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Free MOEMS Olympiad practice test — Grade 6

10 original MOEMS Olympiad-style questions for Grade 6, with answers and full explanations. No signup needed.

Practice in the spirit of MOEMS — five-problem elementary and middle-school math olympiads that stretch problem-solving beyond the classroom.

Each problem rewards a strategy: draw it, simplify it, find the pattern, work backwards.

Question 1Clever Arithmetic (G6)
A sequence of numbers starts with 1, 2, 4, 7, 11. What is the next number in the sequence?
  1. A14
  2. B15
  3. C16
  4. D17
Show answer & explanation

Correct answer: D

The pattern of the sequence is obtained by adding 1, 2, 3, 4,... to the previous term. Therefore, to get the next number, we add 5 to the last term, which is 11. So, 11 + 5 = 16. 💡 Tip: Look for patterns in the differences between consecutive terms.

Question 2Counting & Logic (G6)
In a school, there are 15 clubs, and each club has 8 members. If each member can join at most 3 clubs, what is the maximum number of members in the school?
  1. A80
  2. B120
  3. C160
  4. D200
Show answer & explanation

Correct answer: B

To maximize the number of members, we need to minimize the overlap between clubs. Since each member can join at most 3 clubs, we can divide the 15 clubs into 5 groups of 3 clubs each. Each group can have 8 members, and since each member joins 3 clubs, each group contributes 8 new members. Therefore, the maximum number of members is 5 groups * 8 members/group * 3 clubs/group / 3 clubs/member = 160 / 3 * 3 = 160. 💡 Tip: Divide the clubs into groups to minimize overlap and maximize the number of members.

Question 3Geometry & Measurement (G6)
A rectangular garden measures 15 meters by 8 meters. A path that is 2 meters wide is built around the garden. What is the area of the path?
  1. A92
  2. B100
  3. C108
  4. D116
Show answer & explanation

Correct answer: C

To find the area of the path, first calculate the area of the larger rectangle including the path, which is (15+2+2) * (8+2+2) = 19 * 12 = 228. Then subtract the area of the garden, 15 * 8 = 120. The area of the path is 228 - 120 = 108. 💡 Tip: When calculating the area of the path around a shape, it's helpful to visualize the larger shape that includes the original figure and the path, and then subtract the area of the original figure.

Question 4Number Theory (G6)
What is the smallest 3-digit number that is divisible by 3, 4, and 5, and has exactly two different prime factors?
  1. A120
  2. B100
  3. C105
  4. D102
Show answer & explanation

Correct answer: A

To solve this, first find the least common multiple (LCM) of 3, 4, and 5, which is 60. Then, find the smallest 3-digit multiple of 60, which is 120. Since 120 has only two different prime factors (2 and 3), it satisfies all conditions. 💡 Tip: Remember, the LCM of numbers gives the smallest number that is a multiple of each of the given numbers. Also, prime factorization helps in identifying the number of different prime factors.

Question 5Problem Solving (G6)
A bookstore has three shelves, and each shelf can hold 8 rows of books. If the store currently has 120 books on the shelves and wants to add more books such that each shelf will have the same number of books, what is the minimum number of additional books needed?
  1. A16
  2. B24
  3. C32
  4. D40
Show answer & explanation

Correct answer: B

To find the minimum number of additional books needed, we need to find the least common multiple (LCM) of 3 and 8. Since 3 x 8 = 24, we can add 24 books to make each shelf have 48 books (16 per row x 3 rows). Currently, there are 120 books, so each shelf has 120 / 3 = 40 books. To make each shelf have 48 books, we need 48 - 40 = 8 books per shelf. Since there are 3 shelves, we need 8 x 3 = 24 books. 💡 Tip: Pay attention to the shelf capacity and the current number of books.

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Question 6Clever Arithmetic (G6)
A bookshelf has 5 shelves, and each shelf can hold 8 books. If the bookshelf is currently empty, how many books can be placed on it in total, given that each book has a thickness of 1 cm and the bookshelf has a height of 250 cm?
  1. A40 books
  2. B160 books
  3. C200 books
  4. D400 books
Show answer & explanation

Correct answer: B

Since each book has a thickness of 1 cm and the bookshelf has a height of 250 cm, we can fit 250 books on the bookshelf if we fill it completely. However, the bookshelf has 5 shelves, each of which can hold 8 books. So, the total number of books the bookshelf can hold is 5 * 8 = 40, if we consider the shelves. But the actual limiting factor is the height, and since 250 cm can fit 250 books, and we know that 5 * 8 = 40, we can fit 40 * 4 = 160 books (as 5 shelves would take 5 cm for the shelves themselves, leaving 250 - 5 = 245 cm, which is roughly 4 times the height of 8 books, which is 8 cm). Thus, the answer is 160 books. 💡 Tip: Consider all the given constraints and how they relate to each other.

Question 7Counting & Logic (G6)
There are 5 switches, but they are not labelled. Each switch corresponds to one of five light bulbs in a room. Each light bulb is off at the start. You can turn the lights on and off as many times as you want, but you can only enter the room one time to observe the bulbs. How can you figure out which switch corresponds to which light bulb?
  1. AFlip the switches in a specific sequence and then enter the room
  2. BEnter the room, turn on all the switches, and then turn them off one by one
  3. CTurn on each switch for 5 minutes and then turn it off
  4. DFlip the switches in any sequence and then enter the room
Show answer & explanation

Correct answer: A

To solve this problem, you can flip the switches in a specific sequence, for example: turn switch 1 to ON for 5 minutes, then turn it OFF. Turn switch 2 to ON for 5 minutes, then turn it OFF. Turn switch 3 to ON and leave it ON. Turn switch 4 to ON for 2.5 minutes and then turn it OFF. Turn switch 5 to ON and leave it ON. Then, enter the room and observe the bulbs. The hot bulb (but off) corresponds to switch 2, the bulb that is on corresponds to either switch 3 or switch 5, and the cold bulb (but off) that is not corresponding to switch 2 corresponds to either switch 1 or switch 4. By the process of elimination, you can figure out which switch corresponds to which bulb. 💡 Tip: Use a specific sequence of switch flips to create a unique pattern for each bulb.

Question 8Geometry & Measurement (G6)
A triangle has angles measuring 30, 60, and 90 degrees. If the side opposite the 30-degree angle is 5 inches, what is the length of the hypotenuse?
  1. A5
  2. B10
  3. C10√3
  4. D20
Show answer & explanation

Correct answer: B

In a 30-60-90 triangle, the side opposite the 30-degree angle is half the length of the hypotenuse. Since the side opposite the 30-degree angle is 5 inches, the hypotenuse must be twice that, which is 10 inches. 💡 Tip: Knowing the properties of special triangles like 30-60-90 and 45-45-90 can be very helpful in geometry problems.

Question 9Number Theory (G6)
A number is said to be 'doubly divisible' by 4 and 9 if it is divisible by both 4 and 9. What is the smallest 4-digit number that is doubly divisible by 4 and 9?
  1. A1008
  2. B1024
  3. C1000
  4. D1004
Show answer & explanation

Correct answer: A

First, find the least common multiple of 4 and 9, which is 36. Then, find the smallest 4-digit multiple of 36, which is 1008. Thus, 1008 is the smallest 4-digit number that is doubly divisible by 4 and 9. 💡 Tip: Finding the LCM of the divisors and then the smallest multiple of that LCM which fits the given constraints is key.

Question 10Problem Solving (G6)
A group of friends want to share some candy equally. If they have 48 pieces of candy and there are 8 friends, but 2 friends don't want any candy, how many pieces will each friend get who wants candy?
  1. A5
  2. B6
  3. C7
  4. D8
Show answer & explanation

Correct answer: B

First, subtract the 2 friends who don't want any candy from the total number of friends: 8 - 2 = 6. Then, divide the total number of pieces of candy by the number of friends who want candy: 48 / 6 = 8. 💡 Tip: Identify the number of friends who want candy before dividing the total number of pieces.

MOEMS Olympiad FAQ

What is MOEMS?

Math Olympiads for Elementary and Middle Schools — five monthly contests per school year, run through school teams, for grades 4–8.

More free MOEMS Olympiad practice

Grade 4Grade 5Grade 7Grade 8🖨️ Printable Grade 6 pack (PDF) →Parent's guide to the MOEMS Olympiad →

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