karthikpandian19 wrote:If x, y, and k are positive integers such that (x/(x+y))(10)+(y/(x+y))(20)=k and if x<y, which of the following could be the value of k?
a.10
b.12
c.15
d.18
e.30
PS: i didnt understand the long explanation for the correct answer D
I posted an explanation here:
https://www.beatthegmat.com/tough-algebr ... tml#292229.
As for the more theoretical approach:
Let x = the number of $10 towels purchased and y = the number of $20 towels purchased.
Average cost per towel = (total cost)/(total number of towels) =
(10x + 20y)/(x+y).
This is the value of k in the problem above:
(x/(x+y))(10) + (y/(x+y))(20) = k
(10x + 20y)/(x+y) = k.
Since the price of each towel is either $10 or $20, the value of k -- the AVERAGE cost per towel -- must be between 10 and 20.
Since y>x -- implying that more $20 towels are purchased than $10 towels -- the average cost per towel must be CLOSER TO 20 than to 10.
Thus, the only viable answer choice is
D.
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