Math Olympiad: 25 MCQs with answers

C · 40

Following the order of operations, multiplication is done before addition: $4 \times 5 = 20$, then $20 + 20 = 40$.

B · 7

A prime number has exactly two distinct factors: 1 and itself. 7 is divisible only by 1 and 7, so it is prime. 9, 15, and 21 are composite.

C · 45

1 hour = 60 minutes. $\frac{3}{4} \times 60 = 45$ minutes.

A · 7

Subtract 5 from both sides: $x = 12 - 5 = 7$.

B · 40 cm$^2$

Area of a rectangle = length $\times$ width = $8 \times 5 = 40$ cm$^2$.

B · $\frac{6}{9}$

Multiply numerator and denominator of $\frac{2}{3}$ by 3: $\frac{2 \times 3}{3 \times 3} = \frac{6}{9}$.

A · True

An odd number can be written as $2k+1$. The sum of two odds is $(2k+1)+(2m+1)=2(k+m+1)$, which is even.

B · False

The sum of angles in a triangle is $180^\circ$. Two right angles would sum to $180^\circ$, leaving $0^\circ$ for the third angle, which is impossible.

C · 12

The correct answer is $12$ because $5 + 7 = 12$.

C · Triangle

A triangle is defined as a shape with three sides.

D · 5

The next number is $5$ because the sequence increases by $1$ each time.

C · 8

The correct answer is $8$ because even numbers are divisible by $2$.

C · 6

The value is $6$ because $10 - 4 = 6$.

D · Sphere

A ball is shaped like a sphere, which is round and three-dimensional.

C · 6

A hexagon has $6$ sides by definition.

D · 9

The value of $3^2$ is $9$ because $3 imes 3 = 9$.

D · 30

The correct answer is $30$ because it can be expressed as $5 imes 6$.

A · 42

The differences between consecutive terms are 4, 6, 8, 10, so the next difference is 12. Thus $30 + 12 = 42$.

C · 36

Let the number be $x$. Then $\frac{1}{3}x = 12$, so $x = 12 \times 3 = 36$.

C · 55

The sum of the first $n$ positive integers is $\frac{n(n+1)}{2}$. For $n=10$, it is $\frac{10 \times 11}{2} = 55$.

D · 25 cm$^2$

Perimeter of a square = $4 \times$ side, so side = $20 \div 4 = 5$ cm. Area = side$^2$ = $5^2 = 25$ cm$^2$.

B · 2

A number is divisible by 5 if it ends in 0 or 5. The next multiple of 5 after 123 is 125, so we need to add 2.

D · 17

$2^3 = 8$ and $3^2 = 9$, so $8 + 9 = 17$.

A · 6

Let the number be $x$. Then $2x + 5 = 17$. Subtract 5: $2x = 12$, so $x = 6$.

B · Thursday

100 divided by 7 leaves a remainder of 2 (since $7 \times 14 = 98$). Two days after Tuesday is Thursday.