Data Sufficiency

BTGmoderatorDC wrote: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

Source: e-GMAT

Say Harry's income, expenditure and saving are x, y, and z, respectively, thus, z = (x - y); thus, the portion of Harry's saving = z/x.

Similarly, say Ron's income, expenditure and saving are p, q, and r, respectively, thus, r = (p - q); thus, the portion of Harry's saving = r/p.

We have to determine whether z/x > = < r/p.

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 > p + y => (x - y) > (p - q) => z > r

Though we see that Harry's saving (z) is greater than Ron's saving (r), we cannot conclude that Harry saves a greater portion of their income or z/x > r/p. If x >> p then z/x < r/p. Insufficient.

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

Certainly insufficient.

(1) and (2) together

From (2), we have x = 0.8p

From (1), we have z > r

Thus, z/x = z/0.8p

Thus, we can compare Harry's (z/0.8p = (5/4)*(z/p)) and Ron's portion of saving (r/p).

We can see that (5/4)*(z/p) > r/p since z > r.

The correct answer: C

Hope this helps!

-Jay
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