CAT Arithmetic Short Notes: Chapter-wise Weightage and Solved Questions

CAT Arithmetic: 6 chapters, 0 practice questions and one solved question from each chapter.

Arithmetic Chapter Matrix

Chapter	PYQs	Share of unit PYQs	Practice questions
Arithmetic Word Problems and Quantity Distribution	0	0%	0
Mixtures, Alligation and Replacement	0	0%	0
Profit, Loss, Discounts and Interest	0	0%	0
Ratios, Percentages, Averages and Population	0	0%	0
Time, Speed, Distance, Boats and Trains	0	0%	0
Time, Work, Pipes and Productivity	0	0%	0

One Solved Question from Each Arithmetic Chapter

Question 1 · Quantitative Ability NAT

In a school, $120$ students each choose exactly one of Science, Arts or Commerce. The fees are ₹ $1400$ , ₹ $1000$ and ₹ $700$ respectively. The total fee collected is ₹ $119000$ . If the number of Science students is fewer than the number of Arts students, what is the maximum possible number of Science students?

Correct Answer:

Step-by-Step Solution

Key idea: this is a fee count-value maximization question. The triggers are total students, total fee, and a comparison condition asking for a maximum.

Step 1: Let $S$ , $A$ and $C$ be the numbers of Science, Arts and Commerce students.

Step 2: Write the count equation.

$S + A + C = 120$

Step 3: Write the value equation.

$1400 S + 1000 A + 700 C = 119000$

Step 4: Eliminate $C$ using $C = 120 - S - A$ .

$1400 S + 1000 A + 700 (120 - S - A) = 119000$

$84000 + 700 S + 300 A = 119000$

$700 S + 300 A = 35000$

Divide by $100$ :

$7 S + 3 A = 350$

Step 5: Express $A$ in terms of $S$ .

$A = \frac{350 - 7 S}{3}$

For $A$ to be an integer, $350 - 7 S$ must be divisible by $3$ .

Since $350 \equiv 2 (mod 3)$ and $7 \equiv 1 (mod 3)$ , we need

$2 - S \equiv 0 (mod 3)$

$S \equiv 2 (mod 3)$

Step 6: Apply the strict condition $S < A$ .

$S < \frac{350 - 7 S}{3}$

$3 S < 350 - 7 S$

$10 S < 350$

$S < 35$

Step 7: Find the largest integer less than $35$ that satisfies $S \equiv 2 (mod 3)$ .

The candidates below $35$ are $32, 29, 26, \dots$ , so the largest is $32$ .

Step 8: Check feasibility.

If $S = 32$ , then

$A = \frac{350 - 224}{3} = 42$

and

$C = 120 - 32 - 42 = 46$

All counts are non-negative, and $32 < 42$ .

Answer: $32$ .

Common trap: reading “fewer than” as “not more than” gives the false boundary value $S = 35$ , where $S = A$ . Another trap is choosing $34$ just because it is below $35$ , without checking that $A$ must be an integer.

chapter

CAT Arithmetic Short Notes: Chapter-wise Weightage and Solved Questions

CAT Arithmetic: 6 chapters, 0 practice questions and one solved question from each chapter.

A question from this chapter

Question 1

In a school, 120 students each choose exactly one of Science, Arts or Commerce. The fees are ₹ 1400, ₹ 1000 and ₹ 700 respectively. The total fee collected is ₹ 119000 . If the number of Science students is fewer than the number of Arts students, what is the maximum possible number of Science students?

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