cans wrote:But suppose the options were
A)12
B)13
C)14
D)15
E)16
if we start with C) and then go to D and then to E, it can take sufficient time.
Given your set of answer choices:
Answer choice C (k=14) makes x>y:
10x + 20y = 14x + 14y
6y = 4x
y/x = 4/6.
Answer choice D (k=15) makes x=y:
10x + 20y = 15x + 15y
5y = 5x
y/x = 5/5.
Since k=14 makes x>y and k=15 makes x=y, the process is complete: we know that the next largest answer choice (k=16) makes x<y.
Quick and efficient. And no algebraic insight required.
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