A survey of 600 schools in India was conducted to gather information about their online teaching learning processes (OTLP). The following four facilities were studied.

F1: Own software for OTLP

F2: Trained teachers for OTLP

F3: Training materials for OTLP

F4: All students having Laptops

The following observations were summarized from the survey.

- 80 schools did not have any of the four facilities – F1, F2, F3, F4.
- 40 schools had all four facilities.
- The number of schools with only F1, only F2, only F3, and only F4 was 25, 30, 26 and 20 respectively.
- The number of schools with exactly three of the facilities was the same irrespective of which three were considered.
- 313 schools had F2.
- 26 schools had only F2 and F3 (but neither F1 nor F4).
- Among the schools having F4, 24 had only F3, and 45 had only F2.
- 162 schools had both F1 and F2.
- The number of schools having F1 was the same as the number of schools having F4.

**Question 1: **

What was the total number of schools having exactly three of the four facilities?

- 200
- 50
- 80
- 64

**Show Answer**

**1**

**Question 2: **

What was the number of schools having facilities F2 and F4?

- 185
- 45
- 95
- 85

**Show Answer**

**1**

**Question 3: **

What was the number of schools having only facilities F1 and F3?

**Show Answer**

**42**

**Question 4: **

What was the number of schools having only facilities F1 and F4?

**Show Answer**

**20**

The given information can be represented in the following Venn diagram.

**Question 1:**

Given,

\(F _{2}=( a + x +40+ x )+(30+26+ x +45)=313 .\)

It is also given that \(F_{1}\) and \(F_{2}=a+x+40+x=162\).

Hence, \(30+26+x+45=313-162=151\)

Hence, \(x=151-(30+26+45)=50\)

The number of schools that have exactly three facilities \(=4 x=200\)

Option: 1**Question 2:**

The number of schools having facilities \(F _{2}\) and \(F _{4}\) \(=40+x+45+x=185\)

Option: 1**Question 3:**

Only \(F_{1}\) and \(F_{3}=b\)

Given \(F _{1}= F _{4}\)

\(25+b+x+c+a+x+40+x\)

\(=24+20+x+45+40+x+x+c\)

Hence, \(a+b=64\)

It is given that \(a+x+40+x=162\).

As \(x=50, a=22\)

Hence, only \(F _{1}\) and \(F _{3}= b =64-22=42\).

Answer: 42**Question 4:**

Only \(F _{1}\) and \(F _{4}= c\)

Exactly \(1+\) Exactly \(2+\) Exactly \(3+\) Exactly 4 \(=600-80=520\)

\((25+30+26+20)+\) Exactly \(2+200+40=520\)

Hence, Exactly \(2=179=a+24+b+c+26+45\)

As \(a=22\) and \(b=42, c=\) only \(F_{1}\) and \(F_{4}=20\).

Answer: 20### CAT 2020 LRDI sets with Solutions

CAT 2020 LRDI set 1CAT 2020 LRDI set 2

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