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

Six playing cards are lying face down on a table, two of them are kings. Two cards are drawn at random. Let \(a\) denote the probability that at least one of the cards drawn is a king, and \(b\) denote the probability of not drawing a king. The ratio \(a/b\) is
The radius of a circle with centre \(O\) is \(\sqrt{50}\) cm. \(A\) and \(C\) are two points on the circle, and \(B\) is a point inside the circle. The length of \(AB\) is \(6\) cm, and the length of \(BC\) is \(2\) cm. The angle \(\angle ABC\) is a right angle. Find the square of the distance \(OB\).
Consider \(f(x)=x^{4+x^{3}+x^{2}+x+1\), where \(x\) is a positive integer greater than \(1\). What will be the remainder if \(f(x^{5})\) is divided by \(f(x)\)?}
Consider \((xxx)_b = x^3\), where \(b\) is the base, and \(x\) is any digit in base \(b\). Find \(b\).
Ram, Shyam and Hari went out for a 100 km journey. Ram and Hari started the journey in Ram's car at the rate of 25 kmph, while Shyam walked at 5 kmph. After sometime, Hari got off and started walking at the rate of 5 kmph and Ram went back to pick up Shyam. All three reached the destination simultaneously. The number of hours required for the trip was:
70% of the students who joined XCRI last year play football, 75% play cricket, 80% play basketball and 85% play carrom. The minimum percentage of students who play all four games is:
The central park of the city is 40 metres long and 30 metres wide. The mayor wants to construct two roads of equal width in the park such that the roads intersect each other at right angles and the center of the rectangle coincides with the center of the rectangle formed by the intersection of the two roads. Further, the mayor wants that the area of the two roads to be equal to the remaining area of the park. What should be the width of the roads?
\(p\) and \(q\) are positive numbers such that \(p^{q}=q^{p}\), and \(q=9p\). The value of \(p\) is
The taxis plying in Wasseypur have the following fare structure: Rs 20 for the first two kilometers, Rs 5 for every km in excess of 2 km and up to 10 km, and Rs 8 for every km in excess of 10 km. Bullock carts on the other hand charge Rs 2 per km. Sardar Khan takes a taxi from the Wasseypur railway station to his home. On the way, at a distance of 14 km from the railway station, he meets Faizal Khan, and gets down from the taxi to talk to him. Later he takes a bullock cart to reach his home. He spends a total of Rs 102 to reach his home from the railway station. How far is his home from the railway station (in kilometers)?
Consider the expression \(\dfrac{(a^2+a+1)(b^2+b+1)(c^2+c+1)(d^2+d+1)(e^2+e+1){abcde}\), where \(a,b,c,d\) and \(e\) are positive numbers. The minimum value of the expression is}
In a square \(PQRS\), \(A\) and \(B\) are two points on \(PS\) and \(SR\) such that \(PA = 2AS\), and \(RB = 2BS\). If \(PQ = 6\), the area of the triangle \(ABQ\) is (in sq. cm).
How many whole numbers between 100 and 800 contain the digit 2?
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?
\(p, q\) and \(r\) are three non-negative integers such that \(p+q+r=10\). The maximum value of \(pq+qr+pr+pqr\) is
Albela, Bob and Chulbul have to read a document of seventy eight pages and make a presentation next day. They realize that the article is difficult to understand and they would require teamwork to finish the assignment. Albela can read a page in 2 minutes, Bob in 3 minutes, and Chulbul in 4 minutes. If they divide the article into 3 parts so that all three of them spend the equal amount of time on the article, the number of pages that Bob should read is
At the centre of a city's municipal park there is a large circular pool. A fish is released in the water at the edge of the pool. The fish swims north for 300 feet before it hits the edge of the pool. It then turns east and swims for 400 feet before hitting the edge again. What is the area of the pool?
Mr. Mehra is planning for higher education expenses of his two sons aged 15 and 12. He plans to divide Rs 15 lakhs in two equal parts and invest in two different plans such that his sons may have access to Rs 21 lakhs each when they reach the age of 21. He is looking for plans that will give him a simple interest per annum. The rates of interest of the plans for his younger son and his elder son should be
Ramesh bought a total of 6 fruits (apples and oranges) from the market. He found that he required one orange less to extract the same quantity of juice as extracted from apples. If Ramesh had used the same number of apples and oranges to make the blend, then which of the following correctly represents the percentage of apple juice in the blend?
Sara has just joined Facebook. She has 5 friends. Each of her five friends has twenty five friends. It is found that at least two of Sara's friends are connected with each other. On her birthday, Sara decides to invite her friends and the friends of her friends. How many people did she invite for her birthday party?
Prof. Mandal walks to the market and comes back in an auto. It takes him 90 minutes to make the round trip. If he takes an auto both ways, it takes him 30 minutes. On a Sunday, he decides to walk both ways. How long would it take him?
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
Ram and Shyam form a partnership (with Shyam as working partner) and start a business by investing 4000 and 6000 respectively. The conditions of partnership were as follows:
1. In case of profits till 200,000 per annum, profits would be shared in the ratio of the invested capital.
2. Profits from 200,001 till 400,000 Shyam would take 20% out of the profit, before the division of remaining profits, which will then be based on ratio of invested capital.
3. Profits in excess of 400,000, Shyam would take 35% out of the profits beyond 400,000, before the division of remaining profits, which will then be based on ratio of invested capital.
If Shyam’s share in a particular year was 367000, which option indicates the total business profit (in ₹) for that year?

The following graphs show the revenue (in $ million) of three companies in their initial six years of operations, in an economy which is characterized by a persistent inflation.

Ramya, based in Shanpur, took her car for a 400 km trip to Rampur. She maintained a log of the odometer readings and the amount of petrol she purchased at different petrol pumps at different prices (given below). Her car already had 10 litres of petrol at the start of the journey, and she first purchased petrol at the start of the journey, as given in the table below, and she had 5 litres remaining at the end of the journey

Odometer Reading (Km)Petrol Purchased (Litre)Rate of Petrol (per Litre)
400 (Start of journey)2030
6001535
6501040
800 (End of journey)––

The following pie chart shows the percentage distribution of runs scored by a batsman in a test innings.