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Question

What is the sum of house numbers of all the three X, Y and Z?



Your Answer
A

100

Correct Answer
B

200

Your Answer
C

128

Your Answer
D

Cannot be determined


Solution

The correct option is B

200


Paragraph 2Since X thinks that he has the answer to the house number of Z, he must have got 'yes' as an answer to both questions he asked. In such a case he would think that Z's number is one of 64or 81(the two 2 digit perfect squares which are greater than 50).Also, we can deduce that since he thinks that he knows the answer he must be living in one of the two houses. Hence, X's house number is either 64or 81.Paragraph 3By a similar logic,Y's house number  is either27or 64.Paragraph 4We know Z's house number is greater than 50but less than Y's and X's house numbers. Hence Y's number must  be64and X's number is 81. Also we get that  Z's number must be 55since (81+64+55) is the only addition that satisfies the condition of the sum of the three numbers to be double of a perfect square.

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