Top 100 XAT 2026 QADI Questions PDF With Video Solutions

A manufacturer produces two types of products - A and B, which are subjected to two types of operations, viz. grinding and polishing. Each unit of product A takes 2 hours of grinding and 3 hours of polishing whereas product B takes 3 hours of grinding and 2 hours of polishing. The manufacturer has 10 grinders and 15 polishers. Each grinder operates for 12 hours/day and each polisher 10 hours/day. The profit margin per unit of A and B are Rs. 5/ - and Rs. 7/ - respectively. If the manufacturer utilises all his resources for producing these two types of items, what is the maximum profit that the manufacturer can earn in a day?

Rani bought more apples than oranges. She sells apples at Rs. 23 apiece and makes 15% profit. She sells oranges at Rs. 10 a piece and makes 25% profit. If she gets Rs. 653 after selling all the apples and oranges, find her profit percentage.

The Maximum Retail Price (MRP) of a product is 55% above its manufacturing cost. The product is sold through a retailer, who earns 23% profit on his purchase price. What is the profit percentage (expressed in nearest integer) for the manufacturer who sells his product to the retailer? The retailer gives 10% discount on MRP.

Nikhil’s mother asks him to buy 100 pieces of sweets worth 100/-. The sweet shop has 3 kinds of sweets, kajubarfi, gulabjamun and sandesh. Kajubarfi costs 10/- per piece, gulabjamun costs 3/- per piece and sandesh costs 50 paise per piece. If Nikhil decides to buy at least one sweet of each type, how many gulabjamuns should he buy?

If $$\log_4m + \log_4n = \log_2(m + n)$$ where m and n are positive real numbers, then which of the following must be true?

Consider the equation $$\log_5(x - 2) = 2 \log_{25}(2x - 4)$$, where x is a real number.
For how many different values of x does the given equation hold?

For how many distinct real values of $$x$$ does the equation below hold true? (Consider $$a$$ > 0.)
$$\dfrac{x^2 \log_a(16)}{\log_a(32)} - \dfrac{\log_a(64)}{\log_a(32)} - x = 0 $$

Consider the formula, $$S=\frac{\alpha\times\omega}{\tau+\rho\times\omega}$$ positive integers. If ⍵ is increased and ⍺, τ and ρ are kept constant, then S:

Prof. Suman takes a number of quizzes for a course. All the quizzes are out of 100. A student can get an A grade in the course if the average of her scores is more than or equal to 90.Grade B is awarded to a student if the average of her scores is between 87 and 89 (both included). If the average is below 87, the student gets a C grade. Ramesh is preparing for the last quiz and he realizes that he will score a minimum of 97 to get an A grade. After the quiz, he realizes that he will score 70, and he will just manage a B. How many quizzes did Prof. Suman take?

A teacher noticed a strange distribution of marks in the exam. There were only three distinct
scores: 6, 8 and 20. The mode of the distribution was 8. The sum of the scores of all the students was 504. The number of students in the in most populated category was equal to the sum of the number of students with lowest score and twice the number of students with the highest score. The total number of students in the class was:

Ramesh analysed the monthly salary figures of five vice presidents of his company. All the salary figures are integers. The mean and the median salary figures are 5 lakh, and the only mode is 8 lakh. Which of the options below is the sum (in lakh) of the highest and the lowest salaries?

A computer program was tested 300 times before its release. The testing was done in three stages
of 100 tests each. The software failed 15 times in Stage I, 12 times in Stage II, 8 times in Stage III, 6 times in both Stage I and Stage II, 7 times in both Stage II and Stage III, 4 times in both Stage I and Stage III, and 4 times in all the three stages. How many times the software failed in a single stage only?

A boat, stationed at the North of a lighthouse, is making an angle of 30° with the top of the lighthouse. Simultaneously, another boat, stationed at the East of the same lighthouse, is making an angle of 45° with the top of the lighthouse. What will be the shortest distance between these two boats? The height of the lighthouse is 300 feet. Assume both the boats are of negligible dimensions.

A girl travels along a straight line, from point A to B at a constant speed, $$V_1$$ meters/sec for T seconds. Next, she travels from point B to C along a straight line, at a constant speed of $$V_2$$ meters/sec for another T seconds. BC makes an angle 105° with AB. If CA makes an angle 30° with BC, how much time will she take to travel back from point C to A at a constant speed of $$V_2$$ meters/sec, if she travels along a straight line from C to A?

Two friends, Ram and Shyam, start at the same point, at the same time. Ram travels straight north at a speed of 10km/hr, while Shyam travels straight east at twice the speed of Ram. After 15 minutes, Shyam messages Ram that he is just passing by a large telephone tower and after another 15 minutes Ram messages Shyam that he is just passing by an old banyan tree. After some more time has elapsed, Ram and Shyam stop. They stop at the same point of time. If the straight-line distance between Ram and Shyam now is 50 km, how far is Shyam from the banyan tree (in km)? (Assume that Ram and Shyam travel on a flat surface.)

A hare and a tortoise run between points O and P located exactly 6 km from each other on a straight line. They start together at O, go straight to P and then return to O along the same line. They run at constant speeds of 12 km/hr and 1 km/hr respectively. Since the tortoise is slower than the hare, the hare shuttles between O and P until the tortoise goes once to P and returns to O. During the run, how many times are the hare and the tortoise separated by an exact distance of 1 km from each other?

At any point of time, let x be the smaller of the two angles made by the hour hand with the minute hand on an analogue clock (in degrees). During the time interval from 2:30 p.m. to 3:00 p.m., what is the minimum possible value of x?

Let ABC be an isosceles triangle. Suppose that the sides AB and AC are equal and let the length of AB be x cm. Let b denote the angle ∠ABC and sin b = 3/5. If the area of the triangle ABC is M square cm, then which of the following is true about M?

Rajesh, a courier delivery agent, starts at point A and makes a delivery each at points B, C and D, in that order. He travels in a straight line between any two consecutive points. The following are known: (i) AB and CD intersect at a right angle at E, and (ii) BC, CE and ED are respectively 1.3 km, 0.5 km and 2.5 km long. If AD is parallel to BC, then what is the total distance (in km) that Rajesh covers in travelling from A to D?

The six faces of a wooden cube of side 6 cm are labelled A, B, C, D, E and F respectively. Three of these faces A, B, and C are each adjacent to the other two, and are painted red. The other three faces are not painted. Then, the wooden cube is neatly cut into 216 little cubes of equal size. How many of the little cubes have no sides painted?

ABC is a triangle with integer-valued sides AB = 1, BC >1, and CA >1. If D is the mid-point of AB, then, which of the following options is the closest to the maximum possible value of the angle ACD (in degrees)?

The topmost point of a perfectly vertical pole is marked A. The pole stands on a flat ground at point D. The points B and C are somewhere between A and D on the pole. From a point E, located on the ground at a certain distance from D, the points A, B and C are at angles of 60, 45 and 30 degrees respectively. What is AB : BC : CD?

Two circles P and Q, each of radius 2 cm, pass through each other’s centres. They intersect at points A and B. A circle R is drawn with diameter AB. What is the area of overlap (in square cm) between the circles R and P?

Find the value of
$$\frac{\sin^{6}15^{\circ} + \sin^{6}75^{\circ} + 6\sin^{2}15^{\circ}\sin^{2}75^{\circ}}{\sin^{4}15^{\circ} + \sin^{4}75^{\circ} + 5\sin^{2}15^{\circ}\sin^{2}75^{\circ}}$$

ABC is a triangle with BC=5. D is the foot of the perpendicular from A on BC. E is a point on CD such that BE=3. The value of $$AB^2 - AE^2 + 6CD$$ is:

ABC is a triangle and the coordinates of A, B and C are (a, b-2c), (a, b+4c) and (-2a,3c) respectively where a, b and c are positive numbers.
The area of the triangle ABC is:

A non-flying ant wants to travel from the bottom corner to the diagonally opposite top corner of a cubical room. The side of the room is 2 meters. What will be the minimum distance that the ant needs to travel?

ABCD is a trapezoid where BC is parallel to AD and perpendicular to AB. Kindly note that BC< AD. P is a point on AD such that CPD is an equilateral triangle. Q is a point on BC such that AQ is parallel to PC. If the area of the triangle CPD is $$4\sqrt{\ 3}$$, find the area of the triangle ABQ.

ABCD is a trapezoid where BC is parallel to AD and perpendicular to AB. Kindly note that BC< AD. P is a point on AD such that CPD is an equilateral triangle. Q is a point on BC such that AQ is parallel to PC. If the area of the triangle CPD is $$4\sqrt{\ 3}$$, find the area of the triangle ABQ.

Which of the following will BEST capture the relationship between GDP (x-axis) and Life Satisfaction (y-axis) of countries?

The _____ refers to investments made for product development, marketing, and market research.

An investor lent-out a certain sum on simple interest and the same sum on compound interest at the same rate of interest per annum. He noticed that the ratio of the difference of the compound interest and the simple interest for 4 years to the difference of the compound interest and the simple interest for 3 years is 20:8. The approximate rate of interest per annum is given by,

According to the passage, the subconscious mind .... :

The term "currency manipulation" by the developing and newly industrialized economies a mentioned in the pa sage can be explained as ..............

A number is interesting if on adding the sum of the digits of the number and the product of the digits of the number, the result is equal to the number. What fraction of numbers between 10 and 100 (both 10 and 100 included) is interesting?

p and q are positive numbers such that $$p^q = q^p$$, and $$q = 9p$$. The value of p is

Consider the expression $$(xxx)_{b}=x^3$$, where b is the base, and x is any digit of base b. Find the value of b:

Please read the following sentences carefully:
I — 103 and 7 are the only prime factors of 1000027
II — $$\sqrt[6]{6!}>\sqrt[7]{7!}$$
III — If I travel one half of my journey at an average speed of x km/h, it will be impossible for me to attain an average speed of 2x km/h for the entire journey.

If $$N = (11^{p + 7})(7^{q - 2})(5^{r + 1})(3^{s})$$ is a perfect cube, where $$p, q, r$$ and $$s$$ are positive integers, then the smallest value of $$p + q + r + s$$ is :

A three - digit number has digits in strictly descending order and divisible by 10. By changing the places of the digits a new three - digit number is constructed in such a way that the new number is divisible by 10. The difference between the original number and the new number is divisible by 40. How many numbers will satisfy all these conditions?

If the last 6 digits of [(M)! - (N)!] are 999000, which of the following option is not possible for (M) × (M - N)? Both (M) and (N) are positive integers and M > N. (M)! is factorial M.

$$x, 17, 3x - y^{2} - 2$$, and $$3x + y^{2} - 30$$, are four consecutive terms of an increasing arithmetic sequence. The sum of the four number is divisible by:

Two numbers, $$297_{B}$$ and $$792_{B}$$ , belong to base B number system. If the first number is a factor of the second number then the value of B is:

Read the following instruction carefully and answer the question that follows:
Expression $$\sum_{n=1}^{13}\frac{1}{n}$$ can also be written as $$\frac{x}{13!}$$ What would be the remainder if x is divided by 11?

Consider four natural numbers: x, y, x + y, and x - y. Two statements are provided below:
I. All four numbers are prime numbers.
II. The arithmetic mean of the numbers is greater than 4.
Which of the following statements would be sufficient to determine the sum of the four numbers?

In which year was the increase in spending on CSR, vis - à - vis the previous year, the maximum?

Of the years indicated below, in which year was the ratio of CSR/ Assets the maximum?

The maximum value of spending on CSR activities in the period 2004-2009 is closest to which of the following options?

In which year, did the spending on CSR (measured in Rs) decline, as compared to previous year?

The level in which the Ex-Defence Servicemen are highest in percentage terms is:

If the company decides to abolish all vacant posts at all levels, which level would incur the highest reduction in percentage terms ?

Among all levels, which level has the lowest representation of Ex- policemen?

Which of the following, shows the maximum year to year percentage growth in feedback?

Count the number of instances in which "annual decreasing efforts in research" is accompanied with "annual increase in feedback"?

Research efficiency is the ratio of cumulative number of publication for a period of 3 years to the cumulative number of hours spent on research activity in those 3 years. Which of the following professors is the least efficient researcher for the period 2015 to 2017?

How many students major in chemistry?

If the proportion of physics majors who are from Delhi is the same as the proportion of engineering majors who are from Delhi, how many engineering majors are from Delhi?

12% of all students are from Chennai. What is the largest possible percentage of economics students that can be from Chennai, rounded off to the nearest integer?

Based on the given information, how many nations can be uniquely identified?

Based on the given information, which of the following CANNOT be ruled out?

Which of the following information, when considered in addition to the given information, does not allow us to completely identify the nine nations in the graph?

Given $$A = |x + 3| + | x - 2 | - | 2x -8|$$. The maximum value of $$|A|$$ is:

In a school, the number of students in each class, from Class I to X, in that order, are in an arithmetic progression. The total number of students from Class I to V is twice the total number of students from Class VI to X.

If the total number of students from Class I to IV is 462, how many students are there in Class VI?

Let $$f(x) = \frac{x^2 + 1}{x^2 - 1}$$ if $$x \neq 1, -1,$$ and 1 if x = 1, -1. Let $$g(x) = \frac{x + 1}{x - 1}$$ if $$x \neq 1,$$ and 3 if x = 1.
What is the minimum possible values of $$\frac{f(x)}{g(x)}$$ ?

The figure below shows the graph of a function f(x). How many solutions does the equation f(f(x)) = 15 have?

In a list of 7 integers, one integer, denoted as x is unknown. The other six integers are 20, 4, 10, 4,8, and 4. If the mean, median, and mode of these seven integers are arranged in increasing order, they form an arithmetic progression. The sum of all possible values of x is

The number of point(s) satisfying the above mentioned characteristics and not in the first quadrant is/are

A shop sells bags in three sizes: small, medium and large. A large bag costs Rs.1000, a medium bag costs Rs.200, and a small bag costs Rs.50. Three buyers, Ashish, Banti and Chintu, independently buy some numbers of these types of bags. The respective amounts spent by Ashish, Banti and Chintu are equal. Put together, the shop sells 1 large bag, 15 small bags and some medium bags to these three buyers. What is the minimum number of medium bags that the shop sells to them?

The roots of the polynomial $$P(x) = 2x^3 - 11x^2 + 17x - 6$$ are the radii of three concentric circles.
The ratio of their area, when arranged from the largest to the smallest, is:

If $$x$$ and $$y$$ are real numbers, the least possible value of the expression $$4(x - 2)^{2} + 4(y - 3)^{2} - 2(x - 3)^{2}$$ is :

a, b, c are integers, |a| ≠ |b| ≠|c| and -10 ≤ a, b, c ≤ 10. What will be the maximum possible value of [abc - (a + b + c)]?

When opening his fruit shop for the day a shopkeeper found that his stock of apples could be perfectly arranged in a complete triangular array: that is, every row with one apple more than the row immediately above, going all the way up ending with a single apple at the top.
During any sales transaction, apples are always picked from the uppermost row, and going below only when that row is exhausted.
When one customer walked in the middle of the day she found an incomplete array in display having 126 apples totally. How many rows of apples (complete and incomplete) were seen by this customer? (Assume that the initial stock did not exceed 150 apples.)

Let x and y be two positive integers and p be a prime number. If x (x - p) - y (y + p) = 7p, what will be the minimum value of x - y?

The sum of the cubes of two numbers is 128, while the sum of the reciprocals of their cubes is 2.

What is the product of the squares of the numbers?

Consider the expression $$\frac{(a^2+a+1)(b^2+b+1)(c^2+c+1)(d^2+d+1)(e^2+e+1)}{abcde}$$, where a,b,c,d and e are positive numbers. The minimum value of the expression is

For a positive integer x, define f(x) such that f(x + a) = f(a × x), where a is an integer and f(1) = 4. If the value of f(1003) = k, then the value of ‘k’ will be:

A marble is dropped from a height of 3 metres onto the ground. After hitting the ground, it bounces and reaches 80% of the height from which it was dropped. This repeats multiple times. Each time it bounces, the marble reaches 80% of the height previously reached. Eventually, the marble comes to rest on the ground.

What is the maximum distance that the marble travels from the time it was dropped until it comes to rest?

The mean of six positive integers is 15. The median is 18, and the only mode of the integers is less than 18. The maximum possible value of the largest of the six integers is

If $$x=(9+4\sqrt{5})^{48} = [x] +f$$, where [x] is defined as integral part of x and f is a fraction, then x (1 - f) equals

Consider the four variables A, B, C and D and a function Z of these variables, $$Z = 15A^2 - 3B^4 + C + 0.5D$$ It is given that A, B, C and D must be non-negative integers and thatall of the following relationships must hold:
i) $$2A + B \leq 2$$
ii) $$4A + 2B + C \leq 12$$
iii) $$3A + 4B + D \leq 15$$
If Z needs to be maximised, then what value must D take?

a,  b,  c,  d and  e are integers such that 1 ≤ a < b < c < d < e. If a, b, c, d and e are geometric progression and lcm (m , n) is the least common multiple of m and n, then the maximum value of $$\frac{1}{lcm(a,b)}+\frac{1}{lcm(b,c)}+\frac{1}{lcm(c,d)}+\frac{1}{lcm(d,e)}$$ is

Find z, if it is known that:
a: $$-y^2 + x^2 = 20$$
b: $$y^3 - 2x^2 - 4z \geq -12$$ and
c: x, y and z are all positive integers

Consider the system of two linear equations as follows: $$3x + 21y + p = 0$$; and $$qx + ry - 7 = 0$$, where p, q, and r are real numbers.
Which of the following statements DEFINITELY CONTRADICTS the fact that the lines represented by the two equations are coinciding?

What is the sum of the following series?
-64, -66, -68,............., -100

A chocolate dealer has to send chocolates of three brands to a shopkeeper. All the brands are packed in boxes of same size. The number of boxes to be sent is 96 of brand A, 240 of brand B and 336 of brand C. These boxes are to be packed in cartons of same size containing equal number of boxes. Each carton should contain boxes of same brand of chocolates. What could be the minimum number of cartons that the dealer has to send?

If both the sequences x, a1, a2, y and x, b1, b2, z are in A.P. and it is given that $$y > x$$ and $$z < x$$, then which of the following values can $$\left\{\frac{(a1-a2)}{(b1-b2)}\right\}$$ possibly take?

Consider the function f(x) = (x + 4)(x + 6)(x + 8) ⋯ (x + 98). The number of integers x for which f(x) < 0 is:

The operation ( x ) is defined by
(i) (1) = 2
(ii)(x  + y) = (x).(y)

for all positive integers x and y.
If $$\sum_{x=1}^n(x)$$ = 1022 then n =

If $$2 \leq |x - 1| \times  |y + 3| \leq 5$$ and both $$x$$ and $$y$$ are negative integers, find the number of possible combinations of $$x$$ and $$y$$.

Consider the set of numbers {1, 3, $$3^{2}$$, $$3^{3}$$,…...,$$3^{100}$$}. The ratio of the last number and the sum of the remaining numbers is closest to:

The sum of series, (-100) + (-95) + (-90) + …………+ 110 + 115 + 120, is:

p, q and r are three non-negative integers such that p + q + r = 10. The maximum value of pq + qr + pr + pqr is

The sum of the possible values of X in the equation |X + 7| + |X - 8| = 16 is:

The Guava club has won 40% of their football matches in the Apple Cup that they have played so far. If they play another n matches and win all of them, their winning percentage will improve to 50. Further, if they play 15 more matches and win all of them, their winning percentage will improve from 50 to 60. How many matches has the Guava club played in the Apple Cup so far? In the Apple Cup matches, there are only two possible outcomes, win or loss; draw is not possible.

Find the equation of the graph shown below.

Three truck drivers, Amar, Akbar and Anthony stop at a road side eating joint. Amar orders 10
rotis, 4 plates of tadka, and a cup of tea. Akbar orders 7 rotis, 3 plates of tadka, and a cup of tea. Amar pays 80 for the meal and Akbar pays 60. Meanwhile, Anthony orders 5 rotis, 5 plates of tadka and 5 cups of tea. How much (in ) will Anthony pay?

f is a function for which f(1)= 1 and f(x) = 2x + f(x - 1) for each natural number x$$\geq$$2. Find f(31)

Rahul has just made a $$3 \times 3$$ magic square, in which, the sum of the cells along any row, column or diagonal, is the same number N. The entries in the cells are given as expressions in x, y, and Z. Find N?

Given that a and b are integers and that $$5x+2\sqrt{7}$$ is a root of the polynomial $$x^2 - ax + b + 2\sqrt{7}$$ in $$x$$, what is the value of b?

The y - ordinates of $$A_8$$ is

A polynomial y=$$ax^{3} + bx^{2 }+ cx + d$$ intersects x-axis at 1 and -1, and y-axis at 2. The value of b is:

a, b, c are integers, |a| ≠ |b| ≠|c| and -10 ≤ a, b, c ≤ 10. What will be the maximum possible value of [abc - (a + b + c)]?

Aman decides to buy only onion, in whatever maximum quantity possible (in positive integer kilogram), with the money he has come to the market with. How much money will he be left with after the purchase?

Consider $$a_{n+1} =\frac{1}{1+\frac{1}{a_{n}}}$$ for $$n = 1,2, ....., 2008, 2009$$ where $$a_{1} = 1$$. Find the value of $$a_{1}a_{2} + a_{2}a_{3} + a_{3}a_{4} + ... + a_{2008}a_{2009}$$.

Shireen draws a circle in her courtyard. She then measures the circle’s circumference and its diameter with her measuring tape and records them as two integers, A and B respectively. She finds that A and B are co-primes, that is, their greatest common divisor is 1. She also finds their ratio, A:B, to be: 3.141614161416… (repeating endlessly).

What is A - B ?

Some members of a social service organization in Kolkata decide to prepare 2400 laddoos to gift to children in various orphanages and slums in the city, during Durga puja. The plan is that each of them makes the same number of laddoos. However, on the laddoo-making day, ten members are absent, thus each remaining member makes 12  laddoos more than earlier decided.

How many members actually make the laddoos?

If $$x^2 + x + 1 = 0$$, then $$x^{2018} + x^{2019}$$ equals which of the following:

Consider the quadratic function $$f(x) = ax^2 + bx + a$$ having two irrational roots, with a and b being two positive integers, such that $$a, b \leq 9$$.
If all such permissible pairs (a, b) are equally likely, what is the probability that a + b is greater than 9?

Consider a function $$f(x) = x^4 + x^3 + x^2 + x + 1$$, where x is a positive integer greater than 1. What will be the remainder if $$f(x^5)$$ is divided by f(x)?

Determine the value(s) of “a” for which the point $$(a, a^{2})$$ lies inside the triangle formed by the lines: 2x+ 3y= 1, x+ 2y=3 and 5x-6y= 1

If f(x) = ax + b, a and b are positive real numbers and if f(f(x)) = 9x + 8, then the value of a + b is:

Let $$a_{n} = 1 1 1 1 1 1 1..... 1$$, where 1 occurs n number of times. Then,
i. $$a_{741}$$ is not a prime.
ii. $$a_{534}$$ is not a prime.
iii. $$a_{123}$$ is not a prime.
iv. $$a_{77}$$ is not a prime.

Two different quadratic equations have a common root. Let the three unique roots of the two equations be A, B and C - all of them are positive integers. If (A + B + C) = 41 and the product of the roots of one of the equations is 35, which of the following options is definitely correct?

Consider the real-valued function $$f(x)=\frac{\log{(3x-7)}}{\sqrt{2x^{2}-7x+6}}$$ Find the domain of f(x).

The cost of running a movie theatre is Rs. 10,000 per day, plus additional Rs. 5000 per show. The theatre has 200 seats. A new movie released on Friday. There were three shows, where the ticket price was Rs. 250 each for the first two shows and Rs. 200 for the late-night show.
For all shows together, total occupancy was 80%. What was the maximum amount of profit possible?

Consider the set of numbers {1, 3, $$3^{2}$$, $$3^{3}$$,…...,$$3^{100}$$}. The ratio of the last number and the sum of the remaining numbers is closest to: