the total number of possible outcomes. Fran is going to pick one shirt, and we want to figure out the probability that it will not
be orange. In other words, what is the probability of picking a non-orange shirt? Aside from the orange shirts, there are 4
black shirts and 5 blue shirts, so altogether there are 9 non-orange shirts. So there are 9 possible successful outcomes. The
total number of shirts to choose from, including the orange shirts, is 12, so there are 12 possible outcomes. So the probability
of Fran picking a non-orange shirt is which can be reduced to answer choice (K).
D
You might be tempted to say that is midway between and but that’s not the answer. Even if you don’t know what to
do, you can eliminate choice (A) because is less than so it can’t be between and You can solve this problem by
picturing and on a number line. The fraction we’re looking for is the midpoint between and To find this midpoint,
first we will add the two fractions together, and then we will divide the sum by 2. In order to add the fractions together, we
have to give them the same denominator. The least common denominator is 35. Then is equal to and is equal to
and answer choice (D).
57.
H
The digit 7 is in the ten-thousands place, so the 7 represents 7 × 10,000, or 70,000, choice (H).
58.
B
Draw a chart or table to help organize the information. Newark is two hours later than Denver, so if the time in Denver when
Harry arrives is 2:30 PM, then the time in Newark when he arrives in Denver is 4:30 PM The flight takes 5 hours, so the time
he began in Newark is 5 hours earlier than 4:30 PM, or 11:30 AM, choice (B).
59.
J
Let’s answer this question by trying each answer choice and trying to show that the statement can be true with a negative q. In
choice (F), can q + r = 1 if q is negative? Yes. Let’s say q = −2. Then the equation would read −2 + r = 1, which would mean
that r = 3, an integer. What about (G)? If q is −2, then the equation reads −2 − r = 1. Solving for r we find that r = −3, which
is also an integer. In choice (H), if q is −1, then the equation reads −1r = 1. Solving for r, we find that r = −1, so we can
discard (H). In choice (J), if q is −1, the equation reads (−1)^2 × r = 1, so r = 1. This leaves only choice (K). In choice (K), if
q = −1, then the equation reads (−1) × r^2 = 1. This means that r^2 must equal −1. But any nonzero number squared becomes
positive, so r^2 can’t be −1. The same problem would occur with any negative value of q, so q must be positive, making (K)
the correct answer. You can also prove that q must be positive if qr^2 = 1 because qr^2 = 1, q ≠ 0, and r ≠ 0. The square of any
nonzero number is positive, so r^2 is positive. Since qr^2 = 1, q must be positive.
60.
A
First we have to find out what D is. We are given that D ÷ 25 = 8 with a remainder of 9. So D = (25 × 8) + 9, or 200 + 9, or
209; 209 ÷ 8 = 26 remainder 1, so the answer is choice (A).
61.
62. J
