GATE CS 2025 Set 2 Q.8: Data Interpretation and Graphs

Which one of the following options is correct for the given data in the table?

Iteration (i)	0	1	2	3
Input (I)	20	-4	10	15
Output (X)	20	16	26	41
Output (Y)	20	-80	-800	-12000

$X(i) = X(i - 1) + I(i); \quad Y(i) = Y(i - 1)I(i); \quad i > 0$

$X(i) = X(i - 1)I(i); \quad Y(i) = Y(i - 1) + I(i); \quad i > 0$

$X(i) = X(i - 1)I(i); \quad Y(i) = Y(i - 1)I(i); \quad i > 0$

$X(i) = X(i - 1) + I(i); \quad Y(i) = Y(i - 1)I(i - 1); \quad i > 0$

Official answer and solution

Solution

Check how $X(i)$ and $Y(i)$ are computed from the previous output and current input $I(i)$ for $i = 1, 2, 3$ .

From the table:

For $X(i)$ : $X(1) = 20 + (-4) = 16$ , $X(2) = 16 + 10 = 26$ , and $X(3) = 26 + 15 = 41$ . Thus $X(i) = X(i - 1) + I(i)$ for $i > 0$ .
For $Y(i)$ : $Y(1) = 20 \times (-4) = -80$ , $Y(2) = (-80) \times 10 = -800$ , and $Y(3) = (-800) \times 15 = -12000$ . Thus $Y(i) = Y(i - 1)I(i)$ for $i > 0$ .

Final answer

Option (A)

Common trap

Selecting (D) without noticing $I(i - 1)$ instead of $I(i)$ in the formula for $Y(i)$ .

The answer is the one in the official GATE answer key. The solution is this site's own explanation.

Paper: GATE 2025 Computer Science and Information Technology - Session 2 (CS2)
Question: 8 of 65
Section: General Aptitude

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