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Four friends go to Macy’s for shopping and buy a top each. Three of them buy a pillowcase each too. The prices of the

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by Vincen » Thu Sep 03, 2020 5:49 am

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Difficulty—

Four friends go to Macy’s for shopping and buy a top each. Three of them buy a pillowcase each too. The prices of the seven items were all different integers, and every top cost more than every pillowcase. What was the price, in dollars, of the most expensive pillowcase if the total price of the seven items was $89?

(1) The most expensive top cost $16.

(2) The least expensive pillowcase cost $9.

Answer: A

Source: Veritas Prep
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Source: — Data Sufficiency |

- 4 friends purchased 7 items
- 7 items = 4 tops + 3 pillowcase
- each item are different integers
- every top is more expensive than the pillowcase
- the total price of the 7 items = $89

Target question => What was the price in dollars of the most expensive pillowcase?
Average = 89/7 = 12.7, no price of item can be $12.7 since the price are integers and $12 is not an exact average because 12 * 7 = 84 and not 89 and 13 * 7 = 91 which is now greater than 89
For an average price of $12, another $5 must be spent to get a total of $89
Therefore, the price of each item will be gotten from a sequence of 7 prices with $12 as the average

Statement 1 => The most expensive top cost $16
At an average of 12, the sequence of 7 items is $9, $10, $11, $12, $13, $14, $15. By adding $5 to the items in the sequence to produce different integers/price, have an average of $12 have the highest/most expensive top to be $16 and the total item to be 89.
$1 can be added to every item in the sequences starting from the highest/expensive item to spread the $5. So the prices are $9, $10, $12, $13, $14, $15, $16
The price of the most expensive pillowcase is $12. Statement 1 is SUFFICIENT

Statement 2 => The least expensive pillowcase cost $9
At an average of 12 the sequence of 7 it is $9, $10, $11, $12, $13, $14, $15. By adding $5 to the items in the sequence to produce different integers/price, have an average of $12, have the least expensive pillowcase to be $9 and total item to be 89, $1 can be added to every item in the sequence starting from the most expensive item to spread the $5, so the prices are $9, $10, $12, $13, $14, $15, $16
The price of the most expensive pillowcase is $12 but if the $5 was added to the expensive item alone, the 7 prices will be $9, $10, $11, $12, $13, $14, $20, and price of the most expensive pillow is not definite. Statement 2 is NOT SUFFICIENT

Since only statement 1 is SUFFICIENT,
Answer = A
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