21. | What greatest number can be subtracted from 10000, so that the remainder may be divisible by 32, 36, 48 and 54? | |

A. | 9136 | |

B. | 9036 | |

C. | 9138 | |

D. | 9132 | |

## View Answer
LCM of 32, 36, 48 and 54 is 864 |

22. | What is the least number which when divided by 52 leaves 33 as the remainder, and when divided by 78 leaves 59, and when divided by 117 leaves 98 as the respective remainders. | |

A. | 459 | |

B. | 449 | |

C. | 479 | |

D. | 483 | |

## View Answer
Shortcut: |

23. | Find the greatest number of six digits which on being divided by 6, 7, 8, 9 and 10 leaves 4, 5, 6, 7 and 8 as remainder respectively. | |

A. | 996918 | |

B. | 997918 | |

C. | 997912 | |

D. | 997928 | |

## View Answer
The LCM of 6, 7, 8, 9 and 10 = 2520 |

24. | What is the least multiple of 7, which when divided by 2, 3, 4, 5 and 6 leaves the remainders 1, 2, 3, 4 and 5 respectively? | |

A. | 119 | |

B. | 112 | |

C. | 105 | |

D. | 154 | |

## View Answer
LCM 2, 3, 4, 5 and 6 = 60 |

25. | Find the greatest number of six digits which when divided by 5, 7, 12 and 15 leaves respectively remainders 3, 5, 10 and 13. | |

A. | 999498 | |

B. | 999598 | |

C. | 999898 | |

D. | 999698 | |

## View Answer
LCM of 5, 7, 12 and 15 = 420 |

26. | Find the least number which upon being divided by 2, 3, 4, 5 and 6 leaves in each case a remainder of 1. | |

A. | 61 | |

B. | 47 | |

C. | 43 | |

D. | 71 | |

## View Answer
Shortcut: |

27. | What smallest number must be subtracted from 7894135 so that the remainder when divided by 34, 38, 85 and 95 leaves the same remainder 11 in each case. | |

A. | 8 | |

B. | 2 | |

C. | 6 | |

D. | 4 | |

## View Answer
LCM of 34, 38, 85 and 95 = 3230 |

28. | What is the least multiple of 17, which leaves a remainder of 1 when divided by each of the first twelve integers excepting unity? | |

A. | 138501 | |

B. | 136601 | |

C. | 138601 | |

D. | 138501 | |

## View Answer
LCM of first twelve integers excepting unity is 27720 |

29. | Find the least number of six digits which when divided by 4, 6, 10 and 15, leaves in each case the same remainder 2. | |

A. | 10026 | |

B. | 10022 | |

C. | 10028 | |

D. | 10020 | |

## View Answer
LCM of 4, 6, 10 and 15 = 60 |

30. | Find the greatest number which will divide 410, 751 and 1030 so as to leave remainder 7 in each case. | |

A. | 31 | |

B. | 21 | |

C. | 51 | |

D. | 41 | |

## View Answer
Shortcut:
To find the greatest number that will divide x, y and z leaving the same remainder 'R' in each case. |