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CSAT · 58 questions

Data interpretation & sufficiency

Every UPSC CSAT question on this topic, 2016–2026, newest first. Tap an option to check yourself; the answer and explanation open below it.

Data interpretation & sufficiency questions per year: 2016: 0, 2017: 1, 2018: 13, 2019: 0, 2020: 6, 2021: 5, 2022: 7, 2023: 5, 2024: 10, 2025: 5, 2026: 6 Asked in 9 of 11 years · most in 2018 (13)
Timed · 30 minutes a set Practise Data interpretation & sufficiency as timed tests 3 sets of about 20 questions with UPSC's CSAT marking. Start practising

UPSC syllabus: “Basic numeracy (numbers and their relations, orders of magnitude, etc.) (Class X level), Data interpretation (charts, graphs, tables, data sufficiency etc. — Class X level);” Sub-topics in the detailed syllabus →

CSAT 2024 · Q59

X-Ray · Core #6 Medium

एक प्रश्न दिया गया है जिसके बाद दो कथन I और II दिए गए हैं। प्रश्न और कथनों पर विचार कीजिए।

  1. प्रश्न: m और n के मान क्या हैं, जहाँ m और n धनपूर्ण संख्याएँ हैं?
  2. कथन–I: m + n > mn और m > n.
  3. कथन–II: m और n का गुणनफल 24 है।

उपर्युक्त प्रश्न और कथनों के संबंध में, निम्नलिखित में से कौन-सा सही है?

Read this question in English

A Question is given followed by two Statements I and II. Consider the Question and the Statements.

Question. What are the values of m and n, where m and n are natural numbers?

Statement–I. m + n > mn and m > n.

Statement–II. The product of m and n is 24.

Which one of the following is correct in respect of the above Question and the Statements?

(a) The Question can be answered by using one of the Statements alone, but cannot be answered using the other Statement alone · (b) The Question can be answered by using either Statement alone · (c) The Question can be answered by using both the Statements together, but cannot be answered using either Statement alone · (d) The Question cannot be answered even by using both the Statements together

उत्तर और व्याख्या · explanation in English

Answer: (c) प्रश्न का उत्तर, दोनों कथनों का एक-साथ प्रयोग कर दिया जा सकता है, किन्तु अकेले किसी भी एक कथन का प्रयोग कर नहीं दिया जा सकता है

m + n > mn with m > n forces n = 1, but leaves m open; mn = 24 alone allows several pairs. Together, n = 1 and m = 24.

  1. m + n > mn is the same as mn − m − n + 1 < 1, i.e. (m − 1)(n − 1) < 1.
  2. For natural numbers this means (m − 1)(n − 1) = 0; since m > n ≥ 1, n = 1. Statement I fixes n = 1 but any m ≥ 2 works, so it is not sufficient.
  3. Statement II alone: mn = 24 allows (24, 1), (12, 2), (8, 3), (6, 4) and their reversals, so it is not sufficient.
  4. Together: n = 1 and mn = 24 give m = 24. Check: 24 + 1 = 25 > 24.

Remember · Rewrite m + n > mn as (m − 1)(n − 1) < 1; with natural numbers, one of them must be 1.

Question and answer: UPSC's official GS Paper II (2024, Series A) — paper ↗ · answer key ↗. Explanation: Minimalist IAS, checked 30 Sept 2026 (how we verify). Permalink ·

CSAT 2024 · Q60

X-Ray · Core #6 Easy

एक प्रश्न दिया गया है जिसके बाद दो कथन I और II दिए गए हैं। प्रश्न और कथनों पर विचार कीजिए।

  1. प्रश्न: सॉफ्टवेयर को डाउनलोड करने में कितने समय की आवश्यकता है?
  2. कथन–I: सॉफ्टवेयर की साइज़ 12 मेगाबाइट है।
  3. कथन–II: स्थानांतरण दर 2·4 किलोबाइट प्रति सेकंड है।

उपर्युक्त प्रश्न और कथनों के संबंध में, निम्नलिखित में से कौन-सा सही है?

Read this question in English

A Question is given followed by two Statements I and II. Consider the Question and the Statements.

Question. What is the time required to download the software?

Statement–I. The size of the software is 12 megabytes.

Statement–II. The transfer rate is 2.4 kilobytes per second.

Which one of the following is correct in respect of the above Question and the Statements?

(a) The Question can be answered by using one of the Statements alone, but cannot be answered using the other Statement alone · (b) The Question can be answered by using either Statement alone · (c) The Question can be answered by using both the Statements together, but cannot be answered using either Statement alone · (d) The Question cannot be answered even by using both the Statements together

उत्तर और व्याख्या · explanation in English

Answer: (c) प्रश्न का उत्तर, दोनों कथनों का एक-साथ प्रयोग कर दिया जा सकता है, किन्तु अकेले किसी भी एक कथन का प्रयोग कर नहीं दिया जा सकता है

Download time = size ÷ transfer rate. Statement I gives only the size and Statement II only the rate; together they fix the time.

  1. Time = size of the software ÷ transfer rate.
  2. Statement I gives the size (12 megabytes) but no rate, so it is not sufficient.
  3. Statement II gives the rate (2.4 kilobytes per second) but no size, so it is not sufficient.
  4. Together: 12 megabytes = 12,000 kilobytes (taking 1 MB = 1000 KB), so time = 12,000 ÷ 2.4 = 5,000 seconds; with 1 MB = 1024 KB it is 5,120 seconds. Either way the time is fixed.

Remember · In data sufficiency, write the formula first and tick off which statement supplies each quantity.

Question and answer: UPSC's official GS Paper II (2024, Series A) — paper ↗ · answer key ↗. Explanation: Minimalist IAS, checked 30 Sept 2026 (how we verify). Permalink ·

CSAT 2024 · Q64

X-Ray · Core #6 Medium

एक प्रश्न दिया गया है जिसके बाद दो कथन I और II दिए गए हैं। प्रश्न और कथनों पर विचार कीजिए।

  1. प्रश्न: x और y के अद्वितीय मान क्या हैं जहाँ x, y भिन्न धनपूर्ण संख्याएँ हैं?
  2. कथन–I: x / y विषम है।
  3. कथन–II: xy = 12

उपर्युक्त प्रश्न और कथनों के संबंध में, निम्नलिखित में से कौन-सा सही है?

Read this question in English

A Question is given followed by two Statements I and II. Consider the Question and the Statements.

Question. What are the unique values of x and y, where x, y are distinct natural numbers?

Statement–I. x / y is odd.

Statement–II. xy = 12

Which one of the following is correct in respect of the above Question and the Statements?

(a) The Question can be answered by using one of the Statements alone, but cannot be answered using the other Statement alone · (b) The Question can be answered by using either Statement alone · (c) The Question can be answered by using both the Statements together, but cannot be answered using either Statement alone · (d) The Question cannot be answered even by using both the Statements together

उत्तर और व्याख्या · explanation in English

Answer: (c) प्रश्न का उत्तर, दोनों कथनों का एक-साथ प्रयोग कर दिया जा सकता है, किन्तु अकेले किसी भी एक कथन का प्रयोग कर नहीं दिया जा सकता है

‘x/y is odd’ alone allows endless pairs, and xy = 12 alone allows six ordered pairs. Together, of the pairs with product 12, only x = 6, y = 2 gives an odd quotient (3).

  1. Statement I alone: x = 3y, 5y, 7y, …, for example (3, 1), (5, 1), (6, 2); not unique.
  2. Statement II alone: (1, 12), (2, 6), (3, 4), (4, 3), (6, 2), (12, 1); not unique.
  3. Together, test x/y for each pair: 12/1 = 12 (even), 6/2 = 3 (odd); 4/3, 3/4, 2/6 and 1/12 are not whole numbers.
  4. Only x = 6, y = 2 works, so both statements together answer the question.

Remember · When one statement gives a short list, test each item on it against the other statement.

Question and answer: UPSC's official GS Paper II (2024, Series A) — paper ↗ · answer key ↗. Explanation: Minimalist IAS, checked 30 Sept 2026 (how we verify). Permalink ·

CSAT 2024 · Q65

X-Ray · Core #6 Medium

एक प्रश्न दिया गया है जिसके बाद दो कथन I और II दिए गए हैं। प्रश्न और कथनों पर विचार कीजिए।

एक निश्चित धनराशि X, Y और Z के बीच बाँटी गई।

  1. प्रश्न: किसे सबसे कम धनराशि प्राप्त हुई?
  2. कथन–I: Y और Z को मिलकर जो धनराशि मिली X को उसका 4/5 हिस्सा प्राप्त हुआ।
  3. कथन–II: X और Z को मिलकर जो धनराशि मिली Y को उसका 2/7 हिस्सा प्राप्त हुआ।

उपर्युक्त प्रश्न और कथनों के संबंध में, निम्नलिखित में से कौन-सा सही है?

Read this question in English

A Question is given followed by two Statements I and II. Consider the Question and the Statements.

A certain amount was distributed among X, Y and Z.

Question. Who received the least amount?

Statement–I. X received 4/5 of what Y and Z together received.

Statement–II. Y received 2/7 of what X and Z together received.

Which one of the following is correct in respect of the above Question and the Statements?

(a) The Question can be answered by using one of the Statements alone, but cannot be answered using the other Statement alone · (b) The Question can be answered by using either Statement alone · (c) The Question can be answered by using both the Statements together, but cannot be answered using either Statement alone · (d) The Question cannot be answered even by using both the Statements together

उत्तर और व्याख्या · explanation in English

Answer: (c) प्रश्न का उत्तर, दोनों कथनों का एक-साथ प्रयोग कर दिया जा सकता है, किन्तु अकेले किसी भी एक कथन का प्रयोग कर नहीं दिया जा सकता है

Statement I makes X’s share 4/9 of the total and Statement II makes Y’s share 2/9; together Z gets 3/9, so Y received the least. Either statement alone leaves the split between the other two open.

  1. Statement I: X = (4/5)(Y + Z), so X : (Y + Z) = 4 : 5 and X = 4/9 of the total. Y and Z share 5/9 in an unknown way, so it is not sufficient.
  2. Statement II: Y = (2/7)(X + Z), so Y = 2/9 of the total. X and Z share 7/9 in an unknown way (X could even be less than Y), so it is not sufficient.
  3. Together: X = 4/9 and Y = 2/9, so Z = 1 − 6/9 = 3/9.
  4. Y received the least.

Remember · ‘A gets p/q of what the others get’ means A’s share is p/(p + q) of the total.

Question and answer: UPSC's official GS Paper II (2024, Series A) — paper ↗ · answer key ↗. Explanation: Minimalist IAS, checked 30 Sept 2026 (how we verify). Permalink ·

CSAT 2024 · Q66

X-Ray · Core #6 Medium

एक प्रश्न दिया गया है जिसके बाद दो कथन I और II दिए गए हैं। प्रश्न और कथनों पर विचार कीजिए।

  1. प्रश्न: यदि एक कक्षा में औसत अंक 60 है, तो कक्षा में छात्रों की संख्या कितनी है?
  2. कथन–I: कक्षा में अधिकतम अंक 70 है और न्यूनतम अंक 50 है।
  3. कथन–II: कक्षा में अधिकतम अंक और न्यूनतम अंक को छोड़ देने से औसत में कोई अंतर नहीं आता है।

उपर्युक्त प्रश्न और कथनों के संबंध में, निम्नलिखित में से कौन-सा सही है?

Read this question in English

A Question is given followed by two Statements I and II. Consider the Question and the Statements.

Question. If the average marks in a class are 60, then what is the number of students in the class?

Statement–I. The highest marks in the class are 70 and the lowest marks are 50.

Statement–II. Exclusion of highest and lowest marks from the class does not change the average.

Which one of the following is correct in respect of the above Question and the Statements?

(a) The Question can be answered by using one of the Statements alone, but cannot be answered using the other Statement alone · (b) The Question can be answered by using either Statement alone · (c) The Question can be answered by using both the Statements together, but cannot be answered using either Statement alone · (d) The Question cannot be answered even by using both the Statements together

उत्तर और व्याख्या · explanation in English

Answer: (d) प्रश्न का उत्तर, दोनों कथनों का एक-साथ प्रयोग कर भी नहीं दिया जा सकता

Statement II only tells us that the highest and lowest marks add up to 120 (twice the average). Statement I confirms 70 + 50 = 120, but neither statement says anything about how many students there are.

  1. Let there be n students, with total marks 60n.
  2. Statement II: (60n − H − L) ÷ (n − 2) = 60 gives H + L = 120, which is true for any n.
  3. Statement I: H = 70 and L = 50, consistent with H + L = 120, but n is still free.
  4. Example: marks 50, 60, 70 (n = 3) and 50, 60, 60, 70 (n = 4) both fit everything. So the question cannot be answered.

Remember · If a statement holds for every value of the unknown, it cannot fix that unknown; test two different cases.

Question and answer: UPSC's official GS Paper II (2024, Series A) — paper ↗ · answer key ↗. Explanation: Minimalist IAS, checked 30 Sept 2026 (how we verify). Permalink ·

CSAT 2024 · Q67

X-Ray · Core #6 Medium

एक प्रश्न दिया गया है जिसके बाद दो कथन I और II दिए गए हैं। प्रश्न और कथनों पर विचार कीजिए।

तीन भिन्न अभाज्य संख्याएँ हैं, जिनका योगफल एक अभाज्य संख्या है।

  1. प्रश्न: वे तीन संख्याएँ कौन-सी हैं?
  2. कथन–I: उनका योगफल 23 से कम है।
  3. कथन–II: उनमें से एक संख्या 5 है।

उपर्युक्त प्रश्न और कथनों के संबंध में, निम्नलिखित में से कौन-सा सही है?

Read this question in English

A Question is given followed by two Statements I and II. Consider the Question and the Statements.

There are three distinct prime numbers whose sum is a prime number.

Question. What are those three numbers?

Statement–I. Their sum is less than 23.

Statement–II. One of the numbers is 5.

Which one of the following is correct in respect of the above Question and the Statements?

(a) The Question can be answered by using one of the Statements alone, but cannot be answered using the other Statement alone · (b) The Question can be answered by using either Statement alone · (c) The Question can be answered by using both the Statements together, but cannot be answered using either Statement alone · (d) The Question cannot be answered even by using both the Statements together

उत्तर और व्याख्या · explanation in English

Answer: (a) प्रश्न का उत्तर, दोनों में से अकेले एक कथन का प्रयोग कर दिया जा सकता है, किन्तु अकेले अन्य कथन का प्रयोग कर नहीं दिया जा सकता है

Three distinct primes with a prime sum must all be odd, because including 2 makes the sum even. With the sum below 23, the only possibility is 3 + 5 + 11 = 19, so Statement I alone suffices. Statement II allows 3, 5, 11 and 5, 7, 11 and more.

  1. If 2 is one of them, the sum is 2 + odd + odd = even (and more than 2), so not prime. All three must be odd primes.
  2. Statement I: odd-prime triples with sum below 23 are 3 + 5 + 7 = 15, 3 + 5 + 11 = 19, 3 + 5 + 13 = 21 and 3 + 7 + 11 = 21; only 19 is prime. So the numbers are 3, 5 and 11: sufficient.
  3. Statement II: triples containing 5 with a prime sum include {3, 5, 11} (19), {5, 7, 11} (23) and {3, 5, 23} (31), so it is not sufficient.
  4. So the question can be answered by one statement (I) alone but not by the other.

Remember · A prime sum of three distinct primes cannot include 2 (the sum turns even). Start listing from the smallest odd primes.

Question and answer: UPSC's official GS Paper II (2024, Series A) — paper ↗ · answer key ↗. Explanation: Minimalist IAS, checked 30 Sept 2026 (how we verify). Permalink ·

CSAT 2024 · Q68

X-Ray · Core #6 Medium

एक प्रश्न दिया गया है जिसके बाद दो कथन I और II दिए गए हैं। प्रश्न और कथनों पर विचार कीजिए।

  1. प्रश्न: क्या (x + y) एक पूर्णांक है?
  2. कथन–I: (2x + y) एक पूर्णांक है।
  3. कथन–II: (x + 2y) एक पूर्णांक है।

उपर्युक्त प्रश्न और कथनों के संबंध में, निम्नलिखित में से कौन-सा सही है?

Read this question in English

A Question is given followed by two Statements I and II. Consider the Question and the Statements.

Question. Is (x + y) an integer?

Statement–I. (2x + y) is an integer.

Statement–II. (x + 2y) is an integer.

Which one of the following is correct in respect of the above Question and the Statements?

(a) The Question can be answered by using one of the Statements alone, but cannot be answered using the other Statement alone · (b) The Question can be answered by using either Statement alone · (c) The Question can be answered by using both the Statements together, but cannot be answered using either Statement alone · (d) The Question cannot be answered even by using both the Statements together

उत्तर और व्याख्या · explanation in English

Answer: (d) प्रश्न का उत्तर, दोनों कथनों का एक-साथ प्रयोग कर भी नहीं दिया जा सकता

Neither statement alone fixes x + y. Even together they only make 3(x + y) an integer, so x + y can be a fraction such as 2/3 (x = y = 1/3) or an integer (x = y = 1).

  1. Statement I alone: x = 0.5, y = 0 gives 2x + y = 1 but x + y = 0.5; x = y = 1 gives x + y = 2. Not sufficient.
  2. Statement II alone: the same examples with x and y swapped show it is not sufficient.
  3. Together: adding them, 3x + 3y is an integer, so x + y is only known to be an integer divided by 3.
  4. x = y = 1/3 gives 2x + y = 1 and x + 2y = 1, yet x + y = 2/3; x = y = 1 gives x + y = 2. Both fit, so the answer is still open.

Remember · In ‘is it an integer?’ questions, try fractions like 1/3 or 1/2; they often break an apparent ‘yes’.

Question and answer: UPSC's official GS Paper II (2024, Series A) — paper ↗ · answer key ↗. Explanation: Minimalist IAS, checked 30 Sept 2026 (how we verify). Permalink ·

CSAT 2024 · Q69

X-Ray · Core #6 Medium

एक प्रश्न दिया गया है जिसके बाद दो कथन I और II दिए गए हैं। प्रश्न और कथनों पर विचार कीजिए।

एक व्यक्ति ₹ 50 में तीन वस्तुएँ p, q और r खरीदता है। वस्तु q की कीमत ₹ 16 है जो न्यूनतम है।

  1. प्रश्न: वस्तु p की कीमत क्या है?
  2. कथन–I: p की कीमत, r की कीमत से अधिक नहीं है।
  3. कथन–II: r की कीमत, p की कीमत से अधिक नहीं है।

उपर्युक्त प्रश्न और कथनों के संबंध में, निम्नलिखित में से कौन-सा सही है?

Read this question in English

A Question is given followed by two Statements I and II. Consider the Question and the Statements.

A person buys three articles p, q and r for ₹50. The price of the article q is ₹16 which is the least.

Question. What is the price of the article p?

Statement–I. The cost of p is not more than that of r.

Statement–II. The cost of r is not more than that of p.

Which one of the following is correct in respect of the above Question and the Statements?

(a) The Question can be answered by using one of the Statements alone, but cannot be answered using the other Statement alone · (b) The Question can be answered by using either Statement alone · (c) The Question can be answered by using both the Statements together, but cannot be answered using either Statement alone · (d) The Question cannot be answered even by using both the Statements together

उत्तर और व्याख्या · explanation in English

Answer: (c) प्रश्न का उत्तर, दोनों कथनों का एक-साथ प्रयोग कर दिया जा सकता है, किन्तु अकेले किसी भी एक कथन का प्रयोग कर नहीं दिया जा सकता है

p + r = 50 − 16 = 34, with both more than 16. Statement I gives p ≤ 17 and Statement II gives p ≥ 17, so together p = ₹17; either alone leaves a range, since prices need not be whole rupees.

  1. p + r = 50 − 16 = 34, and p and r are both more than 16 because q is the least.
  2. Statement I (p ≤ r): p ≤ 17, so 16 < p ≤ 17; p could be ₹16.50 or ₹17. Not sufficient.
  3. Statement II (r ≤ p): p ≥ 17, so 17 ≤ p < 18. Not sufficient.
  4. Together, p ≤ r and r ≤ p give p = r = 34 ÷ 2 = ₹17.
  5. Note: only if prices had to be whole rupees would each statement alone give ₹17; the question does not say so.

Remember · In data sufficiency, don’t assume whole numbers unless told. ‘Not more than’ in both directions means equality.

Question and answer: UPSC's official GS Paper II (2024, Series A) — paper ↗ · answer key ↗. Explanation: Minimalist IAS, checked 30 Sept 2026 (how we verify). Permalink ·

CSAT 2024 · Q70

X-Ray · Core #6 Medium

एक प्रश्न दिया गया है जिसके बाद दो कथन I और II दिए गए हैं। प्रश्न और कथनों पर विचार कीजिए।

P, Q, R और S एक परीक्षा में भाग लेते हैं।

  1. प्रश्न: क्या P ने, Q से अधिक अंक प्राप्त किए?
  2. कथन–I: P और Q द्वारा प्राप्त किए गए अंकों का योगफल, R और S द्वारा प्राप्त किए गए अंकों के योगफल के बराबर है।
  3. कथन–II: P और S द्वारा प्राप्त किए गए अंकों का योगफल, Q और R द्वारा प्राप्त किए गए अंकों के योगफल से अधिक है।

उपर्युक्त प्रश्न और कथनों के संबंध में, निम्नलिखित में से कौन-सा सही है?

Read this question in English

A Question is given followed by two Statements I and II. Consider the Question and the Statements.

P, Q, R and S appeared in a test.

Question. Has P scored more marks than Q?

Statement–I. The sum of the marks scored by P and Q is equal to the sum of the marks scored by R and S.

Statement–II. The sum of the marks scored by P and S is more than the sum of the marks scored by Q and R.

Which one of the following is correct in respect of the above Question and the Statements?

(a) The Question can be answered by using one of the Statements alone, but cannot be answered using the other Statement alone · (b) The Question can be answered by using either Statement alone · (c) The Question can be answered by using both the Statements together, but cannot be answered using either Statement alone · (d) The Question cannot be answered even by using both the Statements together

उत्तर और व्याख्या · explanation in English

Answer: (d) प्रश्न का उत्तर, दोनों कथनों का एक-साथ प्रयोग कर भी नहीं दिया जा सकता

Combining the statements gives only P > R and S > Q; nothing compares P with Q directly. Examples with P above Q and with P below Q both satisfy the data.

  1. Statement I alone: P + Q = R + S says nothing about P versus Q.
  2. Statement II alone: P + S > Q + R also depends on S and R, so it is not sufficient.
  3. Together: putting R = P + Q − S into Statement II gives 2S > 2Q, i.e. S > Q; similarly P > R. Neither compares P with Q.
  4. Example: P = 5, Q = 1, R = 4, S = 2 (P > Q) and P = 5, Q = 6, R = 4, S = 7 (P < Q) both satisfy I and II. So the question cannot be answered.

Remember · Combine the equations to see what they really fix, then build two examples that give opposite answers.

Question and answer: UPSC's official GS Paper II (2024, Series A) — paper ↗ · answer key ↗. Explanation: Minimalist IAS, checked 30 Sept 2026 (how we verify). Permalink ·

CSAT 2024 · Q73

X-Ray · Core #6 Medium

एक प्रश्न दिया गया है जिसके बाद दो कथन I और II दिए गए हैं। प्रश्न और कथनों पर विचार कीजिए।

P और Q में से प्रत्येक की आयु 100 वर्ष से कम है किन्तु 10 वर्ष से अधिक है। यदि आप P की आयु के अंकों का विनिमय (इंटरचेंज) कर दें, तो यह संख्या Q की आयु को निरूपित करती है।

  1. प्रश्न: उनकी आयु में कितना अंतर है?
  2. कथन–I: P की आयु, Q की आयु से अधिक है।
  3. कथन–II: उनकी आयु का योगफल, उनकी आयु के अंतर का 11/6 गुना है।

उपर्युक्त प्रश्न और कथनों के संबंध में, निम्नलिखित में से कौन-सा सही है?

Read this question in English

A Question is given followed by two Statements I and II. Consider the Question and the Statements.

Age of each of P and Q is less than 100 years but more than 10 years. If you interchange the digits of the age of P, the number represents the age of Q.

Question. What is the difference of their ages?

Statement–I. The age of P is greater than the age of Q.

Statement–II. The sum of their ages is 11/6 times their difference.

Which one of the following is correct in respect of the above Question and the Statements?

(a) The Question can be answered by using one of the Statements alone, but cannot be answered using the other Statement alone · (b) The Question can be answered by using either Statement alone · (c) The Question can be answered by using both the Statements together, but cannot be answered using either Statement alone · (d) The Question cannot be answered even by using both the Statements together

उत्तर और व्याख्या · explanation in English

Answer: (a) प्रश्न का उत्तर, दोनों में से अकेले एक कथन का प्रयोग कर दिया जा सकता है, किन्तु अकेले अन्य कथन का प्रयोग कर नहीं दिया जा सकता है

With ages 10a + b and 10b + a, Statement II gives 11(a + b) = (11/6) × 9|a − b|, i.e. 2(a + b) = 3|a − b|, whose only solution is 51 and 15. The difference is 36 whichever is older, so Statement II alone suffices; Statement I alone does not.

  1. Let the ages be 10a + b and 10b + a, with a and b non-zero digits. Sum = 11(a + b); difference = 9|a − b|.
  2. Statement I alone only says which one is older, so it is not sufficient.
  3. Statement II: 11(a + b) = (11/6) × 9|a − b|, which simplifies to 2(a + b) = 3|a − b|.
  4. If a > b: 2a + 2b = 3a − 3b, so a = 5b; b = 1 gives a = 5 (b = 2 would need a = 10). The ages are 51 and 15, in some order.
  5. Difference = 36 either way, so Statement II alone answers the question.
  6. Check: 51 + 15 = 66 = (11/6) × 36.

Remember · For a number and its reverse: sum = 11(a + b), difference = 9(a − b). Ask only what the question actually needs.

Question and answer: UPSC's official GS Paper II (2024, Series A) — paper ↗ · answer key ↗. Explanation: Minimalist IAS, checked 30 Sept 2026 (how we verify). Permalink ·

The Syllabus X-Ray of this topic

1 of its 2 sub-topics is Core

1 Core · 1 High · 0 Steady · 0 Rare

  • Core #6Data sufficiency · 38 questions
  • HighTables, charts & graphs · 20 questions

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