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UPSC 1996: The following figure contains three squares with areas of 100, 16 and 49 lying side by side as shown. By how much should the area of the middle square be reduced in order that the total length PQ of the resulting three squares is 19?
(a)12
(b)4
(c)2
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Not attemptedCorrect Answer: (a) 12
Side lengths are √100 = 10, √16 = 4 and √49 = 7, so the original total length PQ is 10 + 4 + 7 = 21. To reduce PQ to 19, the middle square’s side must be 19 − 10 − 7 = 2, giving a new area 2² = 4. The decrease in area is 16 − 4 = 12; the other numeric options give total lengths that are not 19.
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What is the correct answer to this UPSC 1996 Science & Technology question?▼
The correct answer is option (a): 12. Watch the detailed video explanation in our Sherlocking Prelims course on UnlockIAS.
Which year was this Quantitative Aptitude question asked in UPSC Prelims?▼
This question was asked in UPSC CSE Prelims 1996, GS Paper 1, as Question 146. It falls under Science & Technology > Quantitative Aptitude.
What is the difficulty level of this UPSC question?▼
This question is rated "moderate". It requires sound conceptual understanding of the topic.
How many UPSC Prelims questions have been asked from Quantitative Aptitude?▼
UPSC has asked 178 questions from Quantitative Aptitude (under Science & Technology) across multiple years. Visit the topic page to see the full list and year-wise trends.