# Malware in the computer [closed]

You are IT staff working in a company and there are a few amount of computers which have some malwares in them.

• If you clean 3 computers every day starting today, you will be finished at the end of the day on Sunday.
• If you clean 5 computers every day starting today, you will be finished at the end of the day on Friday.

What day is it today?

Since we are finished at the end of the day,

it follows that the number of computers is divisible by 3 and 5. However, we do not know which multiple of 15 the number of computers is.

However,

if we let $a$ be the number of days cleaning 3 computers at a time, and $b$ be the number of days cleaning 5 computers at a time, we see $a\equiv b+2 \pmod 7$, due to the number of days between Friday and Sunday.

Also,

$5b\equiv 3a\equiv 3(b+2) \pmod 7$, so rearranging gives $2b \equiv 6 \pmod 7$, or $b \equiv 3 \pmod 7$. That means 3 days and some weeks will pass since starting to clean computers 5 at a time. Hence, 3 days and some weeks before the end of Friday would be the start of Wednesday.

In conclusion:

Without knowing the total number of computers, today is Wednesday.

• Yeah I got the same answer. – Beastly Gerbil Dec 24 '16 at 15:27
• @BeastlyGerbil Well, but your working assumes that the number of computers is the smallest possible. – Element118 Dec 24 '16 at 22:32
• anything bigger would result in you not finishing this week – Beastly Gerbil Dec 25 '16 at 9:59

Today is

Wednesday

We take the

Lowest Common Multiple (LCM) of 5 and 3 which is 15. We divide that by the computers we clean that day, and then take it away from that day.

So

15/3 = 5. Sunday - 5 days = Wednesday
15/5 = 3. Friday - 3 days = Wednesday

I have included Sunday/Friday in the sums above, as it says 'you will be finished at the end of the day' meaning you worked on that day too.

• @Oray am I correct? – Beastly Gerbil Dec 24 '16 at 13:51