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

Say Rex's income is $100; thus, Paul's income = $100 – 40 = $60.

This gives Quentin's income = 80% of $60 = $48; and Sam's income = 60% of $60 = $36;

After Rex gave 60% of his income to Sam and 40% of his income to Quentin, Sam's income = 36 + 60% of 100 = 36 + 60 = $96 and Quentin's income = 48 + 40% of 100 = 48 + 40 = $88

Quentin's new income is 88/96 = 11/12 fraction of Sam's new income

The correct answer: A

Hope this helps!

-Jay
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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