List of top Quantitative Aptitude Questions

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

For any non-zero real number x, let\( f(x) + 2f\left(\frac{1}{x}\right) = 3x.\)Then, the sum of all possible values of x  for which f(x) = 3, is

A train travelled a certain distance at a uniform speed. Had the speed been 6 km per hour more, it would have needed 4 hours less. Had the speed been 6 km per hour less,it would have needed 6 hours more. The distance, in km, travelled by the train is

Rajesh and Vimal own 20 hectares and 30 hectares of agricultural land, respectively, which are entirely covered by wheat and mustard crops. The cultivation area of wheat and mustard in the land owned by Vimal are in the ratio of 5 : 3. If the total cultivation area of wheat and mustard are in the ratio 11 : 9, then the ratio of cultivation area of wheat and mustard in the land owned by Rajesh is

\( 10^{68} \) is divided by 13, the remainder is  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 \(y\) are real numbers such that \(4x^2 + 4y^2 - 4xy - 6y + 3 = 0\), then the value of \((4x + 5y)\) is

P, Q, R and S are four towns. One can travel between P and Q along 3 direct paths, between Q and S along 4 direct paths, and between P and R along 4 direct paths. There is no direct path between P and S, while there are few direct paths between Q and R, and between R and S. One can travel from P to S either via Q, or via R, or via Q followed by R, respectively, in exactly 62 possible ways. One can also travel from Q to R either directly, or via P, or via S, in exactly 27 possible ways. Then, the number of direct paths between Q and R is

If \(a\), \(b\), and \(c\) are positive real numbers such that \(a > 10 \ge b \ge c\) and\[ \frac{\log_8(a+b)}{\log_2 c} + \frac{\log_{27}(a-b)}{\log_3 c} = \frac{2}{3} \]then the greatest possible integer value of \(a\) is

A fruit seller has a stock of mangoes, bananas and apples with at least one fruit of each type. At the beginning of a day, the number of mangoes make up 40% of his stock. That day, he sells half of the mangoes, 96 bananas and 40% of the apples. At the end of the day, he ends up selling 50% of the fruits. The smallest possible total number of fruits in the stock at the beginning of the day is

Three circles of equal radii touch (but not cross) each other externally. Two other circles, X and Y, are drawn such that both touch (but not cross) each of the three previous circles. If the radius of X is more than that of Y, the ratio of the radii of X and Y is

The sum of the infinite series \( \frac{1}{5} \left( \frac{1}{5} - \frac{1}{7} \right) + \left( \frac{1}{5} \right)^2 \left( \frac{1}{5} - \frac{1}{7} \right)^2 - \left( \frac{1}{7} \right)^2 + \left( \frac{1}{5} \right)^3 \left( \frac{1}{5} - \frac{1}{7} \right)^3 + \dots \) is equal to

A function f maps the set of natural numbers to whole numbers, such that f(xy) = f(x)f(y) + f(x) + f(y) for all x, y and f(p) = 1 for every prime number p. Then, the value of f(160000) is

A vessel contained a certain amount of a solution of acid and water. When 2 litres of water was added to it, the new solution had 50% acid concentration. When 15 litres of acid was further added to this new solution, the final solution had 80% acid concentration. The ratio of water and acid in the original solution was

Bina incurs 19% loss when she sells a product at Rs. 4860 to Shyam, who in turn sells this product to Hari. If Bina would have sold this product to Shyam at the purchase price of Hari, she would have obtained 17% profit. Then, the profit, in rupees, made by Shyam is

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

If m and n are natural numbers such that n > 1, and mⁿ = 2²⁵ × 3⁴⁰, then m − n equals

The roots \(\alpha\), \(\beta\) of the equation \(3x^2 + \lambda x - 1 = 0\), satisfy \( \frac{1}{\alpha^2} + \frac{1}{\beta^2} = 15 \). The value of \( (\alpha^3 + \beta^3)^2 \) is

When 3³³³ is divided by 11, the remainder is

In the $XY$-plane, the area, in sq. units, of the region defined by the inequalities $y \ge x + 4$ and $-4 \le x^2 + y^2 + 4(x - y) \le 0$ is

The sum of all four-digit numbers that can be formed with the distinct non-zero digits $a$, $b$, $c$, and $d$, with each digit appearing exactly once in every number, is $153310 + n$, where $n$ is a single digit natural number. Then, the value of $(a + b + c + d)$ is ?

ABCD is a rectangle with sides AB = 56 cm and BC = 45 cm, and E is the midpoint of side CD. Then, the length, in cm, of radius of incircle of \(\triangle ADE\) is

Let $x$ be a positive real number such that $4 \log_{10} x + 4 \log_{100} x + 8 \log_{1000} x = 13$ , then the greatest integer not exceeding $x$. is