Applications of Congruence

  • 10th Grade
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| By Thames
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Quizzes Created: 8157 | Total Attempts: 9,567,281
| Attempts: 11 | Questions: 10 | Updated: Nov 12, 2025
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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.

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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.

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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.

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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.

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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.

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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.

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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.

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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.

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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.

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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.

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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.

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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...
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