CAT Modern Maths Practice Questions: Chapter-wise Weightage and Solved Questions

CAT Modern Maths: 3 chapters, 0 practice questions and one solved question from each chapter.

Modern Maths Chapter Matrix

Chapter	PYQs	Share of unit PYQs	Practice questions
Permutations, Combinations and Counting	0	0%	0
Progressions, Sequences and Series	0	0%	0
Sets, Venn Diagrams and Functions	0	0%	0

One Solved Question from Each Modern Maths Chapter

Question 1 · Quantitative Ability NAT

Thirty identical candies are to be given to five children. Every child must receive some candies, and no child may receive an odd number of candies. How many distributions are possible?

Correct Answer:

1001

Step-by-Step Solution

Key idea: this is a parity-restricted identical-object distribution question. The phrase "some candies" means each child gets at least one, and "no child may receive an odd number" means each share is even. So each share must be a positive even number.

Step 1: Let child $i$ receive $x_{i}$ candies. We need

$x_{1} + x_{2} + x_{3} + x_{4} + x_{5} = 30$ ,

where each $x_{i}$ is even and positive.

Step 2: Use the substitution $x_{i} = 2 y_{i}$ . Since $x_{i}$ is positive even, $y_{i}$ must be a positive integer: $y_{i} \geq 1$ .

Step 3: Substitute into the total:

$2 y_{1} + 2 y_{2} + 2 y_{3} + 2 y_{4} + 2 y_{5} = 30$ .

Divide by $2$ :

$y_{1} + y_{2} + y_{3} + y_{4} + y_{5} = 15$ .

Step 4: Count positive integer solutions. For $5$ positive variables summing to $15$ , the number is

$(5 - 1 15 - 1) = (4 14)$ .

Step 5: Compute:

$(4 14) = \frac{14 \times 13 \times 12 \times 11}{4 \times 3 \times 2 \times 1} = 1001$ .

Answer: $1001$ .

Common trap: if you allow $y_{i} = 0$ , you are allowing a child to receive zero candies. That violates "every child must receive some candies".

chapter

CAT Modern Maths Practice Questions: Chapter-wise Weightage and Solved Questions

CAT Modern Maths: 3 chapters, 0 practice questions and one solved question from each chapter.

A question from this chapter

Question 1

Thirty identical candies are to be given to five children. Every child must receive some candies, and no child may receive an odd number of candies. How many distributions are possible?

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