One kilogram of a certain coffee blend consists of x kilogram of type

Question

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

Bunuel · Accepted Answer

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?

"One kilogram of a certain coffee blend consists of x kilogram of type I coffee and y kilogram of type II coffee"

So, $x+y=1$. Question: is $x<0.8$.

(1) y > 0.15

Not sufficient.

(2) C >=7.30

Sufficient.

Answer: B.

KarishmaB · Answer

Responding to a pm:

C = Avg cost of the mix = Cost of the blend = 6.5x + 8.5y

If you remember your weighted average formula, Avg = (C1*w1 + C2*w2)/(w1 + w2) = 
Avg Cost = (C1*x + C2*y)/(x + y) 
(x+y) is 1 kg since the weight of the blend is 1 kg.
Avg Cost = C = (C1*x + C2*y) = (6.5x + 8.5y)
So cost of type I coffee is $6.5/kg and cost of type II coffee is $8.5/kg.

So everything is set for you. All you have to do is plug in the values of x and y now.
Question: Is x > 0.8?

(1) y > 0.15
If y is 0.16, x is 0.84
If y is 0.5, x is 0.5
This statement alone is not sufficient.

(2) C >= 7.30
Let's say C = 7.3
x/y = (8.5 - 7.3)/(7.3 - 6.5) = 12/8 = 3/2 (The Scale Method)
x = 3/5 = 0.6
If C is greater than 7.3, x/y will get smaller and hence the value of x will keep getting smaller too. Say if C = 7.5, 
x/y = 1/1
x = 0.5
and so on...

So x can be at most 0.6. Hence it must be less than 0.8.
Statement II alone is sufficient.

Answer (B)

Marcab · Answer

I tried doing this via using the concept of weighted average.
Its given in statement 2 that 6.5x + 8.5y>=7.3.
Now, when x=.5 and y=.5, then the c would be 7.5. (GIVEN FACT IS THAT X+Y=1.)
Total distance in terms of parts is 2 units and in terms of numerical distance is 1. For every 2 part change, there is a 0.1 deviation in the numerical separation.
Since c>=7.3( note the 0.2 deviation), the numerical deviation is 0.1. Hence x must be <=0.6.
Regards.

gmacforjyoab · Answer

x+y=1
c= 6.5x + 8.5y
Question ---- is x<0.8 ?

As seen from above equations , for a given sum of x and y ( =1) , the value of C increases as x decreases and Y increases ( since y is multipled by greater number than x)

If x=0.8 , then y=0.2
and C= (6.5*0.8) + (8.5*0.2) = 6.9 .

Now if we increase value of x above 0.8 , the value of C decreases below 6.9 ( consider x=0.9 , then y would be 0.1 , which pulls down the value of C below 6.9--- as per the highlighted text above).
And if we decrease the value of x below 0.8 , the value of c increases from 6.9 ( cos y is increased when x is reduced).

Statement 1 - y>0.15 , Y could be 0.2 , in which case x=0.8 ( No to the answer)
or Y = 0.3 , in which case x=0.7 ( yes to the answer)
Insufficient

Statement 2 C>=7.5 , as seen from above , for any c > 6.9 demands a x <0.8 . Hence sufficient.

Hope that helps
Jyothi

FRANCISCODake · Answer

It is really nice to find this place as it is full of fun. Looking forward for new friends. Hope I'll definitely enjoy my stay here.
ood question and quite a learning...

Out of curiousity, can this sum be solved in less than 2mins that too under "GMAT exam" conditions that too at first sight??

Bunuel · Answer

Bumping for review and further discussion*. Get a kudos point for an alternative solution!

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Predecessor · Answer

Idk, in my opinion after you figure out that x+y=1 and that C=6.5x+8.5y (knowing that C can be 7.30), we have two equations and we can solve for X.
Please correct me if I'm wrong but this was my line of reasoning and I've chosen B after 1min.

ARUNPLDb · Answer

one kilogram of a certain coffee blend consists of X kilogram of type I and Y kilogram of type II" means that X+Y=1
Combined C=6.5X+8.5Y,

we get:
X=(8.5-C)/2, Y=(C-6.5)/2
Combined C>=7.3, X=(8.5-C)/2<1.2/2=0.6

Answer is B

seabhi · Answer

@Bunuel,
You are just great!!!

honey86 · Answer

Initially I got the answer wrong but there was a calculation mistake. I am posting my approach anyway :D,

Question Says,
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

Sol. x + y = 1 (from question statement)
now, cost C = 6.5x + 8.5y = 6.5 (x + y) + 2y = 6.5 +2y------(eq. 1)
we need to check whether x < 0.8
or y > 0.2 (since x + y = 1)

option 1). y > 0.15
clearly not sufficient alone.

option 2). C >= 7.30
from eq.1, 6.5 + 2y >= 7.30
=> 2y => 0.80
=> y>= 0.40 or x =< 0.60
Hence, sufficient.

littlewarthog · Answer

With x+y = 1, we can simplify the equation for C:

C = 6.5 + 2y

Statement 1: Not sufficient. x can still be anywhere between 0 and 0.85

Statement 2: Sufficient:
7.3 = 6.5 + 2y. This leads to y = 0.4 and x smaller than 0.8. If C is greater than 7.3, this will only increase y and therefore decrease x, which will therefore be smaller than 0.8 in any case.

Answer B.

sananoor · Answer

This question is amazing and i guess dont need any hard calculations.
Statement 1 is clearly insufficient
Statement 2 sufficient...question asks is x < 0.8
Statement 2 tells us that C > or equal to 7.3...so we can write
6.5X + 8.5 y = 7.3 (remember C equals to 7.3 or greater than but not less than that)
Now see that 7.3 is between 6.5 and 8.5
7.3 -6.5 = 0.8 
8.5-7.3 = 1.2
6.5--------7.3-------------8.5
 0.8 1.2
One can see that 7.3 is more close to 6.5 it means the ratio of X is more than the ratio of y type of coffee...the ratio will be equal to 0.8/1.2 = x/y or x/y = 2/3 
we can find the ratio of two coffee blends and thus we an find the ratio of x which is 3/5 =0.6

Jsound996 · Answer

This is essentially a weighted average problem. I tend to go with the visual graph over the formulas.

1.) Statement 1 says that y is greater than 0.15 but there's no info about x, so off the bat it's insufficient!

2.) C ≥ 7.30
I like to use the "see-saw method" so if we draw the graph out (Refer to attached picture): 
Statement 2 is sufficient

Answer is B!!

avinash16 · Answer

The real deal here is x+y = 1

Kimberly77 · Answer

Hi  brunel , what's the reason behind substituting y with 8.5(1−x) here? How will I know to substitue here?Thanks

bumpbot · Answer

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One kilogram of a certain coffee blend consists of x kilogram of type

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