Question

If m and n are positive integers and 4m + 9n is a multiple of 11, which of the following is also a multiple of 11?

• A. 2m+ 3n
• B. 2m + 5n
• C. 3m + 4n
• D. m + n + 11

Answer 1

Answer:

C. 3m + 4n

4m + 9n is multiple of 11 4m + 9n = 11x 9n = 11x - 4m n = (11x - 4m)/9 Consider 3m + 4n = 3m + 4{(11x - 4m)/9} = 3m + (44x - 16m)/9 = (27m + 44x - 16m)/9 = (11m + 44x)/9 = 11(m + 4x)/9 = Multiple of 11