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An animal shelter began the day Tuesday with a ratio of 5

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by BTGmoderatorLU » Wed Aug 29, 2018 3:04 pm

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Difficulty—

Source: Veritas Prep

An animal shelter began the day Tuesday with a ratio of 5 cats for every 11 dogs. If no new animals arrived at the shelter, and the only animals that left the shelter were those that were adopted, what was the ratio of cats to dogs at the end of the day Tuesday?

(1) No cats were adopted on Tuesday.
(2) 4 dogs were adopted on Tuesday.

The OA is E.
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Source: — Data Sufficiency |

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by Jay@ManhattanReview » Wed Aug 29, 2018 9:42 pm
BTGmoderatorLU wrote:Source: Veritas Prep

An animal shelter began the day Tuesday with a ratio of 5 cats for every 11 dogs. If no new animals arrived at the shelter, and the only animals that left the shelter were those that were adopted, what was the ratio of cats to dogs at the end of the day Tuesday?

(1) No cats were adopted on Tuesday.
(2) 4 dogs were adopted on Tuesday.

The OA is E.
Say beginning Tuesday, there were 5x cats and 11x dogs, where x is a positive integer.

Let's take each statement one by one.

(1) No cats were adopted on Tuesday.

No info about the adoption of dogs. Insufficient.

(2) 4 dogs were adopted on Tuesday.

No info about the adoption of cats. Insufficient.

(1) and (2) together

The ratio of cats to dogs at the end of Tuesday: 5x / (11x - 4)

We do not have the value of x. Can't get the unique value of 5x / (11x - 4). Insufficient.

The correct answer: E

Hope this helps!

-Jay
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by fskilnik@GMATH » Thu Aug 30, 2018 5:57 am
BTGmoderatorLU wrote:Source: Veritas Prep

An animal shelter began the day Tuesday with a ratio of 5 cats for every 11 dogs. If no new animals arrived at the shelter, and the only animals that left the shelter were those that were adopted, what was the ratio of cats to dogs at the end of the day Tuesday?
(1) No cats were adopted on Tuesday.
(2) 4 dogs were adopted on Tuesday.
\[\begin{array}{*{20}{c}}
{{\text{cats}} = \,\,5\,k} \\
{{\text{dogs}} = 11\,k}
\end{array}\,\,\,\,\,\,\left( {k > 0\,\,\,\operatorname{int} } \right)\,\,\,\,\,\,\,\left( * \right)\]
\[\left( * \right)\,\,k\,\, = \,\,11k - 2\left( {5k} \right)\,\,\,{\text{ = }}\,\,\,{\text{difference}}\,\,{\text{of}}\,\,{\text{ints}}\]
That´s the k technique, a "killer" tool of our method (when dealing with ratios)!
\[\left( {1 + 2} \right)\,\,\,\,\,{\text{?}}\,\,\, = \,\,\,\frac{{5k}}{{\,11k - 4\,}}\,\,\,\,\, \Rightarrow \,\,\,\,\,\left\{ \begin{gathered}
\,{\text{Take}}\,\,k = 1\,\,\,\, \Rightarrow \,\,\,? = \frac{5}{7} \hfill \\
{\text{Take}}\,\,k = 2\,\,\,\, \Rightarrow \,\,\,? = \frac{{10}}{{18}} \ne \frac{5}{7} \hfill \\
\end{gathered} \right.\]
The above follows the notations and rationale taught in the GMATH method.
Fabio Skilnik :: GMATH method creator ( Math for the GMAT)
English-speakers :: https://www.gmath.net
Portuguese-speakers :: https://www.gmath.com.br
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by Jeff@TargetTestPrep » Wed Sep 05, 2018 9:50 am
BTGmoderatorLU wrote:Source: Veritas Prep

An animal shelter began the day Tuesday with a ratio of 5 cats for every 11 dogs. If no new animals arrived at the shelter, and the only animals that left the shelter were those that were adopted, what was the ratio of cats to dogs at the end of the day Tuesday?

(1) No cats were adopted on Tuesday.
(2) 4 dogs were adopted on Tuesday.
Statement One Alone:

No cats were adopted on Tuesday.

Since we don't know how many dogs were adopted on Tuesday, we can't determine the ratio of cats to dogs at the end of Tuesday.

Statement one alone is not sufficient.

Statement Two Alone:

4 dogs were adopted on Tuesday.

Since we don't know how many cats were adopted on Tuesday, we can't determine the ratio of cats to dogs at the end of Tuesday.

Statement two alone is not sufficient.

Statements One and Two Together:

Even though we know no cats and 4 dogs were adopted on Tuesday, we still can't determine the ratio of cats to dogs at the end of Tuesday. That is because we don't know the number of cats and dogs at the beginning of the day (recall that we know only that the ratio of cats to dogs at the beginning of the day was 5:11). For example, if there were 5 cats and 11 dogs at the beginning of the day, then there would be 5 cats and 7 dogs at the end of the day, making the cats-to-dogs ratio of 5:7. However, if there were 10 cats and 22 dogs at the beginning of the day (still satisfying the ratio of 5 : 11), then there would be 10 cats and 18 dogs at the end of the day, making the cats-to-dogs ratio of 10:18 or 5 to 9.

Answer: E

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