 # Quant and DI Sections of XAT: Concept explained with Examples

In this article, we will discuss the nature of questions generally asked in the XAT Quantitative Ability & Data Interpretation section. Also, we will provide you with a sound strategy to sail through this critical section. In previous years, this section has seen around 32 questions of one mark each. In the recent years, the number of these questions has been reduced to 27.
###### XAT Quantitative Ability
The major areas from which questions have been asked were: Algebra and Functions, Number System, Probability, Mixtures, Geometry, Co-ordinate Geometry, Arithmetic Sequences, Tables Chart, Multiple Graph, Percentage, Profit and Loss, Interest, Average, Logarithm, etc. Within these, XAT examiners have focused on areas of Geometry, Algebra and Number Systems along with questions from Tables and Multiple graphs.
You should learn and practice the basic concepts of all the major topics of Quant with special focus on the above-mentioned areas. Let us take a look at a couple of questions that appeared in previous year XAT
Ace the General Awareness section of XAT
Q. 1. What is the sum of the series -64, -66, -68 ........- 100? (XAT previous year)

As you can see, just having the basic knowledge of Arithmetic Progression (A.P) is sufficient to answer this question.

Solution: Tn= a + (n - 1) d
- 100 = - 64 + (n - 1)( - 2)
Solving this we get, n = 19

S 19 = 19/2 [(-64)+(-100)]
19/2 X(-164) = 19 x (-82) = - 1558

Q. 2. A teacher noticed a strange distribution of marks in the exam. There were only three distinct scores: 6, 8 and 20. The mode of the distribution was 8. The sum of the scores of all the students was 504. The number of students in most populated category was equal to the sum of the number of students with lowest score and twice the number of students with the highest score. What was the total number of students in the class? (XAT previous year)

Now, in order to answer this question, having the basic knowledge of averages is sufficient.

Solution: Let students with 6 marks be z, 8 marks be x, 20 marks be y,

So we get the equation as
8x + 6z + 20y = 504....(i)
and x = z + 2y.... (ii)

Putting the value of x from (ii) you get
8z + 16y + 6z + 20y = 504
⇒ 14z + 36y = 504
⇒ 7z + 18y = 252

Only value of y satisfying this is y = 7 ⇒ z = 18 and x = 32.

Therefore, Total = 7 + 18 + 32 = 57

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Strategy to boost your score in XAT Verbal Section
Q. 3. The figure below has been obtained by folding a rectangle. The total area of the figure (as visible) is 144 square meters. Had the rectangle not been folded, the current overlapping part would have been a square. What would have been the total area of the original unfolded rectangle? ( XAT 2015) [Quant and-DI Sections]
1. 128 square meters
2. 154 square meters
3. 162 square meters
4. 172 square meters
5. None of the above
Solution: Folded part as shown in the first figure is a triangle - a right triangle. The two perpendicular sides of the right triangle measure 6m each. So, the triangle is a right isosceles triangle. When unfolded, the folded area becomes a square as shown in the following figure:

The side of the square will be the width of the larger rectangle and is therefore, 6m.
Area of the square = 6 * 6 = 36 sq.m

When folded, only the area of the right triangle gets counted. However, when unfolded the area of square gets counted. The square comprises two congruent right triangles.

In essence, when folded only half a square is counted. When unfolded the entire square gets counted.

The area of the rectangle when unfolded = area of the rectangle when folded + area of half a square.

So area after unfolding= 144 + 18 = 162 sq.m.

The level of difficulty of the Quant and DI section varies from moderate to tough. Also, in XAT you would find indirect usage of the various mathematical concepts that you have studied while preparing for the exam. In the past, the exam has seen some easy questions based on mathematical logic. But these easy questions or sitters have to be carefully selected, as the language used in questions is sometimes complex and can pose a challenge.

In totality, it can be concluded that the difficulty level of questions is medium to tough, but at the same time do not forget that the total number of questions in this paper is lesser in comparison to other exams. Hence, an optimum use of the available time can make you perform better in this exam.

###### XAT Data Interpretation

In the previous years, there have been 8 - 10 questions of data interpretation in XAT. In XAT, the perceived level of difficulty of DI questions is on the higher side, as XAT examiners provide data either in statement form or in the form of complex diagrams. While these problems appear tough at first, we suggest that you carefully go through each problem. You will see invariably that the questions are not as tough as they appear.

So, the learning is that do not judge the level of the questions from the complexity of the graph only. Further, in XAT DI, questions are simple but a little calculation-intensive. We suggest that you attempt questions from every set individually i.e. it is not necessary to attempt all the questions of a particular set.

###### DI set:

Study the graph below and answer the questions 1--3 that follow:
This graph depicts the last eight years’ annual salaries (in Rs. (lacs.)) offered to students during campus placement. Every year 100 students go through placement process. However, at least one of them fails to get placed. The salaries of all unplaced students are marked zero and represented in the graph.

Q.1. In which year were a maximum number of students offered salaries between Rs.20 to Rs. 30 lacs (both inclusive)?

1. 2008
2. 2009
3. 2010
4. 2012
5. Cannot be determined
At least 25% of the students definitely got salaries between 20-30 lacs in years 2008, 2010 and 2012. However, the graphs do not tell the actual salaries. Hence, no comment can be made on the number of students within a particular salary range.
Option E is the correct answer.

Q.2. Identify the years in which the annual median salary is higher by at least 60% than the average salary of the preceding year?
1. 2009, 2010
2. 2012, 2014
3. 2009, 2010, 2012
4. 2009, 2012, 2014
5. 2009, 2010, 2012, 2014

It is clear from the above table that in 2012 and 2014, the median of existing year is higher than 1.6 times mean of previous years. Hence the correct answer is: 2012 and 2014.
Option B is the correct answer.
Q.3. If the average salary is computed excluding students with no offers, in how many years will the new average salary be greater than the existing median salary? Refer the table below for number of students without offers
 Year 2008 2009 2010 2011 2012 2013 2014 2015 Number without job offers 9 5 20 2 2 4 15 2
1. 3
2. 4
3. 5
4. 6
5. Cannot be solved without additional information.
The answer can be found based on the table given:
New Average Salary = (Old Average Salary)×100/(100-students without jobs)
Based on the additional information, the new average would be higher than the graph average of all the years. During two years old averages were already higher than median (2008 and 2013). With 20 students taken out, the new average salary for 2010 would jump to 23.4, which is clearly higher than median salary of 22. Similarly, the value of 2013 would jump further by at least one hence making new average definitely higher than existing median. In 2008, even the existing mean is visibly higher than median. Hence, the three 3 years are: (2008, 2010, and 2013).
Option A is the correct answer.
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