Question: Children Playing Tennis

Comment on Children Playing Tennis

Wouldn't the correct answer to this question actually be D? How can we know the ratio of girls to boys? It seems dubious to simply assume that half of the school is boys and the other half is girls.
greenlight-admin's picture

We're not assuming that there are 100 boys and 100 girls; we're deducing it.

The big clue here is that 37% of the girls play tennis.

From this information, we can see that MANY of the possible values for the number of girls do not work.

For example, it wouldn't make any sense if there were 10 girls. The reason it wouldn't make sense is that if we find 37% of 10, we get 3.7. In other words, if there are 10 girls in total, then 3.7 of them play tennis.

Since the number tennis players must be an INTEGER, we can see that there can't be 10 girls at the school.

For the same reason, we know that there can't be 11 girls, since 37% of 11 = 4.07, and we can't have 4.7 tennis players.

In fact, there can be only ONE possible value for the number of girls at the school. There MUST be 100 girls, since all other possible values yield NON-INTEGER values for the number of girl tennis players.

Does that help?

Yes, I think it does! Is the crux of the solution, then, recognizing that for 37% of a number to be an integer, it must be a multiple of 100? Am I correct in believing that the only reason this is true of 37 is because it is a prime number?
greenlight-admin's picture

Not quite. The reason is because the fraction 37/100 does not simplify.

So, 37% of x = (37/100)(x) = (37x)/100
In order for (37x)/100 to be an integer, x must be divisible by 100

Likewise, 5% of x = (5/100)(x) = (1/20)(x) = x/20
In order for x/20 to be an integer, x must be divisible by 20

One last example: 25% of x = (25/100)(x) = (1/4)(x) = x/4
In order for x/4 to be an integer, x must be divisible by 4

Cheers,
Brent

Hi,
when we are told that the school has 200 children, will it be possible to assume that .37 of the 200 kids plus .10 of the kids play tennis ?. It says some boys and some girls so .47 of the total of the kids play tennis.
greenlight-admin's picture

That approach will work ONLY in cases in which the number of girls = the number of boys.
So, in this very specific question, the strategy works.

However, let's say the question stated that there are 200 children, and 25% of the girls play tennis and 40% of the boys play tennis.

Since we can't be certain that the number of girls = the number of boys, there are many possible cases that work. For example:

CASE A: There are 40 girls and 160 boys.
So, the number of tennis players = (25% of 40) + (40% of 160)
= 10 + 64
= 74

CASE B: There are 80 girls and 120 boys.
So, the number of tennis players = (25% of 80) + (40% of 120)
= 20 + 48
= 68

CASE C: There are 100 girls and 100 boys.
So, the number of tennis players = (25% of 100) + (40% of 100)
= 25 + 40
= 65

Notice that your approach works for Case C (the number of girls = the number of boys), but not the other cases.

Cheers,
Brent

Thank you

Add a comment

Have a question about this video?

Post your question in the Comment section below, and I’ll answer it as fast as humanly possible.

QC Strategies

When you encounter a Quantitative Comparison question, be sure to consider which strategy might best apply: 

 

Free “Question of the Day” emails!