Angelica and Basil are playing a game with the set of ordered pairs S

Question

Angelica and Basil are playing a game with the set of ordered pairs  S = {(1, 3), (2, 1), (3, 2), (4, 4)} . 
In each ordered pair, the first number is Angelica's preference number for that pair, and the second number is Basil's preference number for that pair. Angelica takes the first turn and removes an ordered pair from set  S . Basil takes the second turn and removes an ordered pair from among those remaining from set  S . They continue taking turns until all the ordered pairs have been removed, at which time the game is over. Each player's final score is equal to the sum of that player's preference numbers for the ordered pairs he or she has removed.

Assume that each player always selects the available ordered pair for which his or her preference number is greatest. In the table, select a value for  Angelica's final score  and a value for  Basil's final score  that are jointly consistent with this assumption and the given information. Make only two selections, one in each column.

egmat · Accepted Answer

A simple question indeed… Another one of those time saver questions – only if you do not get scared of the following scenarios/terms
 
 Ordered pairs. 
 How a game is played.

Now not all students get scared of the above. But some do and that is why mentioning this is very important so that you remove such preconceptions from your mind and recognize this question as a time-saver.

So, watch this solution and observe how easy it is to solve this question.

https://www.youtube.com/watch?v=-JHwrfmI05g

chetan2u · Answer

The numbers are (1,3), (2,1), (3,2) and (4,4)

A would first pick (4,4) and the score would become 4.
Next, B would be pick element containing his highest preferred number that is (1,3), so his score becomes 3.
Then A picks (3,2), making her score 4+3 or 7.
Finally B picks (2,1), making his score 3+1 or 4.

Answer: 7 and 4

JoeKan1234 · Answer

"Assume that each player always selects the available ordered pair for which his or her preference number is greatest."

Angelica takes the first turn. The largest possible pair is (4,4)

In the second turn, the largest pair to Basil is (1,3)

In the third turn, the largest pair to Angelica is (3,2)

In the final turn, the largest pair to Basil is (2,1)

So Angelica's score is 4+3=7
Basil's score is 3+1=4

Vinit800HBS · Answer

Given Ordered Pairs:
Angelica's preferences are in  Red  and Basil's preferences are in  Blue .

S = {( 1 ,  3 ), ( 2,    1 ), ( 3,   2 ), ( 4,    4 )}

Angelica's  turn: She removes ( 4,    4 ). Her score is  4  right now.

Available Ordered Pairs: S = {( 1 ,  3 ), ( 2,    1 ) ,  ( 3,   2 )}.

Basil's  turn: She removes ( 1 ,  3 ). Her score is  3  right now.

Available Ordered Pairs: S = {( 2,    1 ) ,  ( 3,   2 )}.

Angelica's  turn: She removes ( 3,    2 ). Her score is  4+3  =  7  now.

Available Ordered Pairs: S = {( 2,    1 )}.

Basil's  turn: She removes ( 2 ,  1 ). Her score is   3    +   1  =   4  now.

__thisisjay · Answer

It is easy to solve find the best answer so math just logical thinking

PAIR ARE FOR Angelica - { 1, 2, 3, 4}
PAIR ARE FOR Basil ------{ 3, 1 , 2, 4}

First turn A choose highest value - {4} that also remove { 4} for B 
than B chose remaining pair for B

PAIR ARE FOR Angelica - { 1, 2, 3}
PAIR ARE FOR Basil ------{ 3, 1 , 2}

First turn B choses the best pair - {3} that rule out {1} for A

PAIR ARE FOR Angelica - { 2, 3}
PAIR ARE FOR Basil ------{ 1 , 2}

than A choses  
 PAIR ARE FOR Angelica - { 2, 3}
PAIR ARE FOR Basil ------{ 1 , 2}

best pair - A - { 3} that remove { 2} for B
  Total A get - 4 + 3 = 7 
PAIR ARE FOR Angelica - { 2,}
PAIR ARE FOR Basil ------{ 1 }

and B left with = 3 + 1 = 4

GMAT745owner · Answer

this one is much easier than the others

MartyMurray · Answer

Angelica and Basil are playing a game with the set of ordered pairs  S = {(1, 3), (2, 1), (3, 2), (4, 4)} .

In each ordered pair, the first number is Angelica's preference number for that pair, and the second number is Basil's preference number for that pair. Angelica takes the first turn and removes an ordered pair from set  S . Basil takes the second turn and removes an ordered pair from among those remaining from set  S . They continue taking turns until all the ordered pairs have been removed, at which time the game is over. Each player's final score is equal to the sum of that player's preference numbers for the ordered pairs he or she has removed.

Assume that each player always selects the available ordered pair for which his or her preference number is greatest. In the table, select a value for  Angelica's final score  and a value for  Basil's final score  that are jointly consistent with this assumption and the given information. Make only two selections, one in each column.

Getting a question like this one correct doesn't take a lot of thinking. So, even though, in a way, it's not an easy question, a question like this one can be a little bit of a break from the intensity of the DI section.

To get a question like this one correct, we have to understand the outlined procedure, keep things straight, and execute precisely.

Key Aspects of the Procedure

From the passage:

In each ordered pair, the first number is Angelica's preference number for that pair, and the second number is Basil's preference number for that pair.

Angelica takes the first turn, and Basil takes the second turn.

Each player's final score is equal to the sum of that player's preference numbers for the ordered pairs he or she has removed.

From the question stem:

Each player always selects the available ordered pair for which his or her preference number is greatest.

Executing the Procedure

(1, 3), (2, 1), (3, 2), (4, 4)

Angelica - (1, 3), (2, 1), (3, 2), ( 4 , 4)

Basil - (1,  3 ), (2, 1), (3, 2)

Angelica - (2, 1), ( 3 , 2)

Basil - (2,  1 )

Angelica's total: 4 + 3 = 7

Basil's total: 3 + 1 = 4

Correct answer:   7 ,  4

ManishaPrepMinds · Answer

Since  Angelica goes first  and both players play optimally:

Turn 1 (Angelica): She will take (4,4)

Turn 2 (Basil): From remaining {(1,3), (2,1), (3,2)}, he takes (1,3)

Turn 3 (Angelica): From remaining {(2,1), (3,2)}, she takes (3,2)

Turn 4 (Basil): Takes (2,1)

Final scores: Angelica = 4+3 = 7, Basil = 3+1 = 4 
 Answer: Angelica = 7, Basil = 4

Angelica and Basil are playing a game with the set of ordered pairs S

Prep Toolkit

Top 5 GMAT Debrief Videos

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards

GMAT Two-part Analysis (TPA) Questions

Angelica and Basil are playing a game with the set of ordered pairs S

Prep Toolkit

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards