SBI PO Prelims 8 Mar 2025 Shift 1 Paper

Concept:Compare the number of digits between two digits in the given number with the number of digits between them in the natural order $1,2,3,4,5,6,7,8,9$.Explanation:The given number is $1537862$.Write digits with their positions (left to right):$1$ at position $1$, $5$ at $2$, $3$ at $3$, $7$ at $4$, $8$ at $5$, $6$ at $6$, $2$ at $7$.For any pair $(a,b)$, count digits between them in the number = $|\text{pos}(a) - \text{pos}(b)| - 1$.Count digits between them in numerical order = $|a - b| - 1$.The condition is that these two counts are equal, which simplifies to $|\text{pos}(a) - \text{pos}(b)| = |a - b|$.Now check all unordered pairs that satisfy this:• $(1,3)$: positions $1$ and $3$, difference in positions $=2$, numerical difference $=2$. (Digits between: one digit $2$)• $(1,6)$: positions $1$ and $6$, difference $=5$, numerical difference $=5$. (Digits between: $2,3,4,5$)• $(5,7)$: positions $2$ and $4$, difference $=2$, numerical difference $=2$. (Digit $6$)• $(5,8)$: positions $2$ and $5$, difference $=3$, numerical difference $=3$. (Digits $6,7$)• $(3,6)$: positions $3$ and $6$, difference $=3$, numerical difference $=3$. (Digits $4,5$)• $(7,8)$: positions $4$ and $5$, difference $=1$, numerical difference $=1$. (No digit between)Thus total $6$ such pairs.Answer:E. Six