What was the price at which a merchant sold a certain appliance? : Data Sufficiency (DS)

TOUGH GUY

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What was the price at which a merchant sold a certain appliance? [#permalink]

10 Oct 2005, 11:25

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A

B

C

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E

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19% (01:11) wrong

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

(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.

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MHIKER

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What was the price at which a merchant sold a certain appliance? [#permalink]

Updated on: 28 Dec 2020, 09:18

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$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 $C$

Originally posted by MHIKER on 13 May 2011, 06:25.
Last edited by MHIKER on 28 Dec 2020, 09:18, edited 2 times in total.

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subhashghosh

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Re: What was the price at which a merchant sold a certain appliance? [#permalink]

13 May 2011, 06:59

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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
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MHIKER

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Re: What was the price at which a merchant sold a certain appliance? [#permalink]

02 Jan 2012, 06:37

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Jasontuyj2012 wrote:

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

(1) The merchant's gross profit on the appliance was 20% 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.

I chose E.

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

For Both: 0.20s =50
Ans. C

rboots

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Re: What was the price at which a merchant sold a certain appliance? [#permalink]

02 Jan 2012, 08:21

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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

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Re: What was the price at which a merchant sold a certain appliance? [#permalink]

13 Jul 2012, 18:57

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

L

Bunuel

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Posts: 92756

Re: What was the price at which a merchant sold a certain appliance? [#permalink]

14 Jul 2012, 04:00

Expert Reply

dianamao wrote:

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

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.
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dianamao

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Re: What was the price at which a merchant sold a certain appliance? [#permalink]

14 Jul 2012, 15:08

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

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Bunuel

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Re: What was the price at which a merchant sold a certain appliance? [#permalink]

15 Jul 2012, 07:05

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Expert Reply

dianamao wrote:

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

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

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Re: What was the price at which a merchant sold a certain appliance? [#permalink]

07 Aug 2013, 07:43

2

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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

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Re: What was the price at which a merchant sold a certain appliance? [#permalink]

18 May 2014, 11:12

1

Kudos

SP = P + Purchase Price (PP)

Combined we have

SP = X
Profit = 50 = 0.2X

So SP = 250
Hence C

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dave13

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Posts: 1162

Re: What was the price at which a merchant sold a certain appliance? [#permalink]

23 Apr 2018, 13:35

subhashghosh wrote:

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

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.,,,

L

pushpitkc

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Re: What was the price at which a merchant sold a certain appliance? [#permalink]

23 Apr 2018, 13:49

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dave13 wrote:

subhashghosh wrote:

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

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.,,,

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

Quote:

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

(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.

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!

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Re: What was the price at which a merchant sold a certain appliance? [#permalink]

09 Feb 2020, 10:24

Bunuel wrote:

dianamao wrote:

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

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.

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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Re: What was the price at which a merchant sold a certain appliance? [#permalink]

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Re: What was the price at which a merchant sold a certain appliance? [#permalink]

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