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A jeweller sold a watch at a profit. Was his percent...

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A jeweller sold a watch at a profit. Was his percent...

by AAPL » Sat Nov 11, 2017 11:00 am
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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Source: — Data Sufficiency |

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by ErikaPrepScholar » Mon Nov 13, 2017 5:27 am
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.
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