List of top Quantitative Aptitude Questions on Number of integer solutions asked in CAT

The number of integer solutions of equation \(2|x|(x^2+1)=5x^2\) is

The sum of all possible values of \(x\) satisfying the equation \(2^{4x^2} - 2^{2x^2+x+16} + 2^{2x+30} = 0\), is

The number of integer solutions of equation \(2|x|(x^2+1)=5x^2\) is

Let \(0≤a≤x≤100\) and f(x)=\(|x−a|+|x−100|+|x−a−50|\).Then the maximum value of f(x) becomes 100 when a is equal to

For any real number x, let [x] be the largest integer less than or equal to x. If \(\sum_{n=1}^N \left[ \frac{1}{5} + \frac{n}{25} \right] = 25\) then N is

Let \(A\) be the largest positive integer that divides all the numbers of form \(3^k+4^k+5^k\), and \(B\) be the largest positive integer that divides all the numbers of the form \(4^k+3(4^k)+4^{k+2}\), where k is any positive integer. Then \((A+B)\) equals

The number of integer solutions of the equation (x2−10)(x2−3x−10)=1 is

Let \(A\) be the largest positive integer that divides all the numbers of form \(3^k+4^k+5^k\), and \(B\) be the largest positive integer that divides all the numbers of the form \(4^k+3(4^k)+4^{k+2}\), where k is any positive integer. Then \((A+B)\) equals

For any real number x, let [x] be the largest integer less than or equal to x. If \(\sum_{n=1}^N \left[ \frac{1}{5} + \frac{n}{25} \right] = 25\) then N is

The number of integer solutions of the equation \((x^2−10)^{(x2−3x−10)}=1\) is

Let \(0≤a≤x≤100\) and f(x)=\(|x−a|+|x−100|+|x−a−50|\).Then the maximum value of f(x) becomes 100 when a is equal to