Martha bought and armchair and a coffee table....

[james_dennis]

Hi,

Couldn't find this problem on the forum after searching...

Data Sufficiency Problem:
Martha bought an armchair and a coffee table from an auction and sold both items at her store. Her gross profit from the purchase and sale of the armchair was what percent greater than the gross profit from the purchase and sale of the coffee table?

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

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

Answer is E (Neither is sufficient)

Working it out myself, I think I understand why but can someone please validate my reasoning and ensure I haven't over complicated this?

Chair purchase price = Cp
Chair sell price = Cs = (x/100)*Cp (where x should be greater than 100)
Table purchase price = Tp
Table sell price = Ts = (y/100)*Tp (where y should be greater than 100)

Profit on Chair = Pc = Cs - Cp
Profit on table = Pt = Ts - Tp

[(Pc - Pt) / Pt ] * 100 = ? (This is what the question is asking for)

...drill down some more using eqns above you get:

[[(Cs - Cp) - (Ts - Tp)] / (Ts - Tp) ] *100 = ?

...continue to drill down you get the Rephrased Question (RP)...
[[(Cp * x/100 - Cp) - Tp * y/100 - Tp)]/(Tp*y/100 - Tp)]*100=?

From Statement 1: Cp = Tp (110/100)
...Putting this into the RP above, all of the Cp's (or Tp's depending on which you use) will cancel but you are still left with x and y...therefore INSUFFICIENT

From Statement 2: Cs = Ts (120/100)
...Although I didn't explicitly write a rephrased equation above in terms of Cs and Ts, using the same logic discussed in statement 1, all Cs (or Ts) terms would cancel but you would still be left with x and y...therefore INSUFFICIENT

Combining statements: x and y are still unknown...therefore INSUFFICIENT (Answer E)

Is this correct? Is there a simpler way to recognize this?

[mschwrtz]

Well, I certainly agree that you will often profit from first translating from English to algebra, then manipulating algebraically.

But in this case, the rephrased [[(Cp * x/100 - Cp) - Tp * y/100 - Tp)]/(Tp*y/100 - Tp)]*100=? seems to me much harder to evaluate than the original question.

Let's try a different approach:

1 says nothing about sales price, so can't give us a profit to profit comparison.
AD out, BCE still in.

2 says nothing about purchase price, so can't give us a profit to profit comparison. B out, C or E.

Check values to see whether the two statements are sufficient together.

Let's suppose that Martha bought the coffee table for $100 and sold it for $200. These number are easy to work with. That means that she bought the armchair for $110 and sold it for $240. Her profit on the armchair ($130) was 30% greater than her profit on the table ($100).

The trick to testing values is to aim for not sufficient.

The trick for aiming for not sufficient is to pick values most likely to yield a different answer.

In this case that means taking the profits down or up.

Let's suppose that Martha bought the coffee table for $100 and sold it for $150. These number are also easy to work with. That means that she bought the armchair for $110 and sold it for $180. Her profit on the armchair ($70) was 40% greater than her profit on the table ($50).

So even together the two statements are consistent with two different values. E.

[dinesh19aug]

Hi,
I broke down this problem as :

PC = SC - CC
PA = SA -CA

Question asked = (PA - PC)/PC ==??
OR (PA/PC) - 1 ===??

ST 1: Statement 1) Martha paid 10 percent more for the armchair than the coffee table.

No information about Selling price of arm chair and coffe table. INSUFFICIENT

ST2: Statement 2) Martha sold the armchair for 20 percent more than she sold the coffee table.

No information about COST price of arm chair and coffe table. INSUFFICIENT

BOTH: INSUFFICENT - IMP: This is a FIND THE VALUE OF X type of problem and not YES OR NO problem. Adding both tells us that ==> (1.2S - C)/ (S - 1.1C), thus we cannot find a specific value.

Hence the combining both statement is also INSUFFICIENT.

ANS E

[RonPurewal]

dinesh, not bad.

one clarification:

Adding both tells us that ==> (1.2S - C)/ (S - 1.1C), thus we cannot find a specific value.

the value that dinesh has listed here is the value that the problem is asking you to find, once you decode the words and translate them into mathematical language.
since you cannot simplify this expression into a NUMBER, it follows that the value of the expression will change if you change the values of the variables -- therefore insufficient.

(for instance, if the expression were (1.4S - 0.7C)/(2S - C), you could simplify that to just 0.7, so that would be sufficient.)

[arun.jayachander]

Ron,

Need a clarification - If the question was slightly different from what was posted.

IF
"
Martha bought an armchair and a coffee table from an auction and sold both items at her store.Was her gross profit from the purchase and sale of the armchair greater than the gross profit from the purchase and sale of the coffee table?
"
Is the Question then solvable?
Would the answer then be "C"?
I didnt read the question carefully and ended up with "C" assuming that the question was the way i posted above....My mistake :( !!

[RonPurewal]

Ron,

Need a clarification - If the question was slightly different from what was posted.

IF
"
Martha bought an armchair and a coffee table from an auction and sold both items at her store.Was her gross profit from the purchase and sale of the armchair greater than the gross profit from the purchase and sale of the coffee table?
"
Is the Question then solvable?
Would the answer then be "C"?
I didnt read the question carefully and ended up with "C" assuming that the question was the way i posted above....My mistake :( !!

actually ... if you allow negative profits (i.e., losses), then the answer to the problem is still (e). to be precise, if the selling price of the table is less than 1/2 of its purchase price, then the profits will be reversed.

[linkinph1088]

No information about Selling price of arm chair and coffe table. INSUFFICIENT
ST2: Statement 2) Martha sold the armchair for 20 percent more than she sold the coffee table.
No information about COST price of arm chair and coffe table. INSUFFICIENT

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[suhail]

Hi,
I broke down this problem as :

PC = SC - CC
PA = SA -CA

Question asked = (PA - PC)/PC ==??
OR (PA/PC) - 1 ===??

ST 1: Statement 1) Martha paid 10 percent more for the armchair than the coffee table.

No information about Selling price of arm chair and coffe table. INSUFFICIENT

ST2: Statement 2) Martha sold the armchair for 20 percent more than she sold the coffee table.

No information about COST price of arm chair and coffe table. INSUFFICIENT

BOTH: INSUFFICENT - IMP: This is a FIND THE VALUE OF X type of problem and not YES OR NO problem. Adding both tells us that ==> (1.2S - C)/ (S - 1.1C), thus we cannot find a specific value.

Hence the combining both statement is also INSUFFICIENT.

ANS E

Shouldn't PA/PC= (1.2S-1.1C)/(S-C) ?
Pls clarify

[RonPurewal]

Shouldn't PA/PC= (1.2S-1.1C)/(S-C) ?
Pls clarify

yeah, i think that poster switched "before" and "after". good catch.

the point -- namely, that you get an equation that still contains 2 dependent unknowns -- remains unchanged.