Question

Sonal, a mathematician defines a number as 'connected by 6' if it is divisible by 6, or if the sum of digits is 6, or if 6 is one of the digits of the number. Other numbers are 'not connected by 6'. As per the definition, the number of integers, from 1-60 (both inclusive) which are not connected with 6 is

• A. 18
• B. 43
• C. 22
• D. 42

Answer 1

The Correct Option is B

To find the number of integers from 1 to 60 that are not 'connected by 6', we identify the numbers that are 'connected by 6' as per Sonal's definition. An integer is 'connected by 6' if it:

• is divisible by 6
• has digits that sum to 6
• contains the digit 6

Let's consider each condition:

• Divisible by 6:Numbers within 1 to 60 that are divisible by 6 are: 6,12,18,24,30,36,42,48,54,60.
• Sum of digits equals 6: For this, we sum each number's digits:
  • 6, 15 (1+5), 24 (2+4), 33 (3+3), 42 (4+2), 51 (5+1).
• Contains the digit 6: These include: 6,16,26,36,46,56.

Next, we compile a list of unique numbers from these conditions:

6

12

15

16

18

24

26

30

33

36

42

46

48

51

54

56

60

Counting these gives us 17 numbers that are 'connected by 6'. Therefore, the numbers not 'connected by 6' are calculated as follows:

Total numbers from 1 to 60: 60

Numbers 'connected by 6': 17

So, numbers not 'connected by 6': 60 - 17 = 43.

The correct answer is 43.