Number System · Basic Numeracy · UPSC Civil Service

$222^{333} + 333^{222}$ is divisible by which of the following numbers?

Consider the following statements in respect of the sum $S = x + y + z$, where $x, y$ and $z$ are distinct prime numbers each less than 10:

1. The unit digit of $S$ can be 0.

2. The unit digit of $S$ can be 9.

3. The unit digit of $S$ can be 5.

Which of the statements given above are correct?

Let $X$ be a two-digit number and $Y$ be another two-digit number formed by interchanging the digits of $X$. If $(X + Y)$ is the greatest two-digit number, then what is the number of possible values of $X$?

$32^5 + 2^{27}$ is divisible by

Consider the following in respect of prime number p and composite number c.

1. $\frac{\mathrm{p}+\mathrm{c}}{\mathrm{p}-\mathrm{c}}$ can be even.

2. 2p + c can be odd.

3. pc can be odd.

Which of the statements given above are correct?

Consider the following statements in respect of two natural numbers p and q such that p is a prime number and q is a composite number :

1. p × q can be an odd number.

2. q / p can be a prime number.

3. p + q can be a prime number.

Which of the above statements are correct?

The difference between a 2-digit number and the number obtained by interchanging the positions of the digits is 54.

Consider the following statements:

1. The sum of the two digits of the number can be determined only if the product of the two digits is known.

2. The difference between the two digits of the number can be determined.

Which of the above statements is/are correct?