BTGmoderatorDC wrote: ↑Sun May 03, 2020 6:32 pm
Paul's income is 40% less than Rex's income, Quentin's income is 20% less than Paul's income, and Sam's income is 40% less than Paul's income. If Rex gave 60% of his income to Sam and 40% of his income to Quentin, Quentin's new income would be what fraction of Sam's new income?
(A) 11/12
(B) 13/17
(C) 13/19
(D) 12/19
(E) 11/19
OA
A
Source: Manhattan Prep
From the information given in the question, we can create the following equations in which P = Paul’s income, R = Rex’s income, Q = Quentin’s income, and S = Sam’s income.
P = 0.6R, or R = P/0.6
Q = 0.8P
S = 0.6P
Now we have all variables in terms of P.
Let’s choose a convenient value for P. If P = 30, we have:
R = P/0.6 = 30/0.6 = 50
Q = 0.8 x 30 = 24
S = 0.6 x 30 = 18
Since Rex gives 60% of his income to Sam and 40% of his income to Quentin, he gives 0.6 x 50 = 30 dollars to Sam and the remaining 20 dollars to Quentin. Thus, Sam now has 18 + 30 = 48 dollars and Quentin now has 24 + 20 = 44 dollars.
Therefore, Quentin’s new income is 44/48 = 11/12 of Sam’s new income.
Answer: A
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