Overlapping Set: Can we make a double set matrix?

[mazhar.hussain]

Hi team,

The following is a question, I saw on gmat club. I was unable to solve it as I was unable to form a double set matrix for this question. Kindly let me know that is there a way to solve it by double set matrix??

In a particular state, 70% of the counties received some rain on Monday, and 65% of the counties received some rain on Tuesday. No rain fell either day in 25% of the counties in the state. What percent of the counties received some rain on Monday and Tuesday?

A) 12.5%
B) 40%
C) 50%
D) 60%
E) 67.5%

[ps63739]

Let the total counties be 100.

25% received no rain at all. So 75% i.e. 75 counties received rain.
Rain on monday - 70% or 70.
Rain on Tuesday - 65% or 65.

AUB = 75.
A = 70
B = 65
Gives A intersection B = 60. So 60% is the answer.

[tammychow]

Can some provide a more detailed explanation?

[sharok50]

All - none = AUB
=> 100-25 = AUB
=> 75 = A + B - (A intersection B)
=>75 = 70 + 65 - (A intersection B)
=> (A intersection B)= 60(Ans)

hope that helps

[jnelson0612]

A double set matrix is not appropriate for this problem because we cannot account for each possibility once and only once in each grouping. In other words, for each row and each column I must be able to contain all members of the set and have that number add up to the total of the set. For example, I could have girls and boys, and each child is either going to a party or not going to a party. We put the "girls" and "boys" across the top, for example, and the "party" and "not party" on the side. This example is appropriate because every member of the set is counted once in each grouping. A child is either a girl or a boy, and that child is either going or not going to the party.

In this instance, my first group is "rain" and "no rain". That group is okay because all members of the set either did or did not get rain. However, the other grouping is "Monday" and "Tuesday". This one does not work because some counties may have gotten rain on both days. Thus, each individual member is not counted only once in this grouping.

For this type of problem, it is better to use this formula:
Total = Group1 + Group2 + neither - both

Assume there are 100 counties. 70 counties received rain on Monday, 65 received rain on Tuesday, and 25 did not receive rain on either day. Plug into the formula:
100=70 + 65 + 25 - both
100=160 - both
both = 60

Thus, answer choice D is correct.

Thank you,

[guptakshay]

Row headers Tue Y, Tue N, and Total
Column headers Mon Y and Mon N
R1C1 60, R1C2 (not required) R1 Total 70
R2C1 5, R2C2 25, R2Total 30
C1 Total 65 C2(Not required) Total 100

Hi..

I was just trying out the double set matrix on this problem and the above method gives me the correct answer.

@ jnelson0612: I didn't quite understand the "we cannot account for each possibility once and only once in each grouping" bit. Can I use this method?

[LazyNK]

@guptaakshay : I didn't wquite uerstand the "we cannot account for each possibility once and only once in each grouping" bit. Can I use this method?

Your method is correct.
What the statement that u are not able to understand means is that the two categories in any row/columnn should be mutually exclusive. So, in jamie's example, categories rain and no rain are fine but categories rain on monday and rain on tuesday aren't fine as there can be rain on both monday and tuesday in some places, so not mutually exclusive.
-NK

[jnelson0612]

@guptaakshay : I didn't wquite uerstand the "we cannot account for each possibility once and only once in each grouping" bit. Can I use this method?

Your method is correct.
What the statement that u are not able to understand means is that the two categories in any row/columnn should be mutually exclusive. So, in jamie's example, categories rain and no rain are fine but categories rain on monday and rain on tuesday aren't fine as there can be rain on both monday and tuesday in some places, so not mutually exclusive.
-NK

Thanks for the excellent explanation! :-)