Playing with Numbers Test

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Playing with Numbers Test - 3

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Weekly Quiz Competition

Question 1
1 / -0

The number(10ⁿ−1)is divisible by 11 for____.

A
n ∈ N

B
Odd values of n

C
Even values of n

D
n is the multiple of 11

Solution

(10n−1) is divisible by 11 for even values of n as 10² − 1 = 99,
104−1=9999, 106−1=999999 etc.,
are divisible fay 11.
Question 2
1 / -0

The greatest value that must be given to x so that the number 7713x8 is divisible by 4 is______.

A
1

B
6

C
8

D
7

Solution

7713x8 is divisible by 4 if ifs last two digits is divisible by 4.

So, we have x8 to be divisible by 4.

Therefore, greatest value of x is 8.
Question 3
1 / -0

Suppose that the division N÷5 leaves a remainder of 4 and the division N÷2 leaves a remainder of 1. What must be the ones digit of N?

A
7

B
3

C
9

D
4

Solution
Question 4
1 / -0

Given that the number 148101a095 is divisible by 11, where a is single digit number, what are the possible values of a?

A
4

B
1

C
7

D
9

Solution

If 148101a095 is divisible by 11,
then (1+8+0+a+9)−(4+1+1+0+5) is either 0 or a multiple of 11
⇒ (a+18)−11 is either 0 or a multiple of 11
⇒ a+7=0 or a multiple of 11
∴ a+7=11
⇒a=4
Question 5
1 / -0

The largest natural number by which the product of three consecutive even natural numbers is always divisible, is ______.

A
16

B
24

C
48

D
96

Solution

The required number would be the product of three smallest even natural number i.e. 2 × 4 × 6 = 48.
Question 6
1 / -0

If in a number, difference between the sum of digits at its odd places and that of digits at the even places is given 0, then the number is divisible by _____.

A
7

B
9

C
5

D
11
Question 7
1 / -0

A 5-digit number xy235 is divisible by 3 such that x + y < 5, where x and y are single digits, then possible values of (x, y) are _____.

A
(1, 1) or (4, 0)

B
(1, 1) or (2, 0)

C
(1, 1) or (0, 2)

D
(2, 0) or (0, 2)

Solution

xy235 is divisible by 3 so sum of its digits is also divisible by 3,
∴ x + y + 2 + 3 + 5 = x + y + 10 is divisible by 3 and x + y < 5.
So possible values of (x, y) are (1, 1) or (2, 0),

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Re-Attempt Weekly Quiz Competition

Playing with Numbers Test - 3

Result

Playing with Numbers Test - 3

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SHARING IS CARING

Question 1

n ∈ N

Odd values of n

Even values of n

n is the multiple of 11

Solution

Question 2

1

6

8

7

Solution

Question 3

7

3

9

4

Solution

Question 4

4

1

7

9

Solution

Question 5

16

24

48

96

Solution

Question 6

7

9

5

11

Question 7

(1, 1) or (4, 0)

(1, 1) or (2, 0)

(1, 1) or (0, 2)

(2, 0) or (0, 2)

Solution

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