SAT Mc Graw Hill 2011

CHAPTER 9 / SPECIAL MATH PROBLEMS 335

1. For all real numbers d, e,and f,let
   d e f=de+ef+df.If 2 3 x=12, then x=
   (A)

(B)

(C)

(D) 2

(E) 6

2. If b≠0, let. If x#y=1, then which of
   the following statements must be true?
   (A) x=y
   (B) x=|y|
   (C) x=−y
   (D) x^2 −y^2 = 0
   (E) xand yare both positive


3. On a digital clock, a time like 6:06 is called a
   “double” time because the number representing
   the hour is the same as the number represent-
   ing the minute. Other such “doubles” are 8:08
   and 9:09. What is the smallest time period
   between any two such doubles?
   (A) 11 mins. (B) 49 mins.
   (C) 60 mins. (D) 61 mins.
   (E) 101 mins.


4. Two numbers are “complementary” if their
   reciprocals have a sum of 1. For instance, 5 and
   are complementary because.

If xand yare complementary, and if ,

what is y?

(A) − 2 (B) (C)

(D)^1 (E) 3

3

−

1

3

−

1

2

x=

2

3

1

5

4

5

(^5) += 1
4
ab
a
b

# =

2

2

8

5

6

5

5

6

5. For x≠0, let. What is the value of $$5?


6. For all nonnegative real numbers x,let ◊xbe

defined by the equation. For what

value of xdoes ◊x=1.5?

(A) 0.3 (B) 6 (C) 12

(D) 14 (E) 36

7. For any integer n,let [n] be defined as the sum of
   the digits of n.For instance, [341] = 3 + 4 + 1 =8.
   If ais an integer greater than 0 but less than
   1,000, which of the following must be true?
   I. [10a] < [a]+ 1
   II. [[a]] < 20
   III. If ais even, then [a] is even
   (A) none
   (B) II only
   (C) I and II only
   (D) II and III only
   (E) I, II, and III


8. For all integers, n,let

What is the value of 13& &?

(A) 10 (B) 13 (C) 20

(D) 23 (E) 26

n

nn

nn

&=

−

⎧

⎨

⎪

⎩⎪

2

3

if is even

if is odd

◊=x

x

4

$x

x

=

1

SAT Practice 1: New Symbol or Term Problems

....

1 2 3 4 5 7 8 9

6

1

0 2 3 4 5 7 8 9

6

1

0 2 3 4 5 7 8 9

6

1

0 2 3 4 5 7 8 9

6