Vincen 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.
The OA is C.
I don't know how to solve this DS question. I think that the answer is E. Experts, may you help me here? Thanks in advanced. <i class="em em-confused"></i>
Say Harry's income is x and the expenditure is y, while Ron's income is a and the expenditure is b.
Thus, Harry's portion of saving = (x - y)/x and Ron's portion of saving = (a - b)/a
We have to determine which between the two (x - y)/x and (a - b)/a is greater.
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 + b > a + y
=> x - y > a - b
=> Harry's Saving is greater than Ron's
Case 1: Say Harry's Saving = x - y = 100 and Harry's Income = x = 200, then (x - y)/x = 100/200 = 1/2. Again, say Ron's Saving = a - b = 50 and Ron's Income = a = 200, then (a - b)/a = 50/200 = 1/4. We see that 1/2 > 1/4. The answer is Harry.
Case 2: Say Harry's Saving = x - y = 100 and Harry's Income = x = 200, then (x - y)/x = 100/200 = 1/2. Again, say Ron's Saving = a - b = 50 and Ron's Income = a = 75, then (a - b)/a = 50/75 = 2/3. We see that 1/2 < 2/3. The answer is Ron.
No unique answer. Insufficient.
(2) Harry's income is 20% lesser than Ron's income.
We have no information about their expenditures. insufficient.
(1) and (2) combined
=> x = a - 20% of a = 80% of a = 0.8a
Harry's portion of saving = (x - y)/x = (x - y)/(0.8a)
Ron's portion of saving = (a - b)/a
We know that x - y > a - b; say x - y =100 and a - b = 80
Thus, Harry's portion of saving = (x - y)/x = (x - y)/(0.8a) = 100/0.8a = 125/a
Ron's portion of saving = (a - b)/a = 100/a
Since 125/a > 100/a, we conclude that Harry saves a greater portion of their income. Sufficient.
The correct answer:
C
Hope this helps!
-Jay
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