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# How many Mondays are in December of a particular year?

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Math Expert
Joined: 02 Sep 2009
Posts: 51100
How many Mondays are in December of a particular year?  [#permalink]

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22 Jan 2016, 09:34
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(N/A)

Question Stats:

33% (01:12) correct 67% (02:17) wrong based on 23 sessions

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How many Mondays are in December of a particular year?

(1) There are four Tuesdays that December.
(2) There are four Saturdays that December.

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Joined: 19 Jan 2016
Posts: 45
How many Mondays are in December of a particular year?  [#permalink]

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22 Jan 2016, 19:59
Bunuel wrote:
How many Mondays are in December of a particular year?

(1) There are four Tuesdays that December.
(2) There are four Saturdays that December.

It is clear that there are 31 days in human December

31 = 7 x 4 weeks + 3

If December start with Sunday, so the last 3 days of this month are: Sun, Mon, and Tues:
Sun (1/12)
Sun (8/12)
Sun (15/12)
Sun (22/12)
Sun (29/12), Mon (30/12), Tue (31/12)

By this way of reasoning, we know that if December start with Sunday, this month will have 5 Sundays, 5 Mondays, and 5 Tuesdays.
Generalizing, to know how many Mondays in Dec, we must have an idea about how December start (or end)
If December start with Monday, Sunday, or Saturday, this month must have 5 Mondays, if not, 4 only.

(1) There are four Tuesdays that December. ==> NOT SUFFICIENT
it is clear that December can't start with Sunday, Monday, or Tuesdays => we can't decide exactly 5 or 4 Mondays because December may start with Monday - Saturday or Thursday

(2) There are four Saturdays that December ==> NOT SUFFICIENT

Now we combine (1) and (2) ==> December CANNOT start with: Sunday, Monday, Tuesday, Saturday, Friday, Wednesday

=> So it must start with Thursday only => therefore, there are 4 Mondays in December

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Joined: 12 Mar 2015
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Re: How many Mondays are in December of a particular year?  [#permalink]

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22 Jan 2016, 23:02
Bunuel wrote:
How many Mondays are in December of a particular year?

(1) There are four Tuesdays that December.
(2) There are four Saturdays that December.

has to be C.

1st December must be Saturday and 31st December as Tuesday.

therefore 4 Mondays.
Re: How many Mondays are in December of a particular year? &nbs [#permalink] 22 Jan 2016, 23:02
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