SSC CGL Exam > SSC CGL Questions > If the number 678967# is exactly divisible b...
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If the number 678967# is exactly divisible by 72, the minimum value of # is:
- a)1
- b)3
- c)2
- d)4
Correct answer is option 'C'. Can you explain this answer?
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Most Upvoted Answer
If the number 678967# is exactly divisible by 72, the minimum value o...
Given:
The number 678967# is exactly divisible by 72
Concept used:
If the number is divisible by 72 that means it has to be divisible by 8 and 9 as these are the two factors of 72.
Divisibility rules of 8 : when the number made by last three digits of a number is divisible by 8 then the number is also divisible by 8. Apart from this if the last 3 or more digits of a number are zero then the number is divisible by 8.
Divisibility rules of 9 : when the sum of all the digits of a number is divisible by 9 then the number is also divisible by 9.
Calculations:
The number is 678967#, so if we apply the divisibility rules of 8, the last 3 digits have to be divisible by 8.
Now, 67# has to be divisible by 8, so if we put 2 in place # it becomes 672 which is divisible by 8.
Again, applying divisibility rules of 9, by adding all the numbers = 6 + 7 + 8 + 9 + 6 + 7 + # = 43 + #
So, if we take 2 again in place of # the sum of the numbers become = 45 which is divisible by 9.
Thus, two rules satisfies the condition and the number is 2.
∴ The answer is 2.
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If the number 678967# is exactly divisible by 72, the minimum value o...
Divisibility Rule of 72:
To determine if a number is divisible by 72, we need to check if it is divisible by both 8 and 9.
Divisibility Rule of 8:
A number is divisible by 8 if the last three digits of the number are divisible by 8.
Divisibility Rule of 9:
A number is divisible by 9 if the sum of its digits is divisible by 9.
Finding the Minimum Value of #:
Given number: 678967#
Step 1:
Check divisibility by 8:
The last three digits of the number are 967#. To find if this number is divisible by 8, we need to check if 967# is divisible by 8.
By trial and error, we find that # = 2 satisfies the divisibility by 8 (968 is divisible by 8).
Step 2:
Check divisibility by 9:
The sum of the digits of the number is 6+7+8+9+6+7+# = 43+#.
For the sum to be divisible by 9, the minimum value of # should be such that 43+# is divisible by 9.
By trial and error, we find that # = 2 satisfies the divisibility by 9 (45 is divisible by 9).
Conclusion:
Therefore, the minimum value of # that makes the number 6789672 divisible by 72 is 2. So, the correct answer is option 'C' (2).
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If the number 678967# is exactly divisible by 72, the minimum value of # is:a)1b)3c)2d)4Correct answer is option 'C'. Can you explain this answer?
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