# 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