Data Sufficiency

BTGmoderatorLU wrote:Source: Veritas Prep

There are n students in a class. Of them, k boys and k girls (including Harvey and Jessica) are selected for a dance performance in which students will dance in pairs of one boy and one girl. What is the probability that Harvey will be paired with Jessica?

1. Other than Harvey, 5 boys are selected for the dance.
2. 8 of the k boys are not selected for the dance.

The OA is A.

The probability that Harvey will be paired with Jessica = 1/k; note that we do not need the value of n.

Also, note that ≠ (1/k)*(1/k) = 1/k^2

Let's look at this way: There are k girls who can be paired with Harvey (= k number of ways), out of which only one way (pairing with Jessica) is the required ways; thus, the required probability = 1/k.

The question boils down to getting the value of k.

Question rephrased: What's the value of k?

Let's take each statement one by one.

1. Other than Harvey, 5 boys are selected for the dance.

=> k = 1 + 5 = 6. Sufficient.

2. 8 of the k boys are not selected for the dance.

=> n - k = 8. Can't get k. Insufficient.

The correct answer: A

Hope this helps!

-Jay
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BTGmoderatorLU wrote:Source: Veritas Prep

There are n students in a class. Of them, k boys and k girls (including Harvey and Jessica) are selected for a dance performance in which students will dance in pairs of one boy and one girl. What is the probability that Harvey will be paired with Jessica?

1. Other than Harvey, 5 boys are selected for the dance.
2. 8 of the k boys are not selected for the dance.

The OA is A.

Target question: What is the probability that Harvey will be paired with Jessica?

Given: There are n students in a class. Of them, k boys and k girls (including Harvey and Jessica) are selected for a dance performance in which students will dance in pairs of one boy and one girl.

Statement 1: Other than Harvey, 5 boys are selected for the dance.
So, if we include Harvey, there are 6 boys selected for the dance.
In other words, k = 6
If there are 6 boys and 6 girls, then we can DEFINITELY answer the target question with certainty.
So, statement 1 is SUFFICIENT

ASIDE: For "fun" let's determine the actual answer to the target question.
There are 6 girls (1 of which is Jessica) who can be paired with Harvey
So, P(Jessica is selected as Harvey's partner) = 1/6

Statement 2: 8 of the k boys are not selected for the dance.
Since we don't know the value of k, we can't determine the number of boys chosen to be selected for the dance.
So, here are two possible cases:
Case a: k = 10, which means 2 boys WERE selected for the dance. If there are 2 boys and 2 girls, then P(Jessica is selected as Harvey's partner) = 1/2
Case b: k = 11, which means 3 boys WERE selected for the dance. If there are 3 boys and 3 girls, then P(Jessica is selected as Harvey's partner) = 1/3
Since we cannot answer the target question with certainty, statement 2 is NOT SUFFICIENT

Answer: A

Cheers,
Brent