roy_priya wrote:
How to quickly solve this problem. Thanks for your help

If it is 6:27 in the evening on a certain day, what time in the morning was it exactly 2,880,717 minutes earlier? (Assume standard time in one location.)
(A) 6:22
(B) 6:24
(C) 6:27
(D) 6:30
(E) 6:32


There's no need to work out how much time 2,880,717 minutes is. Just look at the last digit of the current time, and the last digit of 2,880,717. Subtract- the answer needs to end in zero. D.

Ian Stewart wrote:I can try.

If we go back in time 2,880,717 minutes from 6:27, we can first go back in time 7 minutes, to get a time that ends in zero, then go back in time 2,880,710 minutes; the time will still end in zero, since we are subtracting a multiple of 10. This is actually what we're doing when we do 'long subtraction': if you want to work out, to take a random example, 496 - 326, you can first take away 6, then take away 20, then take away 300:

496 - 326 = 496 - 6 - 20 - 300

So the answer must end in zero.

It may be easier to think of smaller numbers first, if the above is unclear. If it's 6:27 now, what time was it:

7 minutes ago? 6:20.
17 minutes ago? 6:10.
27 minutes ago? 6:00.
37 minutes ago? 5:50.
2,880,717 minutes ago? Not sure, but it ends in zero!

Ian Stewart wrote:I can try.

If we go back in time 2,880,717 minutes from 6:27, we can first go back in time 7 minutes, to get a time that ends in zero, then go back in time 2,880,710 minutes; the time will still end in zero, since we are subtracting a multiple of 10. This is actually what we're doing when we do 'long subtraction': if you want to work out, to take a random example, 496 - 326, you can first take away 6, then take away 20, then take away 300:

496 - 326 = 496 - 6 - 20 - 300

So the answer must end in zero.

It may be easier to think of smaller numbers first, if the above is unclear. If it's 6:27 now, what time was it:

7 minutes ago? 6:20.
17 minutes ago? 6:10.
27 minutes ago? 6:00.
37 minutes ago? 5:50.
2,880,717 minutes ago? Not sure, but it ends in zero!

san2009 wrote:

Ian Stewart wrote:I can try.

If we go back in time 2,880,717 minutes from 6:27, we can first go back in time 7 minutes, to get a time that ends in zero, then go back in time 2,880,710 minutes; the time will still end in zero, since we are subtracting a multiple of 10. This is actually what we're doing when we do 'long subtraction': if you want to work out, to take a random example, 496 - 326, you can first take away 6, then take away 20, then take away 300:

496 - 326 = 496 - 6 - 20 - 300

So the answer must end in zero.

It may be easier to think of smaller numbers first, if the above is unclear. If it's 6:27 now, what time was it:

7 minutes ago? 6:20.
17 minutes ago? 6:10.
27 minutes ago? 6:00.
37 minutes ago? 5:50.
2,880,717 minutes ago? Not sure, but it ends in zero!

Ian - the way i thought about this question was a bit different. I arrived at 6:24 - but not sure where I went wrong.
If you start with 2,880,000 you end up back at 6:27 pm since 2,880,000 when divided by 60 gives us 48,000. And that constitutes 4,000 full 24 hour cycles or days. Then you're left with 717 minutes --- which is 3 less minutes than 60*12=720 minutes -- which means you fall short of the 6:27 mark by 3 minutes. I am probably complicating this question - but still would appreciate any input you can provide. thanks