GATE CS 2015 Set 2 Q.9 (GA Q.9): Analytical and Logical Reasoning

If $p, q, r, s$ are distinct integers such that:

f(p, q, r, s) = \max(p, q, r, s)

g(p, q, r, s) = \min(p, q, r, s)

h(p, q, r, s) = \text{remainder of } (p \times q) / (r \times s) \text{ if } (p \times q) > (r \times s) \text{ or remainder of } (r \times s) / (p \times q) \text{ if } (r \times s) > (p \times q)

Also a function $fgh(p, q, r, s) = f(p, q, r, s) \times g(p, q, r, s) \times h(p, q, r, s)$ .
Also the same operations are valid with two variable functions of the form $f(p, q)$ .
What is the value of $fg(h(2, 5, 7, 3), 4, 6, 8)$ ?

Your answer

Official answer and solution

Official answer: 8
From: Official GATE 2015 answer key

Solution

Evaluate the innermost custom operation $h(2, 5, 7, 3)$ first, then evaluate the composite function $fg$ .

Step 1: Compute $h(2, 5, 7, 3)$ .
Here, $p = 2, q = 5, r = 7, s = 3$ .

p \times q = 2 \times 5 = 10

r \times s = 7 \times 3 = 21

Since $(r \times s) > (p \times q)$ , the rule specifies taking the remainder of $(r \times s) / (p \times q)$ :

\text{remainder of } 21 / 10 = 1.

Thus, $h(2, 5, 7, 3) = 1$ .

Step 2: Evaluate $fg(h(2, 5, 7, 3), 4, 6, 8) = fg(1, 4, 6, 8)$ .
By the problem's definition, the composite function $fgh$ is the product of $f$ , $g$ , and $h$ . Similarly, $fg$ is the product of $f$ and $g$ :

fg(p, q, r, s) = f(p, q, r, s) \times g(p, q, r, s)

For the input tuple $(1, 4, 6, 8)$ :

f(1, 4, 6, 8) = \max(1, 4, 6, 8) = 8

g(1, 4, 6, 8) = \min(1, 4, 6, 8) = 1

Step 3: Multiply the two results:

fg(1, 4, 6, 8) = 8 \times 1 = 8.

Final answer

Common trap

Computing quotient instead of remainder in function $h$ , which would give $2$ instead of $1$ .

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

Source

Paper: GATE 2015 Computer Science and Information Technology (CS) Session 2
Question: 9 of 65, printed as GA Q.9
Section: General Aptitude

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