In Narora nuclear power plant a technician is allowed an interval of m

1.	In Narora nuclear power plant a technician is allowed an interval of maximum 100 minutes. A timer with a bell rings at specific intervals of time such that the minutes when the timer rings are not divisible by 2, 3, 5 and 7. The last alarm rings with a buzzer to give time for decontamination of the technician. How many times will the bell ring within these 100 minutes and what is the value of the last minute when the bell rings for the last time in a 100 minute shift?
Answer» In order to find how many times the alarm rings we need to find the number of numbers below 100, which are not divisible by 2, 3, 5 or 7. This can be found by: 100 — (numbers divisible by 2) – (numbers divisible by 3 but not by 2) — (numbers divisible by 5 but not by 2 or 3) — (numbers divisible by 7 but not by 2 or 3 or 5). Numbers divisible by 2 up to 100 would be represented by the series 2, 4, 6, 8, 10…100 → A total of 50 numbers. Numbers divisible by 3 but not by 2 up to 100 would be represented by the series 3, 9, 15, 21...99 → A total of 17 numbers. Note use short cut for finding the number of number in this series : [(last term — first term)/ common difference] + 1 = [(99 — 3)/6] + 1 = 16 + 1 = 17. Numbers divisible by 5 but not by 2 or 3: Numbers divisible by 5 but not by 2 up to 100 would be represented by the series 5, 15, 25, 35...95 → A total of 10 numbers. But from these numbers, the numbers 15, 45 and 75 are also divisible by 3. Thus, we are left with 10 — 3 = 7 new numbers which are Divisible by 5 but not by 2 and 3. Numbers divisible by 7, but not by 2, 3 or 5: numbers divisible by 7 but not by 2 upto 100 would be represented by the series 7, 21, 35, 49, 63, 77, 91 → A total of 7 numbers. But from these numbers we should not count 21, 35 and 63 as they are divisible by either 3 or 5. Thus a total of 7 — 3 = 4 numbers are divisible by 7 but not by 2, 3 or 5. Thus we get a total of 100 − 78 = 22 times. Also, the last time the bell would ring would be in the 97th minute (as 98, 99 and 100 are divisible by at least one of the numbers).

In Narora nuclear power plant a technician is allowed an interval of maximum 100 minutes. A timer with a bell rings at specific intervals of time such that the minutes when the timer rings are not divisible by 2, 3, 5 and 7. The last alarm rings with a buzzer to give time for decontamination of the technician. How many times will the bell ring within these 100 minutes and what is the value of the last minute when the bell rings for the last time in a 100 minute shift?

Answer»

In order to find how many times the alarm rings we need to find the number of numbers below 100, which are not divisible by 2, 3, 5 or 7. This can be found by:

100 — (numbers divisible by 2) – (numbers divisible by 3 but not by 2) — (numbers divisible by 5 but not by 2 or 3) — (numbers divisible by 7 but not by 2 or 3 or 5).

Numbers divisible by 2 up to 100 would be represented by the series 2, 4, 6, 8, 10…100 → A total of 50 numbers.

Numbers divisible by 3 but not by 2 up to 100 would be represented by the series 3, 9, 15, 21...99 → A total of 17 numbers. Note use short cut for finding the number of number in this series : [(last term — first term)/ common difference] + 1 = [(99 — 3)/6] + 1 = 16 + 1 = 17.

Numbers divisible by 5 but not by 2 or 3: Numbers divisible by 5 but not by 2 up to 100 would be represented by the series 5, 15, 25, 35...95 → A total of 10 numbers. But from these numbers, the numbers 15, 45 and 75 are also divisible by 3. Thus, we are left with 10 — 3 = 7 new numbers which are Divisible by 5 but not by 2 and 3.

Numbers divisible by 7, but not by 2, 3 or 5: numbers divisible by 7 but not by 2 upto 100 would be represented by the series 7, 21, 35, 49, 63, 77, 91 → A total of 7 numbers. But from these numbers we should not count 21, 35 and 63 as they are divisible by either 3 or 5. Thus a total of 7 — 3 = 4 numbers are divisible by 7 but not by 2, 3 or 5.

Thus we get a total of 100 − 78 = 22 times. Also, the last time the bell would ring would be in the 97th minute (as 98, 99 and 100 are divisible by at least one of the numbers).

Discussion

No Comment Found

Related InterviewSolutions

Reply to Comment