Q23:
One kilogram of a certain coffee blendconsists of x kilogram of type I coffee and y kilogram of type II coffee.
The cost of the blend is C dollars perkilogram, where C = 6.5x + 8.5y.
Is x< 0.8?
(1)

y > 0.15
(2)

C ≥ 7.30


A. Statement (1) ALONE issufficient, but statement (2) alone is not sufficient.
B. Statement (2) ALONE issufficient, but statement (1) alone is not sufficient.
C. BOTH statements TOGETHERare sufficient, but NEITHER statement ALONE is sufficient.
D. EACH statement ALONE issufficient.
E. Statements (1) and (2) TOGETHERare NOT sufficient.
Answer:B



Q27:
The interior of a rectangular carton isdesigned by a certain manufacturer to have a volume of x cubic feet anda ratio of length to width to height of 3 : 2 : 2.
In terms of x, which of the followingequals the height of the carton, in feet?
Answer:(3/2)x^(1/3)



答案是不是给错了?

A.



B

Q23:
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

We are given that x + y = 1.

Let us look at (1) first.  If y > 0.15, then x = 1 − y < 1 − 0.15 = 0.85.  Hence we cannot tell whether x is less than 0.8 or not.

Now let us look at (2).

C = 6.5x + 8.5y = 6.5x + 8.5(1 − x) = 8.5 − 2x ≥ 7.3.
Therefore, 8.5 − 7.3 ≥ 2x.  Simplifying, we obtain 0.6 ≥ x.  This shows that x is indeed less than 0.8.

The correct answer is thus B.

Q27:
The interior of a rectangular carton is designed by a certain manufacturer to have a volume of x cubic feet and a ratio of length to width to height of 3 : 2 : 2.  In terms of x, which of the following equals the height of the carton, in feet?

Suppose the height of the carton is 2y.  Then the length is 3y and the width is 2y.  The volume is then 12y^3.  Since this is equal to x, we have
12y^3 = x
y^3 = x/12
y = (x/12)^(1/3)
2y = 2(x/12)^(1/3) = (8x/12)^(1/3) = (2x/3)^(1/3)

Thus the answer is correct.