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# An animal shelter began the day Tuesday with a ratio of 5 cats for eve

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Math Expert
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An animal shelter began the day Tuesday with a ratio of 5 cats for eve  [#permalink]

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23 Jan 2015, 06:41
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45% (medium)

Question Stats:

58% (01:25) correct 42% (01:13) wrong based on 280 sessions

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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.

Kudos for a correct solution.

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Re: An animal shelter began the day Tuesday with a ratio of 5 cats for eve  [#permalink]

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23 Jan 2015, 07:46
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Bunuel wrote:
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.

Kudos for a correct solution.

1) we don't know how many dogs have been adopted.
not sufficient.

2) we don't know how many cats have been adopted
not sufficient.

1+2) 5x/11x-4 is the ratio; we still don't know what's the value of x. Not sufficient.
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Re: An animal shelter began the day Tuesday with a ratio of 5 cats for eve  [#permalink]

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23 Jan 2015, 08:46
1
Any statement provide enough information about both Dog and Cats is qualified.
1/ Know the number of Cats. (Not Dogs)
2/ The Q did not say: all adopted leave. It just said: if leave, must be adopted => Know nothing about the number of Dogs.
=> E
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Re: An animal shelter began the day Tuesday with a ratio of 5 cats for eve  [#permalink]

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26 Jan 2015, 03:44
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2
Bunuel wrote:
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.

Kudos for a correct solution.

VERITAS PREP OFFICIAL SOLUTION:

A fairly common trap on ratio problems is for students to forget that a change in "actual number" (in this case, -4 dogs) can't necessarily be applied to the change in ratio unless the ratio provides a link to actual number. In this case, consider two hypotheticals that prove that the statements together are not sufficient:

There were exactly 5 cats and 11 dogs at the beginning of the day, meaning that there were 5 cats and 7 dogs at the end of the day, a ratio of 5 : 7.

or

There were 10 cats and 22 dogs at the end of the day. By the end of the day, there would be 10 cats and 18 dogs for a ratio of 5 : 9.

Since multiple ratios are possible, the statements together are not sufficient.

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Re: An animal shelter began the day Tuesday with a ratio of 5 cats for eve  [#permalink]

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05 Sep 2018, 09:52
Bunuel wrote:
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.

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Re: An animal shelter began the day Tuesday with a ratio of 5 cats for eve  [#permalink]

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06 Sep 2018, 08:11
Bunuel wrote:
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.

$$\begin{array}{*{20}{c}} {{\text{cats}} = \,\,5\,k} \\ {{\text{dogs}} = 11\,k} \end{array}\,\,\,\,\,\,\left( {k > 0\,\,\,\operatorname{int} } \right)\,\,\,\,\,\,\,\left( * \right)$$

$$\left( * \right)\,\,{\mkern 1mu} k\,{\mkern 1mu} {\mkern 1mu} = \,\,{\mkern 1mu} {\mkern 1mu} 11k - 2\left( {5k} \right){\mkern 1mu} {\mkern 1mu} {\mkern 1mu} {\text{ = }}{\mkern 1mu} {\mkern 1mu} \operatorname{int} - \operatorname{int} \,\,\, = \,\,\,\operatorname{int}$$

That´s the k technique, a "killer" tool of our method (when dealing with ratios)!

$$\left( {1 + 2} \right)\,\,\,\,\,{\text{?}}\,\,\, = \,\,\,\frac{{5k}}{{\,11k - 4\,}}\,\,\,\,\, \Rightarrow \,\,\,\,\,\left\{ \begin{gathered} \,{\text{Take}}\,\,k = 1\,\,\,\, \Rightarrow \,\,\,? = \frac{5}{7} \hfill \\ {\text{Take}}\,\,k = 2\,\,\,\, \Rightarrow \,\,\,? = \frac{{10}}{{18}} \ne \frac{5}{7} \hfill \\ \end{gathered} \right.$$

This solution follows the notations and rationale taught in the GMATH method.

Regards,
fskilnik.
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Re: An animal shelter began the day Tuesday with a ratio of 5 cats for eve &nbs [#permalink] 06 Sep 2018, 08:11
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