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16. A boy divided the numbers 7654, 8506 and 9997 by a certain largest number and he gets same remainder in each case. What is the common remainder? | |

A. 156 | B. 211 |

C. 231 | D. 199 |

Discuss |

answer with explanation

Answer: Option D

Explanation:

If the remainder is same in each case and remainder is not given, HCF of the differences of the numbers is the required largest number.

9997 - 7654 = 2343

9997 - 8506 = 1491

8506 - 7654 = 852

Hence, the greatest number which divides 7654, 8506 and 9997 and leaves same remainder

= HCF of 2343, 1491, 852

= 213

Now we need to find out the common remainder.

Take any of the given numbers from 7654, 8506 and 9997, say 7654

7654 ÷ 213 = 35, remainder = 199

17. Find the greatest common divisor of 24 and 16 | |

A. 6 | B. 8 |

C. 2 | D. 4 |

Discuss |

answer with explanation

Answer: Option B

Explanation:

Hence, greatest common divisor of 24 and 16 = 8

18. A, B and C start at the same time in the same direction to run around a circular stadium. A completes a round in 252 seconds, B in 308 seconds and C in 198 seconds, all starting at the same point. After what time will they again at the starting point ? | |

A. 46 minutes 12 seconds | B. 36 minutes 12 seconds |

C. 36 minutes 22 seconds | D. 46 minutes 22 seconds |

Discuss |

answer with explanation

Answer: Option A

Explanation:

LCM of 252, 308 and 198 = 2772

Hence they all will be again at the starting point after 2772 seconds.

i.e., after 46 minutes 12 seconds.

19. The ratio of two numbers is 4 : 5. If the HCF of these numbers is 6, what is their LCM? | |

A. 30 | B. 120 |

C. 60 | D. 90 |

Discuss |

answer with explanation

Answer: Option B

Explanation:

Let the numbers be 4k and 5k

HCF of 4 and 5 = 1

Hence HCF of 4k and 5k = k

Given that HCF of 4k and 5k = 6

=> k = 6

Hence the numbers are (4 × 6) and (5 × 6)

= 24 and 30

LCM of 24 and 30 = 120

20. What is the HCF of 2.04, 0.24 and 0.8 ? | |

A. 1 | B. 0.04 |

C. 2 | D. 0.02 |

Discuss |

answer with explanation

Answer: Option B

Explanation:

(Refer *"How to calculate LCM and HCF of Decimals"* here)

Step 1: Make the same number of decimal places in all the given numbers by suffixing zero(s) in required numbers as needed.

=> 2.04, 0.24 and 0.80

Step 2: Now find the HCF of these numbers without decimal.

=> HCF of 204, 24 and 80 = 4

Step 3: Put the decimal point in the result obtained in step 2 leaving as many digits on its right as there are in each of the numbers.

i.e., here we need to put decimal point in the result obtained in step 2 leaving two digits on its right.

=> HCF of 2.04, 0.24 and 0.8 = 0.04

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