hersheycake wrote:

Martha bought an armchair and a coffee table at an action and sold both items at her store. Her gross profit from the purchase and sale of the armchair was what percentage greater than her gross profit from the purchase and sale of the coffee table?

(1) Martha paid 10% more for armchair than for the coffee table.

(2) Martha sold the armchair for 20% more than she sold the coffee table.

Thanks!

Welcome to GMAT Club. Below is a solution to your question.

Let the selling price and cost price of an armchair be \(S_a\) and \(C_a\) respectively;

Let the selling price and cost price of a coffee table be \(S_c\) and \(C_c\) respectively.

Basically we need to get: \(\frac{S_a-C_a}{S_c-C_c}\).

(1) Martha paid 10% more for armchair than for the coffee table --> \(C_a=1.1*C_c\). Not sufficient to get the ratio.

(2) Martha sold the armchair for 20% more than she sold the coffee table --> \(S_a=1.2*S_c\). Not sufficient to get the ratio.

(1)+(2) \(\frac{S_a-C_a}{S_c-C_c}=\frac{1.2*S_c-1.1*C_c}{S_c-C_c}\), still not sufficient to get the ratio.

Answer: E.

Notice though that if the percents in (1) and (2) were the same then the answer would be C, since we would be able to factor out the percent and then reduce by \(S_c-C_c\). For example if (1) were

Martha paid 20% more for armchair than for the coffee table, then we would have: \(\frac{S_a-C_a}{S_c-C_c}=\frac{1.2*S_c-1.2*C_c}{S_c-C_c}=\frac{1.2*(S_c-C_c)}{S_c-C_c}=1.2\), which would mean that Martha's gross profit from the armchair was 20% greater than her gross profit from the coffee table. Or simply if both the cost price and selling price of the armchair were 20% greater than the cost price and selling price of the coffee table then the profit would also be 20% greater.

Hope it's clear.

Great answer, but i have a basic doubt.

Do we not need to calculate [(Sa-Ca) - (Sc-Cc)]/ (Sa-Ca) * 100? If we were to calculate what the exact percentage was.

I know that we only need (Sa- Ca)/(Sc-Cc) and if we get that, we can add it to 100%.

I just want to confirm whether i am thinking wrong or what.

When the questions are like "What % greater" Do we calculate the percentage change? like (X-Y)/X * 100?