GATE 2025 IN GA Q.8: solution and answer

GATE 2025 · INGA Q.8 · 2 marks · MCQ

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 | $- 80$ | $- 800$ | $- 12000$ |

GATE 2025 IN GA question 8: A table with 4 rows and 5 columns. — Figure from the GATE 2025 IN paper. It is part of the question.

(A)
$X (i) = X (i - 1) + I (i); Y (i) = Y (i - 1) I (i); i > 0$
(B)
$X (i) = X (i - 1) I (i); Y (i) = Y (i - 1) + I (i); i > 0$
(C)
$X (i) = X (i - 1) I (i); Y (i) = Y (i - 1) I (i); i > 0$
(D)
$X (i) = X (i - 1) + I (i); Y (i) = Y (i - 1) I (i - 1); i > 0$

Answer and solution

ANSWER

The answer is (A): $X (i) = X (i - 1) + I (i)$ and $Y (i) = Y (i - 1) I (i)$ for $i > 0$ .

Official answer: ASource: Official answer key, GATE 2025 IN (IIT Roorkee)

Start with $X$ . Adding each input to the previous output fits every column: $20 + (- 4) = 16$ , $16 + 10 = 26$ , $26 + 15 = 41$ . So $X (i) = X (i - 1) + I (i)$ .
Multiplying does not fit $X$ : $X (0) I (1) = 20 \times (- 4) = - 80 \neq = 16$ . That rules out (B) and (C).
Now $Y$ . Multiplying the previous output by the current input fits every column: $20 \times (- 4) = - 80$ , $(- 80) \times 10 = - 800$ , $(- 800) \times 15 = - 12000$ . So $Y (i) = Y (i - 1) I (i)$ .
Check the lagged form in (D): $Y (1) = Y (0) I (0) = 20 \times 20 = 400 \neq = - 80$ . That rules out (D).
Only (A) has both rules: $X (i) = X (i - 1) + I (i)$ and $Y (i) = Y (i - 1) I (i)$ for $i > 0$ .

KEY IDEA

Test each candidate rule on the first step ( $i = 1$ ), then confirm the survivor on every later column. $X$ grows by adding the current input and $Y$ grows by multiplying by the current input. Both use $I (i)$ , not the lagged $I (i - 1)$ .

WATCH OUT FOR

Checking only one column, or only one of the two outputs. Option (D) has the right rule for $X$ , so it looks correct until you work out $Y (1) = Y (0) I (0) = 400$ , which is not $- 80$ . A student who checks only $i = 1$ against the wrong row can also be fooled, because $X (0) = Y (0) = I (0) = 20$ all start from the same value.

From the GATE 2025 IN paper. Every question of this paper · Download the full paper · All 9 Data interpretation questions, with notes

GATE 2025 IN GA Q.8: solution and answer

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