Top Important CAT Inequalities Questions [PDF]

Let a, b, c, d be four integers such that a+b+c+d = 4m+1 where m is a positive integer. Given m, which one of the following is necessarily true?

Given that $$-1 \leq v \leq 1, -2 \leq u \leq -0.5$$ and $$-2 \leq z \leq -0.5$$ and $$w = vz /u$$ , then which of the following is necessarily true?

If x, y, z are distinct positive real numbers the $$(x^2(y+z) + y^2(x+z) + z^2(x+y))/xyz$$ would always be

The number of solutions of the equation 2x + y = 40 where both x and y are positive integers and x <= y is:

What values of x satisfy $$x^{2/3} + x^{1/3} - 2 <= 0$$?

If x > 5 and y < -1, then which of the following statements is true?

x and y are real numbers satisfying the conditions 2 < x < 3 and - 8 < y < -7. Which of the following expressions will have the least value?

$$m$$ is the smallest positive integer such that for any integer $$n \geq m$$, the quantity $$n^3 - 7n^2 + 11n - 5$$ is positive. What is the value of $$m$$?

If a, b, c and d are four positive real numbers such that abcd = 1, what is the minimum value of (1 + a)(1+b)(1+c)(1+d)?

Let x and y be two positive numbers such that $$x + y = 1.$$

Then the minimum value of $$(x+\frac{1}{x})^2+(y+\frac{1}{y})^2$$ is

If x>2 and y>-1,then which of the following statements is necessarily true?

If x, y and z are real numbers such that x + y + z = 5 and xy + yz + zx = 3, what is the largest value that x can have?

If $$x^2 + 5y^2 + z^2 = 2y(2x+z)$$, then which of the following statements is(are) necessarily true?

A. x = 2y B. x = 2z C. 2x = z

If u, v, w and m are natural numbers such that $$u^m + v^m = w^m$$, then which one of the following is true?

If pqr = 1, the value of the expression $$1/(1+p+q^{-1}) + 1/(1+q+r^{-1}) + 1/(1+r+p^{-1})$$

From any two numbers $$x$$ and $$y$$, we define $$x* y = x + 0.5y - xy$$ . Suppose that both $$x$$ and $$y$$ are greater than 0.5. Then
$$x* x < y* y$$ if

The number of integers n satisfying -n+2 ≥ 0 and 2n ≥ 4 is

x, y and z are three positive integers such that x > y > z. Which of the following is closest to the product xyz?

Which of the following values of x do not satisfy the inequality $$(x^2 - 3x + 2 > 0)$$ at all?

Given that $$x >y> z> 0$$. Which of the following is necessarily true?