According to Vijay’s mother. Vijay reached Mumbai after 13th January, 2013 but before 19th January, 2013. According to Vijay, he reached Mumbai after 16th January, 2013 but before 22nd January, 2013. If both are correct then on which date Vijay reached Mumbai ?

According to Vijay’s mother, Vijay reached Mumbai after 13th January, 2013 but before 19th January, 2013

=> Date at which Vijay reached Mumbai (Jan, 2013) = {14,15,16,17,18}

According to Vijay, he reached Mumbai after 16th January, 2013 but before 22nd January, 2013

=> Date at which Vijay reached Mumbai (Jan, 2013) = {17,18,19,20,21}

Since both of them correct, thus correct  date on which Vijay reached Mumbai is the intersection of both sets

= 17 or 18 January

Still, we cannot conclude to a specific date, thus the correct data cannot be determined.

=> Ans - (E)