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

Arup and Swarup leave point A at 8 AM to point B. To reach B, they have to walk the first 2 km, then travel 4 km by boat and complete the final 20 km by car. Arup and Swarup walk at a constant speed of 4 km/hr and 5 km/hr respectively. Each rows his boat for 30 minutes. Arup drives his car at a constant speed of 50 km/hr while Swarup drives at 40 km/hr. If no time is wasted in transit, when will they meet again?

Hari’s family consisted of his younger brother (Chari), younger sister (Gouri), and their father and mother. When Chari was born, the sum of the ages of Hari, his father and mother was 70 years. The sum of the ages of four family members, at the time of Gouri’s birth, was twice the sum of ages of Hari’s father and mother at the time of Hari’s birth. If Chari is 4 years older than Gouri, then find the difference in age between Hari and Chari.

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:

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 shop, which sold same marked price shirts, announced an offer - if one buys three shirts then the fourth shirt is sold at a discounted price of ₹ 100 only. Patel took the offer. He left the shop with 20 shirts after paying ₹ 20,000. What is the marked price of a shirt?

Four two-way pipes A, B, C and D can either fill an empty tank or drain the full tank in 4, 10, 12 and 20 minutes respectively. All four pipes were opened simultaneously when the tank is empty. Under which of the following conditions would the tank be half filled after 30 minutes?

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

The grid below captures relationships among seven personality dimensions: "extraversion", "true_arousal_plac", "true_arousal_caff”, "arousal_plac", "arousal_caff”, "performance_plac", and "performance caff”. The diagonal represents histograms of the seven dimensions. Left of the diagonal represents scatterplots between the dimensions while the right of the diagonal represents quantitative relationships between the dimensions. The lines in the scatterplots are closest approximation of the points. The value of the relationships to the right of the diagonal can vary from -1 to +1, with -1 being the extreme linear negative relation and +1 extreme linear positive relation. (Axes of the graph are conventionally drawn).

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:

Company ABC starts an educational program in collaboration with Institute XYZ. As per the agreement, ABC and XYZ will share profit in $60:40$ ratio. The initial investment of rupee 100{,}000 on infrastructure is borne entirely by ABC whereas the running cost of \rupee 400 per student is borne by XYZ. If each student pays rupee 2000 for the program, find the minimum number of students required to make the program profitable, assuming ABC wants to recover its investment in the very first year and the program has no seat limits.

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?

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:

$ABCD$ 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 $150\ \text{cm}^2$?

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.

If $a,b,c$ are three consecutive integers between $-10$ and $+10$ (both inclusive), how many {integer values are possible for} \[ \frac{a^3+b^3+c^3+3abc}{(a+b+c)^2}\,? \]

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?

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 $X$.

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.

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

A square piece of paper is folded three times along its diagonal to get an isosceles triangle whose equal sides are $10$ cm. What is the area of the unfolded original piece of paper?

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 $N$?

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?}

Four persons walk from Point A to Point D following different routes. The one following ABCD takes 70 minutes. Another person takes 45 minutes following ABD. The third person takes 30 minutes following ACD. The last person takes 65 minutes following ACBD. If all walk at the same speed, how long will it take to go from point B to point C?