BTGmoderatorDC wrote:Ted and Barney work for the same company but earn different incomes and have different expenditures. Who saves a greater portion of their income?
(1) The sum of Ted's income and Barney's expenditure is greater than the sum of Barney's income and Ted's expenditure.
(2) Ted's income is 20% lesser than Barney's income.
OA C
Source: e-GMAT
Say the incomes of Ted and Barney are x, and y, respectively; and the expenditures of Ted and Barney are p, and q, respectively.
Thus, the savings of Ted and Barney would be (x - y), and (p - q), respectively.
The portion of savings of Ted and Barney are (x - y)/x = 1 - y/x, and (p - q)/p = 1 - q/p, respectively.
We have to determine which of the two (1 - y/x) and (1 - q/p) is greater.
(1) The sum of Ted's income and Barney's expenditure is greater than the sum of Barney's income and Ted's expenditure.
x + q > p + y
=> x - y > p - q.
(x - y)/x > (p - q)/x
1 - y/x > (p - q)/x
Can't determine whether (1 - y/x) > (1 - q/p). Insufficient.
(2) Ted's income is 20% lesser than Barney's income.
=> x = 80% of p = 0.8p
No information about the expenditures. Insufficient.
(1) and (2) together
From (1), we have 1 - y/x > (p - q)/x
=> 1 - y/x > (p - q)/(0.8p); replacing the value of x
1 - y/x > p/0.8p - q/0.8p
1 - y/x > 1.25 - 1.25q/p
1 - y/x > 1.25(1 - q/p)
=> 1 - y/x > 1 - q/p. Sufficient.
The correct answer:
C
Hope this helps!
-Jay
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