You can find all the CAT Number System questions from the previous papers with detailed video explanations on this page. The number system plays a crucial role in CAT quantitative section. There are many tricks, shortcuts and formulas that help you to solve the questions quickly. One can find those solving tips in the video solutions explained by CAT experts and IIM Alumni. Look no further to get resources for practising the CAT Number systems concept. Take free CAT mocks to understand the exam pattern and also you'll get a fair idea of how questions are asked. Download the CAT number systems questions PDF with detailed video solutions and practice to perform well in the quant section. And the best part is you can download the questions PDF for free without signing up. Click on the link below to download all the number system questions from CAT previous papers PDF.
Year | Weightage |
2023 | 7 |
2022 | 4 |
2021 | 2 |
2020 | 9 |
2019 | 5 |
2018 | 4 |
CAT Number systems is one of the most important topics in the quantitative
aptitude section, and it is vital to have a clear understanding of the
formulas related to them. To help the aspirants to ace this topic, we have
made a PDF containing a comprehensive list of formulas, tips, and
tricks that you can use to solve number systems questions with ease
and speed. Click on the below link to download the CAT Number Systems formulas PDF.
1. Remainder Theorems Formulae
Fermat's Theorem - For any integer $$a$$ and prime number $$p$$, $$a^p-a$$ is always divisible by $$p$$
Wilson's Theorem - For a prime $$p$$, remainder when $$(p-1)!$$ i divided by $$p$$ is $$(p-1)$$
Euler's Theorem - If M and N are co-prime to each other then the remainder when $$M^{\phi(N)}$$ is divided by N is 1
2. HCF and LCM
HCF * LCM of two numbers = Product of two numbers
The greatest number dividing a, b and c leaving remainders of $$x_1$$, $$x_2$$ and $$x_3$$ is the HCF of (a-$$x_1$$), (b-$$x_2$$) and (c-$$x_3$$).
The greatest number dividing a, b and c (a<b<c) leaving the same remainder each time is the HCF of (c-b), (c-a), (b-a).
LCM of fractions = LCM of Numerators ÷ HCF of Denominators.
3. Number of trailing zeros
Number of trailing zeros of n! in base b(b=$$p^m$$, where p is a prime number) is for $$k\ge1$$ $$\frac{1}{m}\left(\Sigma\left[\frac{n}{p^k}\right]\ \right)$$
Let a, b, m and n be natural numbers such that $$a>1$$ and $$b>1$$. If $$a^{m}b^{n}=144^{145}$$, then the largest possible value of $$n-m$$ is
correct answer:-4
Let n be the least positive integer such that 168 is a factor of $$1134^{n}$$. If m is the least positive integer such that $$1134^{n}$$ is a factor of $$168^{m}$$, then m + n equals
correct answer:-2
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
correct answer:-3
The number of positive integers less than 50, having exactly two distinct factors other than 1 and itself, is
correct answer:-15
The sum of the first two natural numbers, each having 15 factors (including 1 and the number itself), is
correct answer:-468
The number of coins collected per week by two coin-collectors A and B are in the ratio 3 : 4. If the total number of coins collected by A in 5 weeks is a multiple of 7, and the total number of coins collected by B in 3 weeks is a multiple of 24, then the minimum possible number of coins collected by A in one week is
correct answer:-42
The number of all natural numbers up to 1000 with non-repeating digits is
correct answer:-3
Consider six distinct natural numbers such that the average of the two smallest numbers is 14, and the average of the two largest numbers is 28. Then, the maximum possible value of the average of these six numbers is
correct answer:-4
Let A be the largest positive integer that divides all the numbers of the form $$3^k + 4^k + 5^k$$, and B be the largest positive integer that divides all the numbers of the form $$4^k + 3(4^k) + 4^{k + 2}$$ , where k is any positive integer. Then (A + B) equals
correct answer:-82
For some natural number n, assume that (15,000)! is divisible by (n!)!. The largest possible value of n is
correct answer:-2
A school has less than 5000 students and if the students are divided equally into teams of either 9 or 10 or 12 or 25 each, exactly 4 are always left out. However, if they are divided into teams of 11 each, no one is left out. The maximum number of teams of 12 each that can be formed out of the students in the school is
correct answer:-150
For all possible integers n satisfying $$2.25\leq2+2^{n+2}\leq202$$, then the number of integer values of $$3+3^{n+1}$$ is:
correct answer:-7
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
correct answer:-4195
How many 3-digit numbers are there, for which the product of their digits is more than 2 but less than 7?
correct answer:-21
How many 4-digit numbers, each greater than 1000 and each having all four digits distinct, are there with 7 coming before 3?
correct answer:-315
Let m and n be natural numbers such that n is even and $$0.2<\frac{m}{20},\frac{n}{m},\frac{n}{11}<0.5$$. Then $$m-2n$$ equals
correct answer:-2
How many integers in the set {100, 101, 102, ..., 999} have at least one digit repeated?
correct answer:-252
Let N, x and y be positive integers such that $$N=x+y,2<x<10$$ and $$14<y<23$$. If $$N>25$$, then how many distinct values are possible for N?
correct answer:-6
How many of the integers 1, 2, … , 120, are divisible by none of 2, 5 and 7?
correct answer:-2
How many pairs(a, b) of positive integers are there such that $$a\leq b$$ and $$ab=4^{2017}$$ ?
correct answer:-1
Video solutions can be a helpful resource for candidates preparing for CAT Number Systems questions. They can provide a step-by-step explanation of how to solve the problem, helping candidates better understand the concept and formula. Also, one can find various tips, tricks and shortcuts to solve the questions quickly.
Usually, the questions in the CAT from Number systems are moderately tricky. But not so tough if you are well versed with the basics and practice a good number of questions from this topic.