CAT Number System questions (2023–2025) — actual Quant questions with solutions

Visual lens G Strategy | Number Systems | Easy

The sum of all the digits of the number (10⁵⁰ + 10²⁵ − 123), is

For a 4 digit number greater than 1000 , sum of the digits in thousands , hundreds and tens places is 15.And the sum of digits in hundreds , tens and units place is 16.Also the digits in tens place is 6 more than the digit in the unit place. The difference between the largest possible and smallest possible value of the number is :

The number of divisors of 2⁶ × 3⁵ × 5³ × 7², which are of the form (3r + 1), where r is a non-negative integer, is

Suppose a, b, c are three distinct natural numbers, such that 3ac = 8(a + b). Then, the smallest possible value of 3a + 2b + c is _______

If m and n are integers such that (m + 2n)(2m + n) = 27, then the maximum possible value of 2m − 3n is ___

The number of distinct pairs of integers (x, y) satisfying the inequalities x > y ≥ 3 and x + y < 14 is ____.

Vedic Pattern + Concepts of Logs DPAC G Strategy | EASY | CAT 2025 Slot 1

The number of distinct integers n for which log_1/4 of (n² − 7n + 11) > 0 is _____.

Visual Lens | Odd even numbers | MEDIUM | CAT 2025 Slot 1

In the set of consecutive odd numbers {1, 3, 5, …, 57}, there is a number k such that the sum of all the elements less than k is equal to the sum of all the elements greater than k. Then, k equals

The number of distinct integers n for which log (1/4) of (n² − 7n + 11) > 0 is _____.

A cafeteria offers 5 types of sandwiches. Moreover, for each type of sandwich, a customer can choose one of 4 breads and opt for either small or large sized sandwich. Optionally, the customer may also add up to 2 out of 6 available sauces. The number of different ways in which an order can be placed for a sandwich, is

The number of distinct integer solutions (x, y) of the equation |x + y| + |x – y| = 2, is

If 10⁶⁸ is divided by 13, the remainder is

Find the number of all positive integers up to 500 with non-repeating digits.

When 3³³³ is divided by 11, the remainder is

A function f maps the set of natural numbers to whole numbers, such that f(xy) = f(x)f(y) + f(x) + f(y) for all x, y and f(p) = 1 for every prime number p. Then, the value of f(160000) is

For any natural number \( n \), let \( a_n \) be the largest integer not exceeding \( \sqrt{n} \). Then the value of \( a_1 + a_2 + \cdots + a_{50} \) is

When 10¹⁰⁰ is divided by 7, find the remainder.

When 3333 is divided by 11, the remainder is:

If m and n are natural numbers such that mn = 225 × 340, then m − n equals:

If (a + b√3)² = 52 + 30√3, where a and b are natural numbers, then a + b equals:

If 10⁶⁸ is divided by 13, the remainder is:

If (a + b√n) is the positive square root of 29 − 12√5, where a and b are integers, and n is a natural number, then the maximum possible value of (a + b + n) is

For any natural number n, let an be the largest integer not exceeding √n. Then the value of a1 + a2 + · · · + a50 is

When 10¹⁰⁰ is divided by 7, the remainder is

The sum of all four-digit numbers that can be formed with the distinct non-zero digits a, b, c, and d, with each digit appearing exactly once in every number, is 153310 + n, where n is a single digit natural number. Then, the value of (a + b + c + d + n) is

The sum of the first two natural numbers, each having 15 factors (including 1 and the number itself), is

Q. For any natural numbers m, n, and k, such that k divides both m + 2n and 3m + 4n, k must be a common divisor of

The number of positive integers less than 50, having exactly two distinct factors other than 1 and itself, is:

A container has 40 liters of milk. 4 liters are removed and replaced with 4 liters of water. This process is repeated. The smallest number of times required for milk to be less than water is:

Let both series \( a_1, a_2, a_3, \ldots \) and \( b_1, b_2, b_3, \ldots \) be in arithmetic progression with common differences as prime numbers. If a5=b9, a19=b19 and b2=0, , then a11 equals, find \( a_{19} \):

Let \( a_n = 13 + 6(n - 1) \) and \( b_n = 15 + 7(n - 1) \). Find the largest three-digit integer common to both sequences:

A lab experiment measures the number of organisms at 8 am every day. Starting with 2 organisms on the first day, the number of organisms on any day is equal to 3 more than twice the number on the previous day. If the number of organisms on the \( n \)-th day exceeds one million, then the lowest possible value of \( n \) is: