List of top Quantitative Aptitude Questions on Properties of Numbers asked in CAT

Any non-zero real numbers \(x, y\) such that \(y ≠ 3\) and \(\frac{x}{y}<\frac{x+3}{y-3}\), will satisfy the condition

Let \(a, b, m\) and \(n\) be natural numbers such that \(a >1\) and \(b >1\) . If \(a^m+b^n = 144^{145}\) , then the largest possible value of \(n − m\) is

For some real numbers \(a\) and \(b\) , the system of equations \(x + y = 4\) and \((a+5)x+(b^2-15)y = 8b\) has infinitely many solutions for \(x\) and \(y\). Then, the maximum possible value of \(ab\) is

If \(p^2+q^2-29=2pq-20=52-2pq\) , then the difference between the maximum and minimum possible value of \((p^3-q^3 ) \)is

For a 4-digit number, the sum of its digits in the thousands, hundreds and tens places is 14, the sum of its digits in the hundreds, tens and units places is 15, and the tens place digit is 4 more than the units place digit. Then the highest possible 4-digit number satisfying the above conditions is

For a 4-digit number, the sum of its digits in the thousands, hundreds and tens places is 14, the sum of its digits in the hundreds, tens and units places is 15, and the tens place digit is 4 more than the units place digit. Then the highest possible 4-digit number satisfying the above conditions is