Recent questions tagged number-systems

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

If the product of three consecutive positive integers is $15600$ then the sum of the squares of these integers is $1777$$1785$$1875$$1877$

Let $a_{1},a_{2},a_{3},a_{4},a_{5}$ be a sequence of five consecutive odd numbers. Consider a new sequence of five consecutive even numbers ending with $2a_{3}$. If the s...

If $n$ is any odd number greater than $1$, then $n(n^2 – 1)$ isdivisible by $96$ alwaysdivisible by $48$ alwaysdivisible by $24$ alwaysNone of these

What is the sum of all two-digit numbers that give a remainder of $3$ when they are divided by $7?$$666$$676$$683$$777$

For the product $n\left ( n+1 \right )\left ( 2n+1 \right ),n \in \mathbf{N}$, which one of the following is not necessarily true? It is evenDivisible by $3$Divisible by ...

A young girl counted in the following way on the fingers of her left hand. She started calling the thumb $1$, the index finger $2$, middle finger $3$, ring finger $4$, li...

When you reverse the digits of the number $13$, the number increases by $18$. How many other two digit numbers increase by $18$ when their digits reversed ___________

If $m$ and $n$ are integers such that $(\sqrt{2})^{19}3^{4}4^{2}9^{m}8^{n}=3^{n}16^{m}(\sqrt[4]{64})$ then $m$ is$-20$$-12$$-24$$-16$

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 i...

Let $\text{P, Q, S, R, T, U}$ and $\text{V}$ represent the seven distinct digits from $0$ to $6$, not necessarily in that order. If $\text{PQ}$ and $\text{RS}$ are both t...

Find the remainder of $2^{1040}$ divided by $131$.$1$$3$$5$$7$

Which of the terms $2^{\frac{1}{3}},3^{\frac{1}{4}},4^{\frac{1}{6}},6^{\frac{1}{8}}$ and $10^{\frac{1}{12}}$ is the largest?$2^{\frac{1}{3}} \\$$3^{\frac{1}{4}} \\$$4^{\f...

What is the sum of all the $2$-digit numbers which leave a remainder of $6$ when divided by $8$?$612$$594$$324$$872$

Let $\text{P} = \{2,3,4,\ldots 100\}$ and $\text{Q}= \{101,102,103,\ldots 200\}.$ How many elements of $\text{Q}$ are there such that they do not have any element of $\te...

$\text{P, Q and R}$ are three consecutive odd numbers in ascending order. If the value of three times $\text{P}$ is three less than two times $\text{R}$, find the value o...

What is the sum of all two-digit numbers that give a remainder of $3$ when they are divided by $7?$$666$$676$$683$$777$