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If A and B are represented by the above diagrams as two circles then shaded area is represented as?
$$A \cap B$$
$$(A \cup B) - A$$
$$(A \cap B) \cup A$$
Option D is correct.
In a school students at Pioneer career Kolkata wrote Mock test which has three subjects DI, VA and QA, here is the result of these students. 80 students cleared cut off in DI, 70 in VA and 60 in QA. Only 40 students cleared all the three subjects. 10 students failed to clear cut off even in one subjects. 50 students cleared cut off in VA and QA. 5 students cleared in cut off in only QA.
What is the minimum number of students who appeared in the Mock test.
With the given information, we can draw the following venn diagram:
For minimum students to appear for the exam, we can maximise the part common to VA and DI.
We will get the following final venn diagram:
So, total students appearing= 80+10+5+10= 105
Staff employed in a UNESCO office in Paris are represented by four intersecting circles as in the given diagram. Each circle represents people who can read and write English, French, Spanish and Russian. Strength of people in each circle is also shown alongside. Study the diagram to answer the questions that follow.
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How many people know only Spanish ?
e is the set of people who only know Spanish.
e=$$\frac{1}{2}$$a
e=20
Option B
Staff employed in a UNESCO office in Paris are represented by four intersecting circles as in the given diagram. Each circle represents people who can read and write English, French, Spanish and Russian. Strength of people in each circle is also shown alongside. Study the diagram to answer the questions that follow.
How many people can read and write any one language except French ?
People who can read and write any one language except French= a+c+e
a= 40
c= 2a
e= (1/2)a
i.e 40+80+20=140
Option C
Staff employed in a UNESCO office in Paris are represented by four intersecting circles as in the given diagram. Each circle represents people who can read and write English, French, Spanish and Russian. Strength of people in each circle is also shown alongside. Study the diagram to answer the questions that follow.
People who can read and write all the language except Spanish, are represented by
'i' can read and write only in Spanish.
Option D
Staff employed in a UNESCO office in Paris are represented by four intersecting circles as in the given diagram. Each circle represents people who can read and write English, French, Spanish and Russian. Strength of people in each circle is also shown alongside. Study the diagram to answer the questions that follow.
People who cannot read and write Russian, English and French, are represented by :
'e' represents the staff who speak & write only Spanish
Option D
Staff employed in a UNESCO office in Paris are represented by four intersecting circles as in the given diagram. Each circle represents people who can read and write English, French, Spanish and Russian. Strength of people in each circle is also shown alongside. Study the diagram to answer the questions that follow.
People who cannot read and write Spanish and French but are conversant with English and Russian are represented by:
b represents the staff who can speak & write English and Russian but cannot in Spanish and French
Option A is correct.
60 employees in an office were asked about their preference for tea and coffee. It was observed that for every 3 people who prefer tea, there are 2 who prefer coffee. For every 6 people who prefer tea, there are 2 who drink both of tea and coffee. The number of people who drink both is the same as those who drink neither.
How many people drink both tea and coffee?
Let number of people who prefer tea =3k
those who prefer = 2k
those who like both =k
5k = 60
=> k=12
A placement company has to assign 1000 SW personnel who are skilled in Java and Dot Net to a prospective outsourcing company. He finds that 750 are having Dot Net skills and 450 have Java skills. Some have skills in both Java and Dot Net. Find the numbers who have skills in both Java and Dot Net.
If 750 are skilled in Java, 250 are skilled only in DotNet. Of the 450 who are skilled in DotNet, we just found out that 250 are skilled only in DotNet, meaning that rest 200 out of the 450 are skilled in both.
Abdul, Mala and Chetan went bird watching. Each of them saw one bird that none of the others did. Each pair saw one bird that the third did not. And one bird was seen by all three. Of the birds Abdul saw, two were yellow. Of the birds Mala saw, three were yellow. Of the birds Chetan saw, four were yellow. How many yellow birds were seen in all? How many non-yellow birds were seen in all?
Each of the three persons- Abdul, Mala, and Chetan saw 1 unique birds each. Therefore, the number of unique birds=3.
Each pair of the three persons saw a bird different to the other. Therefore $$^3C_2$$ =3 birds were seen by a pair of two persons each.
Everyone saw a common bird.
Therefore total birds = 7.
Let the birds which were seen by Abdul, Mala, and Chetan uniquely be shown as A, B and C.
Birds seen by Abdul and Mala, Mala and Chetan, Abdul and Chetan be shown as AM, MC and AC respectively.
Birds seen by all of them be shown as AMC.
Birds seen by Abdul are A, AM, AC and AMC
Birds seen by Mala are M, AM, MC and AMC
Birds seen by Chetan are C, AC, AM and AMC.
It is given that Chetan saw 4 yellow birds. So, C, AC, AM and AMC are yellow birds.
For Abdul, it is given that he saw 2 yellow birds only. So, A and AM are non yellow birds, as he already saw AC and AMC.
For Mala, as he saw 3 yellow birds, and MC and AMC are already among the yellow birds seen by him, and since AM is a non yellow bird. Therefore M has to be a yellow bird.
Therefore, in total, there are 5 Yellow birds- M,C, MC, AC, AMC. And the other two- A and AM are non-yellow birds.
Use the data given below to answer the questions.
The following are the results of a survey conducted on a small cross-section of
students from Symbiosis Group of institutes, to determine the readership of
three magazines. This survey was conducted in Dec. 2006.
- Number of students who read only Business India was 40
- 60 students read only Outlook
- 110 students read only India Today
- 30 students read all three magazines
- 20 read Business India and India Today, but not Outlook
- 50 read Business India and Outlook, but not India Today
- 40 read Outlook and India Today, but not Business India
What was the total no. of students surveyed?
Let s,d and t represent the number of students who like only 1, only 2 and all 3 magazines.
Total Number of Student = s+d+t
s = $$40+60+110\ =\ 210$$
d = $$20+50+40\ =\ 110$$
t = 30
Hence total students = $$210+110+30=350$$
Use the data given below to answer the questions.
The following are the results of a survey conducted on a small cross-section of
students from Symbiosis Group of institutes, to determine the readership of
three magazines. This survey was conducted in Dec. 2006.
- Number of students who read only Business India was 40
- 60 students read only Outlook
- 110 students read only India Today
- 30 students read all three magazines
- 20 read Business India and India Today, but not Outlook
- 50 read Business India and Outlook, but not India Today
- 40 read Outlook and India Today, but not Business India
How many students did not read Business India?
.png)
From the Venn Diagram, we can calculate that the no. of students who do not read Business India = 110 + 40 + 60 = 210
Use the data given below to answer the questions.
The following are the results of a survey conducted on a small cross-section of
students from Symbiosis Group of institutes, to determine the readership of
three magazines. This survey was conducted in Dec. 2006.
- Number of students who read only Business India was 40
- 60 students read only Outlook
- 110 students read only India Today
- 30 students read all three magazines
- 20 read Business India and India Today, but not Outlook
- 50 read Business India and Outlook, but not India Today
- 40 read Outlook and India Today, but not Business India
When another survey was conducted in May 2007 with the same set of students, their
tastes had changed and the findings were different. All of them read India Today. 120 read
Outlook, and no one read Business India. Hence, in May 2007, how many students read
only India Today?
From the statements given in question, the above venn diagrams represents the results of the surveys conducted in 2006 and 2007.
From the venn diagam that represents the 2006 survey, we sum up all the groups of people to get total no. of students which is 350.
The same set of students were surveyed in 2007 and from the statements, we drew the venn diagram for 2007 survey. All 350 students read India Today and among them 120 read Outlook. So, the no. of students who read only India Today = 350-120 = 230
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