List of top Quantitative Aptitude Questions asked in NPAT

A can draw 10 illustrations in 5 days. B is three times as productive in twice the amount of time (in comparison to A). How many illustrations can B draw in a day?
A, B and C have some marbles. The ratio of the number of marbles with A to the number with B is 2:1. Also, the number of marbles with A to the number with C is 1:4. What is the approximate percentage of the total number of marbles that are with C?
If \( p \) and \( q \) are numbers such that the pair of linear equations \( (p + 2)x + (q - 1)y = 10 \) and \( (q + 2)x + (p - 1)y = 10 \) have infinite solutions for \( x \) and \( y \), then \( p = q \).
If \( x \), \( y \), and \( z \) are positive integers and \( p = \left( \left( (x - 1)^2 / |x| \right) + 2 \right) + \left( \left( (y - 1)^2 / |y| \right) + 2 \right) + \left( \left( (z - 1)^2 / |z| \right) + 2 \right), \) then \( p<6 \).
There are four questions based on the table that follows, one of which is asked alongside.
The table shows the data regarding the percentage change in the number of units manufactured by a plant during different months in Year 2.
MonthPercentage change (over last month)Percent point change in percentage change (over last month)
Jan10%-20
Feb18%8
Mar-5%-20
Apr6%8
May6%-8
Jun6%-8
Jul6%-8
Note: Round up the decimal values obtained (if any) during calculations to the nearest integer value.
For a set of \( n \) integers in arithmetic progression, the difference between twice the median of the set and the range of the set is equal to twice the first term.
Given: \( a \) and \( b \) are positive integers and \( a>b \). The median of a set consisting of 5 terms: \( a^2, ab, b^2, (a - b)^2 \) and \( (a + b)^2 \) is \( ab \).
Two sets of numbers having medians \( p \) and \( q \) respectively are combined to form a new set. If \( p>q \), then the median \( m \) of the new set satisfies \( q<m<p \).
If the median of a set consisting of \( n \) consecutive odd positive integers is an even integer, the sum of the mean and the range of the set is an odd integer.
A cone fits perfectly (height-wise) inside a 6 cm × 8 cm × 10 cm cuboid such that the entire base of the cone rests on one of the faces of the cuboid. Also, the circumference of the base of the cone just touches one of the pairs of the opposite sides of the face of the cuboid which is beneath it. The volume of the cone is \( 32 \pi \, \text{cm}^3 \).
Given: A right-angled triangle has sides of lengths 6 cm, 8 cm, and 10 cm. Quantity A: Volume of the cone formed by rotating the triangle about the side of length 6 cm. Quantity B: Volume of the cone formed by rotating the triangle about the side of length 8 cm.
In triangle ABC, AB = 6 cm, AC = BC = 7 cm. Also, CP is a median. Which of the following is the area of triangle ABC?
triangle ABC, AB = 6 cm, AC = BC = 7 cm.
ABC and PQR are 2 identical equilateral triangles overlapping each other.
The area of the overlapping region PXBY is equal to twice the area of triangle AXP.
2 identical equilateral triangles overlapping each other.
A milk and honey mixture is 20% honey. Another 120 ml of honey is added to it. After this addition, the resulting mixture has 150 ml of honey. What is the volume of milk in the final mixture?
Given: \( 3^{2x} - 12 \times 3^{x} + 27 = 0 \).
Quantity A: x
Quantity B: \(3^{x}\)
When working individually, A and B take 6 days and 8 days to paint a fence. They started working together. After 2 days, C also joined them. If the work was completed after 1 more day (3 days in total), in how many days can C paint the entire fence alone?
Given: \( f(x) = \left( 1 + \frac{1}{x} \right) \) and \( f(k) \times f(k+1) \times f(k+2) \times \cdots \times f(k+99) = 11 \). Quantity A: k
Quantity B: 11
Let \( x \) be the median of the data: 13, 17, 52, 56, 65, 35, 77, 39, 15, 37. If 35 is replaced by 53 in the data, then the median of the new data will be \( y \). What is the difference between \( x \) and \( y \)?

If
$ \sec(5^\circ - 2\theta) = \csc(5\theta - 5^\circ),\ 0^\circ < \theta < 90^\circ $,
then what will be the value of 
$ \frac{\sin 3\theta + \tan 2\theta}{\sec 2\theta} $?

In \( \triangle ABC \), \( \angle B = 90^\circ \), \( BC = 6 \, \text{cm} \), and \( AC = 10 \, \text{cm} \). What is the value of \( (\sin 2A - \cos 2A) \)?
A biased coin is such that the probability of getting a head is thrice the probability of getting a tail. If the coin is tossed 4 times, what will be the probability of getting a head all the times?
What is the variance of the following data? \( 9, 10, 13, 14, 6, 11, 8, 7, 4, 18 \)
Two persons, on either side of a tower 45 m high, observe the angles of elevation of the top of the tower to be 30° and 60°, respectively. The distance (in m) between the two persons is:
The expression \( \frac{(2\sin^2\theta - 1)(1 + \tan^2\theta)(\sec\theta + \tan\theta)(1 - \sin\theta)}{(\sec^2\theta - 1)(\tan\theta - \cot\theta)\cos^2\theta} \) for \( 0^\circ<\theta<90^\circ \) is equal to:
\[ \frac{\tan^2 \theta + \cot^2 \theta + 2}{\sec \theta \csc \theta}, \ 0^\circ<\theta<90^\circ, \text{ is equal to:} \]