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28 Sep 2025, 04:36
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I will first try to Answer why statement 2 is Insufficient....
Approach 1.. The Matrix/The Venn....
Unfavourable to both = 10...
Now make a 2X2 Matrix.....You do Unfavourable M, Unfavourable N, Favourable + Not Sure M, Favourable + Not Sure N
FM/FN is favourable and unsure ...
Step 1....Input values
Fill the rest....
You get a lot of values...You want favourable for Both M and N.....
You go the the matrix....See 55 is the intersection..... Great..Is that the answer? No!..
because that is favourable + Unsure..Where as you just want favourable....had the question been How many did not vote as unfavourable for both candidate this would have been the answer...or many other things...So its Insufficient...
Now. Lets go with Algebraic Approach... Approach 2.....
Unfavourable for both = 10.....
Now 100- 10 = 90 ..Now 90 is the total of of Favourable and Unsure of M and N.....But here we don't know which is what.......
90 has....Fav M Only + Fav N Only +Fav Both + Not Sure M only + Not Sure N only + Not Sure Both....
We Don't know what is what....So Not Sufficient....
Statement 1..
Who did not respond favourable for either.is 40 ..Means who responed favourable for atleast 1 is 100-40 = 60
Now make a venn with 60 as total ..and favourable with M and favourable with N....you will get 10 answer
Approach 1.. The Matrix/The Venn....
Unfavourable to both = 10...
Now make a 2X2 Matrix.....You do Unfavourable M, Unfavourable N, Favourable + Not Sure M, Favourable + Not Sure N
FM/FN is favourable and unsure ...
Step 1....Input values
| UM | FM | ||
| UN | 10 | 35 | |
| FN | |||
| 20 |
Fill the rest....
| UM | FM | ||
| UN | 10 | 35 | |
| FN | 10 | 65 | |
| 20 | 100 |
You get a lot of values...You want favourable for Both M and N.....
You go the the matrix....See 55 is the intersection..... Great..Is that the answer? No!..
because that is favourable + Unsure..Where as you just want favourable....had the question been How many did not vote as unfavourable for both candidate this would have been the answer...or many other things...So its Insufficient...
Now. Lets go with Algebraic Approach... Approach 2.....
Unfavourable for both = 10.....
Now 100- 10 = 90 ..Now 90 is the total of of Favourable and Unsure of M and N.....But here we don't know which is what.......
90 has....Fav M Only + Fav N Only +Fav Both + Not Sure M only + Not Sure N only + Not Sure Both....
We Don't know what is what....So Not Sufficient....
Statement 1..
Who did not respond favourable for either.is 40 ..Means who responed favourable for atleast 1 is 100-40 = 60
Now make a venn with 60 as total ..and favourable with M and favourable with N....you will get 10 answer
samrand
15 Nov 2025, 01:02
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Essentially we have to find-
Fav(M and N)
-> Fav (M or N) = Fav(M) + Fav(N) - Fav(M and N) ---------------------------- (1)
from given table, we have Fav(M) = 40, Fav(N) = 30
statement 1:- The number of voters who did not respond "Favorable" for either candidate was 40.
-> this can also be restated as "voters who responded favorable for neither M nor N"
hence, (either or) = total - (neither nor)
-> Fav(M or N) = 100 - 40 = 60
-> Put in (1) -> 60 = 40 + 30 - Fav(M and N)
-> Fav (M and N) = 10 -----------------------sufficient
Fav(M and N)
-> Fav (M or N) = Fav(M) + Fav(N) - Fav(M and N) ---------------------------- (1)
from given table, we have Fav(M) = 40, Fav(N) = 30
statement 1:- The number of voters who did not respond "Favorable" for either candidate was 40.
-> this can also be restated as "voters who responded favorable for neither M nor N"
hence, (either or) = total - (neither nor)
-> Fav(M or N) = 100 - 40 = 60
-> Put in (1) -> 60 = 40 + 30 - Fav(M and N)
-> Fav (M and N) = 10 -----------------------sufficient
29 Mar 2026, 09:54
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55 would be combination of not sure N+ Fav M, Not sure M+ Fav N, Noth sure both, Favourable both right and not just favourable both or not sure both?
KarishmaB
