imadkho wrote:

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

Responding to a pm:

**Quote:**

I could solve most of the problems using the scale method, though I was finding it difficult to solve this particular question using it.

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)

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Karishma

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