List of top Quantitative Aptitude Questions on Algebra asked in CAT

The sum of all distinct real values of x that satisfy the equation \(10^x + \frac{4}{10^x} = \frac{81}{2}\)  is

If \(3^a = 4, 4^b = 5, 5^c = 6, 6^d = 7, 7^e = 8 \) and  \(8^f = 9\),  then the value of the product \(abcdef\)  is

The number of distinct integer solutions (x, y) of the equation |x + y| + |x - y| = 2, is

If $(a + b\sqrt{3})^2 = 52 + 30\sqrt{3}$, where $a$ and $b$ are natural numbers, then $a + b$ equals ?

If x and y satisfy the equations |x| + x + y = 15 and x + |y| − y = 20, then (x − y) equals

Let $x$, $y$, and $z$ be real numbers satisfying
\(4(x^2 + y^2 + z^2) = a,\)
\(4(x - y - z) = 3 + a.\)
Then $a$ equals ?

If $(a + b\sqrt{n})$ is the positive square root of $(29 - 12\sqrt{5})$, where $a$ and $b$ are integers, and $n$ is a natural number, then the maximum possible value of $(a + b + n)$ is ?

A shop wants to sell a certain quantity (in kg) of grains. It sells half the quantity and an additional 3 kg of these grains to the first customer. Then, it sells half of the remaining quantity and an additional 3 kg of these grains to the second customer. Finally, when the shop sells half of the remaining quantity and an additional 3 kg of these grains to the third customer, there are no grains left. The initial quantity, in kg, of grains is

If \( x \) and \( y \) satisfy the equations
\(|x| + x + y = 15 \quad \text{(1)},\)
\(x + |y| - y = 20 \quad \text{(2)}.\)
Find the value of \( x - y \).

\(\sqrt{x + 6\sqrt{2}} - \sqrt{x - 6\sqrt{2}} = 2\sqrt{2}.\)
Find \( x \).