Blair is shopping for a meal. He buys truffles, caviar,

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Blair is shopping for a meal. He buys truffles, caviar, tuna, and grapes. He spends the same amount of money on each item, though he purchases different quantities of each. If the quantities purchased are all integer values greater than 1, and if the product of the weights in ounces of each item is equal to the price in cents paid for each item, what is the median price paid per ounce?

(1) Blair spent a total of $46.20 on items.
(2) Blair purchased a total of 26 ounces of food items.

OA A

Source: Princeton Review

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by Jay@ManhattanReview » Wed Jul 03, 2019 11:16 pm

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BTGmoderatorDC wrote:Blair is shopping for a meal. He buys truffles, caviar, tuna, and grapes. He spends the same amount of money on each item, though he purchases different quantities of each. If the quantities purchased are all integer values greater than 1, and if the product of the weights in ounces of each item is equal to the price in cents paid for each item, what is the median price paid per ounce?

(1) Blair spent a total of $46.20 on items.
(2) Blair purchased a total of 26 ounces of food items.

OA A

Source: Princeton Review
Let the weights of the 4 items be a, b, c and d ounces.

Let's take each statement one by one.

(1) Blair spent a total of $46.20 on items.

=> abcd = $46.20/4 = 4620/4 cents = 1155 cents

=> abcd = 1155 = 3*5*7*11; we cannot have other combination since quantities purchased is greater than 1.

Thus, individual prices per ounces are

1. 1155/3 cents;
2. 1155/5 cents;
3. 1155/7 cents;
4. 1155/11 cents

The median price of items = average of (1155/5) and (1155/7) cents. Sufficient

(2) Blair purchased a total of 26 ounces of food items.

=> a + b + c + d = 26. However, this doe not give the value of individual prices. Not sufficient.

The correct answer: A

Hope this helps!

-Jay
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