A) 1 | B) 2 |

C) 3 | D) 4 |

Explanation:

Let the numbers 13a and 13b.

Then, 13a x 13b = 2028

=>ab = 12.

Now, the co-primes with product 12 are (1, 12) and (3, 4).

[Note: Two integers a and b are said to be coprime or relatively prime if they have no common positive factor other than 1 or, equivalently, if their greatest common divisor is 1 ]

So, the required numbers are (13 x 1, 13 x 12) and (13 x 3, 13 x 4).

Clearly, there are 2 such pairs.

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

A) 1008 | B) 1015 |

C) 1022 | D) 1032 |

Explanation:

Required Number = (L.C.M of 12, 16, 18,21,28)+7

= 1008 + 7

= 1015

A) 4 | B) 7 |

C) 9 | D) 13 |

Explanation:

Required Number = H.C.F of (91- 43), (183- 91) and (183-43)

= H.C.F of 48, 92, and 140 = 4