Each of the questions below consists of a question and two statements numbered I and II given below it. You have to decide whether the data provided in the statements are sufficient to
answer the question. Read both the statements and answer the below questions
a: if the data in Statement I alone are sufficient to answer the question, while the data in Statement II alone are not sufficient to answer the question.
b: if the data in Statement II alone are sufficient to answer the question, while the data in Statement I alone are not sufficient to answer the question.
c: if the data either in Statement I alone or in Statement II alone are sufficient to answer the question.
d: if the data even in both Statements I and II together are not sufficient to answer the question.
e: if the data in both Statements I and II together are necessary to answer the question.
Who amongst the six friends M, N, 0, P, Q and R - is the heaviest?
I. O is heavier than only two friends. P is heavier than Q. P is lighter than N.
II. M is lighter than only two friends. N is heavier than O. N is lighter than R. P is heavier than Q.
Let us give ranks to the 6 friends, where 1 -> heaviest and 6 -> lightest.
I : O is heavier than only two friends, => O = 4
P is heavier than Q and P is lighter than N, => N > P > Q
But, there is no information about R and M. So, we cannot determine who is the heaviest.
Thus, I alone is insufficient.
II : M is lighter than only two friends, => M = 3
N is heavier than O and N is lighter than R, => R > N > O
Here, also the same problem arises.
Thus, II alone is insufficient.
I & II : Combining the above statements, we get :
M = 3 and O = 4
Since, R > N > O, => R = 1 and N = 2
Also, P > Q, => P = 5 and Q = 6
$$\therefore$$ R > N > M > O > P > Q
R is the heaviest.
Thus, I & II together are sufficient.
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