CAT 2025 Slot 1 QA Question 4

Type-in-the-answer (no negative marking) · Number Systems · Integral Solutions · Try it, then check the answer and solution below.

CAT 2025 Slot 1QANumber Systems • Integral SolutionsModerate

The number of distinct pairs of integers

(x, y)

satisfying the inequalities

x > y \geq 3

and

x + y < 14

TITA Answer:

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Official Convenor Answer Key: 16

Answer and solution

Answer: 16

📌 Core Concept

To find the number of integer pairs

(x, y)

satisfying

x > y \geq 3

and $x + y < 14 , we systematically analyze each possible value of $y

starting from 3 and determine the corresponding valid

x$ values.

🔢 Step-by-Step Solution

Fix

y = 3

x > 3

implies

x \geq 4

x + 3 < 14

implies

x < 11

Possible

x

values: 4, 5, 6, 7, 8, 9, 10.

Number of pairs:

2. Fix

y = 4

x > 4

implies

x \geq 5

x + 4 < 14

implies

x < 10

Possible

x

values: 5, 6, 7, 8, 9.

Number of pairs:

3. Fix

y = 5

x > 5

implies

x \geq 6

x + 5 < 14

implies

x < 9

Possible

x

values: 6, 7, 8.

Number of pairs:

4. Fix

y = 6

x > 6

implies

x \geq 7

x + 6 < 14

implies

x < 8

Possible

x

value:

- Number of pairs:

5. For

y \geq 7

x > y

implies

x \geq y + 1

x + y < 14

implies

x < 14 - y

For

y = 7 , x

must be

CAT 2025 Slot 1 QA Question 4

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