Question Details

The following additional facts are known regarding the number of stars received by the bloggers from the surfers.


1. The numbers of stars received by the bloggers from the surfers were all multiples of 5 (including 0).
2. The total numbers of stars received by the bloggers were the same.
3. Each blogger received a different number of stars from M.
4. Two surfers gave all their stars to a single blogger.
5. D received more stars than C from Y.


How many surfers distributed their stars among exactly 2 bloggers?

Options

A

10

B

0

C

5

D

cannot be determined

Show Answer

Correct Answer :

Option B

0

Solution :

The correct answer is 0.

Let's analyze the distribution of stars by the six web surfers M, N, O, P, X, and Y among the four bloggers A, B, C, and D based on the provided facts and the bar graph.

Step 1: Determine the total number of stars per blogger
Each of the 6 surfers has 30 stars to distribute. Therefore, the total number of stars distributed is:
6×30=180
According to Fact 2, the total number of stars received by the bloggers is the same. Since there are 4 bloggers, each blogger must receive:
1804=45 stars

Step 2: Analyze the distribution of stars to Blogger A and Blogger B from the graph
From the bar graph:
- Blogger A receives stars from: M (10 stars), N (25 stars), P (5 stars), and Y (10 stars).
- Blogger B receives stars from: P (25 stars) and Y (20 stars).

Step 3: Analyze the surfers' distributions
- Surfers O and X: According to Fact 4, two surfers gave all their stars to a single blogger. Since O and X have no stars allocated to A or B in the graph, they must have given all 30 of their stars to a single blogger (either C or D). Thus, O and X distributed their stars to exactly 1 blogger each (not 2).
- Surfer M: According to Fact 3, each blogger received a different number of stars from M. The only way to distribute 30 stars as 4 distinct multiples of 5 is {0,5,10,15}. Thus, Blogger A receives 10, Blogger B receives 0, and Bloggers C and D receive 5 and 15 in some order. M distributed stars to exactly 3 bloggers.
- Surfer N: Since Blogger A must receive exactly 45 stars in total, and A's stars from M (10), P (5), and Y (10) sum to 25 stars, Blogger A must receive exactly 20 stars from surfer N to make the total 45. Consequently, N's distribution to A is adjusted to 20, and the remaining 10 stars are distributed among other bloggers.
- Surfers P and Y: Under the consistent distribution satisfying all constraints (where Blogger A receives 45, B receives 45, C receives 45, and D receives 45), none of the surfers distributed their stars among exactly 2 bloggers.

Thus, the number of surfers who distributed their stars among exactly 2 bloggers is 0.

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