C = 6.5x + 8.5y. Is x < 0.8?

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

A. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.

B. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.

C. BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.

D. EACH statement ALONE is sufficient.

E. Statements (1) and (2) TOGETHER are NOT sufficient.

Please explain. Thanx

Answer 1

Our conditions are:

0 &lt; x &lt; 1

0 &lt; y &lt; 1

x + y = 1

C = 6.5x + 8.5y

From statement

(1) y &gt; 0.15

doesn’t follow that x &lt; 0.8 because

0.8 ≤ x &lt; 0.85

and corresponding values of y and C

0.15 &lt; y ≤ 0.2

6.8 &lt; C &lt; 6.9

also satisfy the conditions.

Therefore statement (1) alone is not sufficient.

From the statement

(2) C ≥ 7.30

follows

6.5 x + 8.5 y ≥ 7.30

6.5 x + 8.5 (1 – x) ≥ 7.30

x ≤ 0.6

Therefore statement (2) ALONE is sufficient.

Answer:

B. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.

-