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## Number System

Question 1 [CLICK ON ANY CHOICE TO KNOW THE RIGHT ANSWER] |

Two alarm clocks ring their alarms at regular intervals of 50 seconds and 48 seconds. If they first beep together at 12 noon, at what time will they beep again for first time?

12:12 PM | |

12:10 PM | |

None of these | |

12:11 PM |

Question 1 Explanation:

They will ring together after,

LCM of 48 and 50 secs.

48 = 2*2*2*2*3;

50 = 2*5*5;

LCM = 2*2*2*2*3*5*5 = 1200 secs

= 20 min.

They will beep together at 12:20.

Question 2 [CLICK ON ANY CHOICE TO KNOW THE RIGHT ANSWER] |

In a certain series, each number except the first and second is obtained by adding the previous two numbers. If the first no is 2 and sixth no is 26, then the seventh number is:

52 | |

46 | |

42 | |

40 |

Question 2 Explanation:

1stt no. = 2

2nd no. = x (let)

3rd no. = x+2

4th no. = x+x+2 = 2x+2

5th no. = x+2 + 2x+2 = 3x+4

Sixth no.,

3x+4 + 2x+2 = 26

5x = 20

x = 4

7th no. = 26 + 3x+4 = 26 + 3*4+4 = 42.

Question 3 [CLICK ON ANY CHOICE TO KNOW THE RIGHT ANSWER] |

A string of length 221 metre is cut into two parts such that one part is 9/4

^{th}as long as the rest of the string, then the difference between the larger piece and the shorter piece is :53 m | |

85 m | |

76 m | |

58 m |

Question 3 Explanation:

Let one part of string is x.

Now,

x + (9x/4) = 221 m

x = 68 meter

and, (9x/4) = 153 m

Difference between two parts = 153 - 68 = 85m.

Question 4 [CLICK ON ANY CHOICE TO KNOW THE RIGHT ANSWER] |

The sum of first five prime numbers is:

18 | |

11 | |

28 | |

26 |

Question 4 Explanation:

Required sum = (2 + 3 + 5 + 7 + 11) = 28.

Note: 1 is not a prime number.

**Definition :** A prime number (or a prime) is a natural number that has exactly two distinct natural number divisors: 1 and itself.

Question 5 [CLICK ON ANY CHOICE TO KNOW THE RIGHT ANSWER] |

7

^{6n}- 6^{6n}, where n is an integer >0, is divisible byAll of these | |

127 | |

13 | |

559 |

Question 5 Explanation:

For n = 1,

7^{6n}-6^{6n} = 7^{6} -6^{6}

= (7^{3})^{2}-(6^{3})^{2}

= (7^{3}-6^{3})( 7^{3}+6^{3})

= (343-216)*(343+216)

= 127*559.

= 127 * 13 *43.

Clearly, it is divisible by 127, 13 as well as 559.

There are 5 questions to complete.