130+ CAT Number Systems Questions With Video Solutions PDF

In a 3-digit number N, the digits are non-zero and distinct such that none of the digits is a perfect square, and only one of the digits is a prime number. Then, the number of factors of the minimum possible value of N is

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

The sum of digits of the number $$(625)^{65} \times (128)^{36}$$ is

The sum of all the digits of the number $$(10^{50}+10^{25}-123)$$, is

The number of divisors of $$(2^{6}\times 3^{5}\times 5^{3}\times 7^{2})$$, which are of the form $$(3r+1)$$, where r is a non-negative integer, is

If $$12^{12x}\times 4^{24x+12}\times 5^{2y}=8^{4z}\times 20 ^{12x} \times 243^{3x-6}$$, where x , y and z are
natural numbers, then $$ x + y + z $$ equals

The average of three distinct real numbers is 28. If the smallest number is increased by 7 and the largest number is reduced by 10, the order of the numbers remains unchanged, and the new arithmetic mean becomes 2 more than the middle number, while the difference between the largest and the smallest numbers becomes 64.Then, the largest number in the original set of three numbers is

If $$10^{68}$$ is divided by 13, the remainder is

When $$10^{100}$$is divided by 7, the remainder is

The sum of all real values of k for which $$\left(\cfrac{1}{8}\right)^{k}\times \left(\cfrac{1}{32768}\right)^{\cfrac{1}{3}}=\cfrac{1}{8}\times \left(\cfrac{1}{32768}\right)^{\cfrac{1}{k}}$$, 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

If $$m$$ and $$n$$ are natural numbers such that $$n > 1$$, and $$m^n = 2^{25} \times 3^{40}$$, then $$m - n$$ equals

When $$3^{333}$$ is divided by 11, the remainder is

The number of all positive integers up to 500 with non-repeating digits is

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

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

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

The sum of the first two natural numbers,

each having 15 factors (including 1 and the number itself), is

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