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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An animal shelter began the day Tuesday with a ratio of 5
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BTGmoderatorLU
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Jay@ManhattanReview
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Say beginning Tuesday, there were 5x cats and 11x dogs, where x is a positive integer.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.
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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fskilnik@GMATH
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\[\begin{array}{*{20}{c}}BTGmoderatorLU wrote:Source: Veritas Prep
An animal shelter began the day Tuesday with a ratio of 5 cats for every 11 dogs. If no new animals arrived at the shelter, and the only animals that left the shelter were those that were adopted, what was the ratio of cats to dogs at the end of the day Tuesday?
(1) No cats were adopted on Tuesday.
(2) 4 dogs were adopted on Tuesday.
{{\text{cats}} = \,\,5\,k} \\
{{\text{dogs}} = 11\,k}
\end{array}\,\,\,\,\,\,\left( {k > 0\,\,\,\operatorname{int} } \right)\,\,\,\,\,\,\,\left( * \right)\]
\[\left( * \right)\,\,k\,\, = \,\,11k - 2\left( {5k} \right)\,\,\,{\text{ = }}\,\,\,{\text{difference}}\,\,{\text{of}}\,\,{\text{ints}}\]
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.
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Jeff@TargetTestPrep
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Statement One Alone: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.
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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