Number Theory
What is the smallest prime number greater than 20?
Answer: 23
What is 15% of 240?
Answer: 36
A triangle has angles of 40° and 65°. Find the third angle.
Answer: 75°
If 3x=27, find x.
Answer: 9
A number is increased by 5 and then doubled. The result is 20. What is the number?
Answer: 5
A number is divisible by both 6 and 8. What is the smallest possible positive number?
Answer: 24
Without multiplying directly, find:
25×48
Answer: 1,200
A rectangle has an area of 48 cm² and a length of 8 cm. Find its perimeter.
Answer: 28 cm
If x+y=10 and x−y=4, find x.
Answer: 7
The average of 5 numbers is 18. Four of the numbers are 12, 15, 20, and 25. What is the fifth?
Answer: 18
The sum of two prime numbers is 24. What is the greatest possible product of the two primes?
Answer: 143 (11 × 13)
Without using a calculator:
1/2 + 1/6 + 1/12 + 1/20
Answer: 3/4
A square has diagonal 10sqrt(2) cm. What is its area?
Answer: 100 cm²
If x + 1/x = 5, find:
x2 + 1/x2.
Answer: 23
A two-digit number has digits that add to 11. Reversing the digits increases the number by 27. Find the number.
Answer: 47
What is the units digit of 72026?
Answer: 9
Find the value of:
482−472
Answer: 95
A triangle and a parallelogram have the same base and height. The parallelogram has an area of 60 cm². What is the triangle's area?
Answer: 30 cm²
If a + b = 12 and ab = 35, find a2 + b2.
Answer: 74
Find the smallest positive integer whose digits add up to 10.
Answer: 19
Find the smallest positive integer that leaves a remainder of 2 when divided by 3, a remainder of 3 when divided by 5, and a remainder of 4 when divided by 7.
Answer: 53
Calculate mentally:
1012−992
Answer: 400
A square is inscribed in a circle of radius 5 cm. What is the area of the square?
Answer: 50 cm²
If x2−5x+6=0, what is the sum of the reciprocals of the roots?
Answer: 5/6
A square and an equilateral triangle have the same perimeter. If the square has side length 6 cm, what is the side length of the triangle?
Answer: 8 cm