CAT Number System questions (2017–2025) — 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:

CAT 2021 Slot 3 Question 5

A four-digit number is formed by using only the digits 1, 2 and 3 such that both 2 and 3 appear at least once. The number of all such four-digit numbers is

CAT 2021 Slot 2 Question 6

For a 4-digit number, the sum of its digits in the thousands, hundreds and tens places is 14, the sum of its digits in the hundreds, tens and units places is 15, and the tens place digit is 4 more than the units place digit. Then the highest possible 4-digit number satisfying the above conditions is

CAT 2021 Slot 1 Question 7

The natural numbers are divided into groups as (1), (2, 3, 4), (5, 6, 7, 8, 9), ….. and so on. Then, the sum of the numbers in the 15th group is equal to

CAT 2021 Slot 1 Question 8

How many three-digit numbers are greater than 100 and increase by 198 when the three digits are arranged in the reverse order?

The natural numbers are grouped as: (1), (2,3,4), (5,6,7,8,9), ……… Find the sum of all terms in the 15th group.

CAT 2020 Slot 3 Question 1

How many of the integers 1, 2, … , 120, are divisible by none of 2, 5 and 7?

CAT 2020 Slot 3 Question 9

Let N, x and y be positive integers such that N = x + y, 2 25, then how many distinct values are possible for N?

CAT 2020 Slot 2 Question 10

How many 4-digit numbers, each greater than 1000 and each having all four digits distinct, are there with 7 coming before 3?

CAT 2019 Slot 2 Question 2

How many factors of 2⁴ × 3⁵ × 10⁴ are perfect squares which are greater than 1?

CAT 2019 Slot 1 Question 11

The product of two positive numbers is 616. If the ratio of the difference of their cubes to the cube of their difference is 157 : 3, then the sum of the two numbers is

CAT 2018 Slot 2 Question 3

If N and x are positive integers such that N^N = 2¹⁶⁰ and N² + 2^N is an integral multiple of 2^x, then the largest possible x is

CAT 2018 Slot 2 Question 12

If the sum of squares of two numbers is 97, then which one of the following cannot be their product?

CAT 2018 Slot 2 Question 13

How many two-digit numbers, with a non-zero digit in the units place, are there which are more than thrice the number formed by interchanging the positions of its digits?

CAT 2018 Slot 1 Question 4

The number of integers x such that 0.25 < 2^x < 200, and 2^x + 2 is perfectly divisible by either 3 or 4, is

CAT 2018 Slot 1 Question 14

While multiplying three real numbers, Ashok took one of the numbers as 73 instead of 37. As a result, the product went up by 720. Then the minimum possible value of the sum of squares of the other two numbers is

CAT 2017 Slot 2 Question 15

If the product of three consecutive positive integers is 15600 then the sum of the squares of these integers is