Below are the 2018 MTAP Grade 5 Math Challenge Sectoral level questions and answers. Solutions will be posted later. More reviewers can be found on the **Past Tests** and **All Posts** pages.

Easy

1.) What is the value of

2.) A tank is 3/7 full. If adding 50 gallons of water will fill the tank, what is the tank’s capacity?

3.) By how much is 7/4 greater than 5/6?

4.) Eighteen is what percent of 45?

5.) A race with four laps has a total distance of 4.8 km. If Carlo has run three laps, how far into the race is he?

6.) If Martin’s age will double in 16 years, how old is Martin?

7.) What is 2.8 divided by 1/2?

8.) If the diameter of a circle is reduced by 20%, by how many percent is the area of the circle reduced?

9.) Write the sum 10 + 3/20 + 7/1000 as a decimal.

10.) If , what is ?

11.) If 20 + 1/2 + 2/3 + 3/4 + 4/5 + 5/6 + 6/7 + 7/8 = 7089/280, what is 2 + 1/20 + 1/15 + 3/40 + 2/25 + 5/60 + 3/35 + 7/80?

Average

1.) What is the ratio of the value of the digit 6 in 356 391 to the value of the digit 8 in 371.18?

2.) Chloe’s height increased by 8% in the past year. If Chloe is 129.6 cm tall now, what was her height last year?

3.) Camille’s uses 36 beads to make a bracelet, 60 beads to make a small necklace for children, and 132 beads for a large necklace for adults. If Camille makes only bracelets or only small necklaces, she will have 2 beads left. What is the smallest number of beads Camille can have?

4.) Six pencils and 5 pens cost Php 136. If a pen costs twice as much as a pencil, how much will one pencil and one pen cost?

5.) The GCD of two numbers is 30 and their product is 18 000. What is the smallest possible difference between the two numbers?

6.) The sum of a fraction and its reciprocal is 229/30. What are the possible values of the fraction?

Difficult

1.) If a number is increased by 12% and then increased by 5.75, the result is 24.118. What is the number?

2.) What is the largest three-digit number divisible by 21?

3.) If the area of a square is , estimate to the nearest hundredth the length of the side of the square.

4.) The ratio of Paolo’s age to Roger’s is 3 : 7. In eighteen years, Paolo will be 3/4 as old as Roger. How old is Roger now?

5.) The seven-digit number 1 302 9 *AB* is divisible by 66. What is the two-digit number *AB*?

6.) In how many ways can 6 squares in a row be colored black or white if both colors must be used and no two consecutive squares are colored black?

Tiebreaker

1.) Sandra has 42 hair clips and 70 bracelets. She wants to put them in boxes so that the boxes have equal numbers of hair clips and equal number of bracelets. If each box must have both hair clips and bracelets, at most how many boxes can Sandra use?

2.) If 30 kilos of rice can feed 8 children for 45 days, how long will 9 kilos of rice feed 9 children?

3.) Gary is thinking of a two-digit number with the tens digit equal to 4. If Gary’s number has only 3 divisors, what is the number?

Do-or-Die

1.) List all two-digit numbers with an odd number of divisors.

Answer key

Easy

1.) 930

2.) 87.5 gal

3.) 11/12

4.) 40%

5.) 3.6 km

6.) 16 yrs old

7.) 5.6

8.) 36%

9.) 10.157

10.) 99.54

11.) 7089/2800

Average

1.) 75000 : 1

2.) 120 cm

3.) 1982

4.) Php 25.50

5.) 30

6.) 2/15 or 15/2

Difficult

1.) 16.4

2.) 987

3.) 6.93

4.) 14 years old

5.) 72

6.) 18

Tiebreaker

1.) 14

2.) 12 days

3.) 49

Do-or-Die

1.) 16, 25, 36, 49, 81