There are 50 kids in a locality. On Sunday all of them went together

Question

There are 50 kids in a locality. On Sunday all of them went together to buy toys from a kids’ store and then to play at the park. At kid’s store each one of them bought at most 1 toy and at the park they played either football or basketball but not both. If each of them played at least 1 game, then what percentage of total kids played basketball at the park?

(1) 30% of the kids who bought a toy, played football.

(2) 70% of the kids who didn’t buy a toy, played basketball.

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rosyln · Answer

B is the correct answer.  
1.  30% of the kids who bought a toy played football.  
Let's denote:
T = number of kids who bough a toy. therefore 0.3 * T represents kids who bought a toy and played football. however, this statement only gives information about the kids who bough toys and played football, with no data on the total number who played basketball. Insufficient, on its own.
2.  70% of the kids who didn't buy a toy played basketball.  
N - number of kids who didn't buy a toy. Thus, 0.7 * N represents the kids who didn't buy a toy and played basketball. Since, the total number of kids is 50, we have T+N=50. This statement gives us enough information to determine the percentage of total kids who played basketball because we can calculate N and apply the 70% to find the number of basketball players. Sufficient on its own.
We don't need to combine the statements, as statement 2 alone is sufficient to determine the answer.

Tammy01 · Answer

Total Kids: 50
Each bought either 1 toy or no toy. (Toy=x, No Toy= 50-x)
Each played either Football or Basketball. (Football = y, basketball = 50-y)

St1: 0.3x + (kids who didn't buy a toy but played football) = y (Alone not suff)
St2: 0.7(50-x) + (kids who bought a toy and played basketball) = 50-y (Alone not suff)

Combining both,
Football:
0.3x + 0.3(50-x) = y  
0.7(50-x) + 0.7(x) = 50-y

Now we have 2 equations and 2 unknowns which is easily solvable. (Thus both together are suff)

Ans: C

EshaFatim · Answer

Hi  rosyln

How are you calculating N in the above-highlighted statement, please?

rosyln · Answer

Hi!

Since we're asked to find the % of total kids who played basketball, let's start by calculating how many of these 50 kids played basketball based on Statement 2.
1. According to Statement 2, 70% of kids who didn't buy a toy (N) played basketball. This means that the number of kids who played basketball is 0.7 * N;
2. Now, if we knew the exact value of N, we could calculate the number of kids who played basketball. However, without additional details about how many kids bought a toy (or equivalently, how many didn't), we cannot find N exactly. Thus, Statement 2 alone is sufficient to calculate the % of basketball players once N is known but does not directly provide N.

EshaFatim · Answer

Oh, I see. But unfortunately, we can't reason it like that though. If you cannot answer any statement for lack of information, it simply means that statement alone is insufficient to answer.

Carson31 · Answer

I don't get it. After combining the 2 equations, 0.3x + 0.3(50-x) = y and 0.7(50-x) + 0.7(x) = 50-y, we get x + (50-x)=50 , we still are not able to find the exact figure of x.

ubaid009 · Answer

no of kids buy 1 toy = x, no of kids buy 0 toy= y
x+y=50
no of kids played bb + no of kids played fb = 50
Statement 1- kids who played fb = 0.3x +(we don't know about the kids who bought 0 toy and played fb)
insuff
Statement 2- kids who played bb= 0.7y + (we don't know about the kids who bought 1 toy and played bb)
Insuff
Both 1 & 2
kids played fb = 0.3x + 0.3y
kids played bb = 0.7x + 0.7y
these all values must be in integers choose x and y accordingly 
x=10 y=10 , fb=3+3=6 , bb= 7+7=14, bb+fb ≠ 50 --- wrong
x=20 y=30 , fb = 6+9 = 15, bb= 14+21= 35, bb + fb =50 ---right
x=30 y= 20 same result
by both we can get % of kids played bb i.e bb=35/50*100= 70 %

lisahoang1301 · Answer

We want the percent who played  basketball  = B/50.
 Let T = number who bought a toy, so 50−T didn't. Every kid played exactly one game (football or basketball).
 
 (1)  “30% of the kids who bought a toy played football.”
 Among the T buyers, football = 0.30T ⇒ basketball among buyers = 0.70T.
 But we have no information about how the 50−T non-buyers split between football and basketball. So the total basketball players could vary depending on that unknown split.
  (1) alone is not sufficient. 
 
 (2)  “70% of the kids who didn’t buy a toy played basketball.”
 Among non-buyers (50−T), basketball = 0.70(50−T).
 But we still don’t know the split among the TTT buyers. So  (2) alone is not sufficient. 
 
 (1) and (2) together. 
 Basketball total
B=(basketball among buyers)+(basketball among non-buyers)=0.70T+0.70(50−T)
Factor 0.70:
B=0.70(T+(50−T))=0.70×50=35
So 35 of the 50 kids played basketball ⇒ percentage = 35/50=0.70=70%
Both statements together determine the answer; neither alone does.
 
 Answer: C — Both statements together are sufficient, each alone is not.

haianh · Answer

Summary:  
 
 Every kid played either football or basketball, no overlap.  
 Every kid bought either 0 or 1 toy.  
 X = kids who bought a toy 
 Y = kids who did not buy a toy 
 Total: X + Y = 50.  
  Ask for: basketball / 50?

buy toy 
 not buy toy 
 (1)+(2) 
 
  football 
  0.3X (1)

basketball  
 0.7X 
  0.7Y (2)  
 0.7(X+Y)

X 
 Y 
 50

(1): given by statement (1). This alone is not sufficient.  
 (2): given by statement (2). This alone is not sufficient.

From (1) and (2)  	o  basketball = 0.7(X+Y) = 0.7*50 = 35. Sufficient. 
Answer: C

There are 50 kids in a locality. On Sunday all of them went together

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	buy toy	not buy toy	(1)+(2)
football	0.3X (1)
basketball	0.7X	0.7Y (2)	0.7(X+Y)
	X	Y	50

GMAT Data Sufficiency (DS) Questions

There are 50 kids in a locality. On Sunday all of them went together

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