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# Martha bought an armchair and a coffee table at an action and sold bot

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

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10 Jan 2012, 04:05
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55% (hard)

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65% (01:59) correct 35% (01:45) wrong based on 634 sessions

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

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01 Mar 2012, 16:04
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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!

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.

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.
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Director
Joined: 23 Apr 2010
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Martha bought an armchair and a coffee table at an action and sold bot  [#permalink]

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10 Jan 2012, 14:23
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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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11 Jan 2012, 01:10
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nonameee wrote:
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).

Responding to a pm:

Question: Her gross profit from the purchase and sale of the armchair was what percent greater than her gross profit from the purchase and sale of the coffee table?

Pa - Gross profit on armchair
Pc - Gross profit on coffee table

We need to get (Pa - Pc)/Pc = (Pa/Pc - 1)

Pa = Sa - Ca = Selling price - Cost price of armchair
Pc = Sc - Cc = Selling price - Cost price of coffee table

We need to get (Sa-Ca)/(Sc - Cc) - 1

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

This means Ca = 1.1Cc

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

This means Sa = 1.2Sc

Both statements together give us (1.2Sc - 1.1Cc)/(Sc - Cc) which is still not enough. Hence answer is (E).

In case, instead, we had (1.1Sc - 1.1Cc)/(Sc - Cc) or (1.2Sc - 1.2Cc)/(Sc - Cc) etc, we could have taken the common factor out and cancelled it and we would have got 1.1 - 1 = 10% or 20% etc. In that case, answer would have been (C).

In essence, if the cost price of armchair is more than the cost price of coffee table by some percent x and if the selling price is also more by the same percent x, then the gross profit on the armchair would also be more by the same percent x.

Gross profit = Selling price - cost price
If selling price is 10% more and cost price is also 10% more, then the gross profit will be 10% more too.
New Gross Profit = 1.1*Selling price - 1.1*cost price = 1.1 * (Selling price - cost price) = 1.1*Gross profit
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Re: Martha bought an armchair and a coffee table at an action and sold bot  [#permalink]

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02 Mar 2012, 12:02
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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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02 Mar 2012, 12:15
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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10 Jun 2013, 03:52
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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18 Aug 2013, 19:40
2
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.

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

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07 Apr 2015, 12:19
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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07 Apr 2015, 22:33
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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.

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

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22 Jul 2018, 01:11
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.

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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22 Jul 2018, 01:26
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.

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]

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13 Jul 2019, 05:01
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
Re: Martha bought an armchair and a coffee table at an action and sold bot   [#permalink] 13 Jul 2019, 05:01
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