Question | Answer | Explanation |

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. |

What is the greatest three-digit odd number that can be formed using the digits 6, 8 and 9 once only? | 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. |

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. |

What is the smallest four-digit even number that can be formed using the digits 6, 7, 8 and 9 once only? | 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. |

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. |

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

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

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

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. |

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

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. |

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

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. |

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

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. |

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

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. |

In which of the following numbers is the sum of the digits an even number: 9574, 8313, 7685, 6924? | 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). |

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). |

What is the sum of the even numbers between 41 and 51? | 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). |

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. |

What is the sum of the sixth, the seventh, the eighth and the ninth odd numbers after 30? | 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. |

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. |

What is the difference between the 17th and the 21st even numbers coming after 250? | 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. |

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. |

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

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. |

What is the sum of the 30th and 50th even numbers after 26? | 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. |

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. |

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