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Re: The number of days between May 30, 1917, and May 15, 1996, i [#permalink]
amorphous wrote:
Let us start with quantity A

The counting begins on May 1917 and ends on May 15 1996
For the time being let us consider the year in totality without computation for months.

Total no of years would come to be \(1996 - 1917 = 19 +1 = 80\) years since both years are included.
Now, Among these years let us compute the no of leap years
which would be \(\frac{96-20}{4}+ 1 = 20\) leap years.
Hence we have for qty A \(60\) normal years and \(20\) leap years
and let us not forget that counting begins on may 30 and ends on may 15 so we are short of 15 days as well.

Therefore qty \(A = 365* 60 + 366 *20 - 15\)

Coming to qty B similar process as for qty A leads us to the following findings:

leap years = 20
normal years = 60
and the counting begins on may 15 and ends on may 30 so we add 15 more days.

Therefore qty \(B = 365 * 60 + 20 * 366 + 15\)
Qty A = \(21900 + 7320 - 15 = 29205\)
Qty B = \(22265 + 6954 + 15 = 29235\)



Could you please explain how did you calculate the leap year.
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Re: The number of days between May 30, 1917, and May 15, 1996, i [#permalink]
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Leap yrs are those yrs that are divisible by 4. However those yrs which can be divisible by 4 as well as 100 are not leap yrs. on top of that if any year is divisible by 4 and 100 as well as 400 it is a leap year.

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Re: The number of days between May 30, 1917, and May 15, 1996, i [#permalink]
how did found 96-20 by 4
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Re: The number of days between May 30, 1917, and May 15, 1996, i [#permalink]
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In qty A 1920 is the first leap yr and 1996 is the last leap yr. Hence 1996-1920 which is essentially 96-20. Since the difference between each leap yr is 4 so we divide by 4

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Re: The number of days between May 30, 1917, and May 15, 1996, i [#permalink]
4
A --> 79 years - 15 days
B --> 79 years + 15 days

Hence, B is greater and it is the Answer.
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Re: The number of days between May 30, 1917, and May 15, 1996, i [#permalink]
Sanpreet wrote:
A --> 79 years - 15 days
B --> 79 years + 15 days

Hence, B is greater and it is the Answer.

Could you please explain how you manage to get
-15 for option A.
+ 15 days for option B.

Thanks
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Re: The number of days between May 30, 1917, and May 15, 1996, i [#permalink]
venom004 wrote:
There is a quicker approach.

A) From 1996-1917=79 years + from May 30 - May 15 (15 days less to become a full year/350days) = 79 years and 350 days
B) From 1991-1912=79 years + from May 15 - May 30 (15 days more after becoming a full year/380days) = 79 years and 380 days

Therefore quantity B is bigger.

No need to calculate leap years! :-D :-D


I am not able to understand this 15 days thing with +/- could you explain it again?
Thanks
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Re: The number of days between May 30, 1917, and May 15, 1996, i [#permalink]
3
Aprazors wrote:
venom004 wrote:
There is a quicker approach.

A) From 1996-1917=79 years + from May 30 - May 15 (15 days less to become a full year/350days) = 79 years and 350 days
B) From 1991-1912=79 years + from May 15 - May 30 (15 days more after becoming a full year/380days) = 79 years and 380 days

Therefore quantity B is bigger.

No need to calculate leap years! :-D :-D


I am not able to understand this 15 days thing with +/- could you explain it again?
Thanks


Let's forget the # of years since they are the same, that is likely there to confuse us and make the question sound more daunting. Let's consider a 1 year timeframe:
For Qty A:
May 30 to May 30 is 1 year, but this quantity is 15 days less than 1 year

for Qty B:
May 15 to May 15 is one year, but this quantity is 15 days more than 1 year.

That's where the +/- 15 comes from, and why the answer is B.
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Re: The number of days between May 30, 1917, and May 15, 1996, i [#permalink]
1
CozmoP wrote:
Aprazors wrote:
venom004 wrote:
There is a quicker approach.

A) From 1996-1917=79 years + from May 30 - May 15 (15 days less to become a full year/350days) = 79 years and 350 days
B) From 1991-1912=79 years + from May 15 - May 30 (15 days more after becoming a full year/380days) = 79 years and 380 days

Therefore quantity B is bigger.

No need to calculate leap years! :-D :-D


I am not able to understand this 15 days thing with +/- could you explain it again?
Thanks


Let's forget the # of years since they are the same, that is likely there to confuse us and make the question sound more daunting. Let's consider a 1 year timeframe:
For Qty A:
May 30 to May 30 is 1 year, but this quantity is 15 days less than 1 year

for Qty B:
May 15 to May 15 is one year, but this quantity is 15 days more than 1 year.

That's where the +/- 15 comes from, and why the answer is B.


The way you explained it. uff!! thanks my guy.I understand it completely now.
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Re: The number of days between May 30, 1917, and May 15, 1996, i [#permalink]
1
To compute the days, we can simply count the total number of years that have passed and multiply them by 365, noting the leap years

QA:
May 30, 1917 to May 15, 1996

For the number of leap years:
1996 -> m4, so it is the last leap
1920 -> m4, so it is the first leap

\(\frac{{1996-1920}}{4}+1=20\)

Total number of years from 1917 to 1996:
1996-1917+1=80
Notice however, that 80 years would take us to May 30, 1996. So we need to remove 15 days.

Therefore:
\(QA=366(20)+365(60)-15\)

We now perform a similar operation on QB:

1912 -> m4, so it is the first leap year
1988 -> last m4 in the set, so it is the last leap year
\(\frac{{1988-1912}}{4}+1=20\)

Between 1912 and 1991 there were:
1991-1912+1=80 years
Notice that, 80 years would take us to May 15, 1991. QB is until May 30, so you need to add 15

\(QB=366(20)+365(60)+15\)

QA and QB have the same multiplication, however in QA you subtract by 15 whereas in QB you add by 15. So QB must be bigger.
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Re: The number of days between May 30, 1917, and May 15, 1996, i [#permalink]
First taking the year It says between

so we can say number of years would be (96-17)-1=78
In second case its inclusive so its (91-12)+1=80

Even if we compensate a few days we can evidently see that B>A
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