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Question

# An army base has some soldiers, such that when they stand in rows and columns they form a square. More soldiers were added to the camp and the number of rows and columns increased by 1. If there are 625 soldiers now, how many soldiers were added?

A

64

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B

49

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C

69

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D

54

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Solution

## The correct option is B 49 Number of rows and columns when there are 625 soldiers = √625 = √25×25 = 25 ⇒ Intial number of rows and columns = 25 -1 = 24 (As one more row and column was added) ∴, initial number of soldiers 242 = 576 ∴ number of soldiers added = 625 - 576 = 49

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