Series Problem Logical Reasoning – Page 6

Series 6

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 Question 1
What will be the remainder when (67⁶⁷ + 67) is divided by 68?
 A 1 B 63 C 66 D 67
 Question 2
Which of the following numbers will completely divide (49¹⁵ − 1) ?
 A 8 B 14 C 48 D 50
 Question 3
What will be the remainder when 17²⁰⁰ is divided by 18 ?
 A 17 B 16 C 1 D 2
 Question 4
Which one of the following is the common factor of (47⁴³ + 43⁴³) and (47⁴⁷ + 43⁴⁷) ?
 A (47 − 43) B ( 47 + 43) C (47⁴³ + 43⁴³) D 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 ?
 A (2¹⁶ + 1 ) B (2¹⁶ − 1) C 7 × 2³³ D (2⁹⁶ + 1)
 Question 6
Which one of the following numbers will completely divide (4⁶¹ + 4⁶² + 4⁶³ + 4⁶⁴) ?
 A 3 B 10 C 11 D 13
 Question 7
Which one of the following numbers will completely divide (3²⁵ + 3²⁶ + 3²⁷ + 3²⁸) ?
 A 11 B 16 C 25 D 30
 Question 8
A 3-digit number 4a3 is added to another 3-digit number984 to give a 4-digit number 13b7, which is divisible by 11. Then, (a + b) = ?
 A 10 B 11 C 12 D 15
 Question 9
If the number 653 xy is divisible by 90, then (x + y) = ?
 A 2 B 3 C 4 D 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
 A 1,2 B 2,3 C 3,2 D 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
 A 214 B 476 C 954 D 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
 A 24 B 144 C 292 D 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 ?
 A 339 B 349 C 369 D 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 :
 A 1 B 2 C 8 D 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 :
 A 553681 B 555181 C 555681 D 556581
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