Level-3 Mixed Graph Practice Test -3 Hard

Directions: Study the following table and bar chart carefully and answer the questions given below.

Two cities, namely Agra and Meerut, were tested for COVID-19 cases in three months March, April, and May.

Both the cities have Urban and Rural areas, and the tests were conducted in both areas.

Outcomes of the tests were either positive or negative.

Month Number of Tests in both the cities together Negative outcomes out of total number of tests in both the cities
March 100 30 %
April 200 35 %
May 360 50 %
The column chart below shows some other information about the tests.
P = Number of positive cases in Agra
Q = Number of negative cases in Meerut
R = Number of tests conducted in Urban area of Agra
S = Number of tests conducted in Urban area of Meerut
In a given month, it is also known that number of tests found negative in rural area is equal to the number of tests found negative in urban area (True for both the cities)

1 Find the difference between the total number of positive cases in Urban and Rural areas of Meerut in the three months together.
A 55
B 65
C 70
D 75
E 110
» Explain it
Correct Option: B
From table-3 of common explanation, we have
The number of positive cases in Urban Meerut = 45 + 50 + 80 = 175
The number of positive cases in Rural Meerut = 15 + 45 + 50 = 110
Difference = 65
Hence, option B is correct.

Common explanation :

Using the given table chart in the question, we find the following table.

Table-1)
Month Positive (+ve) Negative (-ve)
March 70 30
April 130 70
May 180 180
Using the values of P and Q from column chart, we have the following information.
 
(Table-2)
Month Positive (+ve) Negative (-ve)
Agra Meerut Agra Meerut
March 10 60 20 10
April 35 95 30 40
May 50 130 100 80

From this table, we have that total number of tests (Urban + Rural) in Agra in

March = 10 + 20 = 30
April = 35 + 30 = 65
May = 50 + 100 = 150
From value of R in March, we have
Urban test in Agra = 20 (+ve and –ve both)
Rural test in Agra = 10
From value of R in April, we have
Urban test in Agra = 50
Rural test in Agra = 15
From value of R in May, we have
Urban test in Agra = 100 (+ve and –ve both)

Rural test in Agra = 50
Now, we have last information that in a given month, number of tests found negative in rural area is equal to the number of tests found negative in urban area.

Consider March of Agra.
Let the number of Rural test found positive/negative = R+/R–; and Urban test found positive = U+/U–
So, we have been given that R– = U–
We have from the calculations above that
(March in Agra)
U+ + U– = 20 ——(i)
R+ + R– = 10 ——(ii)
From table 1, we have
R– + U– = 20 ——(iii)
R+ + U+ = 10 ——(iv)
But since R– = U– = Y (say), we have from (iii)
R– = U– = 10
Putting value of R– = U– = 10 in (i), (ii) and (iv), we get
U+ = 10
R+ = 0
Similarly we find for each month and both the cities.
We fill all the values in the table given below.

(Table-3)
Agra Meerut
Urban Rural Urban Rural
+ve -ve +ve -ve +ve -ve +ve -ve
March 10 10 0 10 45 5 15 5
April 35 15 0 15 50 20 45 20
May 50 50 0 50 80 40 50 40

2 Find the number of positive cases in April in the two cities together is what percent more than the number of negative cases in the two cities in March?
A 120%
B 133.33%
C 233.33%
D 333.33%
E 300%
» Explain it

Correct Option: D
From table-2 in the common explanation, we have

Number of positive cases in April = 35 + 95 = 130

Number of negative cases in March = 20 + 10 = 30

Percentage = (130 – 30) /30× 100 = 333.33%
Hence, option D is correct.

Common explanation :

Using the given table chart in the question, we find the following table.

(Table-1)
Month Positive (+ve) Negative (-ve)
March 70 30
April 130 70
May 180 180
Using the values of P and Q from column chart, we have the following information.
 
(Table-2)
Month Positive (+ve) Negative (-ve)
Agra Meerut Agra Meerut
March 10 60 20 10
April 35 95 30 40
May 50 130 100 80
From this table, we have that total number of tests (Urban + Rural) in Agra in 
 
March = 10 + 20 = 30
 
April = 35 + 30 = 65
 
May = 50 + 100 = 150
 
From value of R in March, we have 
 
Urban test in Agra = 20 (+ve and –ve both)
 
Rural test in Agra = 10
 
From value of R in April, we have 
 
Urban test in Agra = 50
 
Rural test in Agra = 15
 
From value of R in May, we have 
 
Urban test in Agra = 100 (+ve and –ve both)
Rural test in Agra = 50
 
Now, we have last information that in a given month, number of tests found negative in rural area is equal to the number of tests found negative in urban area.
 
Consider March of Agra.
Let the number of Rural test found positive/negative = R+/R–; and Urban test found positive = U+/U–

So, we have been given that R– = U–

We have from the calculations above that

(March in Agra)

U+ + U– = 20 ——(i)

R+ + R– = 10 ——(ii)

From table 1, we have

R– + U– = 20 ——(iii)

R+ + U+ = 10 ——(iv)

But since R– = U– = Y (say), we have from (iii)

R– = U– = 10

Putting value of R– = U– = 10 in (i), (ii) and (iv), we get

U+ = 10

R+ = 0

Similarly we find for each month and both the cities.

We fill all the values in the table given below.

(Table-3)
Agra Meerut
Urban Rural Urban Rural
+ve -ve +ve -ve +ve -ve +ve -ve
March 10 10 0 10 45 5 15 5
April 35 15 0 15 50 20 45 20
May 50 50 0 50 80 40 50 40

3 In which case there was no positive test result:
A Urban area of Meerut in March
B Rural area of Meerut in all the three months
C Rural area of Agra in May
D Urban area of Agra in all the three months
E None of these

C
From table-3 of common explanation, we see that the Rural area of Agra in May has zero case.
 
Hence, option C is correct.

Common explanation : 

Using the given table chart in the question, we find the following table.
 
(Table-1)
Month Positive (+ve) Negative (-ve)
March 70 30
April 130 70
May 180 180
Using the values of P and Q from column chart, we have the following information.
 
(Table-2)
Month Positive (+ve) Negative (-ve)
Agra Meerut Agra Meerut
March 10 60 20 10
April 35 95 30 40
May 50 130 100 80
From this table, we have that total number of tests (Urban + Rural) in Agra in 
 
March = 10 + 20 = 30
 
April = 35 + 30 = 65
 
May = 50 + 100 = 150
 
From value of R in March, we have 
 
Urban test in Agra = 20 (+ve and –ve both)
 
Rural test in Agra = 10
 
From value of R in April, we have 
 
Urban test in Agra = 50
 
Rural test in Agra = 15
 
From value of R in May, we have 
 
Urban test in Agra = 100 (+ve and –ve both)
Rural test in Agra = 50
 
Now, we have last information that in a given month, number of tests found negative in rural area is equal to the number of tests found negative in urban area.
 
Consider March of Agra.
Let the number of Rural test found positive/negative = R+/R–; and Urban test found positive = U+/U–

So, we have been given that R– = U–

We have from the calculations above that

(March in Agra)

U+ + U– = 20 ——(i)

R+ + R– = 10 ——(ii)

From table 1, we have

R– + U– = 20 ——(iii)

R+ + U+ = 10 ——(iv)

But since R– = U– = Y (say), we have from (iii)

R– = U– = 10

Putting value of R– = U– = 10 in (i), (ii) and (iv), we get

U+ = 10

R+ = 0

Similarly we find for each month and both the cities.

We fill all the values in the table given below.

(Table-3)
Agra Meerut
Urban Rural Urban Rural
+ve -ve +ve -ve +ve -ve +ve -ve
March 10 10 0 10 45 5 15 5
April 35 15 0 15 50 20 45 20
May 50 50 0 50 80 40 50 40

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