MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
Determine if the statement is true or false.
| 1) |
1351 0 (mod 7) |
1) |
|
|
A) False |
B) True |
| 2) |
11 |
4 (mod 7) |
2) |
|
|
A) False |
B) True |
| 3) |
66 |
7 (mod 12) |
3) |
|
|
A) False |
B) True |
Find the sum.
| 4) |
(6 + 5) (mod 6) |
|
|
4) |
|
A) 5 |
B) 6 |
C) 11 |
D) 4 |
| 5) |
(48 + 48) (mod 50) |
|
|
5) |
|
A) 4 |
B) 46 |
C) 50 |
D) 96 |
Find the sum or product using the requested clock system.
| 6) |
8 |
+ 10 in 12-hour clock arithmetic |
|
6) |
|
|
A) 2 |
B) 8 |
C) 6 |
D) 0 |
| 7) |
7 |
· 16 in 12-hour clock arithmetic |
|
7) |
|
|
A) 4 |
B) 5 |
C) 16 |
D) 11 |
| 8) |
3 |
+ 221 in 7-day clock arithmetic |
|
8) |
|
|
A) 3 |
B) 5 |
C) 0 |
D) 8 |
| 9) |
1400 + 1900 in the military 24-hour clock system |
|
9) |
|
|
A) 0930 |
B) 12100 |
C) 1900 |
D) 0900 |
| 10) |
0930 + 1640 in the military 24-hour clock system |
|
10) |
|
|
A) 0310 |
B) 2610 |
C) 0210 |
D) 2570 |
Decide whether the congruence statement is true or false.
| 11) |
6 13 (mod 2) |
11) |
|
A) True |
B) False |
| 12) |
0 26 (mod 7) |
12) |
|
A) True |
B) False |
| 13) |
19 77 (mod 5) |
13) |
|
A) True |
B) False |
| 14) |
5 21 (mod 5) |
14) |
|
A) True |
B) False |
1
15) 3 13 (mod 11) 15)
A) True B) False
Perform the modular arithmetic operation.
| 16) |
(46 + 37)(mod 7) |
|
|
16) |
|
A) 6 |
B) 7 |
C) 11 |
D) 5 |
| 17) |
(130 + 106)(mod 9) |
|
|
17) |
|
A) 10 |
B) 26 |
C) 2 |
D) 1 |
| 18) |
(10 · 7)(mod 6) |
|
|
18) |
|
A) 3 |
B) 6 |
C) 11 |
D) 4 |
| 19) |
[(11 + 7) · (7 + 3)](mod 7) |
|
|
19) |
|
A) 4 |
B) 7 |
C) 25 |
D) 5 |
| 20) |
(49 - 25)(mod 5) |
|
|
20) |
|
A) 3 |
B) 0 |
C) 120 |
D) 4 |
| 21) |
(15 - 53)(mod 4) |
|
|
21) |
|
A) 3 |
B) 2 |
C) 1 |
D) 152 |
| 22) |
[(3 · 7) - 5](mod 4) |
|
|
22) |
|
A) 1 |
B) 3 |
C) 2 |
D) 0 |
| 23) |
[(13 · 3) + 9](mod 8) |
|
|
23) |
|
A) 3 |
B) 7 |
C) 0 |
D) 1 |
| 24) |
[(4 - 9) · 7](mod 5) |
|
|
24) |
|
A) 2 |
B) 0 |
C) 4 |
D) 3 |
| 25) |
[(-5) · 6](mod 7) |
|
|
25) |
|
A) -5 |
B) 5 |
C) -2 |
D) 1 |
Find all positive solutions for the equation.
| 26) x 4 (mod 7) |
|
|
26) |
|
A) {1, 18, 25, ...} |
B) {4, 11, 18, ...} |
C) {4, 8, 12, ...} |
D) {11, 18, 91, ...} |
| 27) |
2x 1 (mod 3) |
|
|
27) |
|
A) {2, 6, 10, 14, ...} |
|
B) {1, 4, 7, 10, ...} |
|
|
C) {2, 5, 8, 11, ...} |
|
D) None |
|
| 28) |
2x 8 (mod 10) |
|
|
28) |
|
A) Identity |
|
B) {4, 9, 14, 19, 24, 29, ...} |
|
|
C) {4, 14, 24, ...} |
|
D) {9, 19, 29, ...} |
|
| 29) |
8x 4 (mod 4) |
|
|
29) |
|
A) {4, 8, 12, ...} |
B) {1, 5, 9, ...} |
C) Identity |
D) {2, 6, 5, ...} |
2
| 30) |
10x 1 (mod 10) |
|
|
30) |
|
A) {1, 10, 15, ...} |
B) None |
C) Identity |
D) {2, 7, 12, ...} |
| 31) |
(2 + x) 5 (mod 4) |
|
|
31) |
|
A) {4, 6, 8, 10, 12, 14, ...} |
|
B) {0, 2, 4, 6, 8, 10, ...} |
|
|
C) {3, 7, 11, 15, 19, 23, ...} |
|
D) None |
|
