# 2019 Grade 5 Math Challenge Divisionals Questions and Answers (with PDF)

Below are the 2019 MTAP Grade 5 Math Challenge Division Finals questions and answers. Solutions will be posted later. More reviewers can be found on the Past Tests and All Posts pages.

Easy

1.) If x = 5 + 10 + 15 + 20 + 25 and y = 13 + 14 + 15 + 16 + 17, what is x – y?

2.) If $\dfrac {a + b}{b} = \dfrac {11}{8}$, what is the value of $\dfrac {a}{b}$?

3.) Express as decimal the sum of $1 + \dfrac {1}{2} + \dfrac {1}{3} + \dfrac {1}{4} + \dfrac {1}{5} + \dfrac {1}{6}$.

4.) If x : 8 = y : 32 and x + y = 25, what is y – x?

5.) S = $1 + 1^2 + 1^3 + 1^4 + 1^5 + 1^6.$ How many prime factors does S have?

6.) A bell sounds at the indicated number of times at regular intervals as follows: …, 8, 1, 9, 1, 10, 1, 11, 1, 12, 1, 1, 1, ___, ___… What are the next two numbers?

7.) What is “one hundred thousand and one hundred-thousandths” when written as a decimal number?

8.) If I add a number to 4 and subtract the same number from 5, the result differ by $\dfrac {1}{2}.$ What is the number?

9.) What is the greatest four-digit number that is divisible by 6?

10.) What is the least 5-digit number with no zero digit that rounds of to 45000?

11.) What is the greatest one-digit divisor of $3 \times 4 \times 5 \times 6 \times 7 \times 8 \times 11 \times 13$?

Average

1.) What is the least common multiple of 2, 3, 4, 6, 8, 21, and 60?

2.) The proper fractions $\dfrac {n}{15}, \dfrac {n}{16}$, and $\dfrac {n}{18}$ have the same numerator greater that 1 and are in simplest form. What is the least value of n?

3.) The GCF and LCM of two numbers are 6 and 216, respectively. If one number is 24, what is the other number?

4.) What is $\dfrac {1}{3} + \dfrac {4}{9}$ expressed in percent without decimal.

5.) What is the value of in the sequence 1, 3, 6, 10, 15, n?

6.) What is the difference in the value of 8 and 6 in 456 789 123?

Difficult

1.) What is exactly halfway between $\dfrac {3}{5}$ and $\dfrac {9}{10}?$

2.) What is the last digit of the number $2^{2020}$ when written in standard form?

3.) The average of 12 numbers is 80. If two numbers are discarded, namely 53 and 47, what is the average of the remaining numbers?

4.) The numbers 5 and 29 are the first and fifth terms of an equally spaced sequence of five prime numbers. What are the other three numbers?

5.) What is in n = 100 – 99 + 98 – 97 + 96 – 95 + 94 – 93 + 92 – 91 + … and so on up to + 10 – 9 + 8 – 7 + 6 – 5 + 4 – 3 + 2 – 1?

6.) The sum of the digits of the greatest possible three-digit even number is 26. If the number is multiplied by 1001, what is the product?

Tie-breaker

1.) A coin bank is filled with 25-cent coins amounting to Php 504.75. How many coins are there in all?

2.) What is the value of $(37 037 \times 6) + (37 037 \times 9) + (37 037 \times 12)$?

3.) The LCM of the number pair m and n is 12. Give a complete list of all possible pairs m and n.

Do-or-die

What is the product of $(1 - \dfrac {1}{2}) \times (1 - \dfrac {1}{3}) \times (1 - \dfrac {1}{4}) \times (1 - \dfrac {1}{5}) \times ... \times (1 - \dfrac {1}{99}) \times (1 - \dfrac {1}{100})$

Easy

1.) 0

2.) $\dfrac {3}{8}$

3.) 2.45

4.) 15

5.) 2

6.) 2,1

7.) 100 000.000 01

8.) $\dfrac {1}{4}$

9.) 9996

10.) 44511

11.) 9

Average

1.) 120

2.) 7

3.) 54

4.) $77 \dfrac {7}{9}%$

5.) 21

6.) 5 920 000

Difficult

1.) $\dfrac {3}{4}$

2.) 6

3.) 86

4.) 11, 17, 23

5.) 50

6.) 998 999

Tie-breaker

1.) 2019

2.) 999 999

3.) 3 and 4; 4 and 6; 1 and 12; 2 and 12; 3 and 12; 4 and 12; 6 and 12; 12 and 12

Do-or-die

$\dfrac {1}{100}$