Applications of Congruence

Reviewed by Editorial Team
The ProProfs editorial team is comprised of experienced subject matter experts. They've collectively created over 10,000 quizzes and lessons, serving over 100 million users. Our team includes in-house content moderators and subject matter experts, as well as a global network of rigorously trained contributors. All adhere to our comprehensive editorial guidelines, ensuring the delivery of high-quality content.
Learn about Our Editorial Process
| By Thames
T
Thames
Community Contributor
Quizzes Created: 7288 | Total Attempts: 9,526,473
| Questions: 10 | Updated: Nov 12, 2025
Please wait...
Question 1 / 10
0 %
0/100
Score 0/100
1) A theater rotates 5 shows. If show 1 is today, which show is on the 23rd day?

Explanation

((23 − 1) mod 5) + 1 = (22 mod 5) + 1 = 2 + 1 = 3. Show 3 plays on day 23.

Submit
Please wait...
About This Quiz
Applications Of Congruence - Quiz

From clocks and calendars to races and repeating schedules, congruence shows up everywhere. In this quiz, you’ll solve real-world problems that use congruence to model cycles, rotations, and repeating patterns. Try this quiz and see how a simple congruence relation connects math directly to everyday life.

2)
You may optionally provide this to label your report, leaderboard, or certificate.
2) A bus runs every 18 minutes. If the first bus is at 10:00, when is the 15th bus?

Explanation

There are 14 intervals × 18 min = 252 min = 4 h 12 min. 10:00 + 4:12 = 14:12.

Submit
3) A clock shows 7:00. What time will it show 137 hours later?

Explanation

137 mod 12 = 5. 7 + 5 = 12:00 on the clock.

Submit
4) A sequence follows n ≡ 2 (mod 5). Which of these is in the sequence?

Explanation

7 mod 5 = 2, so 7 fits the rule.

Submit
5) A calendar repeats every 12 months. If an event is in April, when is it again after 50 months?

Explanation

50 mod 12 = 2. Two months after April = June.

Submit
6) A digital clock shows 11:00. What time is it 27 hours later?

Explanation

27 mod 12 = 3. Add 3 hours to 11:00 → 2:00.

Submit
7) A 7-day schedule repeats. If today is Monday, what day will it be in 50 days?

Explanation

50 mod 7 = 1. One day after Monday → Tuesday.

Submit
8) A pizza shop sells slices in packs of 8. If 59 slices are sold, how many are in the last pack?

Explanation

59 mod 8 = 3. Three slices fill the final pack.

Submit
9) A machine beeps every 9 seconds. If it beeps at time 0, when will it next beep at a time ending in 7?

Explanation

Solve 9n ≡ 7 (mod 10). n = 3 works. 9 × 3 = 27 s.

Submit
10) A runner completes 400 m laps. After 2500 m, what distance into the lap are they?

Explanation

2500 mod 400 = 100 → 100 m into the next lap.

Submit
×
Saved
Thank you for your feedback!
10)
Your input helps us improve, and you’ll get your detailed results next.
View My Results
Cancel
  • All
    All (10)
  • Unanswered
    Unanswered ()
  • Answered
    Answered ()
A theater rotates 5 shows. If show 1 is today, which show is on the...
A bus runs every 18 minutes. If the first bus is at 10:00, when is the...
A clock shows 7:00. What time will it show 137 hours later?
A sequence follows n ≡ 2 (mod 5). Which of these is in the sequence?
A calendar repeats every 12 months. If an event is in April, when is...
A digital clock shows 11:00. What time is it 27 hours later?
A 7-day schedule repeats. If today is Monday, what day will it be in...
A pizza shop sells slices in packs of 8. If 59 slices are sold, how...
A machine beeps every 9 seconds. If it beeps at time 0, when will it...
A runner completes 400 m laps. After 2500 m, what distance into the...
Alert!

Advertisement