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A house has a number which need to be identified. The following three statements are given that can help in identifying the house number?

  1. If the house number is a multiple of $3$, then it is a number from $50$ to $59$.
  2. If the house number is NOT a multiple of $4$, then it is a number from $60$ to $69$.
  3. If the house number is NOT a multiple of $6$, then it is a number from $70$ to $79$.

What is the house number?

  1. $54$
  2. $65$
  3. $66$
  4. $76$
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Migrated from GO Mechanical 4 years ago by Arjun

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We can eliminate options to get answer, but complete procedure-

Case 1:If house number is out of range 50-79, then

  • Number has to be Multiple of 4 and 6 
  • Number must NOT be multiple of 3

 But any number which is multiple of 6 will be multiple of 3.Hence no number out of range 50-79 satisfies required conditions.

Case 2:If house number is in range 50-59, then

  • Number has to be Multiple of 4   =>52,56 are possible
  • Number has to be Multiple of 6   =>both 52 and 56 fails.

Hence no number in range 50-59 satisfies required conditions.

Case 3:If house number is in range 60-69, then

  • Number has to be Multiple of 6    =>60,66 are possible
  • Number must NOT be multiple of 3  =>both 60 and 66 fails

Hence no number in range 60-69 satisfies required conditions.            

Case 4:If house number is in range 70-79, then

  • Number has to be Multiple of 4  =>72 and 76 are possible
  • Number must NOT be multiple of 3     =>72 fails

Hence only House number satisfying all the conditions is ‘76’.

Answer:option D. 76

Answer:

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