Bunuel wrote:

When positive integer m is divided by positive integer x, the reminder is 7 and when positive integer n is divided by positive integer y, the reminder is 11. Which of the following is a possible value for x + y?

I. 18

II. 19

III. 20

A. I only

B. II only

C. III only

D. II and III only

E. None

TIP FOR SUCH QUESTIONS: Make Algebraic Equation in the beginning to understand how to proceed further. Then Start thinking the possible values of variables asked abouti.e. "When positive integer m is divided by positive integer x, the reminder is 7" can be understood as

m = ax +7

which means the value of x must be greater than 7 as the remainder 7 is possible only when the Divisor is bigger than the Remainder 7i.e. Min Value of x = 8

AND

i.e. "When positive integer n is divided by positive integer y, the reminder is 11" can be understood as

n = by +11

which means the value of y must be greater than 11 as the remainder 11 is possible only when the Divisor is bigger than the Remainder 11i.e. Min Value of y = 12

i.e. Minimum Value of x+y = 8+12 = 20Hence III only can be True

Answer: Option

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