List of top Quantitative Aptitude Questions asked in CAT

Two boats, traveling at 5 and 10 kms per hour, head directly towards each other. They begin at a distance of 20 kms from each other. How far apart are they (in kms) one minute before they collide.

Directions for the following two questions:

Answer the questions on the basis of the information given below.

\( f_1(x) = x \) if \( 0 \le x \le 1 \) \( f_1(x) = 1 \) if x >= 1 \( f_1(x) = 0 \) otherwise

\( f_2(x) = f_1(-x) \) for all x

\( f_3(x) = -f_2(x) \) for all x

\( f_4(x) = f_3(-x) \) for all x

In NutsAndBolts factory, one machine produces only nuts at the rate of 100 nuts per minute and needs to be cleaned for 5 minutes after production of every 1000 nuts. Another machine produces only bolts at the rate of 75 bolts per minute and needs to be cleaned for 10 minutes after production of every 1500 bolts. If both the machines start production at the same time, what is the minimum duration required for producing 9000 pairs of nuts and bolts?

The remainder, when \( 15^{23} + 23^{23} \) is divided by 19, is

If a man cycles at 10 km/hr, then he arrives at a certain place at 1 p.m. If he cycles at 15 km/hr, he will arrive at the same place at 11 a.m. At what speed must he cycle to get there at noon?

Each family in a locality has at most two adults, and no family has fewer than 3 children. Considering all the families together, there are more adults than boys, more boys than girls, and more girls than families. Then the minimum possible number of families in the locality is

Consider the sequence of numbers \(a_1, a_2, a_3, \dots \) to infinity where \(a_1 = 81.33\) and \(a_2 = -19\) and \(a_j = a_{j-1} - a_{j-2}\) for \(j \geq 3\). What is the sum of the first 6002 terms of this sequence?

In the adjoining figure I and II, are circles with P and Q respectively. The two circles touch each other and have a common tangent that touches them at points R and S respectively. This common tangent meets the line joining P and Q at O. The diameters of I and II are in the ratio 4:3. It is also known that the length of PO is 28 cm.

In an examination, there are 100 questions divided into three groups A, B and C such that each group contains at least one question. Each question in group a carries 1 mark, each question in group B carries 2 marks and each question in group C carries 3 marks. It is known that the questions in group A together carry at least 60% of the total marks

DIRECTIONS for the following three questions: Answer the questions on the basis of the information given below.

A city has two perfectly circular and concentric ring roads, the outer ring road (OR) being twice as long as the inner ring road (IR). There are also four (straight line) chord roads from E1, the east end point of OR to N2, the north end point of IR; from N1, the north end point of OR to W2, the west end point of IR; from W1, the west end point of OR, to S2, the south end point of IR; and from S1 the south end point of OR to E2, the east end point of IR. Traffic moves at a constant speed of \(30\pi\) km/hr on the OR road, \(20\pi\) km/hr on the IR road, and \(15\sqrt{5}\) km/hr on all the chord roads.

A graph may be defined as a set of points connected by lines called edges. Every edge connects a pair of points. Thus, a triangle is a graph with 3 edges and 3 points. The degree of a point is the number of edges connected to it. For example, a triangle is a graph with three points of degree 2 each. Consider a graph with 12 points. It is possible to reach any point from any point through a sequence of edges. The number of edges, e, in the graph must satisfy the condition

Let T be the set of integers {3,11,19,27,…451,459,467} and S be a subset of T such that the sum of no two elements of S is 470. The maximum possible number of elements in S is

The number of positive integers n in the range \( 12 \leq n \leq 40 \) such that the product (n -1)*(n - 2)*…*3*2*1 is not divisible by n is

There are 6 boxes numbered 1,2,... 6. Each box is to be filled up either with a red or a green ball in such a way that at least 1 box contains a green ball and the boxes containing green balls are consecutively numbered. The total number of ways in which this can be done is

In the figure below, the rectangle at the corner measures 10 cm \( \times \) 20 cm. The corner A of the rectangle is also a point on the circumference of the circle. What is the radius of the circle in cm?