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.
This is better5 is closer to 20 than 1 is to
100but i
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 the hour hand has moved
7.5from 1 toward 2 and still ha
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 club must be a multiple of 11: 11,
22, . Since there are
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 = 100,
choices C and E are each 10. Eliminate A, B,
and D,
(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.
3 0.5
4 3 2 1 0 1 2 3 4
2 2.53
1
3
1
2
12-A Basic Arit
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 the blue marble is
or or .5.
*By symmetry, it is equal
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
numbersispositive,all10 ofthenumberscouldbe
negative(E).
Key
Givenanytwonumbersaandb,youcanalwaysfind
theirsum,difference,product,andquotient(withacalculator,
ifnecessary),exceptthatwecanneverdivideby
zero:
07=0 70ismeaningless.
Example 4.
What is the sum of the product and the quotient of 7
and 7?
Solution. Produ
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 necessary. You dont need to solve this system
of equation