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When a positive integer n is divided by 7 the quotient and remainder are equal. What is the largest such value of n?

Class 10Euclid's Division LemmaNumber Systems

A48
B96
C53
D43

Step-by-Step Solution

n = 7 q + r

with

q = r

and

0 <= r < 7

, so

n = 7 r + r = 8 r

. The largest valid remainder is

r = 6

, giving

n = 8 \times 6 = 48

.

Answer: A) 48

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