Euclid's Division Lemma states that
"Given positive integers a and b, there exists unique integers
q and
r satisfying
a = bq+ r where
0 ≤ r < b" (q is quotient and r is remainder)
From the question :
m = x *q
1 + 7 So from theorem 7< x ; x > 7
n = y *q
2 + 11 So from theorem 11< y ; y > 11
So the least value of x = 8 & least value of y = 12
Least value of x+y = 20.
Out of given choices only III is possible.
Answer
C
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Ambarish