Hi,

We have, 1 + x + y +xy = 21 (where x & y are natural numbers/positive integers)

or x(1+y) = 20 -y

or x = (20-y)/(1+y)

Using (1)

y > 3, i.e., y = 4, 5, 6...

when y=4, x = (20-4)/5 = 16/5 (not a natural number)

when y=5, x = (20-5)/6 = 15/6 (not a natural number)

when y=6, x = (20-6)/7 = 14/7 = 2

when y=7, x = (20-7)/8 = 13/8 (not a natural number), and for remaining values of y, there would be no positive integral value of x.

so, (x,y) = (2,6). Sufficient

Using (2)

y = 6, => x = (20-6)/(1+6) = 2

so, (x,y) = (2,6). Sufficient.

Thus, Answer is (D)

Regards,

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