List of top Quantitative Ability and Data Interpretation Questions asked in XAT

In the figure below, $AB = AC = CD$. If $\angle ADB = 20^\circ$, what is the value of $\angle BAD$?

In the figure, two circular arcs subtend $60^\circ$ and $90^\circ$ at their respective centres. If the length of the bottom arc $Y$ is $10\pi$, find the length of the other arc $X$.

The difference between the area of the circumcircle and the area of the incircle of an equilateral triangle is $2156\ \text{cm}^2$. What is the area of the equilateral triangle?

$ABCD$ is a quadrilateral such that $AD=9\ \text{cm}$, $BC=13\ \text{cm}$ and $\angle DAB=\angle BCD=90^\circ$. $P$ and $Q$ are two points on $AB$ and $CD$ respectively, such that $DQ:BP=1:2$ and $DQ$ is an integer. How many values can $DQ$ take, for which the maximum possible area of the quadrilateral $PBQD$ is $150\ \text{cm}^2$?

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

For two positive integers $a$ and $b$, if $(a+b)^{(a+b)}$ is divisible by $500$, then the least possible value of $a\times b$ is:

Study the data given in the table below and answer the question that follow:

Region vs Shop Type

Region \\ Shop Type	North	East	West	South	All India
Grocers	\(34.7\)	\(32\)	\(32.2\)	\(30.2\)	\(32.4\)
Pan Bidi	\(7.1\)	\(21.2\)	\(13.1\)	\(19.1\)	\(14.6\)
Food Shops	\(11.8\)	\(7.9\)	\(14.8\)	\(12\)	\(11.6\)
General Stores	\(12.4\)	\(9.1\)	\(12\)	\(6.6\)	\(10.1\)
Electrical Hardware	\(8.3\)	\(5.6\)	\(7.7\)	\(5.7\)	\(6.7\)
Chemists	\(6\)	\(5.8\)	\(5\)	\(5.7\)	\(5.7\)
Cosmetic Stores	\(3.8\)	\(3.6\)	\(3.3\)	\(3.9\)	\(3.7\)
Others	\(15.8\)	\(14.8\)	\(12\)	\(16.8\)	\(15.2\)
Total	\(100\)	\(100\)	\(100\)	\(100\)	\(100\)

All gures are in percentage Based on survey of ‘shop types’ Kamath categorized Indian states into four geographical regions as shown in the table above. His boss felt that the categorization was inadequate since important labels were missing. Kamath argued that no further labels are required to interpret the data.

A person standing at point $A$ on the ground saw an object at point $B$ on the ground $600$ m away. The object started flying towards him at an angle of $30^\circ$ with the ground. The person saw it the second time at point $C$ when the angle of elevation was $30^\circ$. At $C$, the object changed direction and continued flying upwards. The person saw it the third time when it was directly above him. The object flew at a constant speed of $10$ kmph. Find the angle (with the ground) at which it flew after the second sighting. You may use additional statement(s) if required.

Statement I: After changing direction the object took $3$ more minutes than it had taken before.
Statement II: After changing direction the object travelled an additional $200\sqrt{3}$ metres.
Which of the following is correct?

Pradeep could either walk or drive to office. The time taken to walk to the office is $8$ times the driving time. One day, his wife took the car making him walk to office. After walking $1$ km, he reached a temple when his wife called to say that he can now take the car. Pradeep figures that continuing to walk to the office will take as long as walking back home and then driving to the office. Calculate the distance between the temple and the office.

Each day on Planet M is 10 hours, each hour 60 minutes and each minute 40 seconds. The inhabitants use a 10-hour analog clock. If such a clock shows \(\,3\) hours \(42\) minutes \(20\) seconds in a {mirror, what will be the time on Planet M exactly after \(5\) minutes?}

A water tank has $M$ inlet pipes and $N$ outlet pipes. An inlet pipe can fill the tank in $8$ hours while an outlet pipe can empty the full tank in $12$ hours. If all pipes are left open simultaneously, it takes $6$ hours to fill the empty tank. What is the relationship between $M$ and $N$?

In an amusement park, a visitor gets to ride on three different rides (A, B and C) for free. On a particular day 77 opted for ride A, 55 opted for B and 50 opted for C; 25 visitors opted for both A and C, 22 opted for both A and B, while no visitor opted for both B and C. 40 visitors did not opt for ride A or B (i.e., they were outside $A \cup B$). How many visited the amusement park on that day?

A person is standing at a distance of 1800 meters facing a giant clock at the top of a tower. At 5.00 p.m., he can see the tip of the minute hand of the clock at 30 degree elevation from his eye level. Immediately, the person starts walking towards the tower. At 5.10 p.m., the person noticed that the tip of the minute hand made an angle of 60 degrees with respect to his eye-level. Using three-dimensional vision, find the speed at which the person is walking. The length of the minute hand is \( \frac{200}{\sqrt{3}} \) meters (where \( \sqrt{3} = 1.732 \)).

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 (nearest integer) for the manufacturer who sells his product to the retailer? The retailer gives 10% discount on MRP.

Product $M$ is produced by mixing chemical $X$ and chemical $Y$ in the ratio $5:4$. Chemical $X$ is prepared by mixing two raw materials, $A$ and $B$, in the ratio $1:3$. Chemical $Y$ is prepared by mixing raw materials, $B$ and $C$, in the ratio $2:1$. Then the final mixture is prepared by mixing $864$ units of product $M$ with water. If the concentration of the raw material $B$ in the final mixture is $50%$, how much water had been added to product $M$?

A solid metal cylinder of 10 cm height and 14 cm diameter is melted and re-cast into two cones in the proportion of 3 : 4 (volume), keeping the height 10 cm. What would be the percentage change in the flat surface area before and after?

In an examination, two types of questions are asked: one mark questions and two marks questions. For each wrong answer, of one mark question, the deduction is 1/4 of a mark and for each wrong answer, of two marks question, the deduction is 1/3 of a mark.
Moreover, 1/2 of a mark is deducted for unanswered question. The question paper has 10 one mark questions and 10 two marks questions. In the examination, students got all possible marks between 25 and 30 and every student had different marks. What would be the rank of a student, who scores a total of 27.5 marks?

What is the sum of the following series? $-64, -66, -68, \ldots, -100$

An ascending series of numbers satisfies the following conditions: i. When divided by 3, 4, 5 or 6, the numbers leave a remainder of 2.
ii. When divided by 11, the numbers leave no remainder. The 6th number in this series will be:

A three-digit number has digits in strictly descending order and is 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 options is {not possible for $M \times (M-N)$? Both $M$ and $N$ are positive integers with $M>N$. (Here $M!$ denotes $M$ factorial.)}

Find the equation of the graph shown below.

If \(f(x^{2}-1)=x^{4-7x^{2}+k_{1}\) and \(f(x^{3}-2)=x^{6}-9x^{3}+k_{2}\) then the value of \((k_{2}-k_{1})\) is}

If $a,b,c,d$ are four different positive integers selected from $1$ to $25$, then the highest possible value of \(\dfrac{(a+b)+(c+d){(a+b)+(c-d)}\) would be:}