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11 Jul 2018, 00:12
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Difficulty:
95%
(hard)
Question Stats:
29% (02:19) correct
71%
(02:23)
wrong
based on 86
sessions
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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.
(A) Statement 1 alone is sufficient, but statement 2 alone is not.
(B) Statement 2 alone is sufficient, but statement 1 alone is not.
(C) Both statements together are sufficient, but neither alone is sufficient.
(D) Each statement alone is sufficient.
(E) Neither statement is sufficient, even when combined.
(1) Blair spent a total of $46.20 on items.
(2) Blair purchased a total of 26 ounces of food items.
(A) Statement 1 alone is sufficient, but statement 2 alone is not.
(B) Statement 2 alone is sufficient, but statement 1 alone is not.
(C) Both statements together are sufficient, but neither alone is sufficient.
(D) Each statement alone is sufficient.
(E) Neither statement is sufficient, even when combined.
11 Jul 2018, 02:43
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To find the median price paid per ounce
Statement 1
Blair spent a total of $46.20 on items = 4620 cents
Since Blair pends the same amount of money on each item, the price of each item = \(\frac{4620}{5} = 1155\)
The product of the weights in ounces of each item is equal to the price in cents paid for each item = \(1155 = 11 * 5 * 7 * 3\)
So the weights of the items are 11, 5, 7 and 3
Since we know the weight in ounces for each item and the total price for each item, we can calculate the median of price per ounce for the 4 items
Statement 1 is sufficient
Statement 2
Lets call the weight in ounces of truffles, caviar, tuna, and grapes be a, b, c, d respectively
Blair purchased a total of 26 ounces of food items. => a + b + c + d = 26
Lets call the price paid for each item is P => total price = 4 * P
The product of the weights in ounces of each item is equal to the price in cents paid for each item => a * b * c * d = P
Price per ounce for truffles = \(\frac{P}{a} = \frac{abcd}{a} = bcd\)
Price per ounce for caviar = \(\frac{P}{b} = \frac{abcd}{b} = acd\)
Price per ounce for tuna = \(\frac{P}{c} = \frac{abcd}{c} = abd\)
Price per ounce for grapes = \(\frac{P}{d} = \frac{abcd}{d} = abc\)
Since we don't know the specific values for a, b, c, d the median price per ounce cannot be calculated
Statement 2 is not sufficient
Hence option A
Statement 1
Blair spent a total of $46.20 on items = 4620 cents
Since Blair pends the same amount of money on each item, the price of each item = \(\frac{4620}{5} = 1155\)
The product of the weights in ounces of each item is equal to the price in cents paid for each item = \(1155 = 11 * 5 * 7 * 3\)
So the weights of the items are 11, 5, 7 and 3
Since we know the weight in ounces for each item and the total price for each item, we can calculate the median of price per ounce for the 4 items
Statement 1 is sufficient
Statement 2
Lets call the weight in ounces of truffles, caviar, tuna, and grapes be a, b, c, d respectively
Blair purchased a total of 26 ounces of food items. => a + b + c + d = 26
Lets call the price paid for each item is P => total price = 4 * P
The product of the weights in ounces of each item is equal to the price in cents paid for each item => a * b * c * d = P
Price per ounce for truffles = \(\frac{P}{a} = \frac{abcd}{a} = bcd\)
Price per ounce for caviar = \(\frac{P}{b} = \frac{abcd}{b} = acd\)
Price per ounce for tuna = \(\frac{P}{c} = \frac{abcd}{c} = abd\)
Price per ounce for grapes = \(\frac{P}{d} = \frac{abcd}{d} = abc\)
Since we don't know the specific values for a, b, c, d the median price per ounce cannot be calculated
Statement 2 is not sufficient
Hence option A
11 Jul 2018, 04:31
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Bunuel
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)
