HCF of two numbers is 27 and sum of the two numbers is 216. How many such pairs of numbers are possible?

• A. 2
• B. 4
• C. 1
• D. 3

Answer: (A)

HCF of two numbers =27             Let two numbers are in the ratio a:b , then numbers are 27a  and 27b.             Given that , sum of two numbers is 216                                  27a + 27 b = 216 a+b = 216/27= 8  Writing the possibilities of a and b to be sum is 8                 ( 1,7 ), (2,6),(3,5) and (4,4).              Of these pairs, (1,7) and (3,5) are relatively primes . Therefore, 2 such pairs are possible.And those required numbers are ( 1 x 27 , 7 x 27) and ( 3 x 27, 5 x 27)                                = (27 , 189) and (81,135)