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Bunuel
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The cost of each bottle of water is the same and the cost of each bottle of cola is the same. What is the difference in the cost of 1 bottle of water and 1 bottle of cola?

(1) 2 bottles of water and 5 bottles of cola cost $40
(2) 6 bottles of water and 15 bottles of cola cost $120


As per statement 1
let the water price be x
let be cola price be y

2x+3y=40
here x and y can have various value
Hence not sufficient

As per statement 2
6 bottles of water and 15 bottles of cola cost $120

6x+15Y=120
it is same as statement 1 if we divide by 3
2X+5Y=40

here also x and y can have various value

Even combininf statement we cannot get unique value

Option E is correct neither statement is sufficient
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(1) and (2) are equivalent, meaning they do not provide us with different information, (2) is simply a multiple of (1). As we have two variables to find and only 1 equation, I would say that the correct answer here is E, neither.
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Let \(w \) be the number of bottles of water and \(c \) be the number of bottles of cola.

Statement 1
\(2w+5c=40\)
We have only one equation, but two variables.
Not sufficient

Statement 2
\(6w+15c=120\)
We have only one equation, but two variables.
Not sufficient

Statement 1 + Statement 2
We can observe that if we divide the second equation by 3, we obtain the same as the first equation.
Therefore, again we have only one equation.
Not sufficient


Answer: E
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Correct Answer : E

Target:
Find w - c, where w = water price and c = cola price.
  • Statement (1): 2w + 5c = 40. One equation, two variables. Multiple positive pairs exist Insufficient.
  • Statement (2): 6w + 15c = 120 ; 2w + 5c = 40 (after dividing by 3). This is identical to Statement (1). Insufficient.
  • Combined: Adding a linearly dependent equation gives 0 new information. We remain with 1 unique linear equation for 2 variables. Insufficient.

Bunuel
­The cost of each bottle of water is the same and the cost of each bottle of cola is the same. What is the difference in the cost of 1 bottle of water and 1 bottle of cola?

(1) 2 bottles of water and 5 bottles of cola cost $40
(2) 6 bottles of water and 15 bottles of cola cost $120


­
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I) 1 equation, 2 unknowns ~> N.S.
II) 1 equation, 2 unknowns ~> N.S.
I + II) Notice that the numbers provided in the 2nd statement are just 3 times the numbers in the 1st statement. This means there is no new info and we have 2 equations that are identical in information. We cannot use this to solve. N.S.
Bunuel
­The cost of each bottle of water is the same and the cost of each bottle of cola is the same. What is the difference in the cost of 1 bottle of water and 1 bottle of cola?

(1) 2 bottles of water and 5 bottles of cola cost $40
(2) 6 bottles of water and 15 bottles of cola cost $120


­
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