Problem Solving

How many days after the purchase of Product X does its standard warranty expire?
(1997 is not a leap year.)
(1) When Mark purchased Product X in January 1997, the warranty did not expire
until March 1997.
(2) When Santos purchased Product X in May 1997, the warranty expired in May
1997.

Solution : Rephrase the two statements in terms of extreme possibilities:
(1) Shortest possible warranty period: Jan. 31 to Mar. 1 (29 days later)
Longest possible warranty period: Jan. 1 to Mar. 31 (89 days later)
Note that 1997 was not a leap year.
(2) Shortest possible warranty period: May 1 to May 2, or similar (1 day later)
Longest possible warranty period: May 1 to May 31 (30 days later)
Even taking both statements together, there are still two possibilities-29 days and 30 days -so both
statements together are still insufficient.

I don't understand why are we considering Shortest period from 1st statement and Longest period from 2nd statement?

How do we derive warranty period from above extreme scenarios ?

Anantjit wrote:How many days after the purchase of Product X does its standard warranty expire?
(1997 is not a leap year.)
(1) When Mark purchased Product X in January 1997, the warranty did not expire
until March 1997.
(2) When Santos purchased Product X in May 1997, the warranty expired in May
1997.

Solution : Rephrase the two statements in terms of extreme possibilities:
(1) Shortest possible warranty period: Jan. 31 to Mar. 1 (29 days later)
Longest possible warranty period: Jan. 1 to Mar. 31 (89 days later)
Note that 1997 was not a leap year.
(2) Shortest possible warranty period: May 1 to May 2, or similar (1 day later)
Longest possible warranty period: May 1 to May 31 (30 days later)
Even taking both statements together, there are still two possibilities-29 days and 30 days -so both
statements together are still insufficient.

I don't understand why are we considering Shortest period from 1st statement and Longest period from 2nd statement?

How do we derive warranty period from above extreme scenarios ?

Imagine that the original question was "What is the value of integer x?"

Now imagine the two statements as inequalities.

Statement 1: 28 < x < 90
(Clearly not sufficient. x could be 29 or 30 or 50 or 89, etc.)

Statement 2: 0 < x < 31
(Clearly not sufficient. x could be 1 or 2 or 15 or 30, etc.)

Together, we want to consider the overlap of the two statements. The overlap of 28 < x < 90 and 0 < x < 31 is x = 29 and x = 30. Or, put another way, 29 and 30 are the only integers that would fall within both ranges. Because we cannot derive a unique value of x, the statements together are still not sufficient.