sports?
48.) A shirt costs Php 250 and a dress costs Php 700. A skirt costs Php 260 less than dress. How much more does a skirt costs than a shirt?
49.) Fred sold 12 blue shirts on Monday. He sold twice as many black shirts as blue one. How many shirts were sold altogether?
50.) What is the natural number which can be divided by 8 and 14 will each give remainder equal to 3?