CSAT Solved Papers/ 2022/Q39
2022 CSAT — Q39
Three Statements followed by three Conclusions are given below. You have to take the Statements to be true even if they seem to be at variance from the commonly known facts. Read all the Conclusions and then decide which of the given Conclusions logically follows/follow from the Statements, disregarding the commonly known facts :
Statement-1 : Some doctors are teachers.
Statement-2 : All teachers are engineers.
Statement-3 : All engineers are scientists.
Conclusion-I : Some scientists are doctors.
Conclusion-II : All engineers are doctors.
Conclusion-III : Some engineers are doctors.
Which one of the following is correct?
Thinking pathway
Locate. This is a pure-logic question — there is no passage to read, so a conclusion counts only if the three given statements make it impossible for it to be false. Chain the “all” statements: all teachers are engineers, and all engineers are scientists — so every teacher sits inside the engineers, who sit inside the scientists. And “Some doctors are teachers” puts at least one doctor inside the teachers.
Test — does it follow? Chain the “some” statement through the “all” statements. Take the doctor(s) who are teachers — they exist (S1). Being teachers, they are engineers (S2); being engineers, they are scientists (S3). So there is at least one person who is at once a doctor, a teacher, an engineer, and a scientist.
- C-I “Some scientists are doctors” — that person is a scientist and a doctor. Forced.
- C-III “Some engineers are doctors” — that person is an engineer and a doctor. Forced.
- C-II “All engineers are doctors” — only some doctors are teachers/engineers; engineers may include many non-doctors. You can easily picture an engineer who is not a doctor, and that picture breaks no premise. Not forced.
Eliminate by anatomy. (a) “Only I” drops the equally-forced C-III — it under-counts. (b)/(d) seat C-II, which over-states the case: a “some” premise (“some doctors are teachers”) cannot license an “all” conclusion (“all engineers are doctors”). Both I and III are forced; II is not. Key: (c).
Evidence in the text
Premises chain: Teachers ⊆ Engineers ⊆ Scientists, and Some Doctors are Teachers. The doctor-teachers (they exist, by S1) are therefore engineers (S2) and scientists (S3). C-I (Some scientists are doctors): those doctor-teachers are scientists AND doctors → FORCED. C-III (Some engineers are doctors): those doctor-teachers are engineers AND doctors → FORCED. C-II (All engineers are doctors): not forced — only some doctors are teachers; nothing makes every engineer a doctor. So I and III follow, II does not → (c).
Worked rationale
Premises: some doctors are teachers; every teacher is an engineer, and every engineer is a scientist.
The doctor-teachers (they exist, by S1) belong to every larger group along the chain: they are engineers and scientists.
- C-I Some scientists are doctors — the doctor-teachers are scientists; they are doctors. So some scientists are doctors. Follows.
- C-III Some engineers are doctors — the doctor-teachers are engineers; they are doctors. So some engineers are doctors. Follows.
- C-II All engineers are doctors — nothing forces every engineer to be a doctor (the premise about doctors only says some). An engineer who is not a doctor breaks none of the three premises. Does not follow.
Answer: (c) Both Conclusion-I and Conclusion-III.
Why the other options miss
- A half right, half wrong: I is forced, but this option silently drops C-III, which is forced by the same chaining of the doctor-teachers through the engineers; it under-counts the valid conclusions.
- B over-states the case: takes the “some” statement (“some doctors are teachers”) to license the “all” claim (“all engineers are doctors”) — a some-to-all leap that no premise supports.
- D pairs the genuinely-forced C-I with the too-strong C-II; the C-I half is a lure to make the C-II error feel safe.
Specialist insight
The engine is “push the ‘some’ statement through the ‘all’ statements.” A single “some” premise (“some doctors are teachers”) is enough to make some-conclusions about every larger group in the chain (engineers, scientists), because the one person we found carries all his memberships upward — that gives C-I and C-III together. But a “some” premise can never yield an “all” conclusion about those larger groups, which is why C-II (“all engineers are doctors”) fails. The trap the examiner sets is the half-answer (a) that catches C-I but misses its twin C-III. Find every forced “some”-conclusion, not just the first. (c).
The doctor-teachers are engineers AND scientists, so "some scientists are doctors" and "some engineers are doctors" are BOTH forced — don't stop at C-I; the answer is (c).