7.4: Assessment Module 5: Modular Arithmetic
- Page ID
- 55953
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\(\newcommand{\avec}{\mathbf a}\) \(\newcommand{\bvec}{\mathbf b}\) \(\newcommand{\cvec}{\mathbf c}\) \(\newcommand{\dvec}{\mathbf d}\) \(\newcommand{\dtil}{\widetilde{\mathbf d}}\) \(\newcommand{\evec}{\mathbf e}\) \(\newcommand{\fvec}{\mathbf f}\) \(\newcommand{\nvec}{\mathbf n}\) \(\newcommand{\pvec}{\mathbf p}\) \(\newcommand{\qvec}{\mathbf q}\) \(\newcommand{\svec}{\mathbf s}\) \(\newcommand{\tvec}{\mathbf t}\) \(\newcommand{\uvec}{\mathbf u}\) \(\newcommand{\vvec}{\mathbf v}\) \(\newcommand{\wvec}{\mathbf w}\) \(\newcommand{\xvec}{\mathbf x}\) \(\newcommand{\yvec}{\mathbf y}\) \(\newcommand{\zvec}{\mathbf z}\) \(\newcommand{\rvec}{\mathbf r}\) \(\newcommand{\mvec}{\mathbf m}\) \(\newcommand{\zerovec}{\mathbf 0}\) \(\newcommand{\onevec}{\mathbf 1}\) \(\newcommand{\real}{\mathbb R}\) \(\newcommand{\twovec}[2]{\left[\begin{array}{r}#1 \\ #2 \end{array}\right]}\) \(\newcommand{\ctwovec}[2]{\left[\begin{array}{c}#1 \\ #2 \end{array}\right]}\) \(\newcommand{\threevec}[3]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \end{array}\right]}\) \(\newcommand{\cthreevec}[3]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \end{array}\right]}\) \(\newcommand{\fourvec}[4]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \\ #4 \end{array}\right]}\) \(\newcommand{\cfourvec}[4]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \\ #4 \end{array}\right]}\) \(\newcommand{\fivevec}[5]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \\ #4 \\ #5 \\ \end{array}\right]}\) \(\newcommand{\cfivevec}[5]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \\ #4 \\ #5 \\ \end{array}\right]}\) \(\newcommand{\mattwo}[4]{\left[\begin{array}{rr}#1 \amp #2 \\ #3 \amp #4 \\ \end{array}\right]}\) \(\newcommand{\laspan}[1]{\text{Span}\{#1\}}\) \(\newcommand{\bcal}{\cal B}\) \(\newcommand{\ccal}{\cal C}\) \(\newcommand{\scal}{\cal S}\) \(\newcommand{\wcal}{\cal W}\) \(\newcommand{\ecal}{\cal E}\) \(\newcommand{\coords}[2]{\left\{#1\right\}_{#2}}\) \(\newcommand{\gray}[1]{\color{gray}{#1}}\) \(\newcommand{\lgray}[1]{\color{lightgray}{#1}}\) \(\newcommand{\rank}{\operatorname{rank}}\) \(\newcommand{\row}{\text{Row}}\) \(\newcommand{\col}{\text{Col}}\) \(\renewcommand{\row}{\text{Row}}\) \(\newcommand{\nul}{\text{Nul}}\) \(\newcommand{\var}{\text{Var}}\) \(\newcommand{\corr}{\text{corr}}\) \(\newcommand{\len}[1]{\left|#1\right|}\) \(\newcommand{\bbar}{\overline{\bvec}}\) \(\newcommand{\bhat}{\widehat{\bvec}}\) \(\newcommand{\bperp}{\bvec^\perp}\) \(\newcommand{\xhat}{\widehat{\xvec}}\) \(\newcommand{\vhat}{\widehat{\vvec}}\) \(\newcommand{\uhat}{\widehat{\uvec}}\) \(\newcommand{\what}{\widehat{\wvec}}\) \(\newcommand{\Sighat}{\widehat{\Sigma}}\) \(\newcommand{\lt}{<}\) \(\newcommand{\gt}{>}\) \(\newcommand{\amp}{&}\) \(\definecolor{fillinmathshade}{gray}{0.9}\)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 |