Q.4 Five numbers 10, 7, 5, 4 and 2 are to be arranged in a sequence from left to right following
the directions given below:
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?
(A) 2 (B) 4 (C) 7 (D) 10
10, 7, 5, 4, 2 Number Sequence Puzzle Solution
The numbers 10, 7, 5, 4, and 2 must form a sequence where no two odd or even numbers adjoin, the second equals half the first, and the middle equals twice the last. The valid arrangement is 10-5-4-7-2, making 7 the second from the right.
Odd-Even Constraint
Three even numbers (10, 4, 2) and two odd numbers (7, 5) exist. Even positions (1st, 3rd, 5th) must hold evens to alternate with odds in 2nd and 4th, preventing adjacent pairs.
Second-Half-First Rule
Only 10 (even) halves to 5 (odd), fitting 1st-2nd spots: 10-5-_-_-_. No other pair works, as 4 halves to 2 (both even).
Middle-Twice-Last Rule
Remaining: 4, 2, 7. Fourth must be odd (7), yielding 10-5-_-_7-_. Middle (3rd) as 4 doubles last as 2: 10-5-4-7-2. Alternation holds: E-O-E-O-E.
Option Analysis
| Option | Valid? | Explanation |
|---|---|---|
| (A) 2 | No | Fits 5th only; violates if second-right. |
| (B) 4 | No | Fits 3rd only; even cannot precede 7 (odd-even mismatch). |
| (C) 7 | Yes | Positions fourth exactly. |
| (D) 10 | No | Fits 1st only; even cannot end sequence properly. |
The five numbers 10 7 5 4 2 sequence puzzle tests logical arrangement skills for competitive exams like GATE or banking tests. Candidates arrange them left-to-right under three rules: no adjacent odds/evens, second as half the first, middle twice the last. This number sequence arrangement question demands step-wise elimination.
Keyphrase Usage
Focus on five numbers 10 7 5 4 2 sequence reveals even-odd pattern first. With three evens, place at 1-3-5; odds at 2-4.
Half Rule Breakdown
Only 10/2=5 qualifies, locking 10-5-_-_-_.
Twice Rule Completion
7 fills fourth (odd); 4=2×2 assigns middle-last: 10-5-4-7-2.
Exam Tips
Practice reveals second number from right as 7 (option C). Similar puzzles build speed for IIT JAM or SSC reasoning sections.
