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A jeweler sold a watch at a profit. Was his percent profit on the sal 31 Jul 2020, 00:55
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A jeweler sold a watch at a profit. Was his percent profit on the sale of the watch greater than 25%?

(1) The price at which the jeweler bought the watch was more than 20% less than the price at which the jeweler sold the watch.

(2) The profit the jeweler made on the sale of the watch was greater than 20% of the price at which the jeweler sold the watch.


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D
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A jeweler sold a watch at a profit. Was his percent profit on the sal 31 Jul 2020, 01:10
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Bunuel
A jeweler sold a watch at a profit. Was his percent profit on the sale of the watch greater than 25%?


(1) The price at which the jeweler bought the watch was more than 20% less than the price at which the jeweler sold the watch.

(2) The profit the jeweler made on the sale of the watch was greater than 20% of the price at which the jeweler sold the watch.
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Answer: Option D

Please check the video for the step-by-step solution.

GMATinsight's Solution

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A jeweler sold a watch at a profit. Was his percent profit on the sal 31 Jul 2020, 01:58
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Bunuel
A jeweler sold a watch at a profit. Was his percent profit on the sale of the watch greater than 25%?


(1) The price at which the jeweler bought the watch was more than 20% less than the price at which the jeweler sold the watch.

(2) The profit the jeweler made on the sale of the watch was greater than 20% of the price at which the jeweler sold the watch.
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Solution


Step 1: Analyse Question Stem


    • Let us assume that jeweler sold the watch at p% profit.
    • We need to find out if p is greater than 25%.
      o Or, if \(p > \frac{1}{4}CP ⟹ \frac{p}{CP} > \frac{1}{4}\)
         Where CP is the cost price of the watch.

Step 2: Analyse Statements Independently (And eliminate options) – AD/BCE


Statement 1: The price at which the jeweler bought the watch was more than 20% less than the price at which the jeweler sold the watch.
    • According to this statement: \(CP < 0.8SP……..Eq.(i)\),
      o where SP is the selling price.
    • We know that \(SP = CP + p\), so from Eq.(i), we have,
      o \(CP < 0.8(CP + p) ⟹0.2CP < 0.8p ⟹ \frac{p}{CP} > \frac{1}{4}\)
Hence, statement 1 is sufficient and we can eliminate answer Options B, C and E.

Statement 2: The profit the jeweler made on the sale of the watch was greater than 20% of the price at which the jeweler sold the watch.
    • According to this statement: \(p > 0.2SP……..Eq.(ii)\),
      o where SP is the selling price.
    • We know that \(SP = CP + p\), so from Eq.(ii), we have,
      o \(p > 0.2CP + 0.2p ⟹0.8p >0.2CP ⟹ \frac{p}{CP} > \frac{1}{4}\)
Hence, statement 2 is also sufficient.
Thus, the correct answer is Option D.
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A jeweler sold a watch at a profit. Was his percent profit on the sal 31 Jul 2020, 10:49
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Bunuel
A jeweler sold a watch at a profit. Was his percent profit on the sale of the watch greater than 25%?


(1) The price at which the jeweler bought the watch was more than 20% less than the price at which the jeweler sold the watch.

(2) The profit the jeweler made on the sale of the watch was greater than 20% of the price at which the jeweler sold the watch.

 
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Let us set up the formula \(Profit = Price - Cost\). The price here is the price the watch was sold, and the cost here is the price the watch was bought. We are asking if Profit > 25*Cost.

Statement 1:
This translates to: Cost < 80%*Price. Note "more than 20% less than" is the same as "at least 20% less than" which is "less than 80% of". Then we want to replace price and insert something on profit. Plug in \(Price = Profit + Cost\).
Cost < 80%*(Profit + Cost).
20%* Cost < 80%*Profit
Profit > 25%*Cost. Sufficient.

Statement 2:
Profit > 20%*Price. Again we want to eliminate price and insert cost. Plug in \(Price = Profit + Cost\).
Profit > 20%*(Profit + Cost)
80%*Profit > 20%*Cost
Profit > 25%* Cost. Sufficient.

Ans: D­
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A jeweler sold a watch at a profit. Was his percent profit on the sal 31 Jul 2020, 22:44
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A jeweler sold a watch at a profit. Was his percent profit on the sale of the watch greater than 25%?


(1) The price at which the jeweler bought the watch was more than 20% less than the price at which the jeweler sold the watch.

(2) The profit the jeweler made on the sale of the watch was greater than 20% of the price at which the jeweler sold the watch.
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I have a doubt in the language of one of the statements.

Statement (1) says The price at which the jeweler bought the watch was more than 20% less than the price at which the jeweler sold the watch.

Could someone please explain why can it be translated to:

Cost Price > Selling Price - (20%)Selling Price

The help is appreciated. Thank you!
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A jeweler sold a watch at a profit. Was his percent profit on the sal 31 Jul 2020, 23:26
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Bunuel
A jeweler sold a watch at a profit. Was his percent profit on the sale of the watch greater than 25%?


(1) The price at which the jeweler bought the watch was more than 20% less than the price at which the jeweler sold the watch.

(2) The profit the jeweler made on the sale of the watch was greater than 20% of the price at which the jeweler sold the watch.

I have a doubt in the language of one of the statements.

Statement (1) says The price at which the jeweler bought the watch was more than 20% less than the price at which the jeweler sold the watch.

Could someone please explain why can it be translated to:

Cost Price > Selling Price - (20%)Selling Price

The help is appreciated. Thank you!
Show more



Statement 1: The price at which the jeweler bought the watch was more than 20% less than the price at which the jeweler sold the watch

Thus, this is interpreted as: The cost price was "more than 20%" "less than" the selling price

This means: The cost price was "may be 21% or 22% or 23% ... or 25% etc." "less than" the selling price

=> CP was "(100 - 21)% or (100 - 22)% or (100 - 23)% ... or (100 - 25)% etc." "of" the selling price

=> CP = 0.79*SP or CP = 0.78*SP ... etc.

=> CP < 0.8*SP

If CP = 0.8*SP => SP = CP * (1/0.8) => SP = 1.25*CP => Profit is 25% of CP

Thus, if CP < 0.8*SP, we have:

SP > 1.25*CP

=> Profit is more than 25% of CP ----- Sufficient


Statement 2: The profit the jeweler made on the sale of the watch was greater than 20% of the price at which the jeweler sold the watch

=> Profit > 0.2*SP

=> SP - CP > 0.2*SP

=> 0.8*SP > CP

=> SP > 1.25*CP

Alternatively:

If SP = 100, and if Profit > 0.2*SP, we have: Profit > 20 => CP < 80 => Profit % > (20/80) * 100 = 25%

=> Profit is more than 25% of CP ----- Sufficient


Answer D
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A jeweler sold a watch at a profit. Was his percent profit on the sal 01 Aug 2020, 20:28
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Kindly see the attachment.

Initially, the equation formulation of Part A took me some time. Then I found the trick to solve these questions. Just assume the equality first and then add the > / < symbols.
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A jeweler sold a watch at a profit. Was his percent profit on the sal 03 Sep 2025, 11:59
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