A person X wants to distribute some pens among six children A, B, C, D, E and F. Suppose A gets twice the…
A person X wants to distribute some pens among six children A, B, C, D, E and F. Suppose A gets twice the number of pens received by B, three times that of C, four times that of D, five times that of E and six times that of F. What is the minimum number of pens X should buy so that the number of pens each one gets is an even number?
147
150
294
300
Solution
Let A's pens be the LCM of 2, 3, 4, 5, 6 = 60. Then B = 30, C = 20, D = 15, E = 12, F = 10. D = 15 is odd. To make all counts even, double everything: A = 120, B = 60, C = 40, D = 30, E = 24, F = 20. Total = 120 + 60 + 40 + 30 + 24 + 20 = 294.