XAT 2011 Question Paper - QUANT
For the following questions answer them individually
Ln 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 āmagicā number if $$x_{1}x_{2}x_{3}$$ is exactly the same as $$x_{4}x_{5}x_{6}$$ or $$x_{5}x_{6}x_{7}$$ or both. $$X_{i}$$ can take values from 0 to 9, but 2 followed by seven $$0_{s}$$ is not a valid account number. What is the maximum possible number of customers having a āmagicā account number?
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?
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 feet 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?
are followed by two statements labelled as I and II. Decide if these statements are sufficient to conclusively answer the question. Choose the appropriate answer from the options given below:
A. Statement I alone is sufficient to answer the question.
B. Statement II alone is sufficient to answer the question.
C. Statement I and Statement II together are sufficient, but neither of the two alone is sufficient to answer the question.
D. Either Statement I or Statement II alone is sufficient to answer the question.
E. Neither Statement I nor Statement II is necessary to answer the question.
Let PQRS be a quadrilateral. Two circles O1 and O2 are inscribed in triangles PQR and PSR respectively. Circle O1 touches PR at M and circle O2 touches PR at N. Find the length of MN.
I. A circle is inscribed in the quadrilateral PQRS.
II. The radii of the circles O1 and O2 are 5 and 6 units respectively.
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Given below is an equation where the letters represent digits.
(PQ). (RQ) = XXX. Determine the sum of P + Q + R+ X.
I. X = 9.
II. The digits are unique.
Answer questions based on the following information:
Mulchand Textiles produces a single product of only one quality ā 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 āVariable Cost Estimates of Mulchand Textilesā provided the estimates of labour and material costs.
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.
The estimated material cost given in the table titled āVariable Cost Estimates of Mulchand Textilesā included the cost of material that gets spoiled in the production process. Mr. Sharma decomposed the estimated material cost into material spoilage cost and material usage cost, but he lost the data when his computer crashed. When he saw the following line diagram, here called that he measured the estimate of material spoilage cost per square feet of output on the y - axis and monthly output on the x - axis.
Estimated material usage cost per square feet of output.
Mr. Sharma found some printouts of line diagrams. The axes of the graphs were not marked, but Mr. Sharma remembered that he measured monthly output on the x - axis. Which of the following diagrams would represent the estimates of electricity cost per square feet of output versus monthly output?
answer questions based on the following information:
In the beginning of the year 2010, Mr. Sanyal had the option to invest Rs. 800000 in one or more of the following assets ā gold, silver, US bonds, EU bonds, UK bonds and Japanese bonds. In order to invest in US bonds, one must first 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 first 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 fixed at the beginning of every
month and remained unchanged throughout the month. Refer to the table titled āBullion Prices and Exchange Rates in 2010" for the relevant data.
Ā Ā Ā Ā Ā Ā Ā Ā Ā Ā Ā Ā Ā Ā Ā Ā Ā Ā Ā Ā Ā Ā Ā Ā Ā Ā Ā Ā Ā Ā Ā Ā Ā Ā Ā Ā Ā Ā Ā Ā Ā Ā Ā Ā Ā Ā Ā Ā Bullion Prices and Exchange Rates in 2010
Interest rates on US, EU, UK and Japanese bonds are 10%, 20%, 15% and 5% respectively.
Mr. Sanyal invested his entire fund in gold, US bonds and EU bonds in January 2010. He liquefied his assets on 31st August 2010 and gained 13% on his investments. If instead he had held his assets for an additional month he would have gained l6.25%. Which of the following options is correct?
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