A number of candidates interviewed recently revealed that 142 applied admission into university of Lagos, 122 for Illorin and 118 for Jos, 66 had applied for Lagos and Illorin, 48 for Illorin and Jos and 58 for Lagos and Jos, while 32 had applied for all three universities.
(a) Illustrate the information using a venn diagram
(b) How many candidates were interviewed?
(n) 142+122+118 - (66+48+58) + 32 = ____
142+128+188+66+48+58+32=562
(a) The Venn diagram for the given information would look like this:
```
Lagos (66)
/ \
/ \
/ \
142 (32) 58 (48)
\ /
\ /
\ /
\ /
Jos (118)
```
(b) A total of 562 candidates were interviewed.
(a) Unfortunately, as a bot, I cannot illustrate information using visual aids like Venn diagrams. However, I can describe it for you!
Let's start by creating three overlapping circles to represent the three universities - University of Lagos, Illorin, and Jos.
In the first circle representing University of Lagos, we know that 142 candidates applied.
In the second circle representing Illorin, we know that 122 candidates applied.
In the third circle representing Jos, we know that 118 candidates applied.
Now, for the overlapping regions:
- The region where University of Lagos and Illorin overlap (middle left) has 66 candidates.
- The region where Illorin and Jos overlap (middle right) has 48 candidates.
- The region where University of Lagos and Jos overlap (bottom) has 58 candidates.
- The region where all three universities overlap (center) has 32 candidates.
(b) To find out how many candidates were interviewed, we need to add up the number of candidates for each university and then subtract the overlap.
So, to calculate the total number of candidates interviewed, we can add:
142 (University of Lagos) + 122 (Illorin) + 118 (Jos) - 66 (Lagos and Illorin overlap) - 48 (Illorin and Jos overlap) - 58 (Lagos and Jos overlap) + 32 (all three overlap).
Performing the calculations, we get:
142 + 122 + 118 - 66 - 48 - 58 + 32 = 242.
Therefore, 242 candidates were interviewed in total.
To illustrate the information using a Venn diagram, we will use three intersecting circles representing each university: University of Lagos (L), University of Illorin (I), and University of Jos (J).
(a) Venn Diagram:
Let's label the circles L, I, and J.
In the intersection of L and I: 66 candidates applied for both University of Lagos and University of Illorin.
In the intersection of I and J: 48 candidates applied for both University of Illorin and University of Jos.
In the intersection of L and J: 58 candidates applied for both University of Lagos and University of Jos.
In the intersection of L, I, and J: 32 candidates applied for all three universities.
Now, let's calculate the number of candidates for each individual circle:
In circle L only: 142 (total for University of Lagos) - 66 (intersection with I) - 58 (intersection with J) - 32 (intersection with I, J) = 142 - 66 - 58 - 32 = 108.
In circle I only: 122 (total for University of Illorin) - 66 (intersection with L) - 48 (intersection with J) - 32 (intersection with L, J) = 122 - 66 - 48 - 32 = 118.
In circle J only: 118 (total for University of Jos) - 48 (intersection with I) - 58 (intersection with L) - 32 (intersection with L, I) = 118 - 48 - 58 - 32 = 102.
Now, let's summarize the information in a Venn diagram:
L: 108
/ \
58 66
/ \
/ \
32 32
/ \
/ \
I: 118 ------------------------- J: 102
\ /
\ /
\ /
48 48
\ /
\ /
\ /
\ /
O
(b) To find the number of candidates interviewed, we need to calculate the total number of candidates across all circles.
Total candidates = Candidates in circle L + Candidates in circle I + Candidates in circle J - Candidates in intersection of L and I - Candidates in intersection of I and J - Candidates in intersection of L and J + Candidates in intersection of L, I, J
Total candidates = 108 + 118 + 102 - 66 - 48 - 58 + 32
Total candidates = 258
Therefore, a total of 258 candidates were interviewed.