61). Which of the following numbers always divides the difference between the squares of two consecutive odd integers?
A). 7
B). 3
C). 8
D). 6
View Answer
Correct Answer: 8
Let the two consecutive odd numbers be
(2x + 1) and (2x + 3).
Difference = \( \Large (2x+3)^{2}-(2x+1)^{2} \)
= (2x+3+2x+1)(2x+3-2x-1)
= \( \Large (4x+4)\times 2 \)=8(x+1),
which is exactly divisible by 8.
62). A number divided by 56 gives 29 as remainder. If the same number is divided by 8, the remainder will be
A). 4
B). 5
C). 6
D). 7
View Answer
Correct Answer: 5
Let the number be x.
According to the question,
x = 56k + 29
Then,
x = \( \Large (8\times 7k)+(8\times 3)+5 \)
= \( \Large 8\times (7k+3)+5 \)
Therefore, when x is divided by 8 the required remainder = 5
63). A number when divided by a divisor leaves a remainder of 24. When twice the original number is divided by the same divisor, the remainder is 11. What is the value of the divisor?
A). 13
B). 59
C). 35
D). 37
View Answer
Correct Answer: 37
Let the divisor be x and quotient be y.
Then, number = xy + 24
Twice the number = 2xy + 48
Now, 2xy is completely divisible by x.
On dividing 48 by x remainder is x.
x = 48-11=37
64). The number 58129745812974 is divisible by
A). 11
B). 8
C). 4
D). None of these
View Answer
Correct Answer: 11
We know that, a number is divisible by 11 when the difference between the sum of its digit at even places and sum of digit at odd places is either 0 or the difference is divisible by 11.
So, number is 58129745812974
Sum of digits at odd places
=4+9+1+5+7+2+8=36
Sum of digit at even places
7+2+8+4+9+1+5=36
So, the required difference = 36 - 36 = 0
The number is divisible by 11.
65). How many numbers between - 11 and 11 are multiples of 2 or 3?
A). 11
B). 14
C). 15
D). None of these
View Answer
Correct Answer: 14
Following are the numbers between - 11 and 11 which are multiples of 2 or 3?
-10,-9,-8,-6,-4,
-3, -2, 2, 3, 4, 6, 8, 9, 10.
The numbers of multiples 2 or 3, between
-11 and 11 are 14.
66). Which one of the following numbers is divisible by 11?
A). 45678940
B). 54857266
C). 87524398
D). 93455120
View Answer
Correct Answer: 93455120
we know that, if the difference between the sum of digits at even places
and sum of digits at odd places is (0), then the number is divisible by 11.