XAT 2013 Question Paper with Solutions, Download PDF

Instructions

For the following questions answer them individually

Question 81

The figure below shows the graph of a function f(x). How many solutions does the equation f(f(x)) = 15 have?

Video Solution

Solution

It has been given that f(f(x)) = 15.
From the graph, we can see that the value of f(4) = 15 and f(12) = 15
Therefore, f(x) can be 4 or 12.

When f(x) = 4, x can take 4 values
When f(x) = 12, x can take 3 values.
Therefore, there are 4+3 = 7 solutions in total.
Therefore, option C is the right answer.

Instructions

Question 82

What is the ratio of the current account balance in 2010 to the current account balance in 2005?

Video Solution

Solution

Current account balance = Current account balance percentage of GDP*GDP

Current account balance in 2010 = 3.268% of 73555.34 = 2403.7885
Current account balance in 2005 = 1.272% of 35662.2 = 453.623

Ratio = 2403.7885/453.623 = 5.3 (approximately).
Therefore, option E is the right answer.

Question 83

Read the statements given below:
l.Exports were more than imports in 2006
2.Imports were more than exports in 2009
3.Exports increased at faster rate than imports during the period 2005 to 2010
Which of the above statements is necessarily true?

Video Solution

Solution

The table provides details only regarding the % change in the imports and exports. We do not have any detail regarding the base value. Therefore, we cannot find out the absolute values and hence, statements 1 and 2 cannot be verified.

The percentage change of exports and imports over the given period can be found out. Among the given options, option C is the only viable option now. Since none of the above is not present among the options, option C must be the right answer.

To actually compare the growth rate of export and import. we can multiply the rates to find the net change and then compare.

Question 84

What was the approximate number of unemployed persons in 2006?

Video Solution

Solution

Population = GDP/GDP per capita
In 2006, GDP = Rs.41159.73 billion
GDP per capita = Rs. 36,553.93
=> Population = 41159.73*1000/36553.93
= 1126 million.

From the table, we can see that 8.9% of the total population was unemployed in 2006.
=> Number of unemployed people = 0.089*1126 = 100 million (approx)
Therefore, option A is the right answer.

Instructions

Analyze the railway train chart below:

Question 85

Which is the fastest train between HHH and NNN?

Video Solution

Solution

Except 7777, all other trains take at least 2 hours to cover the distance between the stations HHH and NNN. Therefore, option D is the right answer.

Question 86

Which is the fastest train between AAA and NNN?

Video Solution

Solution

In the graph, the line with the steepest slope should be preferred to travel in the shortest possible time.
The line representing 8800 completes within 2 hour slot and has the steepest slope among the given options. Therefore, option A is the right answer.

Question 87

If you have to travel from AAA and reach HHH at around 9:00 AM, and then further travel to NNN at around 6:00 PM, which is the best combination of trains for you?

Video Solution

Solution

Only 3 trains - 4444, 5555, and 8888 reach HHH before 9 AM. Among these 3 trains, 8888 reaches just before 9 AM and hence, it is the best train to reach HHH from AAA. 8800 reaches HHH at 6 PM exactly. Therefore, it is the best train to travel from HHH to NNN. Therefore, option D is the right answer.

Instructions

Answer questions based on the following information:

Data on an ongoing football league of a country is given below. 20 teams are playing in the league. The rules of the league are as follows:

1. Each team plays all the other teams twice, once in its home ground, and once in the opponent's home ground. These matches are known as the "Home" match and the "Away" match respectively.
2. A win results in 3 points, a draw in 1 point, and a loss in 0 point for the team.
3. The number of goals a team scores is termed as "Goals For" and the number of goals it concedes is termed as "Goals Against". We get the "Goal Difference" by subtracting "Goals Against" from "Goals For".

Question 88

Considering away matches only, which of the following teams is the second ranking team?

Video Solution

Solution

Using the data from both the tables available, we can create the table for away matches as given below:

Thus, the team with rank 2 is SW.

Hence, option D is the answer.

Question 89

Considering away matches only, the least number of teams with either 0 or 1 point is:

Video Solution

Solution

Using the data from both the tables available, we can create the table for away matches as given below:

We have to find the number of teams with 0 or 1 point. From the table, we can see that there are 5 such teams.

Thus, option D is the answer.

Question 90

Let us define a term pos as the difference between "home rank" and "away rank". Which of the following has the maximum value of pos?

Video Solution

Solution

Using the data from both the tables available, we can create the table for away matches as given below:

We have to find the team with the highest difference between home and away rank.

AS: pos = |12 - 1| = 11

WB: pos = |1 - 7| = 6

WH: pos = |2 - 10| = 8

MC: pos = |4 - 7| = 3

SW: pos = |5 - 2| = 3

Thus, the team with the highest value of pos is AS

Thus, option A is the correct answer.

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XAT 2013 Question Paper

The figure below shows the graph of a function f(x). How many solutions does the equation f(f(x)) = 15 have?

What is the ratio of the current account balance in 2010 to the current account balance in 2005?

Read the statements given below:
l.Exports were more than imports in 2006
2.Imports were more than exports in 2009
3.Exports increased at faster rate than imports during the period 2005 to 2010
Which of the above statements is necessarily true?

What was the approximate number of unemployed persons in 2006?

Which is the fastest train between HHH and NNN?

Which is the fastest train between AAA and NNN?

If you have to travel from AAA and reach HHH at around 9:00 AM, and then further travel to NNN at around 6:00 PM, which is the best combination of trains for you?

Considering away matches only, which of the following teams is the second ranking team?

Considering away matches only, the least number of teams with either 0 or 1 point is:

Let us define a term pos as the difference between "home rank" and "away rank". Which of the following has the maximum value of pos?

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