percent problem, TACTIC 7 suggests starting
with b = 100:
100 (100% of 100) = 100 100 = 1,
not 100. In fact, this result is not even close.
Try a much smaller number, say 20:
20 (20% of 20) = 20 4 = 5
at 1. It was pointing
at 1 at 1:00. During
the quarter-hour between 1:00 and 1:15, the
hour hand moved one-fourth of the way from 1
to 2. Since the measure of the angle between 1
and 2 is 30, at 1:15
38. (25) Use TACTIC 7: Choose appropriate numbers.
Since of the girls attended the meeting, the
number of girls in the club must be a multiple
of 7: 7, 14, 21, . Similarly, the number of
boys in the c
prime. (II is true.)
If m = 1, then m2 = m, since both are equal
to 1. (III is true.)
II and III only are true.
30. C. Use TACTICS 6 and 7. Since 100% of 10 is
10, let x = 100 and y = 10. When x = 10
(A) 8 (B) 2 (C) 0 (D) 2 (E) 8
Solution. | |3| |5| | = |3 5| = |2| = 2 (D).
Key Fact A2
For any number a and positive number b:
|a| = b
a = b or a = b.
|a| < b
b < a < b.
|a| > b
a < b or a > b.
BGY, YGB, YBG, GYB, GBY. In 3 of these 6
the yellow comes before the blue, and in the
other 3 the blue comes before the yellow.
Therefore, the probability that the yellow marble
will be removed before
Example 6.
If the product of 10 numbers is positive, what is the
greatest number of them that could be negative?
(A) 0 (B) 1 (C) 5 (D) 9 (E) 10
Solution. SincebyKeyFactA5,theproductof10negative
number
Givenanytwonumbersaandb,youcanalwaysfind
theirsum,difference,product,andquotient(withacalculator,
ifnecessary),exceptthatwecanneverdivideby
zero:
07=0 70ismeaningless.
Example 4.
What is the sum of t
Finally, from 100 to 199 there are 20 more
plus 100 numbers where the digit 1 is used in
the hundreds place. The total is
20 + 20 + 20 + 100 = 160.
33. ( or 2.5) Use TACTIC 10: dont do more than
is ne