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Caselet 3 : In a store, there are 600 women. The store is a collection of precious stones, namely diamond, ruby, and emerald. It is found...

DATA INTERPRETATION For CAT, BANK TESTS - CASELETS - Caselets Solved Problems in Data Interpretation

Caselet 3 :
In a store, there are 600 women. The store is a collection of precious stones, namely diamond, ruby, and emerald. It is found that 40% of women like diamonds, 20% of women like ruby and 10% of women like emeralds.
5% of women like diamond and ruby. 3% of women like ruby and emerald and 4% like emerald and diamond. 2% of women like all three stones.

Explanation :
Total number of women = 600
Number of women who like diamonds = 
40% of total women = 40/100 x 600 = 240
Number of women who like Ruby = 
20% of total women = 20/100 x 600 = 120
Number of women who like Emerald = 
10% of total women = 10/100 x 600 = 60
Number of women who like diamonds & Ruby = 
5% of total women = 5/100 x 600 = 30
Number of women who like diamonds &Emerald = 
5% of total women = 6/100 x 600 = 24
Number of women who like Ruby& Emerald = 
30% of total women = 30/100 x 600 = 18
Number of women who like diamonds, Emerald and Ruby = 
2% of total women= 2/100 x 600 = 120.
Let a = diamond only ,    
 b = Ruby only      
c= Emerald only  
d= Diamond& Ruby only
e=Ruby & Emerald only      
f=Diamond & Emerald only 
g=Diamond, Emerald and Ruby
                                    

  Diamond => a+d+g+f = 240
  Ruby      =>d+b+g+e  =120
  Emerald = c+f+e+g = 60
ð  d + g = 30
ð  g + e =18
ð  g+ f =24
ð  g=12
Therefore, d = 30- 12 = 18     e = 18- 12 =6    
 f=24-12 = 12
 C = 60-(12+12+6)=30         
 b= 120 –(30+6)=84   
 a=240-(30+12)=198
                                


Questions with Explanations :
1.    Find the number of women who like both ruby and diamond.
     a) 30      b) 32       c) 12   d) 6    e) 18
Answer: a
Explanation :
 Number of women who like both Diamond and Ruby = 30

2.    Find The number of women who like emerald only.
a) 32       b) 30    c) 28 d) 198    e) 40
Answer: b
Explanation : Number of women who like Emerald only = 30

3.    Find the number of women who like both diamond and emerald.
     a) 32         b) 30         c) 24            d) 28    e) 27
Answer: C
Explanation :
Number of women who like both Diamond and Emerald = 24

4.    Find the number of women who like diamond only.
     a) 60        b) 240       c) 120     d)198            e) 84
Answer : D
Explanation : 
Number of women who like both only Diamond = 198

5.    Find the number of women who like the only ruby.
     a) 60        b) 240   c) 120         d) 198         e) 84
Answer: E
Explanation : Number of women who like only Ruby = 84



Caselet 4.
A colony of 5500 members, 18% of the people manage their business, and 10% of those who manage their business are females. 65% of the total numbers of people in the colony serve various organizations. 40% of the number of people serving various organizations is females.
12% of the total number of people in the colony is unemployed. 30% of the number of people in the colon- are unemployed is females.
The remaining people in color are children, 60% of whom are females.

Explanation :
Number of members who manage their business
18% of total members = 18/100 x 5500 = 990
Number of females who manage their business = 
10/100 x 990 = 99
Number of males who manage their business = 
990-99 = 891

Number of people who serve varous organizations
65% of total people = 65/100 x 5500 =3575
Number of females who serve various organizations = 
3575 x 40/100 =1430
Number of males who serve various organizations = 
3575 – 1430 = 2145

Number of Unemployed people
12% of total members = 12/100 x 5500 = 660
Number of females who are unemployed = 
30% of total unemployed = 30/100 x 660 =198
Number of males who are unemployed = 660- 198 = 462

Number of children :  
Total members – ( People who manage their business + Serve various organization + Unemployed ) = 
100% - (18% +65% +12%) = 5%
Total number of children =   5% of total members =  
5/100 x 5500 = 275
Number of female children = 275 x 60/100 =165
Number of male children = 275  - 165 = 110


                                        Total
                                      members    Male       Female
Manage their business            990        891          99
Serve Various Organizations  3575       2145        1430
Unemployed                          660         462        198
Children                               275          110        165

Questions and Explanation:
1.    The number of children (both main and females) is approximately what percent of people who manage their business (both males and females )
a)28         b)      24      c)32    d) 21     e) 35
Answer: A
Explanation: Total number of children =275
Total number of people who manage their business = 990
       Therefore, required percentage = 275/990 x 100 =28%

2.    What is the difference between male and female children in the colony?
a) 65       b) 55   c) 45   d) 35   e) None of these
Answer: B
Explanation: Number of male children = 165  
Number of female children = 110
 Difference between male and female children =165–110= 55

3.    What is the total number of adult males in the colony (excluding the children)?
a) 3496    b) 3490              c)3500    d)3504      e)3498
Answer :E
Explanation : 
Total number of adult males ( excluding children) = 
891 + 2145 +462=3498

4.    What is the total number of females in the colony?
a)1884     b)1896 c)1888    d) 1892         e)None
Answer : D
Explanation : 
Total number of females = 165 +198 +1430 +99 = 1892

5.    What is the respective ratio of the unemployed males to the number of males working for various organizations?
a) 3 :13    b) 12 : 65  c) 4:13 d) 16: 65 e) 14:65
Answer :
Explanation : Number of unemployed males =462
   Number of males working for various organizations = 2145

            Therefore, required ratio = 462 : 2145 = 14 :65