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Mathbound · Contest practice

Modular Arithmetic worksheet

Mixed difficulty

Name

Date

1.
How many positive integers $n\le 100$ satisfy $n\equiv 3\pmod{6}$ ?
- A.16
- B.17
- C.18
- D.19
- E.z4
2.
How many positive integers $n\le 100$ satisfy $n\equiv 6\pmod{8}$ ?
- A.11
- B.12
- C.14
- D.13
- E.15
3.
How many positive integers $n\le 100$ satisfy $n\equiv 4\pmod{7}$ ?
- A.14
- B.16
- C.15
- D.17
- E.13
4.
Least positive integer $n$ with $n\equiv 2\pmod{5}$ and $n\equiv 3\pmod{7}$ ?
- A.35
- B.17
- C.16
- D.22
- E.24
5.
How many positive integers $n\le 150$ satisfy $n\equiv 4\pmod{7}$ ?
- A.20
- B.21
- C.23
- D.22
- E.24
6.
How many positive integers $n\le 200$ are divisible by $7$ ?
- A.28
- B.25
- C.29
- D.193
- E.27
7.
How many positive integers $n\le 100$ satisfy $n\equiv 1\pmod{7}$ ?
- A.17
- B.16
- C.14
- D.15
- E.alt4
8.
How many positive integers $n\le 100$ satisfy $n\equiv 2\pmod{5}$ ?
- A.20
- B.22
- C.21
- D.23
- E.19
9.
How many positive integers $n\le 200$ satisfy $n\equiv 7\pmod{8}$ ?
- A.27
- B.26
- C.28
- D.24
- E.25
10.
How many positive integers $n\le 50$ satisfy $n\equiv 7\pmod{8}$ ?
- A.5
- B.6
- C.8
- D.7
- E.9

Answer key · worked solutions

1. B. 17
Arithmetic progression. First 3, step 6. $17$ .
2. B. 12
Arithmetic progression. First 6, step 8. $12$ .
3. A. 14
Arithmetic progression. First 4, step 7. $14$ .
4. B. 17
Chinese Remainder Theorem / scan. Modulus 35. $17$ .
5. B. 21
Arithmetic progression. First 4, step 7. $21$ .
6. A. 28
Count multiples. $\lfloor 200/7\rfloor$ . $28$ .
7. D. 15
Count an arithmetic progression. First 1, common difference 7. $15$ .
8. A. 20
Arithmetic progression. First 2, step 5. $20$ .
9. E. 25
Arithmetic progression. First 7, step 8. $25$ .
10. B. 6
Arithmetic progression. First 7, step 8. $6$ .

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Free AMC Math Worksheet Generator — Mathbound