Data interpretation & sufficiency

Answer: (c) S1 और S2 एकसाथ प्रश्न का उत्तर देने के लिए पर्याप्त नहीं हैं।

S1 caps the book at 2 × 51 = 102 figures and S2 guarantees at least 51. Together they only place the total between 51 and 102, which may or may not exceed 100.

1. S1: at most 2 figures on each of 51 pages, so at most 102 figures — could be above or below 100.
2. S2: at least 1 figure per page, so at least 51 figures — no upper limit.
3. Together: between 51 and 102. Both 101 and 60 are possible, so the Question cannot be answered.

Remember · In data sufficiency, find the range each statement allows; if the range still straddles the question's cut-off, the data are insufficient.

Question and answer: UPSC's official GS Paper II (2020, Series A) — paper ↗ · answer key ↗. Explanation: Minimalist IAS, checked 30 Sept 2026 (how we verify). Permalink · Report an error

Answer: (c) दोनों कथन S1 और S2 एकसाथ प्रश्न का उत्तर देने के लिए पर्याप्त हैं किन्तु न तो अकेला S1 और न ही अकेला S2 प्रश्न का उत्तर देने के लिए पर्याप्त है।

S1 makes R bigger than P and Q but says nothing about S; S2 rules out S but says nothing about P, Q and R. Together, S is not the largest and R beats P and Q, so R is the largest.

1. S1 alone: R > P and R > Q, but S could exceed R — not sufficient.
2. S2 alone: the largest is one of P, Q, R — not sufficient.
3. Together: S is not the largest and R is above P and Q, so R is the largest.

Remember · Test each statement alone, then together; choose (c) only when neither alone works but the pair does.

Question and answer: UPSC's official GS Paper II (2020, Series A) — paper ↗ · answer key ↗. Explanation: Minimalist IAS, checked 30 Sept 2026 (how we verify). Permalink · Report an error

Answer: (d) S1 और S2 एकसाथ प्रश्न का उत्तर देने के लिए पर्याप्त नहीं हैं।

Between 10 and 20 the primes are 11, 13, 17 and 19; of these, 13 and 17 both leave remainder 1 on division by 4. Even together the statements leave two possible values of n, so they are not sufficient.

1. S1: n = 11, 13, 17 or 19.
2. S2: n = 13 or 17 (the numbers between 10 and 20 that are 1 more than a multiple of 4).
3. Together: 13 and 17 both satisfy S1 and S2, so n is still not fixed.

Remember · In number data sufficiency, list every value that fits; if more than one survives, the data are insufficient.

Question and answer: UPSC's official GS Paper II (2020, Series A) — paper ↗ · answer key ↗. Explanation: Minimalist IAS, checked 30 Sept 2026 (how we verify). Permalink · Report an error

Answer: (c) दोनों कथन S1 और S2 एकसाथ प्रश्न का उत्तर देने के लिए पर्याप्त हैं किन्तु न तो अकेला S1 और न ही अकेला S2 प्रश्न का उत्तर देने के लिए पर्याप्त है।

A product of 21 alone allows 3 and 7, 1 and 21 and many other pairs, and a sum of 10 alone allows endless pairs. Together, the numbers are the roots of t² − 10t + 21 = 0, which are exactly 3 and 7.

1. S1 alone: 3 × 7, 1 × 21, 2 × 10·5 … — not unique.
2. S2 alone: 3 + 7, 4 + 6, 5 + 5 … — not unique.
3. Together: the numbers satisfy t² − 10t + 21 = 0, i.e. (t − 3)(t − 7) = 0, so they are 3 and 7.

Remember · Two numbers are fixed by their sum and product together: they are the roots of t² − (sum)t + (product) = 0.

Question and answer: UPSC's official GS Paper II (2020, Series A) — paper ↗ · answer key ↗. Explanation: Minimalist IAS, checked 30 Sept 2026 (how we verify). Permalink · Report an error

Answer: (d) S1 और S3 एकसाथ प्रश्न का उत्तर देने के लिए पर्याप्त हैं।

S1 puts D above C and C above both A and B, so the youngest is A or B. S3 settles that pair: A is older than B, so B is the youngest. S2 adds nothing S1 did not already give.

1. S1: D > C > A and D > C > B, so the youngest is A or B — S1 alone is not enough.
2. S2 only repeats that D is the oldest, so S1 and S2 together still leave A or B.
3. S2 and S3: A > B, but C's position is unknown — C could be youngest.
4. S1 and S3: D > C > A > B, so B is the youngest.

Remember · Find what each statement leaves open, then pick the statement that closes exactly that gap.

Question and answer: UPSC's official GS Paper II (2020, Series A) — paper ↗ · answer key ↗. Explanation: Minimalist IAS, checked 30 Sept 2026 (how we verify). Permalink · Report an error

Answer: (d) 1971–1981

Natural growth rate is birth rate minus death rate. The gaps for the four offered periods are 12·6, 12·5, 22·2 and 22·3, so 1971–1981 is the highest, just ahead of 1961–1971.

1. 1911–1921: 48·1 − 35·5 = 12·6.
2. 1941–1951: 39·9 − 27·4 = 12·5.
3. 1961–1971: 41·1 − 18·9 = 22·2.
4. 1971–1981: 37·1 − 14·8 = 22·3 — the maximum.
5. Check: the periods not offered are lower too (10·1, 14·0, 18·9).

Remember · Natural growth = birth rate − death rate. Compute only the offered periods, and compute the close ones exactly.

Question and answer: UPSC's official GS Paper II (2020, Series A) — paper ↗ · answer key ↗. Explanation: Minimalist IAS, checked 1 Oct 2026 (how we verify). Permalink · Report an error