Logical Reasoning & DI (LRDI) Test

Result

Logical Reasoning & DI (LRDI) Test - 23

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Question 1
3 / -1

Directions For Questions

Directions: Study the given information and answer the following question.

A car servicing company has ten LED boards which are fitted on a wall. Each of them displays the digits from 0-9. They are programmed in such a way that when any car enters the workshop for service, the registration number on the car's number plate will appear on the wall as the digits on the wall-mounted LED boards shall glow to show a 4-digit number. On Monday, 4 cars of different colours, i.e. red, white, black and grey, entered the workshop. Due to faulty software, the only thing that got noted down was the number of times each LED board glowed in total after the 4 cars entered. Hence, the following data was collected.

Further, software provided the following data:

(1) The registration number of each car has a factor 5.

(2) Except the white car, all the other cars have at least three different digits.

(3) The registration number of black car has the highest value numerically.

(4) The registration number of red car has four different digits, three of which are not present in the registration numbers of any of the other 3 cars.

(5) The difference between the registration numbers of red car and grey car has a maximum value of 600 and a minimum value of 500.

(6) The registration number of white car is exactly a factor of the registration number of black car.

(7) The sum of the digits of registration number of white car is 8.

...view full instructions

What is the registration number of white car?

A
1115

B
1120

C
1125

D
1130

Solution

The registration number of white car is 1115.

Given that the registration number of white car has less than 3 different digits. It cannot have only one digit (since no digit occurs 4 times). Hence, the registration number of white car must be a multiple of 5 (i.e. end in a 0 or a 5) and have 2 different digits, i.e. be of the form (aaab/abbb) OR (aabb). Hence, 3a + b = 8 (for which the only possibility is a = 1 and b = 5, since 0 appears only twice) or 2a + 2b = 8 (for which there is no possibility, since 4 does not appear even once and at least one of a and b must be 0 or 5). Hence. only 1115 is possible.

The registration number of white car is exactly a factor of registration number of black car or we can say that the registration number of black car is a multiple of registration number of white car. Multiples of 1115 with four digits are 2230, 3345, 4460, 5575, 6690, 7805 and 8920. Of these, only 6690 is possible (8920 and 7805 are not possible because the registration number of red car should have three digits, which are not in anyone else's registration number, i.e. the registration number of red car should have three digits out of 2, 7, 8 and 9).

Since 9 is present in the registration number of black car, red car's registration number should contain 2, 7, 8 and 5/0. The registration number of grey car will have the digits 3, 3, 5 and 5/0. But, if there are two 5s in the registration number of grey car, it will not have at least three distinct digits. Hence, the registration number of grey car will have the digits 3, 3, 5 and 0 and the registration number of red car will be either 2785 or 2875.

From (5), 2785 + 500 = 3285 and 2875 + 500 = 3375. The registration number of grey car should lie between 3285 and 3475. The only possible values of registration number of grey car are 3350 and 3305. Since both these values are less than 3375, the registration number of red car cannot be 2875. Therefore, the registration number of red car must be 2785 and the registration number of grey car can be 3350 or 3305.
Question 2
3 / -1

Directions For Questions

Directions: Study the given information and answer the following question.

A car servicing company has ten LED boards which are fitted on a wall. Each of them displays the digits from 0-9. They are programmed in such a way that when any car enters the workshop for service, the registration number on the car's number plate will appear on the wall as the digits on the wall-mounted LED boards shall glow to show a 4-digit number. On Monday, 4 cars of different colours, i.e. red, white, black and grey, entered the workshop. Due to faulty software, the only thing that got noted down was the number of times each LED board glowed in total after the 4 cars entered. Hence, the following data was collected.

Further, software provided the following data:

(1) The registration number of each car has a factor 5.

(2) Except the white car, all the other cars have at least three different digits.

(3) The registration number of black car has the highest value numerically.

(4) The registration number of red car has four different digits, three of which are not present in the registration numbers of any of the other 3 cars.

(5) The difference between the registration numbers of red car and grey car has a maximum value of 600 and a minimum value of 500.

(6) The registration number of white car is exactly a factor of the registration number of black car.

(7) The sum of the digits of registration number of white car is 8.

...view full instructions

How many of the four cars have a registration number which is a multiple of 3? Key in the correct value.

A
1

B
2

C
3

D
5

Solution

Only the registration number of black car i.e.6690 is a multiple of 3.

Given that the registration number of white car has less than 3 different digits. It cannot have only one digit (since no digit occurs 4 times). Hence, the registration number of white car must be a multiple of 5 (i.e. end in a 0 or a 5) and have 2 different digits, i.e. be of the form (aaab/abbb) OR (aabb). Hence, 3a + b = 8 (for which the only possibility is a = 1 and b = 5, since 0 appears only twice) or 2a + 2b = 8 (for which there is no possibility, since 4 does not appear even once and at least one of a and b must be 0 or 5). Hence. only 1115 is possible.

The registration number of white car is exactly a factor of registration number of black car or we can say that the registration number of black car is a multiple of registration number of white car. Multiples of 1115 with four digits are 2230, 3345, 4460, 5575, 6690, 7805 and 8920. Of these, only 6690 is possible (8920 and 7805 are not possible because the registration number of red car should have three digits, which are not in anyone else's registration number, i.e. the registration number of red car should have three digits out of 2, 7, 8 and 9).

Since 9 is present in the registration number of black car, red car's registration number should contain 2, 7, 8 and 5/0. The registration number of grey car will have the digits 3, 3, 5 and 5/0. But, if there are two 5s in the registration number of grey car, it will not have at least three distinct digits. Hence, the registration number of grey car will have the digits 3, 3, 5 and 0 and the registration number of red car will be either 2785 or 2875.

From (5), 2785 + 500 = 3285 and 2875 + 500 = 3375. The registration number of grey car should lie between 3285 and 3475. The only possible values of registration number of grey car are 3350 and 3305. Since both these values are less than 3375, the registration number of red car cannot be 2875. Therefore, the registration number of red car must be 2785 and the registration number of grey car can be 3350 or 3305.
Question 3
3 / -1

Directions For Questions

Directions: Study the given information and answer the following question.

A car servicing company has ten LED boards which are fitted on a wall. Each of them displays the digits from 0-9. They are programmed in such a way that when any car enters the workshop for service, the registration number on the car's number plate will appear on the wall as the digits on the wall-mounted LED boards shall glow to show a 4-digit number. On Monday, 4 cars of different colours, i.e. red, white, black and grey, entered the workshop. Due to faulty software, the only thing that got noted down was the number of times each LED board glowed in total after the 4 cars entered. Hence, the following data was collected.

Further, software provided the following data:

(1) The registration number of each car has a factor 5.

(2) Except the white car, all the other cars have at least three different digits.

(3) The registration number of black car has the highest value numerically.

(4) The registration number of red car has four different digits, three of which are not present in the registration numbers of any of the other 3 cars.

(5) The difference between the registration numbers of red car and grey car has a maximum value of 600 and a minimum value of 500.

(6) The registration number of white car is exactly a factor of the registration number of black car.

(7) The sum of the digits of registration number of white car is 8.

...view full instructions

What is the sum of registration numbers of red car and black car?

A
9268

B
9470

C
9565

D
9475

Solution

The sum of the registration numbers of red car and black car is 9475.

Given that the registration number of white car has less than 3 different digits. It cannot have only one digit (since no digit occurs 4 times). Hence, the registration number of white car must be a multiple of 5 (i.e. end in a 0 or a 5) and have 2 different digits, i.e. be of the form (aaab/abbb) OR (aabb). Hence, 3a + b = 8 (for which the only possibility is a = 1 and b = 5, since 0 appears only twice) or 2a + 2b = 8 (for which there is no possibility, since 4 does not appear even once and at least one of a and b must be 0 or 5). Hence. only 1115 is possible.

The registration number of white car is exactly a factor of registration number of black car or we can say that the registration number of black car is a multiple of registration number of white car. Multiples of 1115 with four digits are 2230, 3345, 4460, 5575, 6690, 7805 and 8920. Of these, only 6690 is possible (8920 and 7805 are not possible because the registration number of red car should have three digits, which are not in anyone else's registration number, i.e. the registration number of red car should have three digits out of 2, 7, 8 and 9).

Since 9 is present in the registration number of black car, red car's registration number should contain 2, 7, 8 and 5/0. The registration number of grey car will have the digits 3, 3, 5 and 5/0. But, if there are two 5s in the registration number of grey car, it will not have at least three distinct digits. Hence, the registration number of grey car will have the digits 3, 3, 5 and 0 and the registration number of red car will be either 2785 or 2875.

From (5), 2785 + 500 = 3285 and 2875 + 500 = 3375. The registration number of grey car should lie between 3285 and 3475. The only possible values of registration number of grey car are 3350 and 3305. Since both these values are less than 3375, the registration number of red car cannot be 2875. Therefore, the registration number of red car must be 2785 and the registration number of grey car can be 3350 or 3305.
Question 4
3 / -1

Directions For Questions

Directions: Study the given information and answer the following question.

A car servicing company has ten LED boards which are fitted on a wall. Each of them displays the digits from 0-9. They are programmed in such a way that when any car enters the workshop for service, the registration number on the car's number plate will appear on the wall as the digits on the wall-mounted LED boards shall glow to show a 4-digit number. On Monday, 4 cars of different colours, i.e. red, white, black and grey, entered the workshop. Due to faulty software, the only thing that got noted down was the number of times each LED board glowed in total after the 4 cars entered. Hence, the following data was collected.

Further, software provided the following data:

(1) The registration number of each car has a factor 5.

(2) Except the white car, all the other cars have at least three different digits.

(3) The registration number of black car has the highest value numerically.

(4) The registration number of red car has four different digits, three of which are not present in the registration numbers of any of the other 3 cars.

(5) The difference between the registration numbers of red car and grey car has a maximum value of 600 and a minimum value of 500.

(6) The registration number of white car is exactly a factor of the registration number of black car.

(7) The sum of the digits of registration number of white car is 8.

...view full instructions

If two out of the four registration numbers are multiples of 10, then what is the registration number of grey car?

A
3350

B
3380

C
3390

D
3360

Solution

It is given that the registration number of white car has less than 3 different digits. It cannot have only one digit (since no digit occurs 4 times). Hence, the registration number of white car must be a multiple of 5 (i.e. end in a 0 or a 5) and have 2 different digits, i.e. be of the form (aaab/abbb) OR (aabb). Hence, 3a + b = 8 (for which the only possibility is a = 1 and b = 5, since 0 appears only twice) or 2a + 2b = 8 (for which there is no possibility, since 4 does not appear even once and at least one of a and b must be 0 or 5). Hence, only 1115 is possible.

The registration number of white car is exactly a factor of the registration number of black car or we can say that the registration number of black car is a multiple of the registration number of white car. Multiples of 1115 with four digits are 2230, 3345, 4460, 5575, 6690, 7805 and 8920. Of these, only 6690 is possible (8920 and 7805 are not possible because the registration number of red car should have three digits, which are not in anyone else's registration number, i.e. the registration number of red car should have three digits out of 2, 7, 8 and 9).

Since 9 is present in the registration number of black car, red car's registration number should contain 2, 7, 8 and 5/0. The registration number of grey car will have the digits 3, 3, 5 and 5/0, but if there are two 5s in the registration number of grey car, it will not have at least three distinct digits. Hence, the registration number of grey car will have the digits 3, 3, 5 and 0 and the registration number of red car will be either 2785 or 2875.

From (5), 2785 + 500 = 3285 and 2875 + 500 = 3375. The registration number of grey car should lie between 3285 and 3475. The only possible values of the registration number of grey car are 3350 and 3305. Since both these values are less than 3375, the registration number of red car cannot be 2875. Therefore, the registration number of red car must be 2785 and the registration number of grey car can be 3350 or 3305.
Question 5
3 / -1

Directions For Questions

Directions: Study the given information and answer the following question.

A car servicing company has ten LED boards which are fitted on a wall. Each of them displays the digits from 0-9. They are programmed in such a way that when any car enters the workshop for service, the registration number on the car's number plate will appear on the wall as the digits on the wall-mounted LED boards shall glow to show a 4-digit number. On Monday, 4 cars of different colours, i.e. red, white, black and grey, entered the workshop. Due to faulty software, the only thing that got noted down was the number of times each LED board glowed in total after the 4 cars entered. Hence, the following data was collected.

Further, software provided the following data:

(1) The registration number of each car has a factor 5.

(2) Except the white car, all the other cars have at least three different digits.

(3) The registration number of black car has the highest value numerically.

(4) The registration number of red car has four different digits, three of which are not present in the registration numbers of any of the other 3 cars.

(5) The difference between the registration numbers of red car and grey car has a maximum value of 600 and a minimum value of 500.

(6) The registration number of white car is exactly a factor of the registration number of black car.

(7) The sum of the digits of registration number of white car is 8.

...view full instructions

How many cars have a registration number with either of the middle two digits same as either of the extreme two digits?

A
3

B
5

C
6

D
7

Solution

It is given that the registration number of white car has less than 3 different digits. It cannot have only one digit (since no digit occurs 4 times). Hence, the registration number of white car must be a multiple of 5 (i.e. end in a 0 or a 5) and have 2 different digits, i.e. be of the form (aaab/abbb) OR (aabb). Hence, 3a + b = 8 (for which the only possibility is a = 1 and b = 5, since 0 appears only twice) or 2a + 2b = 8 (for which there is no possibility, since 4 does not appear even once and at least one of a and b must be 0 or 5). Hence, only 1115 is possible.

The registration number of white car is exactly a factor of the registration number of black car or we can say that the registration number of black car is a multiple of the registration number of white car. Multiples of 1115 with four digits are 2230, 3345, 4460, 5575, 6690, 7805 and 8920. Of these, only 6690 is possible (8920 and 7805 are not possible because the registration number of red car should have three digits, which are not in anyone else's registration number, i.e. the registration number of red car should have three digits out of 2, 7, 8 and 9).

Since 9 is present in the registration number of black car, red car's registration number should contain 2, 7, 8 and 5/0. The registration number of grey car will have the digits 3, 3, 5 and 5/0, but if there are two 5s in the registration number of grey car, it will not have at least three distinct digits. Hence, the registration number of grey car will have the digits 3, 3, 5 and 0 and the registration number of red car will be either 2785 or 2875.

From (5), 2785 + 500 = 3285 and 2875 + 500 = 3375. The registration number of grey car should lie between 3285 and 3475. The only possible values of the registration number of grey car are 3350 and 3305. Since both these values are less than 3375, the registration number of red car cannot be 2875. Therefore, the registration number of red car must be 2785 and the registration number of grey car can be 3350 or 3305.

Only in the case of Red car (Registration number: 2785) , neither of the middle 2 digits is the same as either of the extreme 2 digits.
Question 6
3 / -1

Directions For Questions

Directions: Answer the question on the basis of the information given below.

Help Distress (HD) is an NGO involved in providing assistance to people suffering from natural disasters. Currently, it has 37 volunteers. They are involved in three projects: Tsunami Relief (TR) in Tamil Nadu, Flood Relief (FR) in Maharashtra, and Earthquake Relief (ER) in Gujarat. Each volunteer working with Help Distress has to be involved in at least one relief work project.

The highest number of volunteers are involved in the FR project. Among them, the number of volunteers involved in the FR project alone is equal to the number of volunteers having involvement in the ER project alone.

The number of volunteers involved in the ER project alone is double the number of volunteers involved in all the three projects.

A total of 17 volunteers are involved in the TR project.

The number of volunteers involved in the TR project alone is one less than the number of volunteers involved in ER project alone.

Ten volunteers involved in the TR project are also involved in at least one more project.

...view full instructions

Based on the given information, the least number of volunteers involved in both the FR and TR projects but not in the ER project is __________.

A
4

B
5

C
6

D
7
Solution
- A total of 17 volunteers are involved in the TR project and 10 in TR are also involved in other projects. Thus, 7 volunteers are involved only in TR.
- The number of volunteers involved in the TR project alone is one less than the number of volunteers involved in the ER project alone. Eight volunteers are involved in ER alone.
- The number of volunteers involved in the ER project alone is double the number of volunteers involved in all the three projects. So, 4 volunteers are involved in all the three projects.
- Among them, the number of volunteers involved in the FR project alone is equal to the number of volunteers having involvement in the ER project alone. So, 8 volunteers are involved in FR alone.
- Let number of volunteers involved in both TR and FR but not ER = a
Number of volunteers involved in both TR and ER but not FR = b

a + b + 4 = 10

a + b = 6

Let number of volunteers involved in both FR and ER but not TR = x

Total = 17 + x + 8 + 8 = 37

x = 4

Consider the Venn diagram shown below:

Number of volunteers involved in FR > Number of volunteers involved in TR

Number of volunteers involved in FR > Number of volunteers involved in ER

∴ 16 + a > 17 and 16 + a > 16 + b or a > b

∴ a and b can be (6, 0), (5, 1), or (4, 2).

Least number of volunteers involved in both the FR and TR projects but not in the ER project = Least value of a = 4
Question 7
3 / -1

Directions For Questions

Directions: Answer the question on the basis of the information given below.

Help Distress (HD) is an NGO involved in providing assistance to people suffering from natural disasters. Currently, it has 37 volunteers. They are involved in three projects: Tsunami Relief (TR) in Tamil Nadu, Flood Relief (FR) in Maharashtra, and Earthquake Relief (ER) in Gujarat. Each volunteer working with Help Distress has to be involved in at least one relief work project.

The highest number of volunteers are involved in the FR project. Among them, the number of volunteers involved in the FR project alone is equal to the number of volunteers having involvement in the ER project alone.

The number of volunteers involved in the ER project alone is double the number of volunteers involved in all the three projects.

A total of 17 volunteers are involved in the TR project.

The number of volunteers involved in the TR project alone is one less than the number of volunteers involved in ER project alone.

Ten volunteers involved in the TR project are also involved in at least one more project.

...view full instructions

Which of the following additional pieces of information would enable to find the exact number of volunteers involved in the various projects?

A
Twenty volunteers are involved in FR.

B
Four volunteers are involved in all the three projects.

C
Twenty-three volunteers are involved in exactly one project.

D
No need for any additional information.
Solution
- A total of 17 volunteers are involved in the TR project and 10 in TR are also involved in other projects. Thus, 7 volunteers are involved only in TR.
- The number of volunteers involved in the TR project alone is one less than the number of volunteers involved in the ER project alone. Eight volunteers are involved in ER alone.
- The number of volunteers involved in the ER project alone is double the number of volunteers involved in all the three projects. So, 4 volunteers are involved in all the three projects.
- Among them, the number of volunteers involved in the FR project alone is equal to the number of volunteers having involvement in the ER project alone. So, 8 volunteers are involved in FR alone.
- Let number of volunteers involved in both TR and FR but not ER = a
Number of volunteers involved in both TR and ER but not FR = b

a + b + 4 = 10

a + b = 6

Let number of volunteers involved in both FR and ER but not TR = x

Total = 17 + x + 8 + 8 = 37

x = 4

Consider the Venn diagram shown below:

We can obtain the information in options 2 and 3 from the data given in the passage.

The information in option 1 will give us the value of a, which in turn will give us the value of b. Thus, option 1 would enable us to find the exact number of volunteers involved in the various projects.
Question 8
3 / -1

Directions For Questions

Directions: Answer the question on the basis of the information given below.

Help Distress (HD) is an NGO involved in providing assistance to people suffering from natural disasters. Currently, it has 37 volunteers. They are involved in three projects: Tsunami Relief (TR) in Tamil Nadu, Flood Relief (FR) in Maharashtra, and Earthquake Relief (ER) in Gujarat. Each volunteer working with Help Distress has to be involved in at least one relief work project.

The highest number of volunteers are involved in the FR project. Among them, the number of volunteers involved in the FR project alone is equal to the number of volunteers having involvement in the ER project alone.

The number of volunteers involved in the ER project alone is double the number of volunteers involved in all the three projects.

A total of 17 volunteers are involved in the TR project.

The number of volunteers involved in the TR project alone is one less than the number of volunteers involved in ER project alone.

Ten volunteers involved in the TR project are also involved in at least one more project.

After some time, the volunteers who were involved in all the three projects were asked to withdraw from one project. As a result, one of the volunteers opted out of the TR project and one opted out of the ER project, while the remaining ones involved in all the three projects opted out of the FR project.

...view full instructions

Which of the following statements necessarily follows after this rearrangement?

A
The lowest number of volunteers is now in the TR project.

B
More volunteers are now in the ER project as compared to the TR project.

C
More volunteers are now in the TR project as compared to the ER project.

D
More volunteers are now in the FR project as compared to the ER project.
Solution
- A total of 17 volunteers are involved in the TR project and 10 in TR are also involved in other projects. Thus, 7 volunteers are involved only in TR.
- The number of volunteers involved in the TR project alone is one less than the number of volunteers involved in the ER project alone. Eight volunteers are involved in ER alone.
- The number of volunteers involved in the ER project alone is double the number of volunteers involved in all the three projects. So, 4 volunteers are involved in all the three projects.
- Among them, the number of volunteers involved in the FR project alone is equal to the number of volunteers having involvement in the ER project alone. So, 8 volunteers are involved in FR alone.
- Let number of volunteers involved in both TR and FR but not ER = a
Number of volunteers involved in both TR and ER but not FR = b

a + b + 4 = 10

a + b = 6

Let number of volunteers involved in both FR and ER but not TR = x

Total = 17 + x + 8 + 8 = 37

x = 4

Consider the Venn diagram shown below:

Number of volunteers involved in FR > Number of volunteers involved in ER

16 + a > 16 + b

a and b can be (6, 0), (5, 1), or (4, 2).

After the volunteers withdraw as mentioned, the number of volunteers working on different projects is as shown below:

After the volunteers withdraw as mentioned,
- Number of volunteers working on TR = 7 + 6 + 3 = 16
- Number of volunteers working on FR = 14 + a
- Number of volunteers working on ER = 15 + b
From options:

1. The lowest number of volunteers is now in the TR project.

Incorrect: For b = 0, Number of volunteers working on ER = 15

2. More volunteers are now in the ER project as compared to the TR project.

Incorrect: For b = 0, Number of volunteers working on ER = 15

3. More volunteers are now in the TR project as compared to the ER project.

Incorrect: For b = 2, Number of volunteers working on ER = 17

4. More volunteers are now in the FR project as compared to the ER project.

Correct for all possible value of a and b: 14 + a > 15 + b

(a, b) = (6, 0), (5, 1), (4, 2)

∴ More volunteers are now in FR than in ER.

Therefore, option 4 is the correct answer.
Question 9
3 / -1

Directions For Questions

Directions: Answer the question on the basis of the information given below.

Help Distress (HD) is an NGO involved in providing assistance to people suffering from natural disasters. Currently, it has 37 volunteers. They are involved in three projects: Tsunami Relief (TR) in Tamil Nadu, Flood Relief (FR) in Maharashtra, and Earthquake Relief (ER) in Gujarat. Each volunteer working with Help Distress has to be involved in at least one relief work project.

The highest number of volunteers are involved in the FR project. Among them, the number of volunteers involved in the FR project alone is equal to the number of volunteers having involvement in the ER project alone.

The number of volunteers involved in the ER project alone is double the number of volunteers involved in all the three projects.

A total of 17 volunteers are involved in the TR project.

The number of volunteers involved in the TR project alone is one less than the number of volunteers involved in ER project alone.

Ten volunteers involved in the TR project are also involved in at least one more project.

After some time, the volunteers who were involved in all the three projects were asked to withdraw from one project. Some new volunteers joined the NGO. Each one of them was allotted only one project in a manner such that the number of volunteers working on one project alone for each of the three projects became identical.

At that point, it was also found that the number of volunteers involved in the FR and ER projects was the same as the number of volunteers involved in the TR and ER projects.

...view full instructions

Which of the projects now has the highest number of volunteers?

A
Cannot be determined

B
FR

C
TR

D
ER
Solution
- A total of 17 volunteers are involved in the TR project and 10 in TR are also involved in other projects. Thus, 7 volunteers are involved only in TR.
- The number of volunteers involved in the TR project alone is one less than the number of volunteers involved in the ER project alone. Eight volunteers are involved in ER alone.
- The number of volunteers involved in the ER project alone is double the number of volunteers involved in all the three projects. So, 4 volunteers are involved in all the three projects.
- Among them, the number of volunteers involved in the FR project alone is equal to the number of volunteers having involvement in the ER project alone. So, 8 volunteers are involved in FR alone.
- Let number of volunteers involved in both TR and FR but not ER = a
Number of volunteers involved in both TR and ER but not FR = b

a + b + 4 = 10

a + b = 6

Let number of volunteers involved in both FR and ER but not TR = x

Total = 17 + x + 8 + 8 = 37

x = 4

Consider the Venn diagram shown below:

Let m volunteers be added to the TR project and n be added to each of the FR and ER projects.

Then, 7 + m = 8 + n

m = n + 1

Also, b + 2 = 5

∴ b = 3 and a = 3

Number of volunteers working on TR = 7 + n + 1 + 4 + 5 = 17 + n

Number of volunteers working on FR = 17 + n

Number of volunteers working on ER = 18 + n

Thus, ER has the highest number of volunteers.

Hence, option 4 is the correct choice.
Question 10
3 / -1

Directions For Questions

Directions: Answer the question on the basis of the information given below.

Help Distress (HD) is an NGO involved in providing assistance to people suffering from natural disasters. Currently, it has 37 volunteers. They are involved in three projects: Tsunami Relief (TR) in Tamil Nadu, Flood Relief (FR) in Maharashtra, and Earthquake Relief (ER) in Gujarat. Each volunteer working with Help Distress has to be involved in at least one relief work project.

The highest number of volunteers are involved in the FR project. Among them, the number of volunteers involved in the FR project alone is equal to the number of volunteers having involvement in the ER project alone.

The number of volunteers involved in the ER project alone is double the number of volunteers involved in all the three projects.

A total of 17 volunteers are involved in the TR project.

The number of volunteers involved in the TR project alone is one less than the number of volunteers involved in ER project alone.

Ten volunteers involved in the TR project are also involved in at least one more project.

...view full instructions

Which of the following is true?

A
The number of volunteers involved in both the ER and TR projects but not in the FR project can be equal to the number of volunteers involved in both the FR and TR projects but not in the ER project.

B
The number of volunteers involved in both the ER and TR projects but not in the FR project is more than the number of volunteers involved in both the FR and TR projects but not in the ER project.

C
Minimum number of volunteers involved in the FR project is 21.

D
Maximum number of volunteers involved in the ER project is 18.
Solution
- A total of 17 volunteers are involved in the TR project and 10 in TR are also involved in other projects. Thus, 7 volunteers are involved only in TR.
- The number of volunteers involved in the TR project alone is one less than the number of volunteers involved in the ER project alone. Eight volunteers are involved in ER alone.
- The number of volunteers involved in the ER project alone is double the number of volunteers involved in all the three projects. So, 4 volunteers are involved in all the three projects.
- Among them, the number of volunteers involved in the FR project alone is equal to the number of volunteers having involvement in the ER project alone. So, 8 volunteers are involved in FR alone.
- Let number of volunteers involved in both TR and FR but not ER = a
Number of volunteers involved in both TR and ER but not FR = b

a + b + 4 = 10

a + b = 6

Let number of volunteers involved in both FR and ER but not TR = x

Total = 17 + x + 8 + 8 = 37

x = 4

Consider the Venn diagram shown below:

Number of volunteers involved in FR > Number of volunteers involved in TR

Number of volunteers involved in FR > Number of volunteers involved in ER

∴ 16 + a > 17 and 16 + a > 16 + b or a > b

∴ a and b can be (6, 0), (5, 1), or (4, 2).

Maximum number of volunteers involved in both the FR and TR projects but not in the ER project = Maximum value of b = 2

Maximum total number of volunteers involved in ER = 2 + 4 + 4 + 8 = 18