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

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Blair is shopping for a meal. He buys truffles, caviar, tuna, and grap  [#permalink]

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New post 11 Jul 2018, 00:12
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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.

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Blair is shopping for a meal. He buys truffles, caviar, tuna, and grap  [#permalink]

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New post 11 Jul 2018, 02:43
1
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
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Re: Blair is shopping for a meal. He buys truffles, caviar, tuna, and grap  [#permalink]

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New post 11 Jul 2018, 04:31
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)
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Re: Blair is shopping for a meal. He buys truffles, caviar, tuna, and grap  [#permalink]

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New post 11 Jul 2018, 09:50
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 the price paid per ounce for each item be P, Q, R, S

Let X be the total amount of money spent on each item, in cents

Let a, b, c, d be the quantity in ounces of each item, a,b,c,d are integers > 1

Hence, we have X = Pa = Qb = Rc = Sd

P = X/a, Q = X/b, R = X/c, S = X/d

X = a*b*c*d

Statement 1: 4X/100 = 46.20

Hence X = 1155 = 3*5*7*11

we get {a,b,c,d} = {3,5,7,11}...using this we can find out P,Q,R,S & hence the median price.

Statement 1 is Sufficient.


Statement 2: a + b + c + d = 26, we can have multiple values of {a,b,c,d} & no information about X.

Statement 2 is Not Sufficient.



Answer A.



Thanks,
GyM
Re: Blair is shopping for a meal. He buys truffles, caviar, tuna, and grap &nbs [#permalink] 11 Jul 2018, 09:50
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