Data Sufficiency

[GMAT math practice question]

Alice works from Monday to Friday only. How many days does she work in April?

1) April 1 is Saturday or Sunday
2) April 28 is Saturday or Sunday

Max@Math Revolution wrote:[GMAT math practice question]

Alice works from Monday to Friday only. How many days does she work in April?

1) April 1 is Saturday or Sunday
2) April 28 is Saturday or Sunday

Question : How many days does she work in April?

Statement 1: April 1 is Saturday or Sunday

Case 1: April 1 is SUNDAY

April has 30 days in calander

Sunday = April 1, 8, 15, 22, 29
Working days between 1st to 29th April = 5*4 = 20 days
and 30th April is Monday = 1 more working day
i.e. Total Working days = 21

Case 2: April 1 is SATURDAY

April has 30 days in calander

Saturday = April 1, 8, 15, 22, 29
Working days between 1st to 29th April = 5*4 = 20 days
and 30th April Sunday = 0 more working day
i.e. Total Working days = 20

NOT SUFFICIENT

Statement 2:April 28 is Saturday or Sunday

Case 1: April 28 is SUNDAY

April has 30 days in calander

Monday = April 1, 8, 15, 22, 29
Working days between 1st to 28th April = 5*4 = 20 days
and 29th and 30th April Monday and Tuesday = 2 more working day
i.e. Total Working days = 22

Case 2: April 28 is SATURDAY

April has 30 days in calander

Sunday = April 1, 8, 15, 22, 29
Working days between 1st to 29th April = 5*4 = 20 days
and 30th April Monday = 1 more working day
i.e. Total Working days = 21

NOT SUFFICIENT

Combining the two statements:

As per statement 1: Working days = 20 or 21
As per statement 2: Working days = 22 or 21

i.e. Total Working days = 21

SUFFICIENT

Answer: option C

=>

Forget conventional ways of solving math questions. For DS problems, the VA (Variable Approach) method is the quickest and easiest way to find the answer without actually solving the problem. Remember that equal numbers of variables and independent equations ensure a solution.

The first step of the VA (Variable Approach) method is to modify the original condition and the question. We then recheck the question.
When the day on which a specific date, for example, the first of April 2018 is fixed, we can determine the days on which other dates in April fall.
Since we have 1 variable (n) and 0 equations, D is most likely to be the answer. So, we should consider each of the conditions on their own first.

Condition 1)
If April 1st is Saturday, Alice works on the 3rd - 7th, 10th - 14th, 17th - 21st, 24th - 28th. This means she works on 20 days.
If April 1st is Sunday, Alice works on the 2nd - 6th, 9th - 13th, 16th - 20th, 23rd - 27th and 30th. This means she works on 21 days.
Since we don't have a unique solution, condition 1) is not sufficient.

Condition 2)
If April 28th is Saturday, Alice works on the 2nd - 6th, 9th - 13th, 16th - 20th, 23rd - 27th and 30th. This means she works on 21 days.
If April 28th is Sunday, Alice works on the 1st - 5th, 8th - 12th, 15th - 19th, 22nd - 26th, 29th and 30th. This means she works on 22 days.

Since we don't have a unique solution, condition 2) is not sufficient.
Conditions 1) & 2) together:
If the 1st of April is a Saturday or Sunday and the 28th of April is a Saturday or Sunday, the 1st of April must be a Saturday.
So, Alice works on the 2nd - 6th, 9th - 13th, 16th - 20th, 23rd - 27th and 30th. Therefore, she works on 21 days.
Since we have a unique solution, both conditions together are sufficient.

Therefore, C is the answer.
Answer: C

If the original condition includes "1 variable", or "2 variables and 1 equation", or "3 variables and 2 equations" etc., one more equation is required to answer the question. If each of conditions 1) and 2) provide an additional equation, there is a 59% chance that D is the answer, a 38% chance that A or B is the answer, and a 3% chance that the answer is C or E. Thus, answer D (conditions 1) and 2), when applied separately, are sufficient to answer the question) is most likely, but there may be cases where the answer is A,B,C or E.