Bunuel
Bunuel
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.
Kudos for a correct solution.
VERITAS PREP OFFICIAL SOLUTION:There are k boys and k girls selected (including Harvey and Jessica). Harvey can be paired with any one of the k girls. Jessica is one of the girls. The probability that Harvey will be paired with Jessica is 1/k. Notice that n has no role to play here. The required probability only needs the value of k.
Statement 1: We now know that total 5+1 = 6 boys and 6 girls were selected for the dance. So probability that Harvey will be paired with Jessica is 1/6. Sufficient.
Statement 2: This tells us that Total number of boys – k = 8. We don’t know the value of k. Not sufficient.Answer (A)
I think there's an issue with statement 2.
On the GMAT, the two statements in a Data Sufficiency (DS) question will never
contradict each other.
For example, the following question would never be a legitimate DS question:
What is the value of x"
(1) x + 1 = 5
(2) 2x = 6Here, statement 1 tells us that x = 4, and statement 2 tells us that x = 3
As such, this question does not adhere to the format of official DS questions.
In the original question, we learned (from statement 1) that k =
6So, statement 2 is basically telling us that "8 of the
6 boys are not selected for the dance," and this contradicts the information provided in statement 1.
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