Question: How many Mondays are in December of a particular year?

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

1. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.
2. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.
3. BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.
4. EACH statement ALONE is sufficient.
5. Statements (1) and (2) TOGETHER are NOT sufficient.

Answer:
Approach Solution (1):
It is clear that there are 31 days in human December
31 = 7 * 4 weeks + 3
If the December starts with Sunday, so the last 3 days of this month are: Sunday, Monday, and Tuesday:
Sunday\(({1\over12})\)
Sunday\(({8\over12})\)
Sunday\(({15\over12})\)
Sunday\(({22\over12})\)
Sunday\(({29\over12})\), Monday\(({30\over12})\), Tuesday\(({31\over12})\)
By this way of reasoning, we know that if December starts with Sunday, this month will have 5 Sundays, 5 Mondays, and 5 Tuesdays
Generalizing, to know how many Mondays in December, we must have an idea about how December starts (or end)
If December starts 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
December can’t start with Saturday, Friday, or Wednesday, but it may start with Sunday, Monday or Thursday
Now we combine (1) and (2)
December cannot start with: Sunday, Monday, Tuesday, Saturday, Friday, and Wednesday
So it must start with Thursday only
Therefore, there are 4 Mondays in December
Correct option: C

Approach Solution (2):
1st December must be Saturday and 31st December as Tuesday
Therefore, 4 Mondays will be there
(1) There are four Tuesdays that December
Not sufficient
(2) There are four Saturdays that December
Not sufficient
Correct option: C

Approach Solution (3):
(1) There are four Tuesdays that December
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
Not sufficient
(2) There are four Saturdays that December
December can’t start with Saturday, Friday, or Wednesday, but it may start with Sunday, Monday or Thursday
Not sufficient
(1) + (2)
December cannot start with: Sunday, Monday, Tuesday, Saturday, Friday, and Wednesday
So it must start with Thursday only
Therefore, there are 4 Mondays in December
Correct option: C

“How many Mondays are in December of a particular year?”- is a topic of the GMAT Quantitative reasoning section of GMAT. This question has been taken from the book "GMAT Quantitative Review". GMAT Quant section consists of a total of 31 questions. GMAT Data Sufficiency questions consist of a problem statement followed by two factual statements. GMAT data sufficiency comprises 15 questions which are two-fifths of the total 31 GMAT quant questions.

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