2020 · Q2
Two unequal pairs of numbers satisfy the following conditions: (i) The product of the two numbers in each pair is 2160 (ii) The HCF of the two numbers in each pair is 12. If x is the mean of the numbers in the first pair and y is the mean of the numbers in the second pair, then what is the mean of x and y?
Elementary MathematicsHCF and LCM
- A60
- B72
- C75
- D78
Explanation
Write the two numbers of each pair as 12m and 12n with coprime m, n. Then 144mn = 2160 gives mn = 15, so {m, n} is {1, 15} or {3, 5}. The two unequal pairs are therefore (12, 180) and (36, 60). Their means are x = 96 and y = 48, so the mean of x and y is (96 + 48)/2 = 72.