XAT 2016 Question Paper

Let $$DQ = x$$, => $$BP = 2x$$

Acc. to ques,

=> $$ar (\triangle BPD) + ar (\triangle BQD) \leq ar (PBQD)$$

=> $$(\frac{1}{2} \times AD \times BP) + (\frac{1}{2} \times BC \times QD) \leq 150$$

=> $$(\frac{1}{2} \times 9 \times 2x) + (\frac{1}{2} \times 13 \times x) \leq 150$$

=> $$31x \leq 300$$ => $$x \leq \frac{300}{31}$$

=> $$x \leq 9.68$$

Thus, for $$x$$ to be an integer and positive, 9 different values (1 to 9) are possible. 

Since the population of the different areas is unknown, None of the two statements can be inferred.
Hence D is the correct answer.

Since there is no data available about the population of the different areas, all the other options except C can be inferred. Option C cannot be inferred as it talks about the ratio of the customers.
Hence C is the correct answer.

Option  A,B ,C,D talk about the increase or decrease in the number of shops with respect to each other. Since the total number of shops can be different in two different years, hence they cannot be definitely concluded.

Option E compares the numbers of shops of two types in the same year. Since the percentage is given and total number of shops is same, hence E can be concluded. Hence E is the correct answer.

Let's tabulate the information given in the graph, 

For a salary range we can get the highest and the lowest value of the range but cannot get the distribution of individual student. 

In the year 2008 we have a complete salary range(76-100) inside it and some students of the range 51-75. 

In the year 2009 some students of the range 51-75 and some students of the range 75-100. 

In the year 2010 some students of the range 51-75 and some students of the range 75-100. 

In the year 2012 we have a complete salary range 51-75 inside it and some students of the range (76-100) . 

Since we cannot determine the exact students and cannot infer a particular year, Hence answer is E i.e cannot be determined.

Let's tabulate the information given in the graph, 

In all the options since 2009 is given 

Lets check if 2009 is satisfying the given criteria 

Median salary of 2009 = 24 l 

Avg salary of 2008 = 16 l

So Median salary of 2009 is between 40 to 50% higher than 2008 avg salary.

Hence options 1,3,4,5 can be negated . 

Option B is the correct answer

Let's tabulate the information given in the graph, 

The number of years cannot be calculated with precision as the distribution pattern is unknown .

Hence E is the correct answer

Let's tabulate the information given in the graph, 

It is clear from the table that the  mean salary after discarding the unemployed students is greater than the mean salary for the years 2008,2010,2013

Hence A is the correct answer.