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Martha bought an armchair and a coffee table at an action and sold bot [#permalink]
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Is there a quick way to know whether a fraction will cancel the variables, and only an absolute value will remain?

As v1rok has said, had numbers been a little bit different, the answer would have been (C).
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Re: Martha bought an armchair and a coffee table at an action and sold bot [#permalink]
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Also Bunuel,

C would be true even if the percentages are different but if it were product

i .e instead of profit calculation ,if it were a revenue calculation, C would be the answer?

Am i right?
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Re: Martha bought an armchair and a coffee table at an action and sold bot [#permalink]
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shankar245 wrote:
Also Bunuel,

C would be true even if the percentages are different but if it were product

i .e instead of profit calculation ,if it were a revenue calculation, C would be the answer?

Am i right?


I'm not sure understand your point. The question asks about the ratio of the profits, not the value of any profit. If it were asking about the ratio of the revenues then the answer would be B, since (2) directly says that revenue from the armchair was 20% more than the revenue from the coffee table.
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Re: Martha bought an armchair and a coffee table at an action and sold bot [#permalink]
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Bumping for review and further discussion*. Get a kudos point for an alternative solution!

*New project from GMAT Club!!! Check HERE

Theory on Percent and Interest Problems: math-number-theory-percents-91708.html

All DS Percent and Interest Problems to practice: search.php?search_id=tag&tag_id=33
All PS Percent and Interest Problems to practice: search.php?search_id=tag&tag_id=54
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Re: Martha bought an armchair and a coffee table at an action and sold bot [#permalink]
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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.



Question asks for \(\frac{S_a-C_a}{S_c-C_c}\)

(1) Pick number \(C_c=100\) then \(C_a=110\) we don't have information for \(S_c\) and \(S_a\) so insufficient

(2) Pick number \(S_c=200\) then \(S_a=240\) we don't have information for \(C_c\) and \(C_a\) so insufficient

(1)+(2) Although it seems like we can solve the questions using the numbers we picked above for (1) and (2), we need to try to pick a new set of numbers to make the statements insufficient.
For example, pick number \(S_c=300\) then \(S_a=360\). The numerator and denominator change non-proportionally, therefore will result in a different ratio.

Answer is E
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Re: Martha bought an armchair and a coffee table at an action and sold bot [#permalink]
Let sale price / purchase price of armchair be As and Ap resp. Similarly for Coffee table be, Cs and Cp.
To find (As - Ap) * 100 / (Cs - Cp) ?
1) gives us that Ap = 1.1Cp
our eq becomes : (As - 1.1Cp) *100 / (Cs - Cp). NS.

2) gives us that As = 1.2 Cs
our eq becomes : (1.2Cs - Ap) *100 / (Cs - Cp). NS.

1 and 2 , give :
(1.2Cs - 1.1Cp) *100 / (Cs-Cp)
Since we cannot cancel anything, the statements are still not suff.
Thus E.
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Re: Martha bought an armchair and a coffee table at an action and sold bot [#permalink]
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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! :)


You can also try two values to see that both statements together are not sufficient.
It is obvious that neither statement alone is sufficient. The only question is whether the two of them together are sufficient.

Say she paid $100 for table and $110 for chair (10% more). Say she sold table for $200 and chair for $240 (20% more).
Her gross profit from table is $100 while from chair is $130 - i.e. 30% more

Now just vary one set of numbers a bit:
Say she paid $100 for table and $110 for chair (10% more). Say she sold table for $300 and chair for $360 (20% more).
Her gross profit from table is $200 while from chair is $250 - i.e. 25% more

So we see that the percentage by which her gross profit on chair is more than that on table varies with 2 different set of values. So both statements together are not sufficient.

Answer (E)
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Re: Martha bought an armchair and a coffee table at an action and sold bot [#permalink]
Bunuel wrote:
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?
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Re: Martha bought an armchair and a coffee table at an action and sold bot [#permalink]
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Akshit03 wrote:
Bunuel wrote:
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?


Question: What percent is 10 greater than 8?

The answer is: (10 - 8)/8*100 = 25%. If you don't multiply you'll get 0.25, which is numerical value of 25% but you cannot say that 10 is greater than 8 by 0.25.
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Re: Martha bought an armchair and a coffee table at an action and sold bot [#permalink]
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. NS as we dont know the price of AC and CT

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

1+2

We dont have any idea about the prices so we cannot find the ans

E
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Re: Martha bought an armchair and a coffee table at an action and sold bot [#permalink]
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