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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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