A jeweller 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 jeweller bought the watch was more than 20% less that the price at which the jeweller sold the watch.
2) The profit the jeweller made on the sale of the watch was greater than 20% of the price at which the jeweller sold the watch.
The OA is D.
Please, can any expert assist me with this DS question? I don't have it clear and I appreciate if any explain it for me. Thanks.
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A jeweller sold a watch at a profit. Was his percent...
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ErikaPrepScholar
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Hi AAPL,
We can solve this problem by building equations. It's key to remember that 1) profit = sale price - purchase price and 2) we can always write percents as decimals. We want to know whether the profit the jeweler makes off of the watch is greater than 25% of the amount it was bought for. This means that the sale price must be more than 125% of the price it was bought for. In other words, we want to know if:
S > 1.25B
where S = sale price and B = purchase price (amount bought for).
Statement 1
This tells us that B < 0.8S. Dividing 0.8 from both sides gives 1.25B < S. Flipping this around gives S > 1.25B, which is exactly what we wanted to find. Sufficient.
Staetment 2
This tells us that S - B > 0.2S. Rearranging gives us 0.8S > B, which flipped around is B < 0.8S. This is exactly what we found in Statement 1! So we know that it will also be sufficient.
We can solve this problem by building equations. It's key to remember that 1) profit = sale price - purchase price and 2) we can always write percents as decimals. We want to know whether the profit the jeweler makes off of the watch is greater than 25% of the amount it was bought for. This means that the sale price must be more than 125% of the price it was bought for. In other words, we want to know if:
S > 1.25B
where S = sale price and B = purchase price (amount bought for).
Statement 1
This tells us that B < 0.8S. Dividing 0.8 from both sides gives 1.25B < S. Flipping this around gives S > 1.25B, which is exactly what we wanted to find. Sufficient.
Staetment 2
This tells us that S - B > 0.2S. Rearranging gives us 0.8S > B, which flipped around is B < 0.8S. This is exactly what we found in Statement 1! So we know that it will also be sufficient.
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