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At a mathematics competition, a professor gives a new definition that a number is called 'defector' if it is impossible to factorise the given number. He then calls a number 'super defector' if the number formed by breaking the number into as many possible smaller numbers ( without re-ordering) and all the numbers so formed are defectors. For example, 123 can be broken into 1, 2, 3, 12, 23 and 123. Note that 13, 32, 21, 31 etc. are not involved.
How many 3-digit numbers are 'super defectors'?
  • a)
    21
  • b)
    19
  • c)
    13
  • d)
    8
Correct answer is option 'D'. Can you explain this answer?
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Most Upvoted Answer
At a mathematics competition, a professor gives a new definition that...
Let abc be a 3-digit 'super defector' number.So, a, b, c, ab, be and abc are all defectors, a, b and c are prime numbers, b and c cannot be 2 and 5. a, b and c can also take value 1. Values of 'ab' such that ab' is a defector are: 11, 13, 17, 23, 31, 37, 53, 71, 73
For abc to be a 3-digit 'super defector' number, values that c can take for various cases is given below: ab - 11 => c - 3 ab = 13 => c = 1, 7 ab = 17 => c = 3 ab = 31 => c = 1, 3, 7 ab = 37 => c = 3 For ab = 23, 53, 71 and 73, there is no possible value of c for which abc will be a 3-digit 'super defector' number.
Thus, we have 8 such numbers. Hence, option 4.
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At a mathematics competition, a professor gives a new definition that a number is called 'defector' if it is impossible to factorise the given number. He then calls a number 'super defector' if the number formed by breaking the number into as many possible smaller numbers ( without re-ordering) and all the numbers so formed are defectors. For example, 123 can be broken into 1, 2, 3, 12, 23 and 123. Note that 13, 32, 21, 31 etc. are not involved.How many 3-digit numbers are 'super defectors'?a)21b)19c)13d)8Correct answer is option 'D'. Can you explain this answer?
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