On a soccer team consisting of 21 children, some of which are boys and

Question

On a soccer team consisting of 21 children, some of which are boys and some of which are girls, exactly 2/3 of the boys and exactly 1/3 of the girls attended the end of the season pizza party. What is the greatest number of children on the team who could have attended the party?

A. 11
B. 12
C. 13
D. 14
E. 15

A. 11
B. 12
C. 13
D. 14
E. 15

prateek25 · Answer

B= boys total
G = girls total

1.Both B and G will be multiples of 3 
2. B+ G = 21

Since 2/3 of boys went to the party, in order to maximize party total, we have to take the maximum value for B satisfying both 1 and 2.

B (max)= 18 ( cannot take B=21, since some of the players have to be girls), which gives G =3

Maximum party total= 18*2/3 + 3*1/3 = 13

Ans should be C.

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GMATWhizTeam · Answer

Solution 
 • Let us assume that the number of boys in the soccer team is b.
 o So, the number of girls in the soccer team is  21- b . 
• The number of children who attended the party  = b*\frac{2}{3} + \frac{21 -b}{3} = 7 + \frac{b}{3} ………..Eq.(1) 
• Since the team consists of boys as well as girls, so number of boys must be less than 21.
 o Therefore,  b < 21 ⟹ \frac{b}{3} < 7 
o Thus, the greatest value of  \frac{b}{3}  can be 6. 
• Hence from the above and the Eq.(1), we get, the greatest number of children in the team who could attend the party  = 7 + 6 = 13  
Thus, the correct answer is  Option C.

ScottTargetTestPrep · Answer

Solution:

Since we want the greatest number of children on the team who could have attended the party and the fraction of the boys attending the party is greater than that of the girls, we want as many boys in the team as possible. The greatest number of boys could be on the team is 18 (so 2/3 of it is still an integer). That is, there are 18 boys and 3 girls on the team (notice that “some of which are girls” implies there is at least one girl, so we can’t have all 21 members of the team to be boys). Therefore, the greatest number of children on the team who could have attended the party is 2/3 x 18 + 1/3 x 3 = 12 + 1 = 13.

Answer: C

KarishmaB · Answer

2/3rd boys attended and 1/3rd girls attended. We want to maximize the number of attendees so we should maximize the number of boys. 
Since there are some girls too, there must be at least 3 girls (so that 1/3rd could attend the party). So at max there can be 18 boys.

Greatest number of children who attended the party = 2/3 * 18 + 1/3 * 3 = 13

Answer (C)

On a soccer team consisting of 21 children, some of which are boys and

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