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A month with 31 days has the same number of Mondays and Wednesdays.How

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Bunuel
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A month with 31 days has the same number of Mondays and Wednesdays.How [#permalink] New post   31 Mar 2019, 20:47
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A month with 31 days has the same number of Mondays and Wednesdays. How many of the seven days of the week could be the first day of this month?

A. 2
B. 3
C. 4
D. 5
E. 6
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B
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Re: A month with 31 days has the same number of Mondays and Wednesdays.How [#permalink] New post   31 Mar 2019, 21:05
31/7 = 4 full weeks + 3 days.
If the week starts on Sunday then 29th day will again be sun and 31st will be tue having 5 mon and 4 wed. So not possible.
Using the same logic Monday, Thursday, and Friday are possible.
Hence option B 3

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A month with 31 days has the same number of Mondays and Wednesdays.How [#permalink] New post   02 Apr 2019, 07:50
A month with 31 days has 4 full weeks and 3 days .
So we can either have 4 Monday and wed in Full week , or 5 ( Monday -Wednesday , in the last 3 days ).

IF i consider 5 mondays and 5 wednesdays , only 1 possibility , 1st of next month should be Thursday.
:Moday-29,Tues-30,Wed-31 ,Thusday-1st
If I consider 4 mondays and 4 Wednesdays , 2 possibilities , 1st of next month could be Sunday or Monday
: Thursday-29,Fri-30,Sat-31 ,Sun-1st Or Fri-29,Sat-30,Sun-31 ,Mon-1st

Total : 3 possibilities - Option B

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Re: A month with 31 days has the same number of Mondays and Wednesdays.How [#permalink] New post   05 Apr 2019, 07:36
Expert Reply
Bunuel wrote:
A month with 31 days has the same number of Mondays and Wednesdays. How many of the seven days of the week could be the first day of this month?

A. 2
B. 3
C. 4
D. 5
E. 6


Let’s say the month is March (since it has 31 days) and let’s test each day of the week for 3/1.

If 3/1 is Monday, then 3/3 is Wednesday and 3/29 is Monday and 3/31 is Wednesday. We see that in this case, we have the same number of Mondays and Wednesdays. (Note: Here we are trying to look for the earliest Monday and Wednesday of the month and the latest Monday and Wednesday of the month and we want the following sequence: Monday, Wednesday, Monday, Wednesday.)

If 3/1 is Tuesday, then 3/2 is Wednesday and 3/7 is Monday and 3/28 is Monday and 3/30 is Wednesday. We see that in this case, we have one more Wednesday than Monday.

If 3/1 is Wednesday, then 3/6 is Monday and 3/27 is Monday and 3/29 is Wednesday. We see that in this case, we have one more Wednesday than Monday.

If 3/1 is Thursday, then 3/5 is Monday and 3/7 is Wednesday and 3/26 is Monday and 3/28 is Wednesday. We see that in this case, we have the same number of Mondays and Wednesdays.

If 3/1 is Friday, then 3/4 is Monday and 3/6 is Wednesday and 3/25 is Monday and 3/27 is Wednesday. We see that in this case, we have the same number of Mondays and Wednesdays.

If 3/1 is Saturday, then 3/3 is Monday and 3/5 is Wednesday and 3/26 is Wednesday and 3/31 is Monday. We see that in this case, we have one more Monday than Wednesday.

If 3/1 is Sunday, then 3/2 is Monday and 3/4 is Wednesday and 3/25 is Wednesday and 3/30 is Monday. We see that in this case, we have one more Monday than Wednesday.


So 3/1 (or the first day of the month) can be Monday, Thursday or Friday.

Answer: B
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Re: A month with 31 days has the same number of Mondays and Wednesdays.How [#permalink] New post   02 Apr 2021, 07:52
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Re: A month with 31 days has the same number of Mondays and Wednesdays.How [#permalink]
02 Apr 2021, 07:52
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