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.
Since statement 1 is in terms of y, we should rephrase the question stem in terms of y.
x = the number of kilograms of A.
y = the number of kilograms of B.
Since a total of 10 kilograms are purchased:
x + y = 10.
x = 10-y.
Substituting x=10-y into the question stem (
Is x>y?), we get:
10-y > y?
10 > 2y?
5 > y?
Question rephrased: Is y < 5?
Statement 1: y>4.
Since it's possible that y=4.5 or that y=6, no way to determine whether y<5.
INSUFFICIENT.
Statement 2: The cost of the 10 kilograms of material K is less than $40.
Since the cost of each of the x kilograms is $3 and the cost of each of the y kilograms is $5, we get:
3x + 5y < 40.
Substituting x=10-y into 3x+5y<40, we get:
3(10-y) + 5y < 40
30 - 3y + 5y < 40
2y < 10
y < 5.
SUFFICIENT.
The correct answer is
B.
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