List of top Questions asked in XAT- 2009

The regular mathematics faculty could not teach because of being sick. As a stop-gap arrangement, different visiting faculty taught different topics on 4 different days in a week. The scheduled time for class was 7:00 am, with a maximum permissible delay of 20 minutes. The monsoon made the city bus schedules erratic, so the classes started at different times on different days.

Mr. Singh did not teach on Thursday. Calculus was taught in the class that started at 7:20 am. Mr. Chatterjee took the class on Wednesday, but he did not teach probability. The class on Monday started at 7:00 am, but Mr. Singh did not teach it. Mr. Dutta did not teach ratio and proportion. Mr. Banerjee, who did not teach set theory, taught a class that started five minutes later than the class in which probability was taught. The teacher in Friday's class taught set theory. Wednesday's class did not start at 7:10 am. No two classes started at the same time.

77. The class on Wednesday started at:

Raj Travels has the following revenue model for a group package. The owner charges Rs. 20,000 per person for a group size up to 200. For every additional traveller beyond 200, he starts offering a discount of Rs. 50 to ALL members of the group.

The maximum possible income for Raj Travels from the package is:
Four married couples competed in a singing competition. Each couple had a unique team name. Points scored by the teams were 2, 4, 6 and 8. The 'Sweet Couple' won 2 points. The 'Bindas Singers' won two more points than Laxman's team. Mukesh's team won four points more than Lina's team, but Lina's team didn't score the least amount of points. 'Just Singing' won 6 points. Waheda wasn't on the team called 'New Singers'. Sanjeev's team won 4 points. Divya wasn't on the 'Bindas Singers' team. Tapas and Sania were on the same team, but it wasn't the 'Sweet Couple'.

The teams arranged in the ascending order of points are:
Four married couples competed in a singing competition. Each couple had a unique team name. Points scored by the teams were 2, 4, 6 and 8. The 'Sweet Couple' won 2 points. The 'Bindas Singers' won two more points than Laxman's team. Mukesh's team won four points more than Lina's team, but Lina's team didn't score the least amount of points. 'Just Singing' won 6 points. Waheda wasn't on the team called 'New Singers'. Sanjeev's team won 4 points. Divya wasn't on the 'Bindas Singers' team. Tapas and Sania were on the same team, but it wasn't the 'Sweet Couple'.

Laxman's teammate and team's name were:

The regular mathematics faculty could not teach because of being sick. As a stop-gap arrangement, different visiting faculty taught different topics on 4 different days in a week. The scheduled time for class was 7:00 am, with a maximum permissible delay of 20 minutes. The monsoon made the city bus schedules erratic, so the classes started at different times on different days.

Mr. Singh did not teach on Thursday. Calculus was taught in the class that started at 7:20 am. Mr. Chatterjee took the class on Wednesday, but he did not teach probability. The class on Monday started at 7:00 am, but Mr. Singh did not teach it. Mr. Dutta did not teach ratio and proportion. Mr. Banerjee, who did not teach set theory, taught a class that started five minutes later than the class in which probability was taught. The teacher in Friday's class taught set theory. Wednesday's class did not start at 7:10 am. No two classes started at the same time.

79. Probability was taught by:

Four married couples competed in a singing competition. Each couple had a unique team name. Points scored by the teams were 2, 4, 6 and 8. The 'Sweet Couple' won 2 points. The 'Bindas Singers' won two more points than Laxman's team. Mukesh's team won four points more than Lina's team, but Lina's team didn't score the least amount of points. 'Just Singing' won 6 points. Waheda wasn't on the team called 'New Singers'. Sanjeev's team won 4 points. Divya wasn't on the 'Bindas Singers' team. Tapas and Sania were on the same team, but it wasn't the 'Sweet Couple'.

The combination which has the couples rightly paired is:

The regular mathematics faculty could not teach because of being sick. As a stop-gap arrangement, different visiting faculty taught different topics on 4 different days in a week. The scheduled time for class was 7:00 am, with a maximum permissible delay of 20 minutes. The monsoon made the city bus schedules erratic, so the classes started at different times on different days.

Mr. Singh did not teach on Thursday. Calculus was taught in the class that started at 7:20 am. Mr. Chatterjee took the class on Wednesday, but he did not teach probability. The class on Monday started at 7:00 am, but Mr. Singh did not teach it. Mr. Dutta did not teach ratio and proportion. Mr. Banerjee, who did not teach set theory, taught a class that started five minutes later than the class in which probability was taught. The teacher in Friday's class taught set theory. Wednesday's class did not start at 7:10 am. No two classes started at the same time.

78. The option which gives the correct teacher-subject combination is:

Answer the questions on the basis of the data given in the two charts below.

Sodium carbonate, also called soda ash, is an important ingredient for glass, soap, detergents and many other products. There are two ways to produce soda ash. The first is producing soda ash from trona, which is obtained naturally; this is called natural soda ash. The second is producing soda ash from common salt through the Solvay process; soda ash made this way is called synthetic soda ash. Tata Chemicals was one of the largest producers of soda ash. The charts below show Tata Chemicals' own production of the two varieties of soda ash, and the world's total production of the two varieties.


69. Suppose the total global production increased, year on year, from 2006 to 2008 by the same amount that Tata Chemicals' synthetic production increased, year on year, over the same period. By what percentage did the total global production increase from 2007 to 2008?
Tata Chemicals' own natural and synthetic soda ash output was:
YearNatural Soda Ash (MT)Synthetic Soda Ash (MT)
200500.7
20070.42.2
20083.22.2

Suppose total global production of soda ash in 2008 was 40 MT, and Tata Chemicals was the second highest producer of soda ash globally, right after another company called Solvay. FMC Wyoming was the third highest producer. The two Indian giants, Tata Chemicals and Nirma, had a combined soda ash production capacity of 8.8 MT.

Which of the following statements are right?
1. Solvay's market share was more than 20.66%
2. Solvay's market share was more than 13.5%
3. FMC's share was less than 10.33%
4. FMC's share was less than 13.5%
5. Nirma, which was the sixth largest producer, had a share of less than 8.5%
Choose the right option.
Soda ash (sodium carbonate) is made in two ways: from natural trona ore (natural soda ash), and from common salt by the Solvay process (synthetic soda ash). Tata Chemicals is one of the world's largest soda ash producers.

Two charts give the data. The first chart plots WORLD production of natural and synthetic soda ash for the years 2001 to 2006: the synthetic soda ash bars climb every year over this period, while the natural soda ash bars stay roughly flat. The second chart plots Tata Chemicals' own natural and synthetic output:
YearNatural Soda Ash (MT)Synthetic Soda Ash (MT)
200500.7
20070.42.2
20083.22.2

Which of the following statements are true?
1. Proportion of natural soda ash to synthetic soda ash has decreased from 2001 to 2006 globally.
2. Proportion of natural soda ash to synthetic soda ash has increased from 2001 to 2006 globally.
3. Proportion of synthetic soda ash to total soda ash has decreased for Tata Chemicals from 2005 to 2007.
4. Proportion of synthetic soda ash to total ash has increased for Tata Chemicals.
Answer the questions on the basis of the data given in the two charts below.

Sodium carbonate, also called soda ash, is an important ingredient for glass, soap, detergents and many other products. There are two ways to produce soda ash. The first is producing soda ash from trona, which is obtained naturally; this is called natural soda ash. The second is producing soda ash from common salt through the Solvay process; soda ash made this way is called synthetic soda ash. Tata Chemicals was one of the largest producers of soda ash. The charts below show Tata Chemicals' own production of the two varieties of soda ash, and the world's total production of the two varieties.


68. It was expected that global soda ash production would stay the same in 2006, 2007 and 2008 (only for this question). What could be a possible reason for the different patterns of production shown by Tata Chemicals and the world?
Continuing from the soda ash data: Tata Chemicals' own natural and synthetic soda ash output was:
YearNatural Soda Ash (MT)Synthetic Soda Ash (MT)
200500.7
20070.42.2
20083.22.2

The world production chart, however, only plots totals for the years 2001 to 2006.

What is Tata Chemicals' share of global production in 2008?
A police inspector spots a thief standing 7 km away from him on a straight road that runs East-West. The inspector is standing on the eastern side while the thief is on the western side of the road. On spotting the inspector, the thief takes his bicycle and tries to cut across the field next to the road, riding away at a uniform speed of \(9\sqrt{2}\) km/hour in a direction making an angle of \(45^{\circ}\) with the road towards North-East. The inspector starts on his scooter at the same instant, moving at a uniform speed of \(15\) km/hour, and catches the thief.

The distance the inspector has to travel is:
KK, an aspiring entrepreneur wanted to set up a pen drive manufacturing unit. Since technology was changing very fast, he wanted to carefully gauge the demand and the likely profits before investing. Market survey indicated that he would be able to sell 1 lac units before customers shifted to different gadgets. KK realized that he had to incur two kinds of costs: fixed costs (the costs which do not change, irrespective of the number of units of pen drives produced) and variable costs (= variable cost per unit multiplied by the number of units). KK expected the fixed cost to be Rs. 40 lac and the variable cost to be Rs. 100 per unit. He expected each pen drive to be sold at Rs. 200.

KK was skeptical that the variable cost per unit might increase by 10 percent, though the demand might remain the same. What will be the expected change in profit in such a case?
KK, an aspiring entrepreneur wanted to set up a pen drive manufacturing unit. Since technology was changing very fast, he wanted to carefully gauge the demand and the likely profits before investing. Market survey indicated that he would be able to sell 1 lac units before customers shifted to different gadgets. KK realized that he had to incur two kinds of costs: fixed costs (the costs which do not change, irrespective of the number of units of pen drives produced) and variable costs (= variable cost per unit multiplied by the number of units). KK expected the fixed cost to be Rs. 40 lac and the variable cost to be Rs. 100 per unit. He expected each pen drive to be sold at Rs. 200.

What would be the break-even point (defined as no profit, no loss situation) for KK's factory, in terms of sales?
KK, an aspiring entrepreneur, wanted to set up a pen drive manufacturing unit. Since technology was changing very fast, he wanted to carefully judge the demand and the likely profit before investing. A market survey showed he could sell 1 lac (100000) units before customers moved to other gadgets. KK had to bear two kinds of cost: fixed cost (the cost that does not change no matter how many units are made) and variable cost (variable cost per unit times the number of units). He expected the fixed cost to be Rs. 40 lac and the variable cost to be Rs. 100 per unit. He expected to sell each pen drive at Rs. 200.

He discussed his business with a chartered accountant. KK said he was thinking of a loan of Rs. 20 lac at simple interest of \(10\%\) per year to start the business. The chartered accountant told him that in this case KK has to pay interest, followed by \(30\%\) tax. By how much does KK's earnings change with a \(20\%\) growth in sales as against the original sales volume, in both cases considering tax and interest on the loan?
Let X be a four digit number with exactly three consecutive digits being the same, and X is a multiple of 9. How many such X's are possible?
A police inspector spots a thief standing 7 km away from him on a straight road that runs East-West. The inspector is standing on the eastern side while the thief is on the western side of the road. On spotting the inspector, the thief takes his bicycle and tries to cut across the field next to the road, riding away at a uniform speed of \(9\sqrt{2}\) km/hour in a direction making an angle of \(45^{\circ}\) with the road towards North-East. The inspector starts on his scooter at the same instant, moving at a uniform speed of \(15\) km/hour, and catches the thief.

Time taken by the inspector to catch the thief is:
Company BELIANCE hosted a party for 8 members of Company AXIAL. In the party no member of AXIAL had interacted with more than three members of BELIANCE. Out of all the members of BELIANCE, three members each interacted with four members of AXIAL and the remaining members each interacted with two members of AXIAL. The greatest possible number of company BELIANCE members in the party is:
Steel Express stops at six stations between Howrah and Jamshedpur. Five passengers board at Howrah. Each passenger can get down at any station till Jamshedpur. The probability that all five persons will get down at different stations is:
How many differently shaped triangles exist in which no two sides are of the same length, each side is of integral unit length and the perimeter of the triangle is less than 14 units?
ABCD is a square with sides of length 10 units. OCD is an isosceles triangle with base CD. OC cuts AB at point Q and OD cuts AB at point P. The area of trapezoid PQCD is 80 square units. The altitude from O of the triangle OPQ is:

The instructions below apply to this question and the previous one.

In the figure below, the seven letters correspond to seven unique digits chosen from 0 to 9. The relation among the digits is such that:

\(P \times Q \times R = X \times Y \times Z = Q \times A \times Y\)

PX
QAY
RZ

The sum of the digits which are not used is:

The instructions below apply to this question and the next one.

In the figure below, the seven letters correspond to seven unique digits chosen from 0 to 9. The relation among the digits is such that:

\(P \times Q \times R = X \times Y \times Z = Q \times A \times Y\)

PX
QAY
RZ

The value of A is:

In a quadrilateral ABCD, BC = 10, CD = 14, AD = 12 and \(\angle CBA = \angle BAD = 60^{\circ}\). If \(AB = a + \sqrt{b}\), where a and b are positive integers, then \(a + b =\)