The table shows the Six members of a certain chess club, each of whom

Question

The table shows the Six members of a certain chess club, each of whom will play against exactly one other member in a game of chess today. For the person named in the column heading, the column entries indicate which member of the club that person would prefer to have as his or her opponent for today. The number 1 indicates the first choice (most- preferred opponent), 2 the second, and so on. The members of the club have as a goal that Priyanka and Sneha should each have her first choice of opponent.

	Aditi	Dhruv	Priyanka	Raj	Sneha	Vijay
Aditi	-	3	5	5	5	1
Dhruv	1	-	2	2	1	5
Priyanka	3	2	-	1	2	3
Raj	5	4	1	-	3	4
Sneha	2	1	3	3	-	2
Vijay	4	5	4	4	4	-

For each of the following members of the chess club, select Could achieve the stated goal if denying that member’s first and second choice of opponent for today could result in Priyanka and Sneha each having her first choice. Otherwise, select Could NOT achieve the stated goal.

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Could achieve the stated goal	Could NOT achieve the stated goal
		Aditi
		Dhruv
		Raj

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Official Answer

Aditi: Could achieve the stated goal Dhruv: Could NOT achieve the stated goal Raj: Could NOT achieve the stated goal

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KarishmaB · Accepted Answer

GOAL: Priyanka and Sneha should each have her first choice of opponent. Priyanka - Raj Sneha - Dhruv If goal is met, only Aditi and Vijay are left so of course they need to be paired together. Goal is met only if the pairing is the following: Priyanka - Raj Sneha - Dhruv Aditi - Vijay 1. Aditi If Aditi is denied her 1st and 2nd choices, i.e. Dhruv and Sneha, it is possible that she gets Vijay and pairing is as the goal indicates. Hence it is possible to achieve the goal. Not necessary, but possible. Select 'Could achieve the stated goal' 2. Dhruv If Dhruv is denied Sneha and Priyanka, "Sneha - Dhruv" pairing is not possible. Hence goal will not be achieved. Select 'Could NOT achieve the stated goal' 3. Raj If Raj is denied Priyanka and Dhruv, "Priyanka - Raj" pairing is not possible. Hence goal will not be achieved. Select 'Could NOT achieve the stated goal' GMAT-Club-Forum-rxja8wek.png

Bunuel · Answer

The table shows the Six members of a certain chess club, each of whom will play against exactly one other member in a game of chess today. For the person named in the column heading, the column entries indicate which member of the club that person would prefer to have as his or her opponent for today. The number 1 indicates the first choice (most- preferred opponent), 2 the second, and so on. The members of the club have as a goal that Priyanka and Sneha should each have her first choice of opponent.

	Aditi	Dhruv	Priyanka	Raj	Sneha	Vijay
Aditi	-	3	5	5	5	1
Dhruv	1	-	2	2	1	5
Priyanka	3	2	-	1	2	3
Raj	5	4	1	-	3	4
Sneha	2	1	3	3	-	2
Vijay	4	5	4	4	4	-

For each of the following members of the chess club, select Could achieve the stated goal if denying that member’s first and second choice of opponent for today could result in Priyanka and Sneha each having her first choice. Otherwise, select Could NOT achieve the stated goal.

First pin down what the “goal” actually means: the goal is that Priyanka and Sneha each get their first-choice opponent. This does not mean that they have to pick first or that they have any priority over the others; it just means that, in the final matching, we want each of them to be paired with her own first choice. From the table (column = person’s preferences):

• Priyanka’s first choice is Raj
• Sneha’s first choice is Dhruv

So to achieve the goal we must have these pairs:

• Priyanka - Raj
• Sneha - Dhruv

That uses up Priyanka, Raj, Sneha, and Dhruv. The only two people left are Aditi and Vijay, so they must play each other. So there is exactly one pairing that achieves the goal:

• Priyanka - Raj
• Sneha - Dhruv
• Aditi - Vijay

Now, let's check what the question wants from us: for each of Aditi, Dhruv, and Raj, we need to see whether we can still get this exact pairing if that person does not get either their first or second choice of opponent. If we can, then we “Could achieve the stated goal”; if we cannot, then we “Could NOT achieve the stated goal.”

1. Aditi

Aditi’s column:
1st choice: Dhruv
2nd choice: Sneha

To achieve the goal, Aditi is matched with Vijay. Vijay is not one of her top two choices, so we could indeed deny Aditi both her 1st and 2nd choices and still achieve the goal.

So, if Aditi is denied her first and second choice of opponent, the club Could achieve the stated goal.

2. Dhruv

Dhruv’s column:
1st choice: Sneha
2nd choice: Priyanka

To achieve the goal, Dhruv must be paired with Sneha. But Sneha is his 1st choice, and he is not allowed to be paired with either his first or his second choice. So Dhruv cannot be paired with Sneha, and the goal cannot be achieved.

So, if Dhruv is denied his first and second choice of opponent, the club Could NOT achieve the stated goal.

3. Raj

Raj’s column:
1st choice: Priyanka
2nd choice: Dhruv

To achieve the goal, Raj must be paired with Priyanka. But Priyanka is his 1st choice, and he is not allowed to be paired with either his first or his second choice. So Raj cannot be paired with Priyanka, and the goal cannot be achieved.

So, if Raj is denied his first and second choice of opponent, the club Could NOT achieve the stated goal.

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chetan2u · Answer

You should immediately realize the following about the preferences. Priyanka: Her first choice is Raj, while Raj's first choice is also Priyanka. Sneha: Her first choice is Dhruv, while Dhruv's first choice is also Sneha. However, Aditi and Vijay are not the first choice for each other. In options, Dhruv and Raj not getting their first choice will also result in Sneha and Priyanka not getting their first choice . Hence, the answer for these two oprions is Could NOT achieve the stated goal. If Aditi does not get her first two choices, she can always choose Vijay, who happens to be the 4th preference, thereby allowing Priyanka to play against Raj and Sneha to play against Dhruv. Thus, the goal could be achieved. GMAT-Club-Forum-8scsxnch.png

james3000 · Answer

Hi   chetan2u ,  I had a doubt in statement 1 - if Aditi deny her first and second choice (Dhruv and Sneha), she would be then choosing her 3rd choice which is Priyanka. Therefore goal will not be achieved.

nisen20 · Answer

what is the definition of this DENYING action? what will happen specifically following this DENYING action?
after aditi's first two opponent—dhruv and sneha—being denied, he might want to choose the rest as his new opponent. why would priyanka and sneha get affected by denying aditi's choice and therefore change opponents with whom they prefer to play?

abhichatur · Answer

Hi  chetan2u  completely agree with  james3000  here. How can we say that Aditi will play the 4th option if the question says that they skip 1 and 2?

GMAT745owner · Answer

This is game theory. Not GMAT.

bb · Answer

This is a very convoluted question in my humble opinion and it is just not clear - thats the biggest issue is that there are some big gaps.

What I think the test-writer meant is that the denial ONLY counts if it interferes with the first two choices.

Here is what I think that means - Aditi is denied playing with Dhruv and Sneha - that does not interfere with Sneha's and Priyanka's choices immediately because neither S or P wanted to play Aditi. 
 
 Aditi's third choice is Priyanka. However, Aditi may want to play Priyanka as her third but since Priyanka already picked Raj, she is not available, and thus Aditi, will have to move on to her 4th choice.

This has an assumptions however: -  Priyanka and Sneha are the first to choose and the rest of the players choose the remaining available players. This may be logical but it is not stated and if we deny Aditi's first two choices, we could assume that she would automatically get her third, but not based on the answer. For the First question to work, priority has to go to S and P.

I am not sure I love this explanation but this is the only way I am able to solve based on the answers we are given. 
hope it helps.

bb · Answer

Because Priyanka (Aditi's third choice) will be playing Raj. Priyank has priority it appears

sbyongid · Answer

So this question do not care about some people left alone? For instance, if we deny Aditi of her first and second choice, Priya and Sneha will play with their perferred players but Aditi will be left alone

cheshire · Answer

Yes, this question does allow for some players to be left unpaired: the task only asks whether denying the first and second choices of a particular person could result in Priyanka and Sneha getting their first-choice opponents. It does not require everyone to be matched or all players to be paired up.

nbharti · Answer

Aditi will not be left alone. She will still have the pair with vijay. It's just that her preference order will not be respected fully.

avigoesforMBA · Answer

I don't think its as complex as we think it is!

Let's understand the table first: X axis (horizontal names written) display the name of the contenstant who's preferences are given in Y axis (vertically). So Aditi's choices are as follows = 1) Dhruv 2) Sneha 3) Priyanka 4) Vijay 5) Raj.

Hope this is clear until now, if not- first try to spot this.

Now, the question says - If I want to achieve the states goal, whose first and second preference I will have to deny. Mark could achieve for those where I'll have to deny, mark could not for whom, if we ignore the first and second preference, we won't be able to achieve the goal.

Now, let's talk about the goal: Sneha & Priyanka to play with their first preference

So the ideal matches which constitute of our goal, look like:
Sneha - Dhruv
Priyanka - Raj

Moving on the ques->

Do I need to deny Aditi of her first two preferences to make the ideal (goal matches)
-> Aditi has her first two pref as Dhruv & Sneha so yes, I'll need to tell her to buzz off and let these two have a match. So - could have achieved

Talking about Dhruv & Raj
Both of their first preferences are with people whom their ideal matches have been set up with. If I deny them, I'll go against the goal and hence ans become - could not be achieved

Saun2511 · Answer

I thought that if dhruv is denied his first and second pref which is sneha and priyanka I could STILL assign him to sneha, hence goal achieved.
the question stem states that priyanka and sneha will get their first preferences, so how does it matter what dhruv's or raj's preferences are. I could still assign dhruv to sneha and raj to priyanka  Bunuel   KarishmaB   chetan2u

Bunuel · Answer

You’re mixing up two things.

“Priyanka and Sneha get their first choice” does NOT mean they pick first. It just describes the final matching we want: Priyanka - Raj and Sneha - Dhruv.

Then the question asks, for Aditi, Dhruv, and Raj, whether we can still get this exact pairing if that person does not get either their first or second choice of opponent.

Check complete solution  HERE .

KarishmaB · Answer

" denying that member’s first and second choice of opponent for today" means Dhruv is not given his first and second choices - i.e. Sneha and Priyanka today. So Dhruv had Aditi as his opponent. 
It doesn't mean that he asked and was denied and later when Sneha was asked and she said Dhruv, then she was given Dhruv. If that were the case, then Dhruv would have got his first choice too. It would not have been denied to him.

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