Problem Solving

There is one survey testing 60 people who taste the three different flavors of icecream. Vanilla(V), Chocolate(C), and Strawbery(S). All the people participate in the survey and rank them. There is no situation where there two flavors are ranked equally. 3/5 of the people rank V worst. 1/10 of them (i.e. total 60) rank V ahead of C. 1/3 of them (i.e. total 60) rank V ahaed of S. How many people rank V first ?

a) 2
b) 4
c) 6
d) 12
e) 24

[spoiler]OA = A.....can someone please tell how ?[/spoiler]

36 people say that V is at the 3rd position
we are left with 24 people

20 people say v better than S
6 people said V better than C

note that there 2 people who are common in the two previous cases.
so there are 2 people who said V is better than S AND C

answer A

This is the venn diagram (Set like) problem.

Total = 60.
Set A: 20
Set B: 6
Both?
None = 36.

Set A + Set B - Both + None = Total
20 + 6 - Both + 36 = 60
26 - Both = 24.
Both = 2.

Here,
Set A is the set of people who voted V > C
Set B is the set of people who voted V > S
Both is the set of people who voted V > S AND V > C. i.e: V > S > C or V > C > S.
None is the set of people who voted S > C > V or C > S > V.

Hope this helps!

Received a PM. Good answers above, but will try to explain as well.

3/5 of total ranked V last, which means that 2/5 of total ranked V first or second. 2/5 of 60 = 24 people. Possible rankings:

V C S
V S C
S V C
C V S

1/10 ranked V ahead of C, which means that for 1/10 * 60 = 6 people, V is better than C, making V either the second or the first choice they had. These 6 people have one of the following "formations":

V C S
V S C
S V C

1/3 of total, i.e. 20 people ranked V ahead of S, again making V their first or second choice. Possible formations include:

V C S
V S C
C V S

The highlighted portions represent common "formations".

So you have that: 20 + 6 represent:
2*(V C S and V S C) + (S V C) + (C V S)

24, on the other hand, represents:

(V C S and V S C) + (S V C) + (C V S).

So 26 is 24 + 2 or 24 + another set of (V C S and V S C). This makes (V C S and V S C) = 2.

goelmohit2002 wrote:There is one survey testing 60 people who taste the three different flavors of icecream. Vanilla(V), Chocolate(C), and Strawbery(S). All the people participate in the survey and rank them. There is no situation where there two flavors are ranked equally. 3/5 of the people rank V worst. 1/10 of them (i.e. total 60) rank V ahead of C. 1/3 of them (i.e. total 60) rank V ahaed of S. How many people rank V first ?

V is ranked 3rd by (3/5)*60 = 36 --- 1
V is ranked ahead of C by (1/10)*60 = 6 (V C S ) ( V S c) or (S V C)----2
V is ranked ahead of S = (1/3)*60 = 20 (V C S) (V S C) or ( C V S)----3

Now if you add all the 3 you get 36+6+20 = 62 but in reality we have only 60 participants. So there should be some overlapping in the order of the preferences. If you look at the bold part above they are same and if counted twice they duplicate.

26+6+20 =62 (duplication in 26 and 6)

subtracting two in the above eqn gives total people which is 60

Hence 26-2+6+20 = 60 (this 2 can be subtracted only from bold part above as this is where duplication has happened) Hence V is voted first by 2

@mohit I will respond to your 2nd pm later

Thanks,
Quant-Master