The chart above gives prices for different types of cheeses at two different delis. Kimberly made a purchase in Deli B. According to the chart, how much money would Kimberly have saved if she had made the purchase in Deli A instead? (1) She purchased equal amounts of Provolone and Swiss, and twice as much American. (2) She purchased 3.6 kilograms of cheese in all.
A. Statement (1) BY ITSELF is sufficient to answer the question, but statement (2) by itself is not. B. Statement (2) BY ITSELF is sufficient to answer the question, but statement (1) by itself is not. C. Statements (1) and (2) TAKEN TOGETHER are sufficient to answer the question, even though NEITHER statement BY ITSELF is sufficient. D. Either statement BY ITSELF is sufficient to answer the question. E. Statements (1) and (2) TAKEN TOGETHER are NOT sufficient to answer the question, meaning that further information would be needed to answer the question.
(B) Statement (1) is not sufficient by itself because it only gives us the ratio of the amounts of the cheeses. We are not told how much cheese she purchased. The more cheese she purchased, the more money she would have saved had she purchased her cheese at Deli A.
Statement (2) tells us exactly what we need to know: how much cheese was purchased. No matter what the distribution was of cheeses purchased, each kilogram of cheese would cost $1 less at Deli A. So Statement (2) is sufficient alone.
Since Statement (1) is insufficient and Statement (2) is sufficient, the correct answer is choice (B).
I think the solution presented is incorrect and insufficient. The question clearly asks "how much money would kimberly have saved..?" which indicates that we should able to calculate the exact amount from the right answer and that we are cannot from only option B, we need A too.
I still dont get it. As per the explanation given below, with Statement 2, we don't know anything about Deli A so it is insufficient. Where as with Statement 1 we know that the average price of Deli A is less than the least cheese price at Deli B. SO the answer should be A (Statement1 alone is sufficient) right? Am I missing something?
Statement (2) IS SUFFICIENT and Statement (1) IS NOT. Let me explain why.
The main question asks us "How much money would Kimberly have saved ... ?". So information we use is sufficient if we can give a definite answer: "Kimberly have saved ___ dollars.".
First, let me show why statement (1) is insufficient. (1) She bought equal amounts of Provolone and Swiss, and twice that amount of American. Imagine she bought 1kg Provolone, 1kg Swiss and 2kg of American. Then in deli A she paid: 15 × 1 + 17 × 1 + 19 × 2 = 51 dollars In deli B she would pay: 16 × 1 + 18 × 1 + 20 × 2 = 55 dollars In this case she saved 4 dollars.
Imagine she bought 2kg Provolone, 2kg Swiss and 4kg of American. Then in deli A she paid: 15 × 2 + 17 × 2 + 19 × 4 = 102 dollars In deli B she would pay: 16 × 2 + 18 × 2 + 20 × 4 = 110 dollars In this case she saved 8 dollars.
Both imaginable situations are possible (they fit in information we have) but the answer for the main question is different. It means that we can not give a definite answer using Statement (1).
Now, let me show that using Statement (2) we can answer the question. (2) She bought 3.6 kilograms of cheese in all. We know that each kilogram of cheese would be $1 less at Deli A. (No matter what kind of cheese it is). So since she bought 3.6 kilograms of cheese in all she saved 3.6 × 1 = 3.6 dollars.
If this explanation is not clear than we can go general way: Let us denote the amount of cheese of each kind she bought by x, y, z respectively. So x + y + z = 3.6 Then in deli A she paid: 15x + 17y + 19z In deli B she would pay: 16x + 18y + 20z The difference is: (16x + 18y + 20z) – (15x + 17y + 19z) = x + y + z We know that x + y + z = 3.6 So Kimberly have saved 3.6 dollars.
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