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# There are n students in a class. Of them, k boys and k girls (includin

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There are n students in a class. Of them, k boys and k girls (includin  [#permalink]

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29 Jan 2015, 08:25
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64% (01:39) correct 36% (01:38) wrong based on 388 sessions

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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.

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Re: There are n students in a class. Of them, k boys and k girls (includin  [#permalink]

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09 Feb 2015, 07:39
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pacifist85 wrote:
Bunuel wrote:
Bunuel wrote:
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.

I agree with A and the explanations.

What I would like to ask refers to the part in red. If we have 6 boys and 6 girls that will be paired together, don't we have 6*6=36 combinations of possibl pairs? So, 36 possible, different pairs? Out of these 36 pairs, Harvey and Jessica together would make one pair. So, isn't the probability 1/36?

hi pacifist,
selection of harvey is already sure as he is one of the k boys selected..
And he can be paired with any of the 6(k) girls... so it will be 1/6..

1/36 would have been correct in following scenarios..
1) there are 6 boys and 6 girls. Out of these one boy and one girl are to be choosen as a pair for dance. what is the prob of choosing harvey and jessica?
2) there are 6 boys, harvey being one of them. these 6 boys are to be paired with one of 36 girls, jessica being one of them.what is the prob of harvey being paired with jessica?
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Re: There are n students in a class. Of them, k boys and k girls (includin  [#permalink]

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29 Jan 2015, 11:09
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Bunuel wrote:
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.

ans A..
1) statement tells us k=6. sufficient
2) statement 2 not clear as k boys are selected how can 8 out of them not selected... it must be n and not k...insufficient
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Re: There are n students in a class. Of them, k boys and k girls (includin  [#permalink]

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29 Jan 2015, 11:33
chetan2u wrote:
Bunuel wrote:
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.

ans A..
1) statement tells us k=6. sufficient
2) statement 2 not clear as k boys are selected how can 8 out of them not selected... it must be n and not k...insufficient

chetan2u, would you mind explaining how do you get that the answer is A? Statement (1) just gives us k, but we still don't know n... Or k is enough information to tell that the probability of Harvey paired with Jessica is 1/6?
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Re: There are n students in a class. Of them, k boys and k girls (includin  [#permalink]

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29 Jan 2015, 11:38
viktorija wrote:
chetan2u wrote:
Bunuel wrote:
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.

ans A..
1) statement tells us k=6. sufficient
2) statement 2 not clear as k boys are selected how can 8 out of them not selected... it must be n and not k...insufficient

chetan2u, would you mind explaining how do you get that the answer is A? Statement (1) just gives us k, but we still don't know n... Or k is enough information to tell that the probability of Harvey paired with Jessica is 1/6?

hi victorija.... as k boys and girls are already selected so k in itself becomes a certainity and n does not have any role in calculating probability..
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Re: There are n students in a class. Of them, k boys and k girls (includin  [#permalink]

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01 Feb 2015, 15:23
1
Bunuel wrote:
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.

Statement 1: Harvey plus 5 boys = K. So K is 6...so there are six boys and six girls...can calculate probability of one particular pairing. Sufficient.

Statement 2: Unclear. Question states K boys and K girls are selected for the dance...this statement says 8 of those K boys are not selected. Doesn't make any sense to me.

Going with A.
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Re: There are n students in a class. Of them, k boys and k girls (includin  [#permalink]

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02 Feb 2015, 03:40
Bunuel wrote:
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.

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Re: There are n students in a class. Of them, k boys and k girls (includin  [#permalink]

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04 Feb 2015, 11:49
Bunuel wrote:
Bunuel wrote:
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.

I think veritas made a mistake. Number (2) clearly should be 8 of the n boys.
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Re: There are n students in a class. Of them, k boys and k girls (includin  [#permalink]

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09 Feb 2015, 07:28
1
Bunuel wrote:
Bunuel wrote:
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.

I agree with A and the explanations.

What I would like to ask refers to the part in red. If we have 6 boys and 6 girls that will be paired together, don't we have 6*6=36 combinations of possibl pairs? So, 36 possible, different pairs? Out of these 36 pairs, Harvey and Jessica together would make one pair. So, isn't the probability 1/36?
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Re: There are n students in a class. Of them, k boys and k girls (includin  [#permalink]

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09 Feb 2015, 07:48
Oh great chetan2u, thank you very much. I actually thought we were talking about the first of the 2 possibilities you provided as an example of a 1/36 probability. Kudos for your help.

I will definitely keep that one in mind.
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Re: There are n students in a class. Of them, k boys and k girls (includin  [#permalink]

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17 Nov 2016, 10:52
Hi,

I have one doubt in the question.
Option A mentions that Harvey is selected, and we can correctly conclude that there are 6 boys and 6 girls selected.
But how can we come to the conclusion that Jessica is among these 6 girls.
Am I on a wrong track here?

Regards,

Ankur
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Re: There are n students in a class. Of them, k boys and k girls (includin  [#permalink]

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03 Dec 2016, 04:28
AnkurBansal89 wrote:
Hi,

I have one doubt in the question.
Option A mentions that Harvey is selected, and we can correctly conclude that there are 6 boys and 6 girls selected.
But how can we come to the conclusion that Jessica is among these 6 girls.
Am I on a wrong track here?

Regards,

Ankur

Dear Ankur,

We are being told that there are K girls and K boys including Jessica and Harvey out of which we need to select pair for dance performance (one girl can be paired with one boy). Now, statement 1 tells us that a total of 6 boys are selected (including Harvey). Now, this tells us that the total number of girls is also 6 as the question stem tells us that equal number of girls and boys are selected (k) and stem also tells us that Harvey is one of those 6 girls (the question stem tells us that there are K girls and boys including Harvey and Jessica. This means that both of them are included in k). Does that help ?
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Re: There are n students in a class. Of them, k boys and k girls (includin  [#permalink]

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21 Mar 2017, 01:24
Statement 2 is not well phrased. I lost time trying to understand what was meant.
Cheers.
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Re: There are n students in a class. Of them, k boys and k girls (includin  [#permalink]

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28 Apr 2017, 16:37
Bunuel wrote:
Bunuel wrote:
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.

Bunuel I could not understand why we need total number of boys - k?
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Re: There are n students in a class. Of them, k boys and k girls (includin  [#permalink]

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29 Apr 2017, 03:51
ziyuen wrote:
Bunuel wrote:
Bunuel wrote:
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.

Bunuel I could not understand why we need total number of boys - k?

What do you mean why we need this? This is what the second statement is saying. It's not sufficient but it is what it is telling us.
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Re: There are n students in a class. Of them, k boys and k girls (includin  [#permalink]

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23 Sep 2017, 14:19
Top Contributor
Bunuel wrote:
Bunuel wrote:
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.

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 = 6

Here, 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 = 6
So, 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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Re: There are n students in a class. Of them, k boys and k girls (includin  [#permalink]

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