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If a merchant purchased a sofa from a manufacturer for $400 and then s

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If a merchant purchased a sofa from a manufacturer for $400 and then s  [#permalink]

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New post 26 Apr 2019, 03:33
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If a merchant purchased a sofa from a manufacturer for $400 and then sold it, what was the selling price of the sofa?

(1) The selling price of the sofa was greater than 140 percent of the purchase price.
(2) The merchant's gross profit from the purchase and sale of the sofa was 1/3 of the selling price.


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Re: If a merchant purchased a sofa from a manufacturer for $400 and then s  [#permalink]

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New post 26 Apr 2019, 04:15
If a merchant purchased a sofa from a manufacturer for $400 and then sold it, what was the selling price of the sofa?
The cost price and selling price are interconnected through profit or loss. Here, cost price = c=400.

(1) The selling price of the sofa was greater than 140 percent of the purchase price.
The selling price is given as a range, so insuff....s>1.4*c...s>1.4*400....x>560
Insuff

(2) The merchant's gross profit from the purchase and sale of the sofa was 1/3 of the selling price.
If s is the selling price, profit =\(\frac{s}{3}\).
Thus c+\(\frac{s}{3}\)=s, or c=400=\(\frac{2s}{3}\), that is s=600.
Suff

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Re: If a merchant purchased a sofa from a manufacturer for $400 and then s  [#permalink]

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New post 27 Apr 2019, 14:23
1
The Logical approach to this question will focus on finding the profit/lost, which will get us from the cost to the selling price.
Statement (1) uses the term 'greater than' which gives us range, and thus doesn't lead to one definite answer to the question we're asked. (A) and (D) are eliminated.
Statement (2) provides the ratio between the profit and the selling price, which is sufficient: if the profit is a third of the selling price then the cost is the other two thirds. Since we have a ratio and a number (the cost), we have all we need. The correct answer is (B).

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Re: If a merchant purchased a sofa from a manufacturer for $400 and then s  [#permalink]

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New post 29 Apr 2019, 04:55
Bunuel wrote:
If a merchant purchased a sofa from a manufacturer for $400 and then sold it, what was the selling price of the sofa?

(1) The selling price of the sofa was greater than 140 percent of the purchase price.
(2) The merchant's gross profit from the purchase and sale of the sofa was 1/3 of the selling price.


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Hola amigos :cool:

Purchasing price - \(400\)
Selling price - \(x\), so what is \(x\)?

1. \(x\) was greater than \(140\) % of \(400\).
Greater than \(140\) % means that \(x\) can be \(600, 700\), ... or whatever.
Insufficient

2. The merchant's gross profit from the purchase and sale of the sofa was \(1/3 * x\).
Gross profit = \(x - 400\) or \(1/3 * x = x - 400\). So \(x = 600\)
Sufficient

The answer is B
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Re: If a merchant purchased a sofa from a manufacturer for $400 and then s  [#permalink]

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New post 29 Apr 2019, 11:22
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Bunuel wrote:
If a merchant purchased a sofa from a manufacturer for $400 and then sold it, what was the selling price of the sofa?

(1) The selling price of the sofa was greater than 140 percent of the purchase price.
(2) The merchant's gross profit from the purchase and sale of the sofa was 1/3 of the selling price.


Given: A merchant purchased a sofa from a manufacturer for $400 and then sold it

Target question: What was the selling price of the sofa?

Statement 1: The selling price of the sofa was greater than 140 percent of the purchase price.
Let x = selling price of the sofa
We can write: x > $400 + (140% of $400)
Simplify: x > $400 + $560
Simplify: x > $960
If the selling price is greater than $960, then the selling price COULD be $970, $980, $985, . . . etc
Since we cannot answer the target question with certainty, statement 1 is NOT SUFFICIENT

Statement 2: The merchant's gross profit from the purchase and sale of the sofa was 1/3 of the selling price.
Let x = selling price of the sofa
So, the gross profit = x/3

NOTE: Gross profit = selling price - purchase price
For this question, we have: Gross profit = selling price - $400
Replace values to get: x/3 = x - 400
Multiply both sides by 3 to get: x = 3x - 1200
So: -2x = -1200
Solve: x = 600
So, the selling price was $600
Since we can answer the target question with certainty, statement 2 is SUFFICIENT

Answer: B

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Re: If a merchant purchased a sofa from a manufacturer for $400 and then s  [#permalink]

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New post 14 May 2019, 23:55

Solution



Steps 1 & 2: Understand Question and Draw Inferences
In this question, we are given
    • A merchant purchased a sofa from a manufacturer for $400 and then sold it.

We need to determine
    • The selling price of the sofa.

As we have no other relevant information present in the question stem, let us now analyse the individual statements.

Step 3: Analyse Statement 1
As per the information given in statement 1, the selling price of the sofa was greater than 140 percent of the purchase price.
    • However, to determine the exact selling price, we need to know by what exact percentage the selling price is greater than purchase price.

Since we don’t know the exact percentage value, statement 1 is not sufficient to answer the question.

Step 4: Analyse Statement 2
As per the information given in statement 2, the merchant's gross profit from the purchase and sale of the sofa was 1/3 of the selling price.
    • Profit = selling price – purchase price
    Or, 1/3 * selling price = selling price – purchase price
    Or, 2/3 * selling price = purchase price = 400
    Or, selling price = 400 * 3/2 = 600

Hence, statement 2 is sufficient to answer the question.

Step 5: Combine Both Statements Together (If Needed)
Since we can determine the answer from statement 2 individually, this step is not required.
Hence, the correct answer choice is option B.

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Re: If a merchant purchased a sofa from a manufacturer for $400 and then s  [#permalink]

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New post 15 May 2019, 20:22
Hi All,

We're told that a merchant purchased a sofa from a manufacturer for $400 and then sold it. We're asked for the selling price of the sofa. This question is based around a mix of basic Arithmetic and Algebra.

(1) The selling price of the sofa was greater than 140 percent of the purchase price.

Fact 1 tells us that the selling price was GREATER than 140% of $400, so there's clearly a limitless number of possibilities. There's no way to determine the exact selling price, although we know that it would be MORE than (1.4)($400) = $560.
Fact 1 is INSUFFICIENT

(2) The merchant's gross profit from the purchase and sale of the sofa was 1/3 of the selling price.

Based on the information in Fact 2, we can create the following equation:
Profit = (Selling Price) - (Cost)
(1/3)(P) = (P) - 400

This is one variable and one equation, so you CAN solve for P (and there will be just one answer. If you did the extra steps, you would come up with the following:

P = 3P - 1200
1200 = 2P
600 = P
Fact 2 is SUFFICIENT

Final Answer:

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Re: If a merchant purchased a sofa from a manufacturer for $400 and then s   [#permalink] 15 May 2019, 20:22
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