XAT Inequalities Practice Questions With Solutions

Consider the equation $\log_5(x - 2) = 2 \log_{25}(2x - 4)$, where x is a real number.
For how many different values of x does the given equation hold?

FS food stall sells only chicken biryani. If FS fixes a selling price of Rs. 160 per plate, 300 plates of biriyani are sold. For each increase in the selling price by Rs. 10 per plate, 10 fewer plates are sold. Similarly, for each decrease in the selling price by Rs. 10 per plate, 10 more plates are sold. FS incurs a cost of Rs. 120 per plate of biriyani, and has decided that the selling price will never be less than the cost price. Moreover, due to capacity constraints, more than 400 plates cannot be produced in a day.
If the selling price on any given day is the same for all the plates and can only be a multiple of Rs. 10, then what is the maximum profit that FS can achieve in a day?

The addition of 7 distinct positive integers is 1740. What is the largest possible “greatest common divisor” of these 7 distinct positive integers?

Given $A = |x + 3| + | x - 2 | - | 2x -8|$. The maximum value of $|A|$ is:

Let x and y be two positive integers and p be a prime number. If x (x - p) - y (y + p) = 7p, what will be the minimum value of x - y?

Raju and Sarita play a number game. First, each one of them chooses a positive integer independently. Separately, they both multiply their chosen integers by 2, and then subtract 20 from their resultant numbers. Now, each of them has a new number. Then, they divide their respective new numbers by 5. Finally, they added their results and found that the sum is 16. What can be the maximum possible difference between the positive integers chosen by Raju and Sarita?

Wilma, Xavier, Yaska and Zakir are four young friends, who have a passion for integers. One day, each of them selects one integer and writes it on a wall. The writing on the wall shows that Xavier and Zakir picked positive integers, Yaska picked a negative one, while Wilma’s integer is either negative, zero or positive. If their integers are denoted by the first letters of their respective names, the following is true:

$W^{4}+X^{3}+Y^{2}+Z\leq4$
$X^{3}+Z\geq2$
$W^{4}+Y^{2}\leq2$
$Y^{2}+Z\geq3$
Given the above, which of these can $W^{2}+X^{2}+Y^{2}+Z^{2}$ possibly evaluate to?

If both the sequences x, a1, a2, y and x, b1, b2, z are in A.P. and it is given that $y > x$ and $z < x$, then which of the following values can $\left\{\frac{(a1-a2)}{(b1-b2)}\right\}$ possibly take?

Let $f(x) = \frac{x^2 + 1}{x^2 - 1}$ if $x \neq 1, -1,$ and 1 if x = 1, -1. Let $g(x) = \frac{x + 1}{x - 1}$ if $x \neq 1,$ and 3 if x = 1.
What is the minimum possible values of $\frac{f(x)}{g(x)}$ ?

Find z, if it is known that:
a: $-y^2 + x^2 = 20$
b: $y^3 - 2x^2 - 4z \geq -12$ and
c: x, y and z are all positive integers