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Modulo Arithmetic & Congruence · Question 20 of 97

After how many hours does a service next fall at 06:00?

Question 20

MediumOriginal question

A factory runs round the clock. A machine is serviced every 30 hours, the first service at 06:00 on a Monday. The shifts run from 06:00 to 14:00, 14:00 to 22:00 and 22:00 to 06:00.

After how many hours does a service next fall at 06:00?

Options for question 20

Show the answer and explanation
CorrectNot quiteAnswer C

Correct answer: C

Explanation

  1. A service falls at 06:00 when the hours passed are a multiple of both 30 and 24.

  2. LCM(30,24)=120\text{LCM}(30, 24) = 120 hours.

Worth noting

720 is 30×2430 \times 24, a common multiple but not the least.

Concept
When two cycles meet again
Typical time
120 s
Your time
—
The rule this testsThe modulo operation
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Ten questions from Modulo Arithmetic & Congruence, at your own pace.

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Ten questions from Modulo Arithmetic & Congruence, at your own pace.

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