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08 Feb 2024, 02:30
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D
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
15%
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Question Stats:
87% (01:24) correct
13%
(01:46)
wrong
based on 134
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The number of cats in Libby’s house is twice the number of dogs and one third the number of fish. If cats, dogs and fish are the only pets in Libby’s house, what is the probability of randomly selecting two cats?
(1) The number of cats in Libby’s house is 12.
(2) The total number of pets in Libby’s house is 54.
(1) The number of cats in Libby’s house is 12.
(2) The total number of pets in Libby’s house is 54.
08 Feb 2024, 13:29
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I think D should be the option
assume:
dogs = y
cats = 2y
fishes = 6y
Total pets = y+2y+6y = 9y
Sattement1 :
The number of cats in Libby’s house is 12, i.e, 2y = 12 => y = 6
9y = 54
P(Randomly selecting 2 cats) = \(\frac{C(12,2)}{C(54,2)}\)
Statement 2:
The total number of pets in Libby’s house is 54.
that means 9y = 54 => number of cats = 2y = 12
So, P(Randomly selecting 2 cats) = \(\frac{C(12,2)}{C(54,2)}\)
Hence, both of the statements seems to be sufficient.
Hence, option D
assume:
dogs = y
cats = 2y
fishes = 6y
Total pets = y+2y+6y = 9y
Sattement1 :
The number of cats in Libby’s house is 12, i.e, 2y = 12 => y = 6
9y = 54
P(Randomly selecting 2 cats) = \(\frac{C(12,2)}{C(54,2)}\)
Statement 2:
The total number of pets in Libby’s house is 54.
that means 9y = 54 => number of cats = 2y = 12
So, P(Randomly selecting 2 cats) = \(\frac{C(12,2)}{C(54,2)}\)
Hence, both of the statements seems to be sufficient.
Hence, option D
09 Feb 2024, 12:37
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Since this is a DS question, it's worth reminding yourself that the success metric is simply, "do I have enough information to answer the question?" In this case, we're being asked about the probability of randomly selecting two cats, given that there exist cats, dogs, and fish in the sample. So what do we really need? We need to know the number of entities in the sample and the number of cats. That's it. We don't need to bother with the calculations, and we don't really care about whether it's with or without replacement since we're given a ratio. That said, let's break it down.
Step One, Translating the Stimulus:
I always like to translate the stimulus on DS questions where applicable. What this stimulus gives us is a fairly simple ratio of cats to dogs to fish of 2: 1: 6. With this, we just need to know the specific ratio multiplier to find out how many of each entity we have and thus what the total sample size is.
Step Two, Analyzing the Statements:
On to the statements.
Statement One:
We're being told here that there are 12 cats in the sample. Back to the original question: does this give us a ratio multiplier to determine the sample size and number of cats? Yes, in fact, it does. If there are 12 cats, that gives us a ratio multiplier of 6, meaning there are 12 cats, 6 dogs, and 36 fish, for a total of 54. It's not even worth doing any probability calculations. All we need to know is the sample size and the number of cats, and that's it. Whether it's with or without replacement is irrelevant.
Statement Two:
We're being told in Statement 2 that there are a total of 54 animals in the sample. In other words, identical to Statement 1. Because we're working with a provided ratio, that is enough to conclude this is also sufficient. But to further illustrate why: we're being told that our ratio adds to 54: \(2x + x + 6x = 54\). In other words, \(9x = 54\) for a ratio multiplier of \(x = 6\). Once again, we can determine the number of cats as 12, allowing us to determine the probability of selecting two cats.
AC D.
Step One, Translating the Stimulus:
I always like to translate the stimulus on DS questions where applicable. What this stimulus gives us is a fairly simple ratio of cats to dogs to fish of 2: 1: 6. With this, we just need to know the specific ratio multiplier to find out how many of each entity we have and thus what the total sample size is.
Step Two, Analyzing the Statements:
On to the statements.
Statement One:
We're being told here that there are 12 cats in the sample. Back to the original question: does this give us a ratio multiplier to determine the sample size and number of cats? Yes, in fact, it does. If there are 12 cats, that gives us a ratio multiplier of 6, meaning there are 12 cats, 6 dogs, and 36 fish, for a total of 54. It's not even worth doing any probability calculations. All we need to know is the sample size and the number of cats, and that's it. Whether it's with or without replacement is irrelevant.
Statement Two:
We're being told in Statement 2 that there are a total of 54 animals in the sample. In other words, identical to Statement 1. Because we're working with a provided ratio, that is enough to conclude this is also sufficient. But to further illustrate why: we're being told that our ratio adds to 54: \(2x + x + 6x = 54\). In other words, \(9x = 54\) for a ratio multiplier of \(x = 6\). Once again, we can determine the number of cats as 12, allowing us to determine the probability of selecting two cats.
AC D.
