What was the price at which a merchant sold a certain appliance?

Question

(1) The merchant's gross profit on the appliance was 20 percent of the price at which the merchant sold the appliance.
(2) The price at which the merchant sold the appliance was $50 more than the merchant's cost of the appliance.

MHIKER · Accepted Answer

s=   selling price

c =  cost price

p =  profit

p = s - c

(a)  p=20 % s ,

s-c= 0.20s

0.8s = c , no information is given about c. INSUFFICEINT.

(b)  s = c + 50 , no information of C INSUFFICIENT.

CONSIDERING BOTH:
 c + 50 - c = 0.20s

0.2s = 50

s = 250

The answer is  C

subhashghosh · Answer

Profit = SP - CP

(1)

Profit = 0.20SP

=> CP = 0.80SP

Not Sufficient

(2)

50 = SP - CP

Not Sufficient

(1) + (2)

0.20SP = 50

=> SP = 250

Answer - C

MHIKER · Answer

P = s-c
1) p = 0.20s Insufficient
2) p = 50 Insufficient

For Both: 0.20s =50
Ans. C

rboots · Answer

It's C.

(1) The merchant's gross profit on the appliance was 20% of the price at which the merchant sold the appliance.

Let p = profit
Let x = original cost of the appliance to the merchant

p = x + .2x

This alone won't give us the original price. #1 is insufficient.

(2) The price at which the merchant sold the appliance was $50 more than the merchant's cost of the appliance.

Using the original variables...

p = x + 50

This alone won't do it. #2 is insufficient. However, comparing the two equations:

.2x = 50 
x = 250
250 + 50 = 300

Answer: C.

dianamao · Answer

Is "gross profit" equal to the difference between sale price and cost of good?

Bunuel · Answer

Yes,  {Gross Profit} = {Selling Price} - {Cost}

What was the price at which a merchant sold a certain appliance?

Question:  {Selling Price}=?

(1) The merchant's gross profit on the appliance was 20 percent of the price at which the merchant sold the appliance -->  {Selling Price} - {Cost} = 0.2*{Selling Price}  -->  0.8*{Selling Price} = {Cost} . One equation two unknowns. Not sufficient.

(2) The price at which the merchant sold the appliance was $50 more than the merchant's cost of the appliance -->  {Cost} +$50 = {Selling Price} . One equation two unknowns. Not sufficient.

(1)+(2) We have that  0.8*{Selling Price} = {Cost}  and  {Cost} +$50 = {Selling Price} . So, we have two distinct linear equations with two unknowns, hence we can solve for each. Sufficient.

Answer: C.

Hope it's clear.

dianamao · Answer

Okay thanks. What about "profit" is that the same as gross profit in terms of calculation?

Bunuel · Answer

Yes, generally profit and gross profit are the same on the GMAT.

Asifpirlo · Answer

solution:

...........................cost......................................................................sell
 st(1)................... x .................................................................. 120%x insufficient
 st(2)................... p ....................................................................... p+5 insufficient
using both, p × 120% = p+5
 or, p = 25 .
So Answer (C)

gmatkum · Answer

SP = P + Purchase Price (PP)

Combined we have

SP = X 
Profit = 50 = 0.2X

So SP = 250 
Hence C

dave13 · Answer

pushpitkc hello can you explain please how do we combine both statements and how we get this => CP = 0.80SP

perhaps afterwork hours effect me

but somehow cant combine these two statments.,,,

pushpitkc · Answer

Hey  dave13

I'm sure you must be aware of the following definitions but am writing them anyway
SP = CP + Profit -> Profit = SP - CP

Now, coming back to the question

1. Profit was 20% of SP (or) Profit = 0.2*SP 
This can be written as 0.2*SP = SP - CP -> CP = 0.8*SP 
We can't arrive at an unique price at which the appliance was sold(Stmt 1 alone is insufficient)

2. SP = CP + 50(for every unique cost price, the selling price will wary - no unique price)
Now, statement 2 is also insufficient!

On combining the two statements, 
we know that CP = 0.8*SP -> SP - 50 = 0.8*SP -> (1-0.8)SP = 50 -> SP =  \frac{50}{0.2} = \frac{500}{2} = 250

Hope that helps you!

TheUltimateWinner · Answer

Hello  Bunuel 
What if people don't know the highlighted part? i mean: is there any other way to solve this?
Thanks in advanced...

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What was the price at which a merchant sold a certain appliance?

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