1. No two odd or even numbers are next to each other.
2. The second number from the left is exactly half of the left-most number.
3. The middle number is exactly twice the right-most number.
Which is the second number from the right?
Analyzing the Constraints
The problem requires arranging the numbers {10, 7, 5, 4, 2} into a sequence $N_1, N_2, N_3, N_4, N_5$ based on three rules.
- Rule 1: Alternating Parity No two odd or even numbers can be adjacent. The available numbers are {10, 4, 2} (Even) and {7, 5} (Odd). Since there are 3 even and 2 odd numbers, the sequence must follow the pattern: Even, Odd, Even, Odd, Even (E O E O E).
- Rule 2: Left-Most Relation The second number from the left ($N_2$) is half the left-most number ($N_1$). $N_2 = N_1 / 2$.
- Rule 3: Middle Number Relation The middle number ($N_3$) is twice the right-most number ($N_5$). $N_3 = 2 \times N_5$.
Applying Rule 2
We test possible pairs for ($N_1, N_2$) from the set {10, 7, 5, 4, 2} that fit the E O pattern:
- If $N_1 = 10$ (E), then $N_2 = 10 / 2 = 5$ (O). Both numbers are available and fit the E O pattern. This is a valid possibility.
- If $N_1 = 4$ (E), then $N_2 = 4 / 2 = 2$ (E). Both are available, but this violates the E O pattern (Rule 1).
- If $N_1 = 2$ (E), then $N_2 = 2 / 2 = 1$. 1 is not in the set.
Therefore, the sequence must start with 10, 5. Sequence: 10, 5, _, _, _.
Applying Rule 3
The sequence pattern is E O E O E. We have $N_1=10$ and $N_2=5$. The remaining numbers are {7, 4, 2}. The positions $N_3$ and $N_5$ must be filled by the remaining even numbers {4, 2}, and $N_4$ must be the odd number {7}.
We need to check Rule 3 ($N_3 = 2 \times N_5$) using the available even numbers {4, 2} for $N_3$ and $N_5$:
- If $N_5 = 2$, then $N_3 = 2 \times 2 = 4$. Both 4 and 2 are available and fit the required E O E pattern. This works.
- If $N_5 = 4$, then $N_3 = 2 \times 4 = 8$. 8 is not available in the set.
Thus, $N_3 = 4$ and $N_5 = 2$. The only remaining number, 7, must be $N_4$. Sequence: 10, 5, 4, 7, 2.
Determining the Final Answer
The complete sequence is 10, 5, 4, 7, 2.
The question asks for the second number from the right. Counting from the right:
- Right-most number ($N_5$): 2
- Second number from the right ($N_4$): 7
The second number from the right is 7.
Important Questions from Puzzles
In the 4 x 4 array shown below, each cell of the first three rows has either a cross (X) or a number.
1 X 4 3 X 5 5 4 3 X 6 X
The number in a cell represents the count of the immediate neighboring cells (left, right, top, bottom, diagonals) NOT having a cross (X). Given that the last row has no crosses (X), the sum of the four numbers to be filled in the last row is- Three children P, Q, R and two grown-ups X, Y play a badminton doubles tournament. X and Y are parents to two of the children playing. The child of X is not the same as the child of Y. Exactly one of the children does not have a parent playing in the tournament. The following rules are followed:
(i) A parent and his/her child cannot be on the same team.
(ii) A match can feature at most one parent and his/her child, that is, a maximum of one parent-child pair can play in a match.
The following matches were played:TEAM 1 TEAM 2 MATCH 1 P and X Q and R MATCH 2 P and R X and Y MATCH 3 R and X Q and Y
Which one of the following options is correct? - Rishi and Swathi are students of Class 5. Pavan and Tanvi are students of Class 4. Rishi and Pavan are boys. Swathi and Tanvi are girls. The four students played a total of three games of chess. The games were played one after another. A player who lost a game did not participate in any more games. It was observed that:
(i) the first game was the only game where two students of the same class played against each other,
(ii) the students of Class 5 won more games than the students of Class 4, and
(iii) the boys won two games and the girls won one game.
The student who did not lose any game is __________. - In the 2020 summer Olympics’ Javelin throw finals, Neeraj Chopra exhibited a spectacular performance to win the gold medal. The silver medal was won by Jakub Vadlejch and the bronze medal was won by Vitezlav Vesely. There were six rounds of throws with each athlete having one throw per round. The best of all the throws of each athlete is considered for the medal. Following were the observations about the throws:
i. The first and second rounds were dominated by Neeraj Chopra with a gold medal performance in his second throw, while the other two athletes did not have any medal winning throws in these rounds.
ii. The throws in the last round by both Jakub Vadlejch and Vitezlav Vesely were fouls and were not considered for scoring.
iii. After four rounds, Vitezlav Vesely was in the second position and could not improve upon his best throw in the succeeding rounds.
iv. In the fourth round, the throw by Jakub Vadlejch was the best in that round.
In which round did Vitezlav Vesely have his best throw? Students applying for hostel rooms are allotted rooms in order of seniority. Students already staying in a room will move if they get a room in their preferred list. Preferences of lower ranked applicants are ignored during allocation.
Given the data below, which room will Ajit stay in?Names Student seniority Current room Room preference list Amar 1 P R, S, Q Akbar 2 None R, S Anthony 3 Q P Ajit 4 S Q, P, R
