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Mathematics Activity :
Even Numbers and Odd Numbers
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1. How many three-digit odd numbers are there?
450
There are 900 three-digit numbers starting with 100 and ending with 999. Half of these are odd numbers and half of these are even numbers.
3. How many two-digit even numbers are there?
45
There are 90 two-digit numbers starting with 10 and ending with 99. Half of these are even numbers and half of these are even numbers.
5. Which of the following is the smallest odd number: 989, 567, 456, 322?
567
The even numbers are 322 and 456. The odd numbers are 567 and 989. So, the smallest odd number is 567.
7. Which of the following is the greatest even number: 2046, 2406, 2640, 2604?
2640
2640 > 2604 > 2406 > 2046.
9. In how many ways can 48 be expressed as the product of two even numbers?
3
The 3 ways to express 48 as the product of two even numbers are 2 × 24, 4 × 12, 6 × 8. The fourth way is 3 × 16, but 3 is an odd number.
11. Which is the 14th odd number after 192?
219
The next odd number after 192 is 193. The 13th odd number after 193 will be 193 + (13 × 2) = 219.
13. Which of the following numbers when multiplied by 5 gives an odd number: 88, 76, 97, 66?
97
When a number is multiplied by 5, it gives a number with a 0 or 5 in the units place. Only an odd number when multiplied by 5 gives an odd number with a 5 in the units place.
15. If the sum of two odd numbers is divided by 2, what will be the remainder?
0
The sum of two odd numbers will always be an even number. If an even number is divided by 2, the remainder is 0.
17. What should be added to 198 to obtain the fourth odd number serially after it?
7
The fourth odd number serially after 198 is 205. Note that 198 + 7 = 205.
19. What is the sum of the odd numbers between 30 and 40?
175
The odd numbers between 30 and 40 are 31, 33, 35, 37, 39. Their sum is (30 × 5) + (1 + 3 + 5 + 7 + 9) = 150 + 25 = 175. Note that 175 is simply 5 times the middle number (i.e., 5 × 35 = 175).
21. What is the sum of the sixth, the seventh and the eighth even numbers after 70?
252
The sixth, seventh and eighth even numbers after 70 are 82, 84, 86. Their sum is (80 × 3) + (2 + 4 + 6) = 240 + 12 = 252.
23. What is the difference between the 23rd and the 26th odd numbers coming after 25?
6
The difference between consecutive odd numbers is 2. Therefore the difference between the 23rd and the 26th odd numbers will be 2 × (26 − 23) = 6.
25. What is the difference between the sum of the even numbers and the sum of the odd numbers between 20 and 31?
5
The even numbers are 22, 24, 26, 28, 30. The odd numbers are 21, 23, 25, 27, 29. Thus, the answer is
(22 + 24 + 26 + 28 + 30) − (21 + 23 + 25 + 27 + 29)
= (22 − 21) + (24 − 23) + (26 − 25) + (28 − 27) + (30 − 29)
= 1 + 1 + 1 + 1 + 1 = 5.
27. What is the difference between the greatest four-digit even number and the smallest four-digit odd number?
8997
The greatest four-digit even number is 9998. The smallest four-digit odd number is 1001. Their difference is 8997.
29. Using each of the digits 0, 5, 7 once only, how many three-digit odd numbers can be formed?
2
The 2 three-digit odd numbers that can be formed are 507 and 705.
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