Bunuel 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.

Let \(w_1,w_2,w_3, w_4\) are the weights(in ounce) of four ingredients.

& \(C_1,C_2,C_3, C_4\)=C(Given) are the costs(in cents) of four ingredients.

Given, \(w_1*w_2*w_3*w_4\)=unit price=\(\frac{C}{w_1}\) or \(\frac{C}{w_2}\) or \(\frac{C}{w_3}\) or \(\frac{C}{w_4}\) -----------(a)

Question stem:- Median price=?

We need to determine unit price of the four ingredients first.

St1:-4C=$46.20=4620 cents (1$=100 cents)

So, Unit price=\(C=\frac{4620}{4}=1155\)

Or, \(w_1*w_2*w_3*w_4\)=1155

Since each of the quantity purchased is an integer value greater than 1, so we have to perform prime factorization in order to determine individual quantities.

1155=3*5*7*11

So, \(w_1=3,w_2=5,w_3=7,w_4=11\) and value of A is known.Therefore, we can determine unit prices using (A), hence median.

Sufficient.

St2:-\(w_1+w_2+w_3+w_4=26\)

& \(w_1*w_2*w_3*w_4\)=unit price=\(\frac{C}{w_1}\) or \(\frac{C}{w_2}\) or \(\frac{C}{w_3}\) or \(\frac{C}{w_4}\)

Here, two equations & 4 variables , hence quantities can't be determined, hence median can't be obtained.

Insufficient.

Ans. (A)

_________________

Regards,

PKN

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