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Mathematics Activity :
Even Numbers and Odd Numbers

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1. How many three-digit odd numbers are there?
Answer: 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.

2. What is the greatest three-digit odd number that can be formed using the digits 6, 8 and 9 once only?
Answer: 869
For the number to be odd, it must end in 9. Arranging the other two digits in descending order, the greatest three-digit odd number turns out to be 869.

3. How many two-digit even numbers are there?
Answer: 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.

4. What is the smallest four-digit even number that can be formed using the digits 6, 7, 8 and 9 once only?
Answer: 6798
On arranging the digits in ascending order, the smallest number one gets is 6789 (which is an odd number). On swapping the last two digits, the next number is 6798.

5. Which of the following is the smallest odd number: 989, 567, 456, 322?
Answer: 567
The even numbers are 322 and 456. The odd numbers are 567 and 989. So, the smallest odd number is 567.

6. Which of the following is the greatest even number: 678, 786, 768, 867?
Answer: 786
Out of the even numbers (678, 768, 786), the greatest number is 786.

7. Which of the following is the greatest even number: 2046, 2406, 2640, 2604?
Answer: 2640
2640 > 2604 > 2406 > 2046.

8. Which is the 13th even number after 89?
Answer: 114
The next even number after 89 is 90. The 12th even number after 90 will be 90 + (12 × 2) = 114.

9. In how many ways can 48 be expressed as the product of two even numbers?
Answer: 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.

10. Which is the 103rd even number after 118?
Answer: 324
The 103rd even number after 118 will be 118 + (103 × 2) = 324.

11. Which is the 14th odd number after 192?
Answer: 219
The next odd number after 192 is 193. The 13th odd number after 193 will be 193 + (13 × 2) = 219.

12. Which is the 106th odd number after 292?
Answer: 503
The next odd number after 292 is 293. The 105th odd number after 293 will be 293 + (105 × 2) = 503.

13. Which of the following numbers when multiplied by 5 gives an odd number: 88, 76, 97, 66?
Answer: 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.

14. Which of the following numbers when divided by 2 leaves 1 as the remainder: 5626, 6233, 7568, 8970?
Answer: 6233
Only an odd number when divided by 2 leaves 1 as the remainder.

15. If the sum of two odd numbers is divided by 2, what will be the remainder?
Answer: 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.

16. What should be added to 197 to obtain the third odd number serially after it?
Answer: 6
The third odd number serially after 197 is 203. Note that 197 + 6 = 203.

17. What should be added to 198 to obtain the fourth odd number serially after it?
Answer: 7
The fourth odd number serially after 198 is 205. Note that 198 + 7 = 205.

18. In which of the following numbers is the sum of the digits an even number: 9574, 8313, 7685, 6924?
Answer: 7685
9 + 5 + 7 + 4 = 25. s s s 8 + 3 + 1 + 3 = 15.
7 + 6 + 8 + 5 = 26. s s s 6 + 9 + 2 + 4 = 21.
The sum of the digits in 7685 is 26 (an even number).

19. What is the sum of the odd numbers between 30 and 40?
Answer: 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).

20. What is the sum of the even numbers between 41 and 51?
Answer: 230
The even numbers between 41 and 51 are 42, 44, 46, 48, 50. Their sum is (40 × 5) + (2 + 4 + 6 + 8 + 10) = 200 + 30 = 230. Note that 230 is simply 5 times the middle number (i.e., 5 × 46 = 230).

21. What is the sum of the sixth, the seventh and the eighth even numbers after 70?
Answer: 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.

22. What is the sum of the sixth, the seventh, the eighth and the ninth odd numbers after 30?
Answer: 176
The sixth, seventh, eighth and ninth odd numbers after 30 are 41, 43, 45, 47. Their sum is (40 × 4) + (1 + 3 + 5 + 7) = 160 + 16 = 176.

23. What is the difference between the 23rd and the 26th odd numbers coming after 25?
Answer: 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.

24. What is the difference between the 17th and the 21st even numbers coming after 250?
Answer: 8
The difference between consecutive even numbers is 2. Therefore the difference between the 17th and the 21st even numbers will be 2 × (21 − 17) = 8.

25. What is the difference between the sum of the even numbers and the sum of the odd numbers between 20 and 31?
Answer: 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.

26. What is the sum of the greatest four-digit odd number and the greatest three-digit even number?
Answer: 10997
The greatest four-digit odd number is 9999. The greatest three-digit even number is 998. Their sum is 10997.

27. What is the difference between the greatest four-digit even number and the smallest four-digit odd number?
Answer: 8997
The greatest four-digit even number is 9998. The smallest four-digit odd number is 1001. Their difference is 8997.

28. What is the sum of the 30th and 50th even numbers after 26?
Answer: 212
The 30th even number after 26 is 26 + (2 × 30). The 50th even number after 26 is 26 + (2 × 50). The sum of these gives
(2 × 26) + (2 × 30) + (2 × 50)
= 2 (26 + 30 + 50) = 2 × 106 = 212.

29. Using each of the digits 0, 5, 7 once only, how many three-digit odd numbers can be formed?
Answer: 2
The 2 three-digit odd numbers that can be formed are 507 and 705.

30. Using each of the digits 2, 3, 6 once only, how many three-digit even numbers can be formed?
Answer: 4
The 4 three-digit even numbers that can be formed are 236, 326, 362 and 632.

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