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15 Mar 2022, 07:56
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B
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30% (03:06) correct
70%
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The average (arithmetic mean) of the original six prices for six coats at a clothing store was $85. After two of the six coats were each discounted by 20%, the average price of the six coats was $76. Was the coat with the lowest original price one of the two coats that were discounted?
1) One of the discounted coats was the one with the highest original price.
2) Before the discount, none of the coats had a price greater than $180.
1) One of the discounted coats was the one with the highest original price.
2) Before the discount, none of the coats had a price greater than $180.
22 Apr 2022, 01:41
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AbhiroopGhosh
Original avg of 6 coats = $85
New average of 6 coats = $76
So there was a $9 reduction in the average i.e. a reduction of 9*6 = $54 in total price. So when 2 coats were reduced by 20%, it led to a reduction of total $54.
We need to find if the lowest value coat was one of the two coats.
Note that 20% of $85 is $17 (it is 2*8.5). So if the coats were average priced at $85 each, then reduction would have been $34. But the reduction is $54 so it means at least one coat was very expensive.
1) One of the discounted coats was the one with the highest original price.
If both coats were equally priced, the reduction of $54 means a reduction of $27 in each coat which means that 20% of the price is $27. Since 10% is $13.5, each coat would be at $135.
It is possible that one coat was $136 and the other $134. So the lowest value coat is not one of two in this case.
It is also possible that $54 reduction came from one coat only so that coat's price was $270 and the other was priced at almost $0. In this case, the lowest value coat is one of two.
Not sufficient.
2) Before the discount, none of the coats had a price greater than $180.
20% of $180 price is $36. So the maximum reduction that could have come from one coat is $36. Then $18 would have come from the other coat which means that the other coat cost would be $90. Since the average is $85, some coats must cost less than $85 (since all are not equally priced). So it is not possible that the lowest price coat was one of the two.
Sufficient.
Answer (B)
29 Jun 2025, 13:28
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