Five numbers 10, 7, 5, 4, 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
GATE 2019 · General Aptitude · Logical Reasoning · medium
Answer: C. 7
Determine the parity pattern: Numbers: 10 (even), 7 (odd), 5 (odd), 4 (even), 2 (even). Count: 3 even, 2 odd. For no two adjacent numbers of the same parity, with 3 even and 2 odd among 5 positions, the only valid pattern is E-O-E-O-E (positions 1, 3, 5 = even; positions 2, 4 = odd).
Apply Constraint 2: position 2 = position 1 / 2: Position 2 must be odd (from step 1). Odd numbers: {7, 5}. Check which even number halves to give an odd number in our set: 10 / 2 = 5 (yes, 5 is in set and odd). 4 / 2 = 2 (even, not allowed for position 2). So: Position 1 = 10, Position 2 = 5.
Apply Constraint 3: position 3 = 2 x position 5: Remaining even numbers for positions 3 and 5: {4, 2} (since 10 is used at position 1). Check: 4 = 2 * 2 (yes). So Position 3 = 4, Position 5 = 2.
Place remaining number at position 4: Numbers used: 10 (pos 1), 5 (pos 2), 4 (pos 3), 2 (pos 5). Remaining number: 7. Position 4 = 7. Final arrangement: 10, 5, 4, 7, 2.
Read off the second number from the right: Sequence: pos1=10, pos2=5, pos3=4, pos4=7, pos5=2. Second from right = position 4 = 7.