Playing with Numbers Test

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Playing with Numbers Test - 3

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Weekly Quiz Competition

Question 1
1 / -0

For what value(s) of N is the number N(10²⁰- 1) divisible by 9?

A
Any natural number

B
Only odd values of N

C
Only even values of N

D
Only if N is multiple of 9

Solution

N(10²⁰ - 1) is divisible by 9 for every natural number (n) as:

10¹ - 1 = 9
10²- 1 = 99
10³ - 1 = 999
...
...
...

10²⁰ - 1 = 999 ..., etc. are divisible by 9.
Question 2
1 / -0

Which of the following numbers is divisible by 8?

A
21,61,316

B
15,41,418

C
13,21,532

D
11,11,640

Solution

According to the divisibility rule of 8, if the number formed by the last three digits is divisible by 8, it means the entire number is divisible by 8.

Option 1: 21,61,316 - 316 is not divisible by 8.
Option 2: 15,41,418 - 418 is not divisible by 8.
Option 3: 13,21,532 - 532 is not divisible by 8.
Option 4: 11,11,640 - 640 is divisible by 8.
Question 3
1 / -0

When an integer k is divided by 6, the remainder is 2. What will be the remainder if 8k is divided by 6?

A
7

B
3

C
9

D
4

Solution

When k is divided by 6, the remainder will be 2.
It can be written as:

k = 6n + 2; where k is the number and n is the quotient.
Multiply all terms by 8.

8k = 8(6n + 2) = 6(8n) + 16
Write 16 as 12 + 4 since 12 = 6 × 2.

8k = 6(8n) + 12 + 4
8k = 6(8n + 2) + 4

The above equation indicates that if 8k is divided by 6, the remainder will be 4.
Question 4
1 / -0

Which of the following can be the values of x and y in 8754x15y4 if it is divisible by 11?

A
x = 3 and y = 2

B
x = 7 and y = 2

C
x = 3 and y = 3

D
x = 4 and y = 2

Solution

If the difference between the sum of the digits at odd places and the sum of the digits at even places is 0 or 11, then the number will be divisible by 11.
Now, (8 + 5 + x + 5 + 4) - (7 + 4 + 1 + y) = 0 or 11

Using option: x = 3 and y = 2;
25 - 14 = 11
Question 5
1 / -0

The largest number by which the product of any four consecutive odd natural numbers is always divisible is ___.

A
9

B
7

C
5

D
3

Solution

When considering four consecutive odd numbers, i.e. (3, 5, 7, 9) or (23, 25, 27, 29) or (107, 109, 111, 113), one of the four numbers would always be a multiple of 3 as every third odd number is a multiple of 3. If we think about 5, every fifth odd number is a multiple of 5 and hence it is not always possible that the product of four consecutive odd numbers is divisible by 5.

Hence, the product of any four consecutive odd numbers will always be divisible by 3 and 1 only.

Hence, the required number is 3.
Question 6
1 / -0

If the total of all the digits in a number is 9 or any multiple of 9, then the number is definitely divisible by

A
18

B
9

C
6

D
27

Solution

In a number, if the total of all the digits is 9 or any multiple of 9, then the number is definitely divisible by 9. (Divisibility rule of 9)
E.g. 9297

Sum of the digits = 9 + 2 + 9 + 7 = 27 (which is a multiple of 9)

Hence, 9297 is divisible by 9.
Question 7
1 / -0

A 6-digit number ab9698 is divisible by 9 such that a + b < 6, where a and b are single-digit numbers. Find the possible values of a and b.

A
a = 1 and b = 2

B
a = 2 and b = 1

C
a = 2 and b = 2

D
a = 2 and b = 3

Solution

When the total of all the digits is divisible by 9, then the number is divisible by 9.
ab9698

a + b + 9 + 6 + 9 + 8 = a + b + 32
Putting a = 2 and b = 2,

2 + 2 + 32 = 36
2,29,698 is divisible by 9.

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Re-Attempt Weekly Quiz Competition

Playing with Numbers Test - 3

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Playing with Numbers Test - 3

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SHARING IS CARING

Question 1

Any natural number

Only odd values of N

Only even values of N

Only if N is multiple of 9

Solution

Question 2

21,61,316

15,41,418

13,21,532

11,11,640

Solution

Question 3

7

3

9

4

Solution

Question 4

x = 3 and y = 2

x = 7 and y = 2

x = 3 and y = 3

x = 4 and y = 2

Solution

Question 5

9

7

5

3

Solution

Question 6

18

9

6

27

Solution

Question 7

a = 1 and b = 2

a = 2 and b = 1

a = 2 and b = 2

a = 2 and b = 3

Solution

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