Data Analysis and Comparison Questions for XAT
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Instructions
Study the following graph carefully to answer these questions.
Per cent rise in population of two states from the previous year
Question 1: What was the effective percentage increase in population of state ‘A’ from 1999 to 2001 ?
a) 103
b) 85
c) 118
d) Cannot be determined
e) None of these
1) Answer (A)
Solution:
Let the population of State A in 1999 = $100x$
=> Population in 2000 = $\frac{140}{100} \times 100x = 140x$
Population in 2001 = $\frac{145}{100} \times 140x = 203x$
$\therefore$ Effective % increase = $\frac{203x – 100x}{100x} \times 100$
= $\frac{103}{100} \times 100$ = 103%
Question 2: If the population of state A in 1998 was 67.5 lakhs, what was its population in 1996 ?
a) 50 lakhs
b) 42 lakhs
c) 45 lakhs
d) 40 lakhs
e) None of these
2) Answer (D)
Solution:
Let the population of State A in 1996 = $100x$ lakhs
=> Population in 1997 = $\frac{125}{100} \times 100x = 125x$ lakhs
Population in 2008 = $\frac{135}{100} \times 125x = 168.75x$ lakhs
Acc to ques,
=> $168.75x = 67.5$
=> $x = 0.4$
$\therefore$ Population of State A in 1996 = 100 * 0.4 = 40 lakhs
Question 3: If population of state B in 1996 was 20 lakhs, what was the average population of the state in 1997 and 1998 ?
a) 22.5 lakhs
b) 25 lakhs
c) 27.6 lakhs
d) 24 lakhs
e) None of these
3) Answer (C)
Solution:
Population of State B in 1996 = 20 lakhs
=> Population in 1997 = $\frac{120}{100} \times 20 = 24$ lakhs
Population in 1998 = $\frac{130}{100} \times 24 = 31.20$ lakhs
$\therefore$ Required Average
= $\frac{24 + 31.2}{2} = 27.6$ lakhs
Question 4: Total population of the two states in 1996 was 87.5 lakhs, what was the total population of the two states in 1998 ?
a) 107 lakhs
b) 22 lakhs
c) 105 lakhs
d) Cannot be determined
e) None of these
4) Answer (D)
Solution:
We do not know the individual population of the two states. Thus, we cannot calculate the % increase in population of each states.
=> Ans – (D)
Question 5: If the ratio between the population of states A & B in year 2000 was 3 : 4 respectively, what was the respective ratio in 2001 ?
a) 7 : 9
b) 29 : 36
c) 81 : 116
d) Cannot be determined
e) None of these
5) Answer (B)
Solution:
Let the population of State A in 2000 = $300x$
Population of State B in 2000 = $400x$
=> Population of State A in 2001 = $\frac{145}{100} \times 300x = 435x$
Population of State B in 2001 = $\frac{135}{100} \times 400x = 540x$
$\therefore$ Required ratio = $\frac{435x}{540x}$
= 29 : 36
Instructions
Study the following table to answer these questions. Number of Officers in various Departments of an Organization in different Scales
Question 6: What percentage of Scale IV officers are deployed in ‘Operations’ department ?
a) 26.5
b) 28
c) 28.5
d) 27
e) None of these
6) Answer (B)
Solution:
Total number of scale IV employees = 40 + 126 + 144 + 60 + 30 + 50
= 450
$\therefore$ Required % = $\frac{126}{450} * 100$
= 28 %
Question 7: Out of the total number of employees in ‘Personnel’ department, approximately what per cent of employees are in scale II ?
a) 30
b) 28
c) 22
d) 20
e) 25
7) Answer (E)
Solution:
Number of employees in Personnel department = 225 + 120 + 75 + 40 + 25 + 4
= 489
Number of employees in Scale II = 120
$\therefore$ Required % = $\frac{120}{489} * 100$
$\approx \frac{120}{490} * 100 = 24.48$
= 25% (approx.)
Question 8: In Public Relations department the number of employees in Scale II is less than that in Scale I by what percent? (rounded off to two digits after decimal).
a) 14.67
b) 16.67
c) 14.29
d) 16.27
e) None of these
8) Answer (C)
Solution:
Number of employees in Public Relations department in :
Scale I = 175
Scale II = 150
Difference = 175 – 150 = 25
=> Required % = $\frac{25}{175} * 100$
= 14.29%
Question 9: Total number of employees in Scale VI is what per cent of the total number of employees in Scale-I ?
a) 2.8
b) 2.4
c) 3.6
d) 3.2
e) None of these
9) Answer (D)
Solution:
Total number of employees in Scale I = 225 + 725 + 750 + 300 + 325 + 175 = 2500
Total number of employees in Scale VI = 4 + 20 + 28 + 15 + 8 + 5 = 80
=> Required % = $\frac{80}{2500} * 100$
= $\frac{80}{25}$ = 3.2 %
Question 10: What is the ratio between the total number of employees in Scale III and Scale IV respectively?
a) 19 : 9
b) 9 : 19
c) 17 : 9
d) 9 : 17
e) None of these
10) Answer (A)
Solution:
Number of employees in Scale III = 75 + 250 + 320 + 120 + 85 + 100 = 950
Number of employees in Scale IV = 40 + 126 + 144 + 60 + 30 + 50 = 450
=> Required ratio = $\frac{950}{450}$
= 19 : 9
