Modular Arithmetic Basics in DSA Python - Interactive Practice

Practice - 5 Tasks

1fill in blank

easy

Complete the code to compute the remainder when 17 is divided by 5.

DSA Python

result = 17 [1] 5
print(result)

Drag options to blanks, or click blank then click option'

A%

B//

C*

D+

Attempts:

3 left

💡 Hint

Common Mistakes

Using // instead of % returns the quotient, not remainder.

The % operator gives the remainder of division, which is the core of modular arithmetic.

2fill in blank

medium

Complete the code to check if 23 is divisible by 7 using modular arithmetic.

DSA Python

if 23 [1] 7 == 0:
    print("Divisible")
else:
    print("Not divisible")

Drag options to blanks, or click blank then click option'

A//

B%

C*

D+

Attempts:

3 left

💡 Hint

Common Mistakes

Using // returns quotient, not remainder.

Using % checks the remainder. If remainder is 0, the number is divisible.

3fill in blank

hard

Fix the error in the code to correctly compute (a + b) mod m.

DSA Python

a = 10
b = 15
m = 6
result = (a [1] b) % m
print(result)

Drag options to blanks, or click blank then click option'

A*

B-

C+

D//

Attempts:

3 left

💡 Hint

Common Mistakes

Using - or * changes the operation meaning.

To add numbers before taking modulo, use the plus operator +.

4fill in blank

hard

Fill both blanks to create a dictionary of numbers and their squares modulo 5 for numbers 1 to 5.

DSA Python

squares_mod = {x: (x [1] x) [2] 5 for x in range(1, 6)}
print(squares_mod)

Drag options to blanks, or click blank then click option'

A*

B+

C%

D-

Attempts:

3 left

💡 Hint

Common Mistakes

Using + instead of * changes the operation.

Use * to multiply x by itself, then % to take modulo 5.

5fill in blank

hard

Fill all three blanks to create a dictionary with keys as numbers squared modulo 7 and values as the original numbers for 1 to 6.

DSA Python

result = [1]: [2] for [3] in range(1, 7)}
print(result)

Drag options to blanks, or click blank then click option'

Ax**2 % 7

Bx

Di

Attempts:

3 left

💡 Hint

Common Mistakes

Using different variable names inconsistently.

Keys are squares modulo 7 (x**2 % 7), values are original numbers (x), and loop variable is x.

Practice

1. What is the result of 17 % 5 in modular arithmetic?

easy

A. 3

B. 2

C. 5

D. 12

Solution

1. Step 1: Understand the modulo operation

   The modulo operator (%) gives the remainder when the first number is divided by the second.

2. Step 2: Calculate 17 divided by 5

   17 divided by 5 is 3 with a remainder of 2.

3. Final Answer:

   2 -> Option B

4. Quick Check:

   17 % 5 = 2 [OK]

Hint: Modulo gives remainder after division [OK]

Common Mistakes:

• Confusing modulo with division
• Using subtraction instead of modulo
• Mixing up dividend and divisor

2. Which of the following is the correct syntax to compute the remainder of 25 divided by 4 in Python?

easy

A. remainder = 25 % 4

B. remainder = 25 mod 4

C. remainder = 25 // 4

D. remainder = 25 / 4

Solution

1. Step 1: Recall Python modulo operator

   In Python, the modulo operator is the percent sign (%).

2. Step 2: Check each option

   remainder = 25 % 4 uses 25 % 4 which correctly computes the remainder. remainder = 25 mod 4 uses 'mod' which is not valid syntax. remainder = 25 // 4 uses floor division (//) which gives quotient, not remainder. remainder = 25 / 4 uses normal division (/), which gives a float result.

3. Final Answer:

   remainder = 25 % 4 -> Option A

4. Quick Check:

   Use % for modulo in Python [OK]

Hint: Use % symbol for modulo in Python [OK]

Common Mistakes:

• Using 'mod' keyword
• Confusing // with %
• Using / instead of %

3. What is the output of the following Python code?

for i in range(1, 6):
    print(i % 3, end=' ')

medium

A. 0 1 2 0 1

B. 1 2 3 1 2

C. 1 2 0 1 2

D. 1 2 0 2 1

Solution

1. Step 1: Understand the loop and modulo

   The loop runs i from 1 to 5. For each i, we compute i % 3.

2. Step 2: Calculate each modulo

   1 % 3 = 1, 2 % 3 = 2, 3 % 3 = 0, 4 % 3 = 1, 5 % 3 = 2.

3. Final Answer:

   1 2 0 1 2 -> Option C

4. Quick Check:

   Modulo cycles every 3 numbers [OK]

Hint: Modulo repeats remainder pattern every divisor [OK]

Common Mistakes:

• Starting loop at 0 instead of 1
• Miscomputing modulo for 3
• Confusing modulo with division

4. Find the error in the following code snippet that tries to compute n % 4 for n = 10:

n = 10
result = n %
print(result)

medium

A. Missing operand after % operator

B. Incorrect variable name

C. Using print without parentheses

D. No error, code runs fine

Solution

1. Step 1: Analyze the modulo expression

   The line 'result = n %' is incomplete because modulo requires two operands: dividend and divisor.

2. Step 2: Identify syntax error

   Without a number or variable after %, Python will raise a syntax error.

3. Final Answer:

   Missing operand after % operator -> Option A

4. Quick Check:

   Modulo needs two numbers: a % b [OK]

Hint: Modulo operator needs both numbers [OK]

Common Mistakes:

• Leaving out divisor after %
• Using print without () in Python 3
• Typos in variable names

5. You want to find the remainder when the sum of numbers from 1 to 100 is divided by 7. Which Python expression correctly computes this using modular arithmetic?

hard

A. sum(i for i in range(1, 101)) // 7

B. (sum(range(1, 101)) // 7) % 7

C. sum(i % 7 for i in range(1, 101))

D. sum(range(1, 101)) % 7

Solution

1. Step 1: Understand the problem

   We want the remainder of the sum of numbers 1 to 100 divided by 7.

2. Step 2: Evaluate each option

   sum(range(1, 101)) % 7 correctly sums all numbers then applies modulo 7. (sum(range(1, 101)) // 7) % 7 first does floor division to get quotient then % 7, which is incorrect. sum(i % 7 for i in range(1, 101)) sums remainders but does not apply modulo to the total sum, so it gives a wrong result. sum(i for i in range(1, 101)) // 7 uses floor division (//) which gives quotient, not remainder.

3. Final Answer:

   sum(range(1, 101)) % 7 -> Option D

4. Quick Check:

   Sum then modulo gives remainder [OK]

Hint: Sum first, then modulo for remainder [OK]

Common Mistakes:

• Applying modulo inside sum without final modulo
• Using floor division instead of modulo
• Using floor division before modulo