SAT Mc Graw Hill 2011

CHAPTER 7 / ESSENTIAL PRE-ALGEBRA SKILLS 293

1. For all real numbers b,−(−b−b−b−b) =
   (A) − 4 b (B) 4b (C) b^4
   (D) −b^4 (E) 4b^4


2. If k=(m−1)(m−2)(m−3), then for which of
   the following values of mis kgreater than 0?
   (A) 2.47
   (B) 1.47
   (C) 0.47
   (D) 1.47
   (E) 2.47


3. For all real numbers w,−w^2 −(−w)^2 =
   (A) −w^4
   (B) − 2 w^2
   (C) 0
   (D) 2w^2
   (E) w^4


4. If > 1, which of the following must be true?

I. m> n

II. > 0

III. m> 1

(A) I only

(B) II only

(C) III only

(D) I and II only

(E) I and III only

5. If x=−yand x≠0, then which of the following
   must be true?

I. x^2 y^3 < 0

II. (x+y)^2 = 0

III. < 0

(A) III only

(B) I and II only

(C) II and III only

(D) I and III only

(E) I, II, and III

x

y

m

n

m

n

6. If mn^4 p^5 > 0 and m< 0, then which of the fol-
   lowing expressions must be negative?
   (A) mn
   (B) m^2
   (C) p^5
   (D) mp
   (E) np


7. If 0 < a< b< c< d< e< fand
   (a−b)(c−d) (e−f)(x) =(b−a)(d−c)(f−e),
   then x=
   (A)  4
   (B)  3
   (C)  2
   (D)  1
   (E) 0


8. If the sum of the integers from 15 to 50, inclu-
   sive, is equal to the sum of the integers from n
   to 50, inclusive, and n< 15, then n=
   (A)  50
   (B)  49
   (C)  35
   (D)  15
   (E)  14


9. If − 2 x< −7 and y< 2.5, then which of the fol-
   lowing must be true?
   I. xy> 0
   II. x−y> 0
   III. x> 3

(A) II only

(B) I and II only

(C) II and III only

(D) I and III only

(E) I, II, and III

10. A sequence of numbers begins with the num-
    bers −1, 1, 1, ..., and each term afterward is
    the product of the preceding three terms. How
    many of the first 57 terms of this sequence are
    negative?
    (A) 19 (B) 20 (C) 28
    (D) 29 (E) 30

SAT Practice 6: Negatives