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The number of days between May 30, 1917, and May 15, 1996, i

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The number of days between May 30, 1917, and May 15, 1996, i [#permalink] New post 27 May 2018, 09:29
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Question Stats:

58% (00:53) correct 41% (01:11) wrong based on 136 sessions
Quantity A
Quantity B
The number of days between May 30, 1917,
and May 15, 1996, inclusive
The number of days between May 15, 1912,
and May 30, 1991, inclusive


A)The quantity in Column A is greater.
B)The quantity in Column B is greater.
C)The two quantities are equal.
D)The relationship cannot be determined from the information given.
[Reveal] Spoiler: OA

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Re: The number of days between May 30, 1917, and May 15, 1996, i [#permalink] New post 17 Jul 2018, 08:57
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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 = \(22265 + 6954 + 15 = 29235\)
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Re: The number of days between May 30, 1917, and May 15, 1996, i [#permalink] New post 06 Sep 2018, 12:22
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] New post 06 Sep 2018, 19:04
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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] New post 22 Mar 2019, 18:04
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] New post 22 Mar 2019, 21:50
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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] New post 06 Oct 2019, 12:45
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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
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Re: The number of days between May 30, 1917, and May 15, 1996, i [#permalink] New post 24 Oct 2019, 22:40
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A --> 79 years - 15 days
B --> 79 years + 15 days

Hence, B is greater and it is the Answer.
Re: The number of days between May 30, 1917, and May 15, 1996, i   [#permalink] 24 Oct 2019, 22:40
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