Data Sufficiency

12.One kilogram of a certain coffee blend consists of x kilogram of type I coffee and y kilogram of type II coffee. The cost of the blend is C dollars per kilogram, where C = 6.5x + 8.5y. Is x < 0.8?
(1) y > 0.15
(2) C >=7.30
i solved and found the answer but when i checked, some said its B some said its E so how do you think? is it E or B? and why is it B?

I think it should be E. Here is my why:
Clearly, none of the statements alone is not enough to solve the question. Together let's see:
Assume C=7.3 (the lowest possible value)
Assume x is 0.8 (which is the highest value which i know is not inclusive but let's see if it was)
That means that the share spent on x is 5.2 (max - meaning slightly lower because of <), this means that the share of Y is 7.3-5.2=2.1. Now, what would be the quantity of y if it costs 8.5 per kilo, then 2.1 for how many kilos? it is approximately 0.25. That means that if the condition that y>0.15 is not enough. If it is below 0.25, then the conditions do not hold. So, it is not possible to solve it.

diebeatsthegmat wrote:12.One kilogram of a certain coffee blend consists of x kilogram of type I coffee and y kilogram of type II coffee. The cost of the blend is C dollars per kilogram, where C = 6.5x + 8.5y. Is x < 0.6?
(1) y > 0.15
(2) C >=7.30
i solved and found the answer but when i checked, some said its B some said its E so how do you think? is it E or B? and why is it B?

The answer should be B. But before I explain how I've done it, I want you to solve the problem by taking into account the change I introduced.[Look at the bolded part in the copy of the original question above]

I think its E as well.As it said Cost >=7.30..it could be any value on which the quantity of X & Y differ..But we would have got the answer if it had mentioned the exact Cost of it..

breakkgmat wrote:I think its E as well.As it said Cost >=7.30..it could be any value on which the quantity of X & Y differ..But we would have got the answer if it had mentioned the exact Cost of it..

I edited my previous post for I noticed a mistake while specifying the answer.

While the answer for the original question has to be B, the answer for the modified question is E.

One efficient way of addressing questions involving inequalities is by using the graphical method.

Let's work on the original problem:

Given: X + Y = 1
6.5X + 8.5Y = C
Required: Is X < 0.8

Statement 1: Y> 0.15
This tells us that X< 0.85[ Because of the first given]
Therefore, insufficient as X can be 0.81, which is greater than 0.8, or X can be 0.4, which is less than 0.8.[ Here I took 'X' values arbitrarily]
Statement 2: C>= 7.3
Combining it with the second given, 6.5X + 8.5Y >=7.3
Now draw the graphs of X + Y = 1 and 6.5X + 8.5Y >=7.3 [ Multiply both sides by 10 to simplify the process]

Find the common region, and you shall see that the portion from line X + Y =1 that is included in the common region is that where X<=0.6.[0.6 is a value of X at the intersection of the two lines drawn.]

Therefore, we know that the maximum X can be is 6, which is definitely less than 8. So, Sufficient!

Therefore,the answer is B.

Now let's see the modified version of the problem:
The question was modified as follows: Is X < O.6?

See that? We early on found that X<=0.6. So, what shall we conclude? X can be 0.6, in which case our answer is 'No!', but X can also be 0.5, in which case our answer is 'Yes!'. Therefore, insufficient.

Both: Since statement 1 adds no unique information, Insufficient.

So, the answer is E.

diebeatsthegmat wrote:12.One kilogram of a certain coffee blend consists of x kilogram of type I coffee and y kilogram of type II coffee. The cost of the blend is C dollars per kilogram, where C = 6.5x + 8.5y. Is x < 0.8?
(1) y > 0.15
(2) C >=7.30
i solved and found the answer but when i checked, some said its B some said its E so how do you think? is it E or B? and why is it B?

The question asks if x < 0.8? So in other words, it asks is y> 0.2 bevcause x + y must add up to 1 kilo.

(1) This stamnet says y greater than 0.15. So it can be 0.17 or 0.22. SO is not sufficient to conclude whether it is greater thann 0.2 or not. NOT SUFF
(2) We know the cost. And also we have the formula. 7.30 = 6.5x + 8.5y
By plug in numbers we can determine whether x is greater than 0.8 or not. So SUFF

Hence B