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# At a certain circus, every child was given either two or three balloon

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Math Expert
Joined: 02 Sep 2009
Posts: 54369
At a certain circus, every child was given either two or three balloon  [#permalink]

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14 Nov 2014, 09:55
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15% (low)

Question Stats:

82% (01:10) correct 18% (01:14) wrong based on 138 sessions

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Tough and Tricky questions: Word Problems.

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 390 balloons were given out to children at the circus.

Kudos for a correct solution.

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Joined: 10 Sep 2014
Posts: 96
Re: At a certain circus, every child was given either two or three balloon  [#permalink]

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14 Nov 2014, 12:06
1
statement 1: not sufficient
We don't have a value to know how many children.

statement 2: not sufficient
Many different possibilities for the # of children that got 3 balloons.

Down to C and E.

Together we have a total # of balloons given out and a ratio of how many children received 2 to how many children received 3. We should be able to use these statements to answer the question but no need to calculate.

Math Expert
Joined: 02 Sep 2009
Posts: 54369
At a certain circus, every child was given either two or three balloon  [#permalink]

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17 Nov 2014, 12:11
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1
Bunuel wrote:

Tough and Tricky questions: Word Problems.

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 390 balloons were given out to children at the circus.

Kudos for a correct solution.

Official Solution:

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

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 390 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 $$2 \times 180 = 390$$ balloons), or there could be 0 children with 2 balloons and 120 with 3 (giving $$3 \times 120 = 390$$ 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 390 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 390, we have: $$2(\frac{2}{5}x) + 3(\frac{3}{5}x) = 390$$. 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.

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Re: At a certain circus, every child was given either two or three balloon  [#permalink]

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15 Jun 2016, 18:11
Bunuel: Would it be wrong to assume that even the ballons would be divided in the ratio of children i.e. 40% of the ballons be distributed in 2s and remaining 60% in 3s?
Intern
Joined: 08 Feb 2017
Posts: 7
Re: At a certain circus, every child was given either two or three balloon  [#permalink]

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19 Feb 2017, 12:52
2
Bunuel wrote:
Bunuel wrote:

Tough and Tricky questions: Word Problems.

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.

Kudos for a correct solution.

Official Solution:

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

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.

Hi Bunuel ,
When S-1 and S-2 combined are combined, we have the equation $$2(\frac{2}{5}x) + 3(\frac{3}{5}x) = 360$$. Here x turns out to be in a fraction. (1800/13). But the number of children cannot be a fraction. So does it mean the Answer is E?
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Re: At a certain circus, every child was given either two or three balloon  [#permalink]

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12 Aug 2017, 13:28
1
I have the same doubt, If we solve till end, the number of children is coming in fraction.
In that case answer should be E.

Posted from my mobile device
Math Expert
Joined: 02 Sep 2009
Posts: 54369
Re: At a certain circus, every child was given either two or three balloon  [#permalink]

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13 Aug 2017, 07:30
appylov wrote:
I have the same doubt, If we solve till end, the number of children is coming in fraction.
In that case answer should be E.

Posted from my mobile device

It should have been 390 instead of 360. Edited. Thank you.
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Re: At a certain circus, every child was given either two or three balloon   [#permalink] 13 Aug 2017, 07:30
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# At a certain circus, every child was given either two or three balloon

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