Data Sufficiency

In a 10-point (worth) debate at a certain High School, 36 students participated in the debate. If the overall points earned by the girls were 24 more than that of the boys, how many girls participated in the debate at the High School?

(1) The average (arithmetic mean) of the overall points earned by the girls in the debate at the High School was 7.

(2) The average (arithmetic mean) of the overall points earned by the boys in the debate at the High School was 5.


Made Up!

Girls = x
Boys = 36-x

Avg of girls * x = 24 + Avg of boys* (36-x)

TO find: Number of Girls, x

Statement 1:
7x = 24 + A*(36-x)
7x = 24 + 36A - Ax
x(7+A) = (24+36A)
x = (24 + 36A)/(7+A)
we can have many value of A so as to make INT x
INSUFFICIENT

Statement 2:
B*x = 24 + 5(36-x)
Similar Logic of Statement 1
INSUFFICIENT

Combining...
7*x = 24 + 5 *(36-x)
SUFFICIENT
{C} ?

Or, it's a C Trap Question

Brent@GMATPrepNow wrote:Hey Sanju,

I'm not 100% sure about a few things:
- If 36 students participated in the debate, does this mean there were 18 individual (2-person debates), or is there some other team-type configuration (e.g., 3 vs 3)?
- What do you mean by a 10-point debate? Does this mean there are 10 points to award to either person/team in the debate (e.g., team A gets 3 points and team B gets 7 points), or can a team/person earn up to 10 points, so that it's possible that not all 10 points are awarded in a debate?

Cheers,
Brent

Hi Brent,

Your questions have put my question under doubt without doubt. I think the use of the term 'debate' won't be fair here. It should have been kind of individual performance where each performer is rated on an integral scale of 0-10, there's always a chance that a performer may receive 10 points. Please suggest me proper wordings in order to make it sound the way I wanted it to. Rahul has probably read my mind the way it worked while designing this question.

My answer is to be C only, with no C trap!

Regards

Brent@GMATPrepNow wrote:Ah, I see. Good question!
All we need to do is find a way to attribute a value from 0 to 10 (inclusive) for each of the 36 students.
How about something like,

36 students participated in a competition in which each student received a score from 0 to 10 inclusive. If the total points earned by the girls was 24 more than the total points earned by the boys, how many girls participated in the competition?

(1) The average (arithmetic mean) of the girls' scores was 7.
(2) The average (arithmetic mean) of the boys' scores was 5.

Cheers,
Brent

[spoiler]Great Brent! I want to thank you in private, hence I didn't click the shining button. Regards[/spoiler]