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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?

  1. $2$
  2. $4$
  3. $7$
  4. $10$
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  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.
    So, the left most number must be even and its half must be odd which comes next. Only options are $10,5$
  3. The middle number is exactly twice the right-most number.
    Middle number must be even and only options left are $2$ and $4$. Since $1$ is not there, $4$ must be the middle and $2$ the right most. 

Thus we get $$10\quad 5 \quad 4 \quad 7 \quad 2$$

Required answer is $7.$

Option C.


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