GATE CS 2025 Set 2 Q8 — General Aptitude

To find the correct relation, we can test the options by substituting the values for $i > 0$ from the given table.

Step 1: Verify the relation for $X(i)$

Let us test the relation $X(i) = X(i-1) + I(i)$ for $i = 1, 2, 3$:

• For $i = 1$: $$X(1) = X(0) + I(1) = 20 + (-4) = 16$$ This matches the table value $X(1) = 16$.
• For $i = 2$: $$X(2) = X(1) + I(2) = 16 + 10 = 26$$ This matches the table value $X(2) = 26$.
• For $i = 3$: $$X(3) = X(2) + I(3) = 26 + 15 = 41$$ This matches the table value $X(3) = 41$.

Thus, the relation $X(i) = X(i-1) + I(i)$ is correct.

Step 2: Verify the relation for $Y(i)$

Let us test the relation $Y(i) = Y(i-1) \times I(i)$ for $i = 1, 2, 3$:

• For $i = 1$: $$Y(1) = Y(0) \times I(1) = 20 \times (-4) = -80$$ This matches the table value $Y(1) = -80$.
• For $i = 2$: $$Y(2) = Y(1) \times I(2) = -80 \times 10 = -800$$ This matches the table value $Y(2) = -800$.
• For $i = 3$: $$Y(3) = Y(2) \times I(3) = -800 \times 15 = -12000$$ This matches the table value $Y(3) = -12000$.

Thus, the relation $Y(i) = Y(i-1) \times I(i)$ is also correct.

Conclusion

Both relations in Option A match the given data perfectly.