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#1 2016-04-21 16:39:34

coolbee
Member
Registered: 2016-04-05
Posts: 19

sid's new year resolution

For the year 2016, Sid has taken a New Year resolution for being very fit. Therefore, starting with January 1, 2016, he has decided to go for swimming every second day gym every third day and jogging every fifth day. The three activities are very energy intensive and require, respectively, 130 calories, 140 calories, 110 calories. If January 1, 2016 happens to be a Sunday,then, on how many days, does Sid not go for any of the three activities?

a) 95   b) 96   c) 97   d) 98




P.S. Considering he doesn't go to any of the activities on 1st jan. I am getting the answer 70 days , i.e, all the prime numbers between 1 to 366 leaving 2,3 and 5.But that's not given in the option.HELP!!

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#2 2016-04-21 19:27:21

bobbym
bumpkin
From: Bumpkinland
Registered: 2009-04-12
Posts: 109,606

Re: sid's new year resolution

Hi;


In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

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#3 2016-04-21 19:42:42

Nehushtan
Member
Registered: 2013-03-09
Posts: 957

Re: sid's new year resolution

The number of days he goes for at least one of the activities is

[list=*]
[*]

[/*]
[/list]

so the number of days he goes for none of them is 366 minus that.

Last edited by Nehushtan (2016-04-21 19:54:11)


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#4 2016-04-22 14:00:17

Relentless
Member
Registered: 2015-12-15
Posts: 631

Re: sid's new year resolution

Hi! big_smile

The above two answers are correct (I simply listed the days and their results in a spreadsheet). You counted all the primes up to 366, plus 1. The 27 non-prime numbers for the days you missed are:
49
77
91
119
121
133
143
161
169
187
203
209
217
221
247
253
259
287
289
299
301
319
323
329
341
343
361

I suppose these numbers have the property that they have only prime divisors not 2, 3 or 5? You may check that.

(Incidentally, he only swims 98 days, only gyms 49 days, only jogs 25 days, swims and gyms 49 days, swims and jogs 24 days, gyms and jogs 12 days, and does all three 12 days)

Last edited by Relentless (2016-04-22 14:08:51)

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#5 2016-04-22 15:20:13

coolbee
Member
Registered: 2016-04-05
Posts: 19

Re: sid's new year resolution

thank you !(I really missed it) big_smile

@relentless
according to my work out he jogs for 25 days.

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#6 2016-04-22 15:50:31

Relentless
Member
Registered: 2015-12-15
Posts: 631

Re: sid's new year resolution

Hey, (: He does indeed only jog for 25 days. If you include days in which he jogs and does something else, he jogs a total of 73 days. smile

Oh, what else is there... the total number of calories burned in the year is 48,900 (133 + 37/61 per day).
Also, the 1st of January 2016 was a Friday tongue

Last edited by Relentless (2016-04-22 15:54:50)

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