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

In a bank the account numbers are all 8-digit numbers, and they all start with the digit 2. So, an account number can be represented as $2x_1x_2x_3x_4x_5x_6x_7$. An account number is considered to be a ‘magic’ number if $x_1x_2x_3$ is exactly the same as $x_4x_5x_6$ or $x_5x_6x_7$ or both. $x_i$ can take values from 0 to 9, but 2 followed by seven 0’s is not valid. What is the maximum possible number of customers having a ‘magic’ account number?
In a plane rectangular coordinate system, points $L, M, N,$ and $O$ are represented by the coordinates $(-5,0), (1,-1), (0,5),$ and $(-1,5)$ respectively. Consider a variable point $P$ in the same plane. The minimum value of $PL + PM + PN + PO$ is:
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:
Prof. Bee noticed something peculiar while entering the quiz marks of his five students into a spreadsheet. The spreadsheet was programmed to calculate the average after each score was entered. Prof. Bee entered the marks in a random order and noticed that after each mark was entered, the average was always an integer. In ascending order, the marks of the students were 71, 76, 80, 82 and 91. What were the fourth and fifth marks that Prof. Bee entered?
The micromanometer in a certain factory can measure the pressure inside the gas chamber from 1 unit to 999999 units. Lately this instrument has not been working properly. The problem with the instrument is that it always skips the digit 5 and moves directly from 4 to 6. What is the actual pressure inside the gas chamber if the micromanometer displays 003016?
Consider a square $ABCD$ of side $60$ cm. It contains arcs $BD$ and $AC$ drawn with centres at $A$ and $D$ respectively. A circle is drawn such that it is tangent to side $AB$, and the arcs $BD$ and $AC$. What is the radius of the circle?
There are 240 second year students in a B-School. The Finance area offers 3 electives: Financial Derivatives (FD), Behavioural Finance (BF), and Security Analysis (SA). - 4 students have taken all three electives. - 48 students have taken FD. - The number of students who study FD and SA but not BF is twice the number of students who study FD and BF but not SA, and 4 times the number of students who study all three. - 124 students study SA. - 59 students do not take any of these subjects. - The number of students who study FD and SA but not BF is equal to the number of students who study BF and SA but not FD. Question: How many students study Behavioural Finance (BF) only?
In the country of Twenty, there are exactly twenty cities, and there is exactly one direct road between any two cities. No two direct roads have an overlapping road segment. After the election dates are announced, candidates from their respective cities start visiting the other cities. Following are the rules that the election commission has laid down for the candidates:
1. Each candidate must visit each of the other cities exactly once.
2. Each candidate must use only the direct roads between two cities for going from one city to another.
3. The candidate must return to his own city at the end of the campaign.
4. No direct road between two cities would be used by more than one candidate.
The maximum possible number of candidates is:
Mulchand Textiles produces a single product of only one quality – waterproof synthetic fabric. Mr.Sharma, the cost accountant of Mulchand Textiles, estimated the costs of Mulchand Textiles for different possible monthly output levels. Before he could tabulate his estimates his computer crashed, and Mr. Sharma lost all data. Fortunately he had some printouts of some incomplete tables, charts and diagrams. The table titled “Variable Cost Estimates of Mulchand Textiles” provided the estimates of labour and material costs.
Variable Cost Estimates of Mulchand Textiles
Output (Square feet)Labour cost (Rs.)Material cost (Rs.)
250002150011050
500004150022000
750006000033000
1000007800044000
1250009500054750
15000011100065700
17500013300076650
20000016000088000
Apart from labour and material costs Mulchand Textiles incurs administrative costs of Rs. 40,000 per month, and electricity costs. Mr. Sharma recalled that estimate data of variable electricity cost had certain peculiar characteristics. Values at every 25000 sq ft of output increased in geometric progression till 150000 sq ft of output, after which values increased in arithmetic progression for every 25000 sq ft of output. Mr. Sharma remembered that the electricity cost was estimated to be Rs. 3800 for 25000 sq.ft. of output, Rs. 5700 for 50000 square feet of output and Rs. 38856.50 for 175000 square feet of output.

In the beginning of the year 2010, Mr. Sanyal had the option to invest Rs. 800000 in one or more of the following assets – gold, silver, US bonds, EU bonds, UK bonds and Japanese bonds. In order to invest in US bonds, one must rst convert his investible fund into US Dollars at the ongoing exchange rate. Similarly, if one wants to invest in EU bonds or UK bonds or Japanese bonds one must rst convert his investible fund into Euro, British Pounds and Japanese Yen respectively at the ongoing exchange rates. Transactions were allowed only in the beginning of every month. Bullion prices and exchange rates were xed at the beginning of every month and remained unchanged throughout the month. Refer to the table titled “Bullion Prices and Exchange Rates in 2010" for the relevant data.
                                                                    Bullion Prices and Exchange Rates in 2010

DateGold prices
Rs/ 10 gram		Silver prices
Rs/ 10 gram		US$
Rs/ US$		€
Rs/ €		£
Rs/ £		¥
Rs/ ¥
1-Jan2000030040 60700.5
1-Feb201003024161.5710.51
1-Mar202503074162710.52
1-Apr203303104262710.52
1-May204003124262.5720.53
1-Jun205003184265720.54
1-Jul206503304463730.55
1-Aug207203354563730.55
1-Sep208503404764740.57
1-Oct209203424965740.58
1-Nov20950345506574.50.59
1-Dec210003505065750.60
Let $PQRS$ be a quadrilateral. Two circles $O_1$ and $O_2$ are inscribed in triangles $PQR$ and $PSR$ respectively. Circle $O_1$ touches $PR$ at $M$ and circle $O_2$ touches $PR$ at $N$. Find the length of $MN$. % Statement I A circle is inscribed in the quadrilateral $PQRS$. % Statement II The radii of the circles $O_1$ and $O_2$ are 5 and 6 units respectively.
Given below is an equation where the letters represent digits: \[ (PQ)\,(RQ) = XXX \] Determine the sum of $P+Q+R+X$. % Statement I $X = 9$. % Statement II The digits are unique.
Rakhal is looking for a field where he can graze his cow. He finds a local farmer, Gopal, who agrees to rent his field to Rakhal for Rs. 1000 a year. Rakhal finds a post in the field and ties his cow to the post with a 25-foot rope. After some months, Gopal tells Rakhal that he will build a shed with four walls on the field with the post as one of the corner posts. The shed would be 15 feet by 10 feet. Rakhal agrees but he realizes that this arrangement would reduce the available area for grazing. What should be the modified rent to compensate for this loss of grazing area if Rakhal has to keep the cow tied to the same post with the same rope?
Prof. Bee noticed something peculiar while entering the quiz marks of his five students into a spreadsheet. The spreadsheet was programmed to calculate the average after each score was entered. Prof. Bee entered the marks in a random order and noticed that after each mark was entered, the average was always an integer. In ascending order, the marks of the students were 71, 76, 80, 82 and 91. What were the fourth and fifth marks that Prof. Bee entered?
In a bank the account numbers are all 8-digit numbers, and they all start with the digit 2. So, an account number can be represented as $2x_1x_2x_3x_4x_5x_6x_7$. An account number is considered to be a ‘magic’ number if $x_1x_2x_3$ is exactly the same as $x_4x_5x_6$ or $x_5x_6x_7$ or both. $x_i$ can take values from 0 to 9, but 2 followed by seven 0’s is not valid. What is the maximum possible number of customers having a ‘magic’ account number?
In a plane rectangular coordinate system, points $L, M, N,$ and $O$ are represented by the coordinates $(-5,0), (1,-1), (0,5),$ and $(-1,5)$ respectively. Consider a variable point $P$ in the same plane. The minimum value of $PL + PM + PN + PO$ is:
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:
Consider a square $ABCD$ of side $60$ cm. It contains arcs $BD$ and $AC$ drawn with centres at $A$ and $D$ respectively. A circle is drawn such that it is tangent to side $AB$, and the arcs $BD$ and $AC$. What is the radius of the circle?
There are 240 second year students in a B-School. The Finance area offers 3 electives: Financial Derivatives (FD), Behavioural Finance (BF), and Security Analysis (SA). - 4 students have taken all three electives. - 48 students have taken FD. - The number of students who study FD and SA but not BF is twice the number of students who study FD and BF but not SA, and 4 times the number of students who study all three. - 124 students study SA. - 59 students do not take any of these subjects. - The number of students who study FD and SA but not BF is equal to the number of students who study BF and SA but not FD. Question: How many students study Behavioural Finance (BF) only?
The micromanometer in a certain factory can measure the pressure inside the gas chamber from 1 unit to 999999 units. Lately this instrument has not been working properly. The problem with the instrument is that it always skips the digit 5 and moves directly from 4 to 6. What is the actual pressure inside the gas chamber if the micromanometer displays 003016?
In the country of Twenty, there are exactly twenty cities, and there is exactly one direct road between any two cities. No two direct roads have an overlapping road segment. After the election dates are announced, candidates from their respective cities start visiting the other cities. Following are the rules that the election commission has laid down for the candidates:
1. Each candidate must visit each of the other cities exactly once.
2. Each candidate must use only the direct roads between two cities for going from one city to another.
3. The candidate must return to his own city at the end of the campaign.
4. No direct road between two cities would be used by more than one candidate.
The maximum possible number of candidates is:

The following graphs give annual data of Assets, Sales (as percentage of Assets) and Spending on Corporate Social Responsibility (CSR) (as percentage of Sales), of a company for the period 2004 - 2009. 

Five years ago Maxam Glass Co. had estimated its staff requirements in the ve levels in their organization as: Level - 1: 55; Level - 2: 65; Level - 3: 225 ; Level - 4: 255 & Level - 5: 300. Over the years the company had recruited people based on ad-hoc requirements, in the process also selecting ex-defence service men and ex policemen. The following graph shows actual staff strength at various levels as on date. 

Based on the following information
Income - Tax Rates for Financial Year 2009 - 10
Individual & HUF below age of 65 yearsWomen below age of 65 yearsTax Rates 
Income up to Rs. 1,60,000/-Income up to Rs. 1,90,000/-Nil 
Rs. 1,60,001 to Rs. 3,00,000/-Rs. 1,90,001 to Rs. 3,00,000/-10% 
Rs. 3,00,001 to Rs. 5,00,000/-Rs. 3,00,001 to Rs. 5,00,000/-20% 
Above Rs. 5,00,001Above Rs. 5,00,00130% 

Total income tax payable is obtained by adding two additional surcharges on calculated income tax.
Education Cess : An additional surcharge called ‘Education Cess’ is levied at the rate of 2% on the amount of income tax.
Secondary and Higher Education Cess : An additional surcharge called ‘Secondary and Higher Education Cess` is levied at the rate of 1% on the amount of income tax.
A man standing on a boat south of a lighthouse observes his shadow to be 24 meters long, as measured at sea level. On sailing 300 meters eastwards, he finds his shadow as 30 meters long, measured in a similar manner. The height of the man is 6 meters above sea level. The height of the lighthouse above sea level is: