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At a certain circus, every child was given either two or three balloons. How many children received three balloons?


(1) At the circus, 40 percent of the children received two balloons.

(2) A total of 360 balloons were given out to children at the circus.
[Reveal] Spoiler: OA

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New post 16 Sep 2014, 01:50
Official Solution:


We must determine the number of children who received 3 balloons, given that every child received either 2 or 3 balloons.

Statement 1 says that \(40%\), or \(\frac{2}{5}\), of the children received 2 balloons. This means that \((100 - 40)% = 60% = \frac{3}{5}\) of the children received 3 balloons. However, since we lack any information about the total number of balloons (or about the total number of children), it is not possible to solve for the number of children who received 3 balloons. There could be 2 children with 2 balloons and 3 children with 3 balloons, or 2,000 with 2 balloons and 3,000 with 3 balloons. Statement 1 is NOT sufficient to answer the question. Eliminate answer choices A and D. The correct answer choice is B, C, or E.

Statement 2 says that a total of 360 balloons were given out to children at the circus. However, since we have no information about how many children got 3 balloons and how many got 2 balloons, we cannot determine a unique value for the number of children who received either quantity of balloons. There could be 180 children with 2 balloons and 0 children with 3 (giving \(2 \times 180 = 360\) balloons), or there could be 0 children with 2 balloons and 120 with 3 (giving \(3 \times 120 = 360\) balloons). Statement 2 is NOT sufficient to answer the question. Eliminate answer choice B. The correct answer choice is either C or E.

Taking the statements together, we have the following facts: \(\frac{2}{5}\) of the children got 2 balloons, \(\frac{3}{5}\) of the children got 3 balloons, and there were 360 total balloons given out to children. If we label the number of children \(x\), then the total number of balloons is \(2(\frac{2}{5}x) + 3(\frac{3}{5}x)\) -- that is, 2 balloons for \(\frac{2}{5}\) of the children and 3 balloons for the other \(\frac{3}{5}\).

Setting this expression equal to 360, we have: \(2(\frac{2}{5}x) + 3(\frac{3}{5}x) = 360\). This is a single-variable equation, and so we can solve for \(x\), the total number of children. Once we have \(x\), we will be able to solve for the number of children with 3 balloons: \(\frac{3}{5}x\). Therefore, we have enough information to answer the question.


Answer: C
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New post 20 Jan 2015, 12:02
This can't be a 600+ question!

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New post 31 Jul 2015, 21:41
The question is too easy but I am seriously confused here.
If we solve the equation after combining statements 1 & 2, the number of children come out as a fraction (not a whole number). Now since the number of children cannot be a fraction, so I marked E. Kindly clarify.

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New post 17 Aug 2015, 02:35
mudit20111989 wrote:
The question is too easy but I am seriously confused here.
If we solve the equation after combining statements 1 & 2, the number of children come out as a fraction (not a whole number). Now since the number of children cannot be a fraction, so I marked E. Kindly clarify.


The number of children who received 3 balloons each is 270/3 = 90. Please show your work.
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New post 19 Aug 2015, 22:11
The number of children who received 3 balloons each is 270/3 = 90. Please show your work.[/quote]

Let number of total children = x

Combining statement 1 and 2:

2(2/5)x+3(3/5)x=360

(13/5)x = 360

solving for x gives us fraction since 360 is not divisible by 13.

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New post 28 Aug 2015, 23:37
I think this is a poor-quality question and I don't agree with the explanation. Does the value of x (as used in explanation) comes out to be an integer ?

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New post 16 Oct 2015, 07:31
I think this is a poor-quality question and I don't agree with the explanation. this question is wrong as the number of children does not equals an integer.

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sandip1611 wrote:
I think this is a poor-quality question and I don't agree with the explanation. this question is wrong as the number of children does not equals an integer.


The number of children who received 3 balloons each is 270/3 = 90. Please show your work.
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New post 10 Jan 2017, 10:13
I think this is a high-quality question and I don't agree with the explanation. The single valued expression when solved would give a fractional value for x.
This is not possible since the number of children (x) cannot be fraction.
So answer would be E.
or there is an issue with the question.

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New post 05 Aug 2017, 13:59
Bunuel, where did you get the 270 number from? Bunuel

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New post 05 Aug 2017, 14:26
The number of children does work out to be a fraction here if you actually solve fully using both statements, so there's something wrong with the numbers in the question. Perhaps they meant Statement 2 to say "390 balloons" instead of "360 balloons". Then you'd have 90 children receiving three balloons, and 60 children receiving two balloons.

Or maybe they meant, in Statement 1, to say "40% received 3 balloons" (instead of 2 balloons). Then you'd have 60 getting 3 balloons, and 90 getting 2 balloons, for a total of 360.
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New post 05 Aug 2017, 18:36
IanStewart thank you!

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New post 14 Sep 2017, 03:25
I think this is a high-quality question and I don't agree with the explanation. As per the solution provided: Total no. of Children = (360*5)/14
which gives a non-integral value. Hence, it cannot represent number of Children.

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Re S95-36   [#permalink] 14 Sep 2017, 03:25
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