(i) There is a group of five girls.
(ii) Kamini is second in height but younger than Rupa.
(iii) Pooja is taller than Monika but younger in age.
(iv) Rupa and Monika are of the same age but Rupa is tallest between them.
(v) Neelam is taller than Pooja and elder Rupa.
To answer the question "who is the youngest person in the group", which of the given statements is superfluous ?
Answer: A
We first find the sequence of height :
By (iii), we have : M < P.
By (v), we have : P < N.
Now, Rupa is tallest and Kamini is is second in height.
So, the sequence of heights is : M < P < N < K < R.
Now, we determine the age sequence :
By (ii), we have : K < R.
By (iii), we have : P < M.
By (iv), we have : R = M.
By (v), we have : R < N.
So, the sequence of ages is : N < R = M < K < P or N < R = M < P < K.
Clearly, only statement (i) is not necessary.
Hence, the answer is (a).
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All the roads of a city are either perpendicular or parallel to one another. The roads are all straight. Roads A, B, C, D and E are parallel to one another. Roads G, H, I, J, K, L and M are parallel to one another.
(i). Road A is 1 km east of road B.
(ii). Road B is ½ km west of road C.
(iii). Road D is 1 km west of road E.
(iv). Road G is ½ km south of road H.
(v). Road I is 1 km north of road J.
(vi). Road K is ½ km north of road L.
(vii). Road K is 1 km south of road M. Which is necessarily true ?
Answer: D
Clearly from statements (1) and (2), figure 1 follows; from statement (3), figure 2 follows; from statement (4), figure 3 follows; and from statement (5), figure 4 follows; and from statements (6) and (7), figure 5 follows.
It follows from figure 5 that distance of M from L = LK + KM = ½ + 1 = 1.5 km and M is to the north of L.
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