ISRO EC 2025 Q.90: solution and answer

Official answer: CSource: ISRO's final answer key of 15 May 2026

1. Read the sectors in order, clockwise from the sector holding 3: $3,5,8,13,22,?$.

2. Take successive differences: $5-3=2,8-5=3,13-8=5,22-13=9$, giving $2,3,5,9,\dots$

3. Take the differences of those: $3-2=1,5-3=2,9-5=4$, so the second differences are $1,2,4$ and double each time.

4. The next second difference is $8$, so the next first difference is $9+8=17$. (Equivalently, the first differences are $2^0+1,2^1+1,2^2+1,2^3+1$, and the next is $2^4+1=17$.)

5. Hence $?=22+17=39$.

6. Check against the options: $45$, $25$ and $78$ would need first differences of $23$, $3$ and $56$, none of which fit the pattern $2,3,5,9,17$. Only $39$ does.