SAT Mc Graw Hill 2011

CHAPTER 7 / ESSENTIAL PRE-ALGEBRA SKILLS 297

1. When an integer nis di-
   vided by 10, the remain-
   der is 7. What is the
   remainder when nis di-
   vided by 5?
   6. Which of the following is a counterexample to
   the statement: All prime numbers are odd?

(A) 2 (B) 3 (C) 9

(D) 11 (E) 12

7. If and are both positive integers, then

which of the following must also be an integer?

(A) (B) (C)

(D) (E)

8. If a, b, c, d,and eare consecutive integers, then
   which of the following statements must be
   true?
   I. This set contains 3 odd numbers.
   II. This set contains a number divisible
   by 5.
   III. bc+1 is odd.

(A) I only (B) II only

(C) I and II only (D) II and III only

(E) I, II, and III

9. mand nare positive integers. If mis divided by
   n,the quotient is 7 with a remainder of 4. Which
   of the following expresses min terms of n?
   (A) 4n− 7 (B) 7n−4(C)4n+ 7

(D) (E) 7n+ 4

10. If aand bare positive integers and ,

then which of the following must be true?

I. (a+b) is odd

II. (a+b) is a multiple of 7

III. is an integer

(A) II only (B) I and III only

(C) I and II only (D) II and III only

(E) I, II, and III

5 b

a

a

b

=25.

n

7

+ 4

k

10

k

15

k

19

k

24

k

42

k

12

k

7

SAT Practice 7: Divisibility

....

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

2. When 8 is divided by 12, the remainder is

(A) (B) (C) 4

(D) 8 (E) 12

3. If pis odd and qis even, then which of the fol-
   lowing must be an odd number?
   I. p^2 +q^2

II.

III. p^2 q^2

(A) none (B) I only

(C) I and II only (D) I and III only

(E) I, II, and III

4. 1, 3, 5, 7, 9, 1, 3, 5, 7, 9, 1,...

If the sequence above follows the pattern

shown, what is the 103rd term of the sequence?

(A) 1 (B) 3 (C) 5

(D) 7 (E) 9

5.

remainder 3

In the division problem shown above, if aand

bare positive, which of the following must be

true?

(A) a=3(B)a= 3 b (C) b= 0

(D) b=3(E)b= 3 a

ab)

0

p

q

2

2

2

3

1

3