Score Plus

rchuck21 wrote:
Hey Bhavin.

Thanks!! I feel bad that I am not able to log in to the forum as I used to do before. My preps have also hit a road block as work pressure has gone up. But I am trying Lets see....

Always good to see you on the forum.

Thanks for pointing out the subtle difference.
Taking an excerpt from the solution you had provided to the QOTD before:

no. of ppl registering for exactly 2 classes = Only Grp 12 + Only Grp 13 + Only Grp 23
And, Grp12 + Grp13+ Grp23 = Only Grp 12 + Only Grp 13 + Only Grp 23 + 3 Grp 123
=> Only Grp 12 + Only Grp 13 + Only Grp 23 = 19 - 3(3) =10

Option (C).

perfect answer Rahul !! exactly 2 groups is different than more than 1 group. The latter includes the possibility of all 3 groups as well...

u have already given the solution..i shall just reiterate...

Total = Grp1 + Grp 2 + Grp 3 – ( Grp12 + Grp 13 + Grp 23 ) + Grp 123

Hence,

68 = 25+ 25 + 34 – (Grp12 + Grp 13 + Grp 23 ) + 3

Hence, (Grp12 + Grp 13 + Grp 23 ) = 87-68 = 19

Now,
Grp12 = Only Grp 12 + Grp 123
Grp 23 = Only Grp 23 + Grp 123
Grp 13 = Only Grp 13 + Grp 123

Hence,
Only Grp 12 + Only Grp 23 + Only Grp 13 + 3 Grp 123 = 19
Grp 12 + Only Grp 23 + Only Grp 13 = 19 – 3*3
= 19-9
= 10

hope this solves your query binish...i am sorry am unable to post a video solution at the moment...as and when it is poss, i shall do so..sorry for inconvenience...

Cheers !!

Now its clear.......Thanks Bhavin and Rahul for ur help........


Regards
Binish

One more question.........

Each of three charities in county X has 8 persons serving on its board of directors.If exactly 4 persons serve on 3 boards each and each pair of charities has 5 person in common on their boards of directors,then how many distant persons serve on one or more boards of directors.?

Ans 13

Pls help.......

Not sure if this has been answerwed.
Here is my approache of solving it and the solution:
- Let toal number of rooms = 100
- Suites = X, Painted Light Blue = Y
- Total = X + Y + Neither - Both, Both = X + Y + Neither - Total
- For both to be minimum, Neither = 0
Therefore, Both (light blue painted suites) Minimum = X + Y - 100 (Values >= 0)

Another possibility:
- Well you can argue that if Neither = 100 then light blue painted suites = 0.
- And you can think of 1- combinations, but my answer should hopld good

Answer option {4}

binish wrote:
One more question.........

Each of three charities in county X has 8 persons serving on its board of directors.If exactly 4 persons serve on 3 boards each and each pair of charities has 5 person in common on their boards of directors,then how many distinct persons serve on one or more boards of directors.?

Ans 13

Pls help.......

Hey Binish,

I haven't used any formula to solve this question. Just draw the statement out and you will get the answer. I have made a correction to the question. I am sure that was a typo. Have replaced 'distant' with 'distinct' in the question.

Let the 4 persons serving on 3 board of directors(BOD) be ABC and D.

So, lets divide the total distinct number of people in three groups for Charity 'A', 'B' and 'C'.

So
Charity A will have ABCDXXXX (X is unknown)
Charity B will have ABCDXXXX (X is unknown)
and Charity C will have ABCDXXXX (X is unknown)

Now we have to satisfy the condition that 5 persons are common in each pair of charities BOD.

Four are already there.

Start filling up Charity A - ABCDEFGH

To fill charity B, one more common member is required to satisfy the condition.

Fill Charity B - ABCDEIJK

To fill charity C, one member should be from Charity A and one from Charity C to satisfy the condition.

Fill Charity C - ABCDFILM
(Note: We have not considered E as E will be common to both Charity A and Charity B. If we take E, then it will violate the condition. Hence take F from Charity A and I from Charity B

Finally, count the distinct members : ABCDEFGHIJKLM

They are 13 in number. Hence answer is 13.

Cheers,
Rahul.

rchuck21 wrote:
binish wrote:
One more question.........

Each of three charities in county X has 8 persons serving on its board of directors.If exactly 4 persons serve on 3 boards each and each pair of charities has 5 person in common on their boards of directors,then how many distinct persons serve on one or more boards of directors.?

Ans 13

Pls help.......

Hey Binish,

I haven't used any formula to solve this question. Just draw the statement out and you will get the answer. I have made a correction to the question. I am sure that was a typo. Have replaced 'distant' with 'distinct' in the question.

Let the 4 persons serving on 3 board of directors(BOD) be ABC and D.

So, lets divide the total distinct number of people in three groups for Charity 'A', 'B' and 'C'.

So
Charity A will have ABCDXXXX (X is unknown)
Charity B will have ABCDXXXX (X is unknown)
and Charity C will have ABCDXXXX (X is unknown)

Now we have to satisfy the condition that 5 persons are common in each pair of charities BOD.

Four are already there.

Start filling up Charity A - ABCDEFGH

To fill charity B, one more common member is required to satisfy the condition.

Fill Charity B - ABCDEIJK

To fill charity C, one member should be from Charity A and one from Charity C to satisfy the condition.

Fill Charity C - ABCDFILM
(Note: We have not considered E as E will be common to both Charity A and Charity B. If we take E, then it will violate the condition. Hence take F from Charity A and I from Charity B

Finally, count the distinct members : ABCDEFGHIJKLM

They are 13 in number. Hence answer is 13.

Cheers,
Rahul.

good explanation Rahul..yes, there is no direct formula...we have to segregate people in different groups...

There are 3 charities in the country..we have to count distinct people...

Now, Charity 1 = only charity 1 + only charity 12 + only charity 13 + charity 123

Or simply, we have to break down total people in one of the 3 categories..

1) people in exactly 1 charity (i.e charity 1 only OR charity 2 only OR charity 3 only )
2) people in exactly 2 charities (i.e charity 12 only OR charity 13 only OR charity 23 only )
3) people in exactly 3 charities (i.e people in charity 123)

there are 8 people in each of the 3 charities...
Of these 8, 4 belong to all 3 categories, and 1 is in common to other 2 charities...i.e 2 different people...hence the remaining 2 people belong to only that charity..

Same is applicable to other 2 charities as well...

Hence,
Exactly 1 charity = 2*3 = 6
Exactly 2 charities = 3
Exactly 3 charities = 4
_____________
Total = 13

i may not have worded it correctly, but i hope the solution is understood...this becomes really simple when we represent with venn diagrams..
if poss, will try to upload venn diagram tomm...

Keep going !!