CHAPTER 9 / SPECIAL MATH PROBLEMS 335
- 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
- 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 - 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. - 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
- For x≠0, let. What is the value of $$5?
- 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
- 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 - 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
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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