BPSC 69th CCE Prelims Q147: Read the given statement and conclusions carefully. Decide

Q: What is the answer to BPSC 69th CCE Prelims Q147?

D. Correct — D, Neither 1 nor 2 follows the statement. The rule in this family is that a conclusion follows only if it cannot be false while the statement is true, and each conclusion must be put through that test on its own. Take conclusion 1 first. The statement supplies two quantities, both of them runs: 200 in total and 160 by spinners. 160 out of 200 is indeed 80 per cent — but 80 per cent of the runs, not of the players. The conclusion silently moves that figure onto a different population. One counter-example is enough to defeat it: two spinners batting at numbers seven and eight could between them make all 160 runs, and two players out of an eleven-man side is 18 per cent, not 80. The conclusion is not even literally available, since 80 per cent of eleven is 8.8 players. Now conclusion 2. The statement never mentions the batting order at all — it records who scored the runs, not when they came in. Spinners occupying positions eight to eleven and scoring 160 between them is entirely consistent with everything the statement says, so the conclusion can be false while the statement is true. Note the exact reason it fails: not that it is untrue in the real match, but that the statement is silent, and silence is not support. Both conclusions fail the necessity test, so the answer is (d).

BPSC 69th CCE Prelims General Studies · Question 147 of 144

Verified against the official question booklet. Answer as per the official BPSC answer key.

Answers derived, not from the official key. BPSC published an answer key for BPSC 69th CCE at the time, but it is no longer available from the Commission or in any web archive. The answers here are our best-supported answers — solved from the question itself and cross-checked against primary sources — and each card says how certain it is. The question text is verbatim from the official booklet. These are not the Commission's answer key.

Question order, option order and answers follow the official BPSC Booklet Series A (booklet 201-A), paper code 19-C/FI/CC/PT-2023.

Read the given statement and conclusions carefully. Decide which of the given conclusions logically follow(s) from the statement. Statement : In a one-day cricket match, the total runs made by a team were 200, of which 160 runs were made by spinners. Conclusions : 1. 80% of the team consisted of spinners. 2. The opening batsmen were spinners. Select the correct answer.

(a)Only 1 follows the statement
(b)Only 2 follows the statement
(c)Both 1 and 2 follow the statement
(d)Neither 1 nor 2 follows the statement

Answer

Why

Correct — D, Neither 1 nor 2 follows the statement. The rule in this family is that a conclusion follows only if it cannot be false while the statement is true, and each conclusion must be put through that test on its own. Take conclusion 1 first. The statement supplies two quantities, both of them runs: 200 in total and 160 by spinners. 160 out of 200 is indeed 80 per cent — but 80 per cent of the runs, not of the players. The conclusion silently moves that figure onto a different population. One counter-example is enough to defeat it: two spinners batting at numbers seven and eight could between them make all 160 runs, and two players out of an eleven-man side is 18 per cent, not 80. The conclusion is not even literally available, since 80 per cent of eleven is 8.8 players. Now conclusion 2. The statement never mentions the batting order at all — it records who scored the runs, not when they came in. Spinners occupying positions eight to eleven and scoring 160 between them is entirely consistent with everything the statement says, so the conclusion can be false while the statement is true. Note the exact reason it fails: not that it is untrue in the real match, but that the statement is silent, and silence is not support. Both conclusions fail the necessity test, so the answer is (d).

Why the others are wrong

(a)Only 1 follows the statement — The trap this item is built around, because the arithmetic in conclusion 1 is genuinely correct — 160 of 200 really is 80 per cent. What is wrong is the base: the percentage is computed over runs and then asserted about players. Swapping the base while keeping the number is the single commonest planted error in statement-and-conclusion items, and it is designed to feel like a calculation rather than an inference.
(b)Only 2 follows the statement — Chosen by candidates who reason that scoring 160 of 200 runs means the spinners must have batted for a long time, and therefore must have opened. That is a judgement about what is likely, not about what must be so — a side's numbers seven and eight can bat through an innings after an early collapse. Plausibility is not entailment, and the statement fixes no batting position for anyone.
(c)Both 1 and 2 follow the statement — This option requires both errors at once: transferring a percentage from runs to players, and importing a batting order the statement never gives. It attracts candidates who read the two conclusions as a package and ask whether the picture as a whole sounds reasonable, instead of testing each conclusion separately against the statement alone.

Concept

Statement-and-conclusions items test deductive discipline, not general knowledge. You are given a short passage and asked which of the listed conclusions logically follow from it, and the standard is necessity: a conclusion follows only if, granting the statement, it is impossible for the conclusion to be false. Three working rules make the family tractable. First, use only what the statement says — no outside knowledge, no assumed background, however obvious it seems. Second, a conclusion that goes beyond the statement does not follow even if it is true in the real world; conversely, 'does not follow' is not a claim that the conclusion is false, only that the statement does not establish it. Third, test one conclusion at a time and in isolation, because the option list is built to reward exactly that and to punish reading the two together as a story. The errors examiners plant are a small set: swapping the base of a percentage, adding a detail the statement omits, reversing an implication, and turning a correlation into a cause.

The reliable procedure is to convert each conclusion into a yes-or-no question — can the statement be true while this conclusion is false? — and answer it with a concrete counter-example rather than a feeling. For conclusion 1 the counter-example is immediate: put two spinners at numbers seven and eight, let them add 160 while the other nine make 40, and the statement holds word for word while the team is 18 per cent spinners. For conclusion 2 the counter-example is just as easy: the same two spinners come in at eight and nine, so the openers are not spinners and the statement is still exactly true. Once both counter-examples exist, the answer is fixed. The discriminating fact for this particular item is that every number in the statement is a number of runs, and neither conclusion is about runs — conclusion 1 is about the composition of the team and conclusion 2 about the batting order, and the statement measures neither. Two extra cautions are worth carrying. Cricket knowledge is a liability here: knowing that spinners usually bat low is not what defeats conclusion 2, and knowing that a team occasionally plays four spinners is not what defeats conclusion 1. And the fourth option, 'neither follows', is a real answer in this family, not a last resort — setters use it precisely because candidates are reluctant to conclude that nothing follows.

Key facts

160 out of 200 is 80 per cent of the runs; the statement gives no figure at all for how many players were spinners, so the 80 per cent has no team-composition meaning
A cricket team fields eleven players, so '80% of the team' would be 8.8 players — not a whole number, which makes conclusion 1 unavailable even before the logic is examined
One counter-example defeats a conclusion: two spinners scoring 160 of the 200 runs is 18 per cent of an eleven-man side and contradicts nothing in the statement
The test in this family is necessity, not plausibility — a conclusion follows only if it cannot be false while the statement is true
'Does not follow' is not the same as 'is false': conclusion 2 might be true in the actual match, but it fails because the statement never mentions the batting order

Each conclusion tested against the statement, one at a time

What the statement gives→Two quantities, both of them runs — 200 total, 160 by spinners. Nothing about how many players there are, who they are, or in what order they batted.

Conclusion 1 — 80% of the team consisted of spinners→Does not follow. The 80 per cent is a share of runs, not of players. Counter-example: two spinners at seven and eight score all 160 — that is 18 per cent of an eleven-man side, and the statement still holds.

Conclusion 2 — The opening batsmen were spinners→Does not follow. The statement is silent on batting order. Counter-example: the spinners bat at eight and nine, the openers are seamers, and every word of the statement remains true.

Therefore→Neither conclusion survives the necessity test → option (d).

Both conclusions are defeated the same way — by constructing one scenario in which the statement is true and the conclusion is not. Note that conclusion 2 fails for silence, not for falsity.

Study next

Syllogisms and the Venn-diagram method for 'all', 'some' and 'no' statementsStatement and assumptions — what must be taken for granted for a statement to make sense, as against what follows from itStatement and courses of action, where the test is whether the action addresses the problem statedCause and effect items, and the difference between correlation and entailmentStatement and arguments, and the strong-versus-weak argument test

Common traps

Carrying a percentage across to a different base — 80 per cent of the runs read as 80 per cent of the players
Using outside knowledge of cricket, either to support a conclusion or to reject it; only the statement counts
Treating 'likely' or 'possible' as 'follows', and treating 'neither follows' as a coward's option rather than a real answer

BPSC keeps this family in the short reasoning block at the end of the General Studies paper, in its plainest two-conclusion form with the standard four-way option set — only 1, only 2, both, neither — and builds the trap out of a number that is correct but attached to the wrong base. UPSC puts logical reasoning and analytical ability in CSAT Paper II, where the same discipline appears more often as a syllogism or as a statement-and-assumption item than as this two-conclusion format.

Related PYQs

No directly related past PYQ was found.

Practice

practice — not a real PYQ
Statement : Of the 400 books sold by a shop last month, 320 were textbooks. Conclusions : 1. Textbooks make up 80% of the shop's stock. 2. The shop sells only textbooks. Which of the conclusions follow(s) from the statement?
- (a)Only 1 follows
- (b)Only 2 follows
- (c)Both 1 and 2 follow
- (d)Neither 1 nor 2 follows
Answer(d) Neither 1 nor 2 follows — 320 of 400 is 80 per cent of the books sold, not of the stock held, and the remaining 80 books sold were not textbooks, which contradicts conclusion 2 outright.
practice — not a real PYQ
Statement : Every player in the team who scored a century was an opening batsman. Rohan is a player in the team who scored a century. Conclusions : 1. Rohan was an opening batsman. 2. Every opening batsman in the team scored a century. Which of the conclusions follow(s) from the statement?
- (a)Only 1 follows
- (b)Only 2 follows
- (c)Both 1 and 2 follow
- (d)Neither 1 nor 2 follows
Answer(a) Only 1 follows — conclusion 1 simply applies the rule to a named case, while conclusion 2 reverses it: 'all century-makers were openers' does not give 'all openers made centuries'.