Harry and Ron work for the same company but earn different incomes and

Question

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.

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Answer Choices

A. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient to answer the question asked.
B. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient to answer the question asked.
C. BOTH statements (1) and (2) TOGETHER are sufficient to answer the question asked, but NEITHER statement ALONE is sufficient to answer the question asked.
D. EACH statement ALONE is sufficient to answer the question asked.
E. Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data specific to the problem are needed.

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Saquib
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Official Answer

C

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broall · Accepted Answer

Harry's income $I_1$ and Harry's expenditure $E_1$. The saving portion is $\frac{I_1-E_1}{I_1}$
Ron's income $I_2$ and Ron's expenditure $E_2$. The saving portion is $\frac{I_2-E_2}{I_2}$

we need to compare $\frac{I_1-E_1}{I_1}$ vs $\frac{I_2-E_2}{I_2}$

(1) $I_1+E_2 > I_2+E_1$. We can't get enough information to conclude. Insufficient.

(2) $I_1 = 80\%I_2$. We still don't have enough information. Insufficient.

Combine (1) and (2).
$I_1+E_2 > I_2+E_1 \implies I_1-E_1 > I_2-E_2$

$(I_1 = 80\%I_2 \implies I_1 < I_2 \implies \frac{1}{I_1} > \frac{1}{I_2} \implies \frac{I_1-E_1}{I_1} > \frac{I_2-E_2}{I_2}$ or Harry's saving portion is larger than Ron's saving portion . Sufficient.

The answer is C.

Mahmud6 · Answer

C.

1: Let income of Harry is 100 and income of Ron is 10

If expenditure of Harry is 90 and expenditure of Ron is 0, then saving of Harry (100-90=10) is greater than that of Harry (10-10=0). Harry's income>Ron's income

Again let income of Harry is 10 and income of Ron is 100

If expenditure of Harry is 10 and expenditure of Ron is 90, then saving of Ron (100-90=10) is greater than that of Harry (10-10=0). Ron's income>Harry's income

So, statement 1 is insufficient.

2. No information about expenditure. Insufficient.

1+2:

Let Ron's Income 100 and Harry's Income is 80

If expenditure of Ron is 90, expenditure of Harry will be  less than  70 => Saving of Harry (80-less than 70= Greater than 10> Saving of Ron (100-90=10)
Again, if expenditure of Ron is 100, expenditure of Harry will be  less than  80 => Saving of Harry (80-less than 80= Greater than 0> Saving of Ron (100-100=0)

So, 1+2 is sufficient.

hellosanthosh2k2 · Answer

Harry: Savings - a, expenditure - b, income = a + b
Ron: Savings - c, expenditure - d, income = c + d

question  \frac{a}{(a+b)} > \frac{c}{(c+d)}  ?

Statement 1: The sum of Harry’s income and Ron’s expenditure is greater than the sum of Ron’s income and Harry’s expenditure.
 => a + b + d > c + d + b
 => a > c
Harry's savings > Ron's savings, but no idea about incomes of both => insuff

Statement 2: Harry’s income is 20% lesser than Ron’s income
 a + b = 0.8(c+d)

1 + 2,
  \frac{a}{(a+b)} > \frac{c}{(c+d)}  ? (original question)
  \frac{a}{0.8(c+d)} > \frac{c}{c+d)}  ? (from statement 2)
 a > 0.8 c ? Answer Yes (from statement 1)

(C)

StressTest · Answer

I have a simpler approach:

1) HI + RE > RI + HE => Insufficient
2) HI > RI => Insufficient

1 + 2) Multiply 2) with -1:
-HI<-RI
add 2) to 1)
 HI + RE > RI + HE
+ -HI >-RI
= RE > HE
=> Sufficient

Engineer1 · Answer

I think the term "portion" of their income is the catch here?
Because otherwise, the answer would be A.

Income = I, Expenditure = E

Option 1, Ih + Er > Ir + Eh; Therefore, Ih-Eh > Ir - Er (suff).
However, the question prompt asks for portion, so we need to prove if (Ih-Eh)/Ih > (Ir - Er)/Ir or reverse is true. That's what the relation between Ir and Ih is necessary, making option A insuff by itself.

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Harry and Ron work for the same company but earn different incomes and

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