Data Sufficiency

BTGmoderatorLU wrote:Source: e-GMAT

Harry and Ron 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 Harry's income and Ron's expenditure is greater than the sum of Ron's income and Harry's expenditure.
2) Harry's income is 20% lesser than Ron's income.

OA C

Say, Harry's income and expenditures are x, and y, respectively. And Ron's income and expenditures are p, and q, respectively.

Harry's saving = x - y and his proportion of saving = (x - y)/x = 1 - y/x.
Ron's saving = p - q and his proportion of saving = (p - q)/p = 1 - q/p.

We are asked to compare 1 - y/x and 1 - q/p.

Since 1 is a constant, we need to compare y/x and q/p.

Note that y/x = Harry's expenditure/ Harry's income and q/p = Ron's expenditure / Ron's income

Let's take each statement one by one.

1) The sum of Harry's income and Ron's expenditure is greater than the sum of Ron's income and Harry's expenditure.

x + q > y + p
x - y > p - q => Harry's expnditure > Ron's expnditure

Insufficient to compare y/x and q/p.

2) Harry's income is 20% lesser than Ron's income.

x = 0.8p. Insufficient to compare y/x and q/p.

(1) and (2) together

From (1), we know that Harry's expenditure is greater than that of Ron's and from (2), we know that Harry's income is less than that of Ron's. Thus, Ron saves a greater portion of his income. Sufficient.

The correct answer: C

Hope this helps!

-Jay
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