Area
A right triangle has legs 15 cm and 20 cm.
Find the area.
150 cm2
Three consecutive numbers have a sum of 75. What is the smallest number?
The smallest number is 24.
1, 2, 4, 7, 11, 16, ___
22
(Add consecutive integers +1, +2, +3, +4, +5, +6…)
I am a three-digit number.
My hundreds digit is twice my ones digit.
My tens digit is one less than my ones digit.
The sum of my digits is 11.
623
1-2-3 → one digit correct and in the right position.
4-5-6 → none correct.
1-4-7 → one digit correct but in the wrong position.
8-9-0 → none correct.
321
An isosceles trapezoid has bases 18 cm and 8 cm, with each leg 13 cm.
Find the area.
156 cm2
Austin scored 78 and 85 on his first two tests. What score does he need on the third test so his average is 87?
Austin needs to score a 98.
0, 2, 6, 12, 20, 30, ___
42
(Add consecutive even numbers: +4, +6, +8, +10, +12…)
I am a three-digit number.
My hundreds digit is equal to the sum of my tens and ones digits.
My tens digit is three less than my hundreds digit.
The sum of all my digits is 12.
What number am I?
633
2-3-3 → none right.
1-2-3 → one right and at the right position.
5-2-9 → one right and at the right position.
6-6-0 → one right and at the right position.
169
A rectangle is 20 cm by 14 cm. A centered isosceles triangle with base 14 cm and height 7 cm is removed from one long side (the triangle’s base sits along the 14-cm side).
Find the remaining area.
231 cm2
If the side lengths of a triangle are three consecutive odd numbers, and the perimeter is 51 cm, what is the length of the longest side?
The longest side is 19 cm.
4, 9, 19, 39, 79, ___
159
(Double the previous number, then add 1)
I am a three-digit number.
My hundreds digit is one less than twice my tens digit.
My ones digit is two more than my hundreds digit.
The sum of all digits is 20.
749
9-6-3 → none right.
5-2-0 → two right but not at the right position.
7-9-0 → none right.
2-4-7 → two right and at the right position.
245
A rectangle is 18 cm by 10 cm. From one corner a right triangle with legs 6 cm and 8 cm is removed. From the opposite corner a small rectangle 4 cm by 5 cm is also removed.
Find the area of the remaining shape.
136 cm2
The length of a rectangle is 3 cm less than twice its width. If the perimeter is 66 cm, what are the dimensions of the rectangle?
Width: 12 cm
Length: 21 cm
Find the next number in the sequence:
2, 4, 3, 6, 4, 8, ___
5
The sequence alternates between two simple rules:
Odd positions (1st, 3rd, 5th): increase by 1
2 → 3 → 4 → 5
Even positions (2nd, 4th, 6th): increase by 2
4 → 6 → 8
So, the 7th term follows the odd-position pattern: 4 → 5
I am a three-digit number.
My tens digit is one less than my hundreds digit.
My ones digit is twice my tens digit minus 1.
The sum of all digits is 16.
547
9-2-4 → none right.
0-1-8 → one right and at the right position.
7-6-6 → one right but not at the right position.
7-8-9 → one right and at the right position.
688
A rectangle is 24 cm by 20 cm.
A centered isosceles triangle with base 12 cm and height 9 cm is removed from one long side.
From the opposite corner a right triangle with legs 5 cm and 12 cm is also removed.
Find the area of the remaining shape.
396 cm2
The sum of three consecutive multiples of 5 is 255. What are the numbers?
80, 85, 90
Find the next number in the sequence:
1, 11, 21, 1211, 111221, ___
312211
This is the famous “Look-and-say” sequence. Each term describes the digits of the previous term:
1 → "one 1" → 11
11 → "two 1s" → 21
21 → "one 2, one 1" → 1211
1211 → "one 1, one 2, two 1s" → 111221
111221 → "three 1s, two 2s, one 1" → 312211
I am a three-digit number.
My hundreds digit is twice my ones digit minus 1.
My tens digit is one less than my ones digit.
The sum of all digits is 18.
945
8-6-7 → one right but not at the right position.
5-0-2 → none right.
7-3-7 → two right but not at the right position.
3-9-3 → two right and at the right position.
373