DILR Test 4 Practice

The order of the race finish can be Alice > Bob > Chris. Therefore, the correct statement is option 1)

To find the number of people who do not like pizza or burgers, we need to subtract the number of people who like both from the total number of people. So, 50 - 40 = 10 people do not like pizza or burgers. Therefore, the correct answer is option 3) 10.

From the given information, we can see that the points scored by the players in a round has the following possibilities:

HHHH: (-1, -1, -1, -1)

HHHL: (1, 1, 1, -3)

HHLL: (2, 2, -2, -2)

HLLL: (3, -1, -1, -1)

LLLL: (1, 1, 1, 1)

Also, the total points scored by the four players in a round can only be -4 or 0 or 4.

From (1), the total points scored by the four players combined in the first three rounds is 6 + 2 - 2 - 2 = 4.

Hence, in the first three rounds, the total points scored by the four players must be either (-4, 4, 4) OR (0, 0, 4), in any order.

Also, from (1), in the first three rounds, Arun scored 6 points. And from (2), Arun scored 7 points at the end of round 6. Hence, in the 4th, 5th, and 6th rounds, he must have scored 1 point.

From (4), Arun scored 3 points in exactly 2 rounds.

These two rounds cannot both be among the 4th, 5th, and 6th rounds because he scored a net of only 1 point in these three rounds combined.

Hence, Arun must have scored 3 points in one round in the 1st, the 2nd, and 3 rd rounds. If Arun scored 3 points in the first three rounds, then in that round, the total points scored by the four players combined must be 0 (in the case of HLLL).

Hence, the total points scored by the four players in the first three rounds must be (0, 0, 4). Among the first three rounds, in one round, the three players must have scored (3, -1, -1, -1), with Arun scoring 3 points.

Since in another round, the four players scored a total of 4 points, they must have bid LLLL (as it is the only case in which they can score 4 points in total). They must have scored (1, 1, 1, 1).

Since Arun scored a total of 6 points in the first three rounds, and he scored 3 points and 1 point in two of these rounds, he must have scored 2 points in the other round. This is possible only if the players bid HHLL and the scores of the four players must be (2, 2, - 2, - 2).

In the round that the players scored (3, - 1, - 1, - 1), Dipak must have scored - 1 point (since Arun scored 3 points).

In the round that the players scored (1, 1, 1, 1), Dipak must have scored 1 point.

In the round that the players scored (2, 2, - 2, - 2), Dipak must have scored 2 points (since the total points that Dipak scored in the first three rounds is 2).

From (3), Dipak must have scored 2 points in the first round, - 1 point in the second round, and 1 point in the third round.

From this, we can fill in the points for the first three rounds, as shown below

(Note that with this information, the first question of the set can be answered)

In the next three rounds, from (1) and (2), Arun must have scored 1 point, Bankim must have scored 1 point, Charu must have scored - 3 points and Dipak must have scored - 3 points.

The total points scored by the four players are - 4. This is possible if the total points scored by the four players in the three rounds are (0, 0, - 4) OR (4, - 4, - 4) in any order.

However, we know that Arun must have scored 3 points in one of these three rounds (from (4)). Hence, the total points scored by the players in this round must be 0.

Hence, the four players must have scored (0, 0, - 4) points in these three rounds. In one round the points scored by the players must be (3, - 1, - 1, - 1), with Arun scoring 3 points.

In the round in which the total points scored by the four players is 4, they must have scored ( - 1, - 1, - 1, - 1).

Since Bankim scored a total of 1 point in these three rounds, and he scored - 1 point and - 1 point in the two rounds mentioned above, he must have scored 3 points in the other third.

Hence, in the remaining round, the four players must have scored (3, - 1, - 1, - 1), with Bankim scoring 3 points.

However, with the given information, we cannot deduce the round number corresponding to the above rounds.

Hence, we get the following table:

The bids by Arun, Bankim, Charu, Dipak in the first round were Hi, Lo, Lo, Hi.

Arun bid Hi in 4 rounds

Bankim bid Lo in 4 rounds

All four players made identical bids in 2 rounds

Dipak gained exactly 1 point in 1 round

In the second round, Arun was the only player to bid Hi.

From the given information, we can see that the points scored by the players in a round has the following possibilities:

HHHH: (-1, -1, -1, -1)

HHHL: (1, 1, 1, -3)

HHLL: (2, 2, -2, -2)

HLLL: (3, -1, -1, -1)

LLLL: (1, 1, 1, 1)

Also, the total points scored by the four players in a round can only be -4 or 0 or 4.

From (1), the total points scored by the four players combined in the first three rounds is 6 + 2 - 2 - 2 = 4.

Hence, in the first three rounds, the total points scored by the four players must be either (-4, 4, 4) OR (0, 0, 4), in any order.

Also, from (1), in the first three rounds, Arun scored 6 points. And from (2), Arun scored 7 points at the end of round 6. Hence, in the 4th, 5th, and 6th rounds, he must have scored 1 point.

From (4), Arun scored 3 points in exactly 2 rounds.

These two rounds cannot both be among the 4th, 5th, and 6th rounds because he scored a net of only 1 point in these three rounds combined.

Hence, Arun must have scored 3 points in one round in the 1st, the 2nd, and 3 rd rounds. If Arun scored 3 points in the first three rounds, then in that round, the total points scored by the four players combined must be 0 (in the case of HLLL).

Hence, the total points scored by the four players in the first three rounds must be (0, 0, 4). Among the first three rounds, in one round, the three players must have scored (3, -1, -1, -1), with Arun scoring 3 points.

Since in another round, the four players scored a total of 4 points, they must have bid LLLL (as it is the only case in which they can score 4 points in total). They must have scored (1, 1, 1, 1).

Since Arun scored a total of 6 points in the first three rounds, and he scored 3 points and 1 point in two of these rounds, he must have scored 2 points in the other round. This is possible only if the players bid HHLL and the scores of the four players must be (2, 2, - 2, - 2).

In the round that the players scored (3, - 1, - 1, - 1), Dipak must have scored - 1 point (since Arun scored 3 points).

In the round that the players scored (1, 1, 1, 1), Dipak must have scored 1 point.

In the round that the players scored (2, 2, - 2, - 2), Dipak must have scored 2 points (since the total points that Dipak scored in the first three rounds is 2).

From (3), Dipak must have scored 2 points in the first round, - 1 point in the second round, and 1 point in the third round.

From this, we can fill in the points for the first three rounds, as shown below

(Note that with this information, the first question of the set can be answered)

In the next three rounds, from (1) and (2), Arun must have scored 1 point, Bankim must have scored 1 point, Charu must have scored - 3 points and Dipak must have scored - 3 points.

The total points scored by the four players are - 4. This is possible if the total points scored by the four players in the three rounds are (0, 0, - 4) OR (4, - 4, - 4) in any order.

However, we know that Arun must have scored 3 points in one of these three rounds (from (4)). Hence, the total points scored by the players in this round must be 0.

Hence, the four players must have scored (0, 0, - 4) points in these three rounds. In one round the points scored by the players must be (3, - 1, - 1, - 1), with Arun scoring 3 points.

In the round in which the total points scored by the four players is 4, they must have scored ( - 1, - 1, - 1, - 1).

Since Bankim scored a total of 1 point in these three rounds, and he scored - 1 point and - 1 point in the two rounds mentioned above, he must have scored 3 points in the other third.

Hence, in the remaining round, the four players must have scored (3, - 1, - 1, - 1), with Bankim scoring 3 points.

However, with the given information, we cannot deduce the round number corresponding to the above rounds.

Hence, we get the following table:

The bids by Arun, Bankim, Charu, Dipak in the first round were Hi, Lo, Lo, Hi.

Arun bid Hi in 4 rounds

Bankim bid Lo in 4 rounds

All four players made identical bids in 2 rounds

Dipak gained exactly 1 point in 1 round

In the second round, Arun was the only player to bid Hi.

From the given information, we can see that the points scored by the players in a round has the following possibilities:

HHHH: (-1, -1, -1, -1)

HHHL: (1, 1, 1, -3)

HHLL: (2, 2, -2, -2)

HLLL: (3, -1, -1, -1)

LLLL: (1, 1, 1, 1)

Also, the total points scored by the four players in a round can only be -4 or 0 or 4.

From (1), the total points scored by the four players combined in the first three rounds is 6 + 2 - 2 - 2 = 4.

Hence, in the first three rounds, the total points scored by the four players must be either (-4, 4, 4) OR (0, 0, 4), in any order.

Also, from (1), in the first three rounds, Arun scored 6 points. And from (2), Arun scored 7 points at the end of round 6. Hence, in the 4th, 5th, and 6th rounds, he must have scored 1 point.

From (4), Arun scored 3 points in exactly 2 rounds.

These two rounds cannot both be among the 4th, 5th, and 6th rounds because he scored a net of only 1 point in these three rounds combined.

Hence, Arun must have scored 3 points in one round in the 1st, the 2nd, and 3 rd rounds. If Arun scored 3 points in the first three rounds, then in that round, the total points scored by the four players combined must be 0 (in the case of HLLL).

Hence, the total points scored by the four players in the first three rounds must be (0, 0, 4). Among the first three rounds, in one round, the three players must have scored (3, -1, -1, -1), with Arun scoring 3 points.

Since in another round, the four players scored a total of 4 points, they must have bid LLLL (as it is the only case in which they can score 4 points in total). They must have scored (1, 1, 1, 1).

Since Arun scored a total of 6 points in the first three rounds, and he scored 3 points and 1 point in two of these rounds, he must have scored 2 points in the other round. This is possible only if the players bid HHLL and the scores of the four players must be (2, 2, - 2, - 2).

In the round that the players scored (3, - 1, - 1, - 1), Dipak must have scored - 1 point (since Arun scored 3 points).

In the round that the players scored (1, 1, 1, 1), Dipak must have scored 1 point.

In the round that the players scored (2, 2, - 2, - 2), Dipak must have scored 2 points (since the total points that Dipak scored in the first three rounds is 2).

From (3), Dipak must have scored 2 points in the first round, - 1 point in the second round, and 1 point in the third round.

From this, we can fill in the points for the first three rounds, as shown below

(Note that with this information, the first question of the set can be answered)

In the next three rounds, from (1) and (2), Arun must have scored 1 point, Bankim must have scored 1 point, Charu must have scored - 3 points and Dipak must have scored - 3 points.

The total points scored by the four players are - 4. This is possible if the total points scored by the four players in the three rounds are (0, 0, - 4) OR (4, - 4, - 4) in any order.

However, we know that Arun must have scored 3 points in one of these three rounds (from (4)). Hence, the total points scored by the players in this round must be 0.

Hence, the four players must have scored (0, 0, - 4) points in these three rounds. In one round the points scored by the players must be (3, - 1, - 1, - 1), with Arun scoring 3 points.

In the round in which the total points scored by the four players is 4, they must have scored ( - 1, - 1, - 1, - 1).

Since Bankim scored a total of 1 point in these three rounds, and he scored - 1 point and - 1 point in the two rounds mentioned above, he must have scored 3 points in the other third.

Hence, in the remaining round, the four players must have scored (3, - 1, - 1, - 1), with Bankim scoring 3 points.

However, with the given information, we cannot deduce the round number corresponding to the above rounds.

Hence, we get the following table:

The bids by Arun, Bankim, Charu, Dipak in the first round were Hi, Lo, Lo, Hi.

Arun bid Hi in 4 rounds

Bankim bid Lo in 4 rounds

All four players made identical bids in 2 rounds

Dipak gained exactly 1 point in 1 round

In the second round, Arun was the only player to bid Hi.

From the given information, we can see that the points scored by the players in a round has the following possibilities:

HHHH: (-1, -1, -1, -1)

HHHL: (1, 1, 1, -3)

HHLL: (2, 2, -2, -2)

HLLL: (3, -1, -1, -1)

LLLL: (1, 1, 1, 1)

Also, the total points scored by the four players in a round can only be -4 or 0 or 4.

From (1), the total points scored by the four players combined in the first three rounds is 6 + 2 - 2 - 2 = 4.

Hence, in the first three rounds, the total points scored by the four players must be either (-4, 4, 4) OR (0, 0, 4), in any order.

Also, from (1), in the first three rounds, Arun scored 6 points. And from (2), Arun scored 7 points at the end of round 6. Hence, in the 4th, 5th, and 6th rounds, he must have scored 1 point.

From (4), Arun scored 3 points in exactly 2 rounds.

These two rounds cannot both be among the 4th, 5th, and 6th rounds because he scored a net of only 1 point in these three rounds combined.

Hence, Arun must have scored 3 points in one round in the 1st, the 2nd, and 3 rd rounds. If Arun scored 3 points in the first three rounds, then in that round, the total points scored by the four players combined must be 0 (in the case of HLLL).

Hence, the total points scored by the four players in the first three rounds must be (0, 0, 4). Among the first three rounds, in one round, the three players must have scored (3, -1, -1, -1), with Arun scoring 3 points.

Since in another round, the four players scored a total of 4 points, they must have bid LLLL (as it is the only case in which they can score 4 points in total). They must have scored (1, 1, 1, 1).

Since Arun scored a total of 6 points in the first three rounds, and he scored 3 points and 1 point in two of these rounds, he must have scored 2 points in the other round. This is possible only if the players bid HHLL and the scores of the four players must be (2, 2, - 2, - 2).

In the round that the players scored (3, - 1, - 1, - 1), Dipak must have scored - 1 point (since Arun scored 3 points).

In the round that the players scored (1, 1, 1, 1), Dipak must have scored 1 point.

In the round that the players scored (2, 2, - 2, - 2), Dipak must have scored 2 points (since the total points that Dipak scored in the first three rounds is 2).

From (3), Dipak must have scored 2 points in the first round, - 1 point in the second round, and 1 point in the third round.

From this, we can fill in the points for the first three rounds, as shown below

(Note that with this information, the first question of the set can be answered)

In the next three rounds, from (1) and (2), Arun must have scored 1 point, Bankim must have scored 1 point, Charu must have scored - 3 points and Dipak must have scored - 3 points.

The total points scored by the four players are - 4. This is possible if the total points scored by the four players in the three rounds are (0, 0, - 4) OR (4, - 4, - 4) in any order.

However, we know that Arun must have scored 3 points in one of these three rounds (from (4)). Hence, the total points scored by the players in this round must be 0.

Hence, the four players must have scored (0, 0, - 4) points in these three rounds. In one round the points scored by the players must be (3, - 1, - 1, - 1), with Arun scoring 3 points.

In the round in which the total points scored by the four players is 4, they must have scored ( - 1, - 1, - 1, - 1).

Since Bankim scored a total of 1 point in these three rounds, and he scored - 1 point and - 1 point in the two rounds mentioned above, he must have scored 3 points in the other third.

Hence, in the remaining round, the four players must have scored (3, - 1, - 1, - 1), with Bankim scoring 3 points.

However, with the given information, we cannot deduce the round number corresponding to the above rounds.

Hence, we get the following table:

The bids by Arun, Bankim, Charu, Dipak in the first round were Hi, Lo, Lo, Hi.

Arun bid Hi in 4 rounds

Bankim bid Lo in 4 rounds

All four players made identical bids in 2 rounds

Dipak gained exactly 1 point in 1 round

In the second round, Arun was the only player to bid Hi.

From the given information, we can see that the points scored by the players in a round has the following possibilities:

HHHH: (-1, -1, -1, -1)

HHHL: (1, 1, 1, -3)

HHLL: (2, 2, -2, -2)

HLLL: (3, -1, -1, -1)

LLLL: (1, 1, 1, 1)

Also, the total points scored by the four players in a round can only be -4 or 0 or 4.

From (1), the total points scored by the four players combined in the first three rounds is 6 + 2 - 2 - 2 = 4.

Hence, in the first three rounds, the total points scored by the four players must be either (-4, 4, 4) OR (0, 0, 4), in any order.

Also, from (1), in the first three rounds, Arun scored 6 points. And from (2), Arun scored 7 points at the end of round 6. Hence, in the 4th, 5th, and 6th rounds, he must have scored 1 point.

From (4), Arun scored 3 points in exactly 2 rounds.

These two rounds cannot both be among the 4th, 5th, and 6th rounds because he scored a net of only 1 point in these three rounds combined.

Hence, Arun must have scored 3 points in one round in the 1st, the 2nd, and 3 rd rounds. If Arun scored 3 points in the first three rounds, then in that round, the total points scored by the four players combined must be 0 (in the case of HLLL).

Hence, the total points scored by the four players in the first three rounds must be (0, 0, 4). Among the first three rounds, in one round, the three players must have scored (3, -1, -1, -1), with Arun scoring 3 points.

Since in another round, the four players scored a total of 4 points, they must have bid LLLL (as it is the only case in which they can score 4 points in total). They must have scored (1, 1, 1, 1).

Since Arun scored a total of 6 points in the first three rounds, and he scored 3 points and 1 point in two of these rounds, he must have scored 2 points in the other round. This is possible only if the players bid HHLL and the scores of the four players must be (2, 2, - 2, - 2).

In the round that the players scored (3, - 1, - 1, - 1), Dipak must have scored - 1 point (since Arun scored 3 points).

In the round that the players scored (1, 1, 1, 1), Dipak must have scored 1 point.

In the round that the players scored (2, 2, - 2, - 2), Dipak must have scored 2 points (since the total points that Dipak scored in the first three rounds is 2).

From (3), Dipak must have scored 2 points in the first round, - 1 point in the second round, and 1 point in the third round.

From this, we can fill in the points for the first three rounds, as shown below

(Note that with this information, the first question of the set can be answered)

In the next three rounds, from (1) and (2), Arun must have scored 1 point, Bankim must have scored 1 point, Charu must have scored - 3 points and Dipak must have scored - 3 points.

The total points scored by the four players are - 4. This is possible if the total points scored by the four players in the three rounds are (0, 0, - 4) OR (4, - 4, - 4) in any order.

However, we know that Arun must have scored 3 points in one of these three rounds (from (4)). Hence, the total points scored by the players in this round must be 0.

Hence, the four players must have scored (0, 0, - 4) points in these three rounds. In one round the points scored by the players must be (3, - 1, - 1, - 1), with Arun scoring 3 points.

In the round in which the total points scored by the four players is 4, they must have scored ( - 1, - 1, - 1, - 1).

Since Bankim scored a total of 1 point in these three rounds, and he scored - 1 point and - 1 point in the two rounds mentioned above, he must have scored 3 points in the other third.

Hence, in the remaining round, the four players must have scored (3, - 1, - 1, - 1), with Bankim scoring 3 points.

However, with the given information, we cannot deduce the round number corresponding to the above rounds.

Hence, we get the following table:

The bids by Arun, Bankim, Charu, Dipak in the first round were Hi, Lo, Lo, Hi.

Arun bid Hi in 4 rounds

Bankim bid Lo in 4 rounds

All four players made identical bids in 2 rounds

Dipak gained exactly 1 point in 1 round

In the second round, Arun was the only player to bid Hi.

From the given information, we can see that the points scored by the players in a round has the following possibilities:

HHHH: (-1, -1, -1, -1)

HHHL: (1, 1, 1, -3)

HHLL: (2, 2, -2, -2)

HLLL: (3, -1, -1, -1)

LLLL: (1, 1, 1, 1)

Also, the total points scored by the four players in a round can only be -4 or 0 or 4.

From (1), the total points scored by the four players combined in the first three rounds is 6 + 2 - 2 - 2 = 4.

Hence, in the first three rounds, the total points scored by the four players must be either (-4, 4, 4) OR (0, 0, 4), in any order.

Also, from (1), in the first three rounds, Arun scored 6 points. And from (2), Arun scored 7 points at the end of round 6. Hence, in the 4th, 5th, and 6th rounds, he must have scored 1 point.

From (4), Arun scored 3 points in exactly 2 rounds.

These two rounds cannot both be among the 4th, 5th, and 6th rounds because he scored a net of only 1 point in these three rounds combined.

Hence, Arun must have scored 3 points in one round in the 1st, the 2nd, and 3 rd rounds. If Arun scored 3 points in the first three rounds, then in that round, the total points scored by the four players combined must be 0 (in the case of HLLL).

Hence, the total points scored by the four players in the first three rounds must be (0, 0, 4). Among the first three rounds, in one round, the three players must have scored (3, -1, -1, -1), with Arun scoring 3 points.

Since in another round, the four players scored a total of 4 points, they must have bid LLLL (as it is the only case in which they can score 4 points in total). They must have scored (1, 1, 1, 1).

Since Arun scored a total of 6 points in the first three rounds, and he scored 3 points and 1 point in two of these rounds, he must have scored 2 points in the other round. This is possible only if the players bid HHLL and the scores of the four players must be (2, 2, - 2, - 2).

In the round that the players scored (3, - 1, - 1, - 1), Dipak must have scored - 1 point (since Arun scored 3 points).

In the round that the players scored (1, 1, 1, 1), Dipak must have scored 1 point.

In the round that the players scored (2, 2, - 2, - 2), Dipak must have scored 2 points (since the total points that Dipak scored in the first three rounds is 2).

From (3), Dipak must have scored 2 points in the first round, - 1 point in the second round, and 1 point in the third round.

From this, we can fill in the points for the first three rounds, as shown below

(Note that with this information, the first question of the set can be answered)

In the next three rounds, from (1) and (2), Arun must have scored 1 point, Bankim must have scored 1 point, Charu must have scored - 3 points and Dipak must have scored - 3 points.

The total points scored by the four players are - 4. This is possible if the total points scored by the four players in the three rounds are (0, 0, - 4) OR (4, - 4, - 4) in any order.

However, we know that Arun must have scored 3 points in one of these three rounds (from (4)). Hence, the total points scored by the players in this round must be 0.

Hence, the four players must have scored (0, 0, - 4) points in these three rounds. In one round the points scored by the players must be (3, - 1, - 1, - 1), with Arun scoring 3 points.

In the round in which the total points scored by the four players is 4, they must have scored ( - 1, - 1, - 1, - 1).

Since Bankim scored a total of 1 point in these three rounds, and he scored - 1 point and - 1 point in the two rounds mentioned above, he must have scored 3 points in the other third.

Hence, in the remaining round, the four players must have scored (3, - 1, - 1, - 1), with Bankim scoring 3 points.

However, with the given information, we cannot deduce the round number corresponding to the above rounds.

Hence, we get the following table:

The bids by Arun, Bankim, Charu, Dipak in the first round were Hi, Lo, Lo, Hi.

Arun bid Hi in 4 rounds

Bankim bid Lo in 4 rounds

All four players made identical bids in 2 rounds

Dipak gained exactly 1 point in 1 round

In the second round, Arun was the only player to bid Hi.

The correct statement is option 1) Shape X has three sides. Since all triangles have three sides and Shape X is a triangle, it can be inferred that Shape X has three sides.

In the Fibonacci sequence, each term is obtained by adding the two preceding terms. To find the next term, we add the last two terms. 5 + 3 = 8 & 8 + 5 = 13

Therefore, the next term in the series is 8, 13.