Reasoning Percent DS Question

[championspunch]

In year x, it rained on 40% of all Mondays and 20% of all Tuesdays. On what percentage of all the weekdays in year x did it NOT rain?
(1) During year x, it rained on 10% of all Wednesdays.

(2) During year x, it did not rain on 70% of Thursdays and it did not rain on 95% of all Fridays.

[srcc25anu]

IMO E

St1: Rains 10% of all Wednesdays. but we dont know about Thursday and Fridays rain %. hence Insufficient

St2: Did not rain 70% Thursday and did not rain 95% of all fridays. dont know about wednesdays hence insufficient

St1 and St2 together: we dont know how many # of mondays, Tues, Wed, Thu and Fri are we looking at. A year has 365 days which is 52 weeks + 1 day (in case of leap year 2 days). dont know what this extra day is which is why i would say its INSUFFICIENT to answer.

Hence E

[Anju@Gurome]

In year x, it rained on 40% of all Mondays and 20% of all Tuesdays. On what percentage of all the weekdays in year x did it NOT rain?

(1) During year x, it rained on 10% of all Wednesdays.
(2) During year x, it did not rain on 70% of Thursdays and it did not rain on 95% of all Fridays.

Clearly none of the statements are individually sufficient.

1 & 2 Together: Now we know on what percentage of each weekdays it did rain or did not rain. However, we do not know how how many weekdays are there in year X. Hence, we cannot answer the question.

This is because, there are either 365 or 366 days in the year X.
If there are 365 days in the year X : Dividing 365 days by 7, we get 52 weeks and 1 extra day. This one extra day may be a weekday or a Saturday/Sunday. Hence, the required percentage will change depending upon whether it is weekday or not and even if it is weekday, which weekday it is. Same is the case with 366 days.

Not sufficient

The correct answer is E.

[Brent@GMATPrepNow]

In year x, it rained on 40% of all Mondays and 20% of all Tuesdays. On what percentage of all the weekdays in year x did it NOT rain?
(1) During year x, it rained on 10% of all Wednesdays.

(2) During year x, it did not rain on 70% of Thursdays and it did not rain on 95% of all Fridays.

Here's a little challenge question on the side:
The above question could never be an official GMAT question. Why not?

Cheers,
Brent

[Brent@GMATPrepNow]

Here's a little challenge question on the side:
The above question could never be an official GMAT question. Why not?

Cheers,
Brent

I have to head out for the day, so here's the reason.

In any given year, there will be either 52 or 53 Mondays, Tuesdays, etc.
So, it's impossible to say that it rained on 40% of all Mondays or 20% of all Tuesdays, etc.
For example, if there are 52 Mondays, then 40% of 52 = 20.8, which means that it rained on 20.8 days (impossible).

Cheers,
Brent