## Series 6

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*Series 6*. You scored %%SCORE%% out of %%TOTAL%%. Your performance has been rated as %%RATING%%
Your answers are highlighted below.

Question 1 |

**What will be the remainder when (67**

**⁶⁷**

**+ 67) is divided by 68?**

1 | |

63 | |

66 | |

67 |

Question 2 |

**Which of the following numbers will completely divide (49¹⁵ − 1) ?**

8 | |

14 | |

48 | |

50 |

Question 3 |

**What will be the remainder when 17²⁰⁰ is divided by 18 ?**

17 | |

16 | |

1 | |

2 |

Question 4 |

**Which one of the following is the common factor of (47⁴³ + 43⁴³) and (47⁴⁷ + 43⁴⁷) ?**

(47 − 43) | |

( 47 + 43) | |

(47⁴³ + 43⁴³) | |

none of these |

Question 5 |

**It is being given that (2³² + 1) is completely divisible by a whole number. Which of the following numbers is completely divisible by this number ?**

(2¹⁶ + 1 ) | |

(2¹⁶ − 1) | |

7 × 2³³ | |

(2⁹⁶ + 1) |

Question 6 |

**Which one of the following numbers will completely divide (4⁶¹ + 4⁶² + 4⁶³ + 4⁶⁴) ?**

3 | |

10 | |

11 | |

13 |

Question 7 |

**Which one of the following numbers will completely divide (3²⁵ + 3²⁶ + 3²⁷ + 3²⁸) ?**

11 | |

16 | |

25 | |

30 |

Question 8 |

**A 3-digit number 4**

*a*3 is added to another 3-digit number984 to give a 4-digit number 13*b*7, which is divisible by 11. Then, (*a*+*b*) = ?10 | |

11 | |

12 | |

15 |

Question 9 |

**If the number 653**

*xy*is divisible by 90, then (*x*+*y*) = ?2 | |

3 | |

4 | |

6 |

Question 10 |

**A number when divided by successively by 4 and 5 leaves remainders 1 and 4 respectively. When it is successively divided by 5 and 4, then the respective remainders will be**

1,2 | |

2,3 | |

3,2 | |

4,1 |

Question 11 |

**A number was divided successively in order by 4,5 and 6. The remainders were respectively 2,3 and 4. The number is**

214 | |

476 | |

954 | |

1908 |

Question 12 |

**In dividing a number by 585, a student employed the method of short division. He divided the number successively by 5, 9 and 13 (factors of 585) and got the remainders 4,8,12 respectively. If he had divided the number by 585, the remainder would have been**

24 | |

144 | |

292 | |

584 |

Question 13 |

**When a number is divided by 13, the remainder is 11. When the same number is divided by 17, the remainder is 9. What is the number ?**

339 | |

349 | |

369 | |

data inadequate |

Question 14 |

**A number when divided by 296 leaves 75 as remainder. When the same number is divided by 37, the remainder will be :**

1 | |

2 | |

8 | |

11 |

Question 15 |

**A boy multiplied 987 by a certain number and obtained 559981 as his answer. If in the answer both 98 are wrong and the other digits are correct, then the correct answer would be :**

553681 | |

555181 | |

555681 | |

556581 |

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