p2sec1.05
5. In the figure above, a path from point A to point D is determined by moving upward or to the right along the grid lines. How many different paths can be drawn from A to D that do not include either B to C?
(A) Two
(B) Four
(C) Six
(D) Eight
(E) Sixteen

6. If \[\frac{3}{7}\] of \[n\] is 42, what is \[\frac{5}{7}\] of \[n\] ?
(A) 70
(B) 45
(C) 30
(D) 18
(E) 10

p2sec1.07
7. In the figure above shows the top view of an open square box that is divided into 6 compartments with walls of equal height. Each of the rectangles D, E, and F has twice the area of each of the equal squares random, it falls into one of the compartments. What is the probability that it will fall into compartment F?
(A) \[\frac{1}{12}\]

(B) \[\frac{1}{8}\]

(C) \[\frac{1}{6}\]

(D) \[\frac{2}{11}\]

(E) \[\frac{2}{9}\]

8. If \[a\] and \[b\] are odd integers, which of the following must also be an odd integer?
I. \[(a + 1)b\]
II. \[(a + 1) + b\]
III. \[(a + 1) - b\]

(A) I only
(B) II only
(C) III only
(D) I and II
(E) II and III

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