Five numbers 10, 7, 5, 4 and 2 are to be arranged in a sequence left to right following:
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?
Options:
(A) 2
(B) 4
(C) 7
(D) 10
Official Answer Key:
C
Step-by-Step Solution & Explanation
Numbers: 10,7,5,4,2 (odd: 7,5; even: 10,4,2). Rule 1 forces strict alternation O-E-O-E-E is impossible with 3 evens/2 odds unless the pattern is E-O-E-O-E. Rule 2: position2 = position1/2, so position1 must be even and twice position2. Testing E-O-E-O-E with position1=10, position2=5 (10/2=5 ✓, both valid parities). Remaining numbers {7,4,2} fill positions 3,4,5 with position3 even, position4 odd(=7), position5 even. Rule 3: middle (position3) = 2×position5(right-most). From {4,2} for positions 3 and 5: 4=2×2 ✓, so position3=4, position5=2. Sequence: 10,5,4,7,2. Second from the right = position 4 = 7. Answer: (C) 7.
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