UPSC (Prelims) 2026 Quantitative Aptitude Number System Previous Year Questions

How many times does 5 appear in all two-digit positive integers?

X receives three coins of different denominations: 1, 2, 5, 10 and 20. If the total amount received by X is $m$, does X receive a coin of denomination 5?

Statement I : $m$ is not a prime number.

Statement II : The sum of the digits of $m$ is greater than 5.

If $x$ and $y$ are integers, then is $x$ even?

Statement I : $x^2{y}^2$ is even.

Statement II : $1+x^2+y^2$ is odd.

X is a collection of certain odd numbers whereas Y is a collection of certain even numbers. T consists of the numbers all of which are either from X or from Y. Is every number of T from Y?

Statement I : The sum of any two numbers belonging to T is even.

Statement II : If both $p$ and $q$ are picked from T, then $(p-1)q$ is even.

If $x,y$ and $z$ are integers, each greater than 1, then is $x$ a prime number?

Statement I : $x{y}^2=116$

Statement II : $xz=261$

Three variables $x$, $y$ and $z$ take values 2, 3, 4 or 5 such that their values are always distinct. If $M$ and $N$ denote the largest possible value and the smallest possible value, respectively, for the expression $(x\times y)+z$, then $M-N$ is

The digit in the unit place of the number $6^{129}\times 7^{307}$ is

How many three-digit numbers can be expressed as an integral power of 2?

In a sequence of numbers, each number other than the first two is the sum of the two immediately preceding numbers from it. If the first two numbers in the sequence are 4 and 7, then the sixth number is

If the product of the HCF and LCM of two distinct numbers is the cube of one of the numbers, then which of the following statements is/are correct?
I. The difference of the numbers is an even number.
II. One of the numbers is a perfect square.
Select the answer using the code given below.

If $x$ and $y$ are two digits and the number $4x5y790$ is divisible by 11, then what is the remainder, if $x+y$ is divided by 11?

A is a 2-digit number with different digits. B is also a 2-digit number and is obtained by reversing the digits of A. If $A-B$ is a multiple of 27, where $A>B$, how many such different A's are possible?