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UPSC 2006: Each of the persons A, B, C, D and E possesses unequal number (<10) of similar items. A, B and C possess 21 items in all, while C, D and E possess 7 items in all. How many items do A and B possess in all?
(a)15
(b)17
(c)18
(d)Data is insufficient
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Not attemptedCorrect Answer: (b) 17
Let the five distinct numbers (<10) be a, b, c, d, e for A–E respectively. Given a + b + c = 21 and c + d + e = 7, so a + b = 21 − c and d + e = 7 − c. Testing allowable values of c (1–9) that keep all numbers positive, distinct and <10 shows only c = 4 works: then a + b = 17 and d + e = 3 with {a, b} = {9, 8} and {d, e} = {1, 2}. Hence A and B together possess 17 items.
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Frequently Asked Questions
What is the correct answer to this UPSC 2006 Science & Technology question?▼
The correct answer is option (b): 17. Watch the detailed video explanation in our Sherlocking Prelims course on UnlockIAS.
Which year was this Logical Reasoning & Puzzles question asked in UPSC Prelims?▼
This question was asked in UPSC CSE Prelims 2006, GS Paper 1, as Question 96. It falls under Science & Technology > Logical Reasoning & Puzzles.
What is the difficulty level of this UPSC question?▼
This question is rated "difficult". It is a challenging question that demands deep subject knowledge and analytical thinking.
How many UPSC Prelims questions have been asked from Logical Reasoning & Puzzles?▼
UPSC has asked 71 questions from Logical Reasoning & Puzzles (under Science & Technology) across multiple years. Visit the topic page to see the full list and year-wise trends.