IQ Test
Vikram and Muthu befriended a girl. Asks her what is her birthday. She does not give a straight forward answer, but some hints
She gives them the following 10 dates to pick the right one from
May: 15, 16, 19
June: 17, 18
July: 14, 16
August: 14, 15, 17
She disclosed correct month to Vikram alone and correct date to Muthu.
Asks Vikram to guess the right birthday. He says sorry I can't, but I am sure even Muthu won't be able to guess it right.
Now Muthu says, I was a bit confused but with Vikram's statement, I know what is her birthday.
Now Vikram says if that is the case, I also know what is it.
Both guessed it right. Use simple logic to guess the right birthday. Go ahead
Answers
Given : list of 10 Dates . and month told to Vikram and date told to Muthu
To find : Exact Date of Birth
Solution:
Dates
MAY 15 , 16 19
JUNE 17 , 18
JULY 14 ,16
AUGUST 14 , 15 , 17
Vikram knows month only so Vikram does not know the correct date of birth as each month has more than one date
But Vikram say Muthu also do not know the correct date of birth
hence the Month known to Vikram does not have unique date ( which is only in a particular month like 18th june & 19th May)
hence MAY & JUNE can not be Month
So now Muthu knows that
Month is JULY or AUGUST only ( which was not known to him earlier)
14 Can not be date as then Muthu would not know which month ( July or august)
Hence possible date are 16 JULY , 15 AUGUST & 17 AUGUST
but now Vikram says he also know date of birth
it means month is not august as if it would have been august then Vikram could not know which date
Hence 16 JULY is the DOB
Her birthday on 16 July
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The way to solve this problem is to look carefully at the question and then work through each statement in turn and see what we can deduce from it.
From the question we know that Vikram has been told May, June, July or August.
Muthu has been told 14, 15, 16, 17, 18, or 19.
Vikram : I don't know when her birthday is, but I know that Muthu does not know too.
Muthu has been told the day of her birthday. There are only two days, 18 and 19 that appear once on her list. This means that her birthday cannot be May 19th or June 18th as if it was then Muthu would know the answer.
Remember that Vikram has been told a month and from the statement he knows that Muthu does not know the birthday. For Vikram to be certain that Muthu does not know her birthday, the month Vikram had been told must not have been May or June.
Therefore her birthday must fall in July or August.
Muthu: At first I don't know when her birthday is, but I know now.
Based on the above Muthu has worked out that birthday is in July or August.
If Muthu now knows her birthday the day he must have been told would be 15, 16 or 17. It cannot be 14 as this falls in both July and August and as such he wouldn't know her birthday for certain.
Vikram: Then I also know when her birthday is.
Based on the above Vikram has worked out that girl's birthday is one of the following:
July 16
August 15
August 17
If Vikram now knows for certain when her birthday is he must have been told the month of July, as if it was August there would be two possible options.
Therefore the answer is July 16.