A) 123 | B) 127 |

C) 235 | D) 305 |

Explanation:

Required number = H.C.F. of (1657 - 6) and (2037 - 5)

= H.C.F. of 1651 and 2032 = 127.

A) 26 | B) 24 |

C) 18 | D) 12 |

Explanation:

Gold coins = 18000 , Silver coins = 9600 , Bronze coins = 3600

Find a number which exactly divide all these numbers

That is HCF of 18000, 9600& 3600

All the value has 00 at end so the factor will also have 00.

HCF for 180, 96 & 36.

Factors of

180 = 3 x 3 x 5 x 2 x 2

96 = 2 x 2 x 2 x 2 x 2 x 3

36 = 2 x 2 x 3 x 3

Common factors are 2x2×3=12

Actual HCF is 1200

Gold Coins will be in 15 rooms

Silver Coins will be in 8 rooms

Bronze Coins will be in 3 rooms

Total rooms will be (15+8+3) = 26 rooms.

A) 40 | B) 60 |

C) 100 | D) 120 |

Explanation:

Let the numbers be 3x, 4x, 5x.

Then, their L.C.M = 60x.

So, 60x=3600 or x=60.

The numbers are (3 x 60), (4 x 60), (5 x 60).

Hence,required H.C.F=60

A) 35 | B) 36 |

C) 37 | D) 38 |

Explanation:

If we want to pack the drinks in the least number of cans possible, then each can should contain the maximum numbers of liters possible.As each can contains the same number liters of a drink, the number of liters in each can is a comman factor for 80,144 and 368; and it is also the highest such factor, as we need to store the maximum number of liters in each can.

So, the number of liters in each can = HCF of 80,144 and 368 = 16 liters.

Now, number of cans of Maaza = 80/16 = 5

Number of cans of Pepsi = 144/16 = 9

Number of cans of Sprite = 368/16 = 23

Thus, the total number of cans required = 5 + 9 + 23 = 37

A) 107 | B) 117 |

C) 127 | D) 137 |

Explanation:

Let us calculate both the length and width of the room in centimeters.

Length = 6 meters and 24 centimeters = 624 cm

width = 4 meters and 32 centimeters = 432 cm

As we want the least number of square tiles required, it means the length of each square tile should be as large as possible.Further,the length of each square tile should be a factor of both the length and width of the room.

Hence, the length of each square tile will be equal to the HCF of the length and width of the room = HCF of 624 and 432 = 48

Thus, the number of square tiles required = (624 x 432 ) / (48 x 48) = 13 x 9 = 117

A) 1677 | B) 1683 |

C) 2523 | D) 3363 |

Explanation:

L.C.M of 5, 6, 7, 8 = 840

Required Number is of the form 840k+3.

Least value of k for which (840k+3) is divisible by 9 is k = 2

Required Number = (840 x 2+3)=1683