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(x + y) = 10[email protected] wrote:101. Material A costs $3 per kilogram, and Material B costs $5 per kilogram. If 10 kilograms of Material K consists of x kilograms of Material A and y kilograms of Material B, is x > y ?
(1) y > 4
(2) The cost of the 10 kilograms of Material K is less than $40.
Statement 1: Consider the following two cases,
- x = 4, y = 6 ---> NO
x = 5.5, y = 4.5 ---> YES
Statement 2: Cost of 10 kg of K is less that $40.
So, cost of 1 kg of K is less than $4.
Now, 4 is midway between 3 and 5.
So, if there were same amount of A and B in K, the cost of 1 kg of K would have been $4. As the cost of 1kg of K is less than $4, there must be more A in K than B.
Hence, x > y
Sufficient
The correct answer is B.
Algebraic analysis of statement 2:
Statement 2: Cost 10 kg of K is $(3x + 5y).
So, (3x + 5y) < 40
--> 3x + 5(10 - x)) < 40
--> 3x + 50 - 5x < 40
--> 2x > 10
--> x > 5
As (x + y) = 10, y must be less than 5 for x to be greater than 5.
So, x > 5 > y ---> x > y
Sufficient
