Mtap g6 National

MMC 2019 Grade 6 National
E1 By how much is the number 10 000 − 9 × 1111 smaller than 1250 − 125 × 9?
E2 Adding the whole numbers from 1 to 10 gives a sum of 55. Using this result, what is the sum of 3 + 6 +
9 + 12 + 15 + 18 + 21 + 24 + 27 + 30?
E3 During a summer sale, Vivian bought a pair of slippers for ₧200. If the original price of the slippers was
₧250, what percent discount did she get?
E4 The price of an adult’s ticket to an amusement park is ₧250. The ratio between the prices of an adult’s ticket
to a child’s ticket is 5 ∶ 4. How much is a child’s ticket?
E5 On a test consisting of 30 questions, Sue had 50% more right answers than she had wrong answers. Each
answer was either right or wrong. How many questions did Sue answer correctly?
E6 Joel’s car uses 12 liters of gas to make a 144 km tip. How many liters of gas is required by this car to travel
336 km?
E7 The total cost of P articles is Q pesos. What is, then, the cost, in pesos, of R articles, of the same type?
E8 A rectangle has a length of 6 cm and a width of 5 cm. A square has been cut out from each of the four corners
of the rectangle. Each of the squares has a perimeter of 4 cm. How many square centimeters is the area of the
resulting figure?
E9 The degree measure of the three angles of a triangle are consecutive multiples of 5. What is the degree
measure of the largest angle?
E10 A single 6-sided die is rolled. Find the probability of getting a prime number.
A1 A survey shows that 5.6% of the people making flight reservations do not keep them. Out of 125 people
who made reservations, how many can be expected to cancel?
A2 The product of three prime numbers was added to 1 and the result was 1222. Calculate the sum of these prime
numbers.
A3 Three signal lights were set to flash every certain specific time. The first light flashes every 12 seconds,
the second every 30 seconds, and the third every 66 seconds. The signal lights flash simultaneously at
8:30 am. At what time will the signal lights next flash together again?
A4 The base of a right triangle has length 9 cm and the altitude to this base is 12 cm. What is the length of
the altitude to the longest side of the triangle?
A5 When A is increased by 20% and B is decreased by 2-%, the resulting values are equal. What is the ratio of A to
B?
D1 In a class of 30 students, 12 played in the band, and 17 played volleyball. Of these, 5 students did both.
How many students did not participate in either activity?
D2 If the nine-digit number A12 345 67B is divisible by 45, determine all possible values of A and B.
D3 The areas of two squares are 3481 cm2 and 1681 cm2 , respectively. Find the difference of their perimeters
in centimeters.
D4 The total number of ducks and chickens in the garden is 335. If the number of chickens is two-thirds
of the number of ducks, how many chickens are there in the garden?
E1 When 20 is divided by n, the resulting quotient is 3 and the remainder is 2. What number is n?
E2 If 30% of a number is 150, what is 25% of the same number?
E3 John always gives a 10% tip every time he dines in a restaurant. How much tip did John give if he paid
a total of ₧2750 for his meal, including tips? Assume no taxes.
E4 A cereal mixture contains rice, wheat, and corn in the ratio of 2 ∶ 3 ∶ 5. If a bag of the mixture contains
4 kilograms of rice, how many kilograms of corn does the mixture contain?
E5 A robot produces sweets that are identical in size and taste. It takes an hour and a half for it to produce
24 tons of sweets. How many tons will it produce in 2 hours?
E6 A car can go x kilometers on y liters of gasoline. How many liters of gasoline will the car need for a
journey of z kilometers?
E7 What is the greatest possible value of the smallest of four different counting numbers with a sum of 34?
E8 What is the answer to 2019 − 2009 + 1999 − 1989 + 1979 − 1969 + ⋯ + 39 − 29 + 19 − 9?
E9 The surface of a cube is to be painted so that no two faces of the same color share a common edge. What
is the minimum number of different colors needed to paint the cube?
E10 The area of circle A is 9 times smaller than the area of circle B. By how much smaller is the circumference
of circle A smaller than that of circle B?
A1 When the numbers 5.02, 5.18, 5.2, 5.007, and 5.018 are arranged from least to greatest, determine the middle number.
A2 The difference between a 4-digit number and the sum of its digits is also a 4-digit number 658X. What is the value of X?
A3 Mr. Valdez gives his students 6 examinations in each grading period. The scores of Paul in the first 5 exams are 80, 79,
84, 87, and 93. If Paul hopes to get an average score for the 6 exams to be at least 4 marks than his average score for the
first 4 exams, find the least score that he must get in the sixth exam.
A4 Matt, a race driver, drove a 6 kilometer track. For the first 3 kilometers, his speed was 150 kilometers per hour; for the
next 2 kilometers, his speed was 200 kilometers per hour; and for the final kilometer, his speed was 300 kilometers per hour.
What is his average speed for the complete circuit?
A5 A wire 60 centimeters in length is cut into two parts in the ratio 2 ∶ 1. Each part is bent to form a square.
What is the total area of the two squares?
D1 Water pours into a tank at a constant rate. One day, the tank was 36% full at 2:00 pm and it became
100% full at 10:00 pm. How full was the tank at noon that day?
D2 When Gerry arrived at a party, two-thirds of those invited had already arrived. Six more people arrived just after Gerry,
bringing the fraction of those invited already present to five-sixths. What was the total number of invited guests?
D3 Bids have to be housed in cages so that each cage contains at least one bird and no two cages contain the same number
of birds. What is the maximum number of cages that can be used to house 100 birds?
D4 A PIN code consists of exactly 4 digits. How many different PIN codes can be constructed in which the sum of the digits is
34 or greater?
D5 Each of the circles shown has an area of 60 cm2 . One-fourth of the area of circle A is shaded. One-fifth of the area of circle
B is shaded. One-sixth of the area of circle C is shaded. What is the sum of the areas of the shaded region in square
centimeters?
A B
C

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MMC 2019 Grade 6 National

E2 If 30% of a number is 150, what is 25% of the same number?

E8 What is the answer to 2019 − 2009 + 1999 − 1989 + 1979 − 1969 + ⋯ + 39 − 29 + 19 − 9?

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