Seven students: P, Q, R, S, T and V.
Different test dates: 1st, 5th, 6th, 7th, 8th and 10th.
From statement I:
The one, whose test is on 8th November is taller than only one person. P is the tallest among all and has test on 10th November. Q is taller than those, whose tests are on 7th and 1st November.
From the given information,
P(10th) > _ > _ > _ > _(8th) > _.
Q’s test cannot be on 1st, 7th, 8th and 10th November.
So, statement I alone is not sufficient.
From statement II:
The difference in the test dates of Q and T is 2. R’s test is on odd date. S is taller than Q and V.
From the given information,
The test dates of Q and T are 5th and 7th November but not necessarily in the same order or 6th and 8th November but not necessarily in the same order. R’s test is on odd date i.e. 1st, 5th or 7th November.
So, statement II alone is not sufficient.
From statement III:
T is not the shortest. Q’s test is just before S’s test. S’s test is not on any prime date.
From the given information,
S’s test can be on 5th, 6th, 8th or 10th November.
So, statement II alone is not sufficient.
On combining I and II,
From the given information,
We get three different possibilities,
(i) P(10th) > S() > Q(6th) > _ (1st) > T(8th) > _ (7th)
(ii) P(10th) > S() > Q(6th) > _ (7th) > T(8th) > _ (1st)
(iii) P(10th) > S(6th) > Q(5th) > T(7th) > V(8th) > R(1st)
So, we cannot determine exactly that whose test is on 6th November and who is the shortest.
On combining I and III,
From the given information,
We get two different possibilities,
(i) P(10th) > _ > Q() > _(1st/7th) > _ (8th) > _ (7th/1st)
(ii) P(10th) > Q()> _ > _ > _(8th) > _
So, we cannot determine exactly that whose test is on 6th November and who is the shortest.
On combining II and III,
From the given information,
_ > _ > _ > _ > _ >_(**×**T)
So, we cannot determine exactly that whose test is on 6th November and who is the shortest.
Combining all statements together we get:
P(10th) > S(6th) > Q(5th) > T(7th) > V(8th) > R(1st)
So, S has test on 6th November and R is the shortest.
Hence, the data in statement I, II and III together are required to answer the question.