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Harry and Ron work for the same company but earn different

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Harry and Ron work for the same company but earn different

by Gmat_mission » Sat Apr 06, 2019 5:03 am

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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.

[spoiler]OA=C[/spoiler]

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Source: — Data Sufficiency |

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by Ian Stewart » Sat Apr 06, 2019 1:26 pm

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Say Harry earns $H, and has $E in expenses, while Ron earns $R, and spends $S. Then Harry saves H-E dollars, and Ron saves R-S dollars.

Statement 1 tells us:

H + S > R + E
H - E > R - S

or in other words, Harry's savings exceed Ron's savings.

Now, it's not clear what is meant by the question "who saves a greater portion of their income", since "portion" can simply mean "amount". So because the wording of the question is so imprecise, there's no way to know if Statement 1 is sufficient alone, or if instead they mean to ask "who saves a greater proportion of their income". If they just want to know who saves the larger amount, then the answer is A. If we care who saves the greater fraction of his income, then Statement 1 is not sufficient alone; if Harry saves more, but also earns a lot more, then he might not save the higher percentage of his income. But combining Statements 1 and 2, we know Harry saves more than Ron, and earns less than Ron, so clearly saves the higher fraction of his income.
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