Averages Problem

20 + 35 + 40 + 45 + 70 = 210

If the average price of a stock in the portfolio increases by 2%, the total will also increase by 2%.

210 * 0.02 = 4.2

We need to find the combination of stock prices that increases the total by $4.20 when we increase one stock by 15% and decrease the other by 35%.

The difference between the two prices must be relatively large, since 35% is so much larger than 15%, so 70 and 20 make the most sense to check first.

70 * 0.15 = 10.5
20 * 0.35 = 7

10.5 - 7 = 3.5

The difference is only $3.50, but comes close to the $4.20 increase required. No other combination will increase this difference, so we can go with answer choice E.

old average = 210/5 = 42
new average = 42*1.02 = 42.84
thus increase = 42.84-42 = 0.84
increased sum = 0.84*5 = 4.2

now, (A+B+constant)/5 = 42 and (1.15A+ 0.65B+constant)/5 = 42.84

thus, [(1.15A+ 0.65B+ constant)- (A+B+constant)]/5 = 0.84
hence,
0.15 A - 0.35 B = 4.2 (approx)

for A = 70 and B = 20 we have RHS = 3.5.(max difference possible)

hence constant = E = 35,40 and 45.