Monday, 12 October 2015

Reasoning
Who is the Liar?

The problems based on truth and lie or Sacha and Jhuta are very common in CAT and similar exams. You will be able to understand the related concepts better with the help of the following example.
Example 1:
In an isolated island there live two tribes:
  • SACHAS
  • JHUTAS
The SACHAS always speak the truth, whereas the JHUTAS never do.
One day SUNIL, a stranger in the island, met four tribesmen. He asked one of them whether the second was a SACHA or a JHUTA. The reply was JHUTA. Similarly, the second tribesman said that the third was a JHUTA and the third said the same about the fourth.
When he asked the fourth as to what would the first tribesman have said about the third, the reply once again was JHUTA. Who’s who?

Solution:
Before solving this question, here are some important deductions that you can make.
1. If you asked the question to any tribesman ‘Are you a “SACHA” or a “JHUTA”?’ from that island irrespective of the tribe he belongs to, his reply would always be ‘SACHA’, because
  • if he were a ‘SACHA’, he will always speak the truth about himself, that he belongs to ‘SACHA’ tribe and
  • if he were a ‘JHUTA’ he will lie about his actual tribe and, say that he belongs to ‘SACHA’ tribe.
2. If two tribesmen, A & B, belong to the same tribes, either both ‘SACHAS’ or both ‘JHUTAS’, and you asked the question from A ‘Is B a “SACHA” or a “JHUTA” ?’, his reply will always be ‘SACHA’, because
  • If they were belongs to ‘SACHA’ tribe then they always speak the truth, that other one belongs to ‘SACHA’ tribe and
  • if both belongs to ‘JHUTA’ tribe then they always lie about themselves as well as about others, and would say that other belongs to ‘SACHA’ tribe.
3. If two tribesmen, A & B belong to different tribes and you asked the question from A ‘Is B a “SACHA” or a “JHUTA”?’, his reply will always be ‘JHUTA’, because
  • if A is ‘SACHA’ then he is speaking the truth about B, and answering that B is ‘JHUTA’ or
  • if A is ‘JHUTA’ then he is telling alie about B, and answering that B is ‘JHUTA’
Note: In conclusion, we can say that,if two persons belong to same tribe they will always say ‘SACHA’ about other and if two belongs to different tribe always say ‘JHUTA’ about the other.
  1. Now, coming back to the problem:
  2. As the first tribesman told Sunil, that the second was a ‘JHUTA’, it means that first & second tribesmen belonged to different tribes.Similarly, the second and third tribesmen were also from different tribes.
  3. Moreover, the third and fourth tribesmen were also from different tribes, and
  4. But as there are only two tribes, it implies that the first and third belonged to the same tribe eitherboth ‘SACHAS’ or both‘JHUTAS’, and the second and fourth also belonged to the same tribe either both ‘JHUTAS’ or both ‘SACHAS’.
  5. When Sunil asked from the fourth tribesman‘what would the first tribesman have said about the third?’, we know from the second point mentioned above, that the answer given by third would always be Sacha, as they belong to the same tribe. But as you asked this question from the fourth person, he will also manipulate the answer as per HIS OWN TRIBE. The fourth said ‘Jhoota’.
  6. It means the fourth tribesman, himself must be a ‘JHUTA’ because if he belongs to tribe ‘SACHA’  then his reply would be‘SACHA’, as he know that fist and third tribes belongs to same tribe and same tribe always say ‘SACHA’ about other.
  7. Hence, the first and third tribesmen were both ‘SACHAS’ and the second and fourth were both ‘JHUTAS’.

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