P, Q, R, S, T and U are six friends. Which of the following is/are sufficient to compare heights of S and T ? 1. R is shorter than P but taller than other friends. 2. U is taller than Q but shorter than S although Q is not the shortest among the friends. Select the correct answer using the code given below :
- (a)1 alone is sufficient
- (b)2 alone is sufficient
- (c)Both 1 and 2 are not sufficient
- (d)1 and 2 together are sufficient
Correct — D, (d) 1 and 2 together are sufficient. Test each statement alone first, then together — that is the whole discipline of a data-sufficiency item, and skipping the first half is how candidates lose them. Statement 1 alone. 'R is shorter than P but taller than other friends' gives P > R > each of Q, S, T and U. It fixes the top two places and says nothing whatever about how the remaining four rank among themselves. S and T are both merely somewhere below R. Not sufficient. Statement 2 alone. 'U is taller than Q but shorter than S' gives S > U > Q. The clause 'Q is not the shortest' tells us somebody stands below Q, but taken by itself statement 2 never mentions T at all — T could be the tallest of all six, or the shortest. Not sufficient. Both together. Statement 1 places P and R above every other friend, so P > R > {Q, S, T, U}. Statement 2 orders three of those four: S > U > Q. Now apply the clause that looks like decoration. Q is not the shortest, so at least one friend is shorter than Q — and we can name every friend who is not: P and R are above Q by statement 1, and S and U are above Q by statement 2. The only person left who can be below Q is T. Therefore T < Q, and the full order is P > R > S > U > Q > T. S is taller than T, so the comparison the question asks for is settled. Sufficient. Notice how the two statements interlock. 'Q is not the shortest' is useless on its own — it merely says someone is below Q. It becomes decisive only once statement 1 has exhausted the other candidates, leaving T as the only person the clause can be referring to. That is the mark of a well-built 'together' answer: neither statement is redundant, and the combination does something neither could do alone.
- (a)1 alone is sufficient — Statement 1 puts S and T in the same undifferentiated bucket — 'other friends', all of them shorter than R. It orders the top of the list and leaves the bottom four completely unranked, which is precisely the part of the list the question asks about. Sufficient for 'who is tallest', useless for 'S or T'.
- (b)2 alone is sufficient — Statement 2 never names T. It gives S > U > Q and adds that somebody is below Q, but that somebody could be P, R or T, and nothing bars T from standing above S. With T unplaced, S and T cannot be compared. This is the option for a candidate who reads 'Q is not the shortest' as though it said 'T is the shortest', which is a conclusion available only after statement 1 has been used.
- (c)Both 1 and 2 are not sufficient — Read against option (d), this option has to mean that even the two statements taken together fail — and they do not, since together they yield the complete order P > R > S > U > Q > T. On its own the printed phrasing is ambiguous English, since 'both 1 and 2 are not sufficient' could also be read as the true statement that neither is individually sufficient. The option set resolves the ambiguity: (d) is the 'together works' option, so (c) must be the 'together still fails' option, and that is false here.
Data sufficiency asks whether the information given is enough to answer a question, not what the answer is. The method is fixed and worth following mechanically: evaluate statement 1 alone, evaluate statement 2 alone, and only then evaluate them together, never letting knowledge from one leak into the assessment of the other. Underneath, this particular item is a linear-arrangement puzzle in which every clause is a constraint on one chain. The technique for those is to write the chain out with the strongest constraint first — here statement 1 fixes the top two — and then to slot the remaining people in, treating negative clauses like 'is not the shortest' as elimination instructions rather than as facts about position.
The EO/AO reasoning block mixes arrangement puzzles, sequences and data sufficiency, and the sufficiency items are the ones that reward discipline over speed. The trap in this question is not the arithmetic of the ordering, which is easy, but the temptation to assess the statements jointly from the start — a candidate who reads both and immediately builds the full chain will get the right order and then have no principled way of choosing between options (a), (b) and (d). The habit rewarded is the separation of the three tests.
- Statement 1 gives P > R > Q, S, T, U — it fixes the top two places only.
- Statement 2 gives S > U > Q and asserts that Q is not the shortest.
- Combined, the only friend who can be shorter than Q is T, because P and R are above Q by statement 1 and S and U by statement 2.
- The resulting complete order is P > R > S > U > Q > T.
- S > T, so the two statements together answer the question and neither does so alone.
- Data-sufficiency method: test statement 1 alone, then statement 2 alone, then both together, in that order and without carrying information between the first two tests.
- A negative clause such as 'X is not the shortest' is an elimination instruction; its value depends entirely on how many candidates the other statements have already removed.
- Building the combined chain first and then trying to work backwards to judge each statement alone.
- Treating 'Q is not the shortest' as though it identified who the shortest is. It only says it is not Q.
- Assuming a statement that mentions neither of the two people being compared can still settle the comparison. Statement 2 never mentions T.
- Misreading option (c). Against option (d) it must mean 'not sufficient even together', not 'neither is sufficient alone'.
The reasoning block runs five items at a time, three or four times through the paper, and the puzzle types repeat: ranking, circular seating, blood relations, sequences and data sufficiency. They are the fastest marks in the paper for a prepared candidate, since none of them requires outside knowledge — only a method applied without shortcuts.
No directly related past PYQ was found.
- practice — not a real PYQ
A, B, C, D and E are five friends. Which of the following is/are sufficient to compare the heights of C and E ? 1. A is taller than B but shorter than C. 2. D is shorter than B, and E is the tallest of the five.
- (a)1 alone is sufficient
- (b)2 alone is sufficient
- (c)Neither 1 nor 2 is sufficient
- (d)1 and 2 together are needed
Answer(b) 2 alone is sufficient
- practice — not a real PYQ
P, Q, R, S and T are five friends. R is taller than P and shorter than Q. T is shorter than P. S is taller than Q. Who among them is the tallest ?
- (a)P
- (b)Q
- (c)R
- (d)S
Answer(d) S