Quantitative Ability Test

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Quantitative Ability Test - 2

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Weekly Quiz Competition

Question 1
4 / -1

What are the total number of ways in which 10 boys can be seated in a row if two particular boys must always have exactly 3 boys in between them?

A
⁸P₃ x 5!

B
⁸P₃ x 1440!

C
⁸P₃ x 300

D
⁶P₃ x 8!

Solution

Let the two particular boys be A and B.

They can be arranged in 2 ways after keeping a gap of 3 seats between them.

Three boys who are to be seated in between A and B can be selected from remaining 8 boys and arranged in 8P3 ways.

The remaining 5 boys can be arranged in 5! ways.

The group of 5 boys including A and B and the ones sitting between them can be seated in the arrangement in 6 ways.

The total number of ways in which all the 10 boys can be seated is 2 x 8P3 x 5! x 6 = 8P3 x 6! x 2 = 8P3 x 1440 Hence, option 2.
Question 2
4 / -1

Directions For Questions

Answer the following question based on the information given below.

Eight friends Raju, Ravi, Ramesh, Rahul, Arjun, Arvind, Anish and Atul are skilled at making Handicraft items. In order to make money using their skills, they decide to make a certain number of handicraft items and sell them at a Handicraft Expo. They decided to minimize time and maximize their productivity by forming two groups. The people whose names start with the letter ‘R’ form Group 1 and the people whose names start with the letter ‘A’ form Group 2. Each person from Group 1 forms a team each person from Group 2 to produce a certain number of handicraft items of a particular type, the details of which are given in the tables below.

Table 1 gives details of the type of handicraft item produced by each team.

Table 2 gives details of the number of handicraft items produced by each team

Table 3 gives the cost price and selling price of one item of each typ

The money (Cost Price and Profit) is shared according to the number of items each one has worked on. For example, if Rahul and Arvind made 175 pots, the total cost price and the profit made by selling those pots would be shared equally.

...view full instructions

Who has worked on the maximum number of handicraft items?

A
Raju

B
Rahul

C
Arvind

D
Anish

Solution

The number of handicraft items worked on by any person is directly given in table 2.

Raju, Rahul, Arvind and Anish have worked on 525, 500, 550 and 450 items respectively.

Thus, among these four people, Arvind has worked on the maximum number of handicraft items.

Hence, option 3.
Question 3
4 / -1

Directions For Questions

Answer the following question based on the information given below.

Eight friends Raju, Ravi, Ramesh, Rahul, Arjun, Arvind, Anish and Atul are skilled at making Handicraft items. In order to make money using their skills, they decide to make a certain number of handicraft items and sell them at a Handicraft Expo. They decided to minimize time and maximize their productivity by forming two groups. The people whose names start with the letter ‘R’ form Group 1 and the people whose names start with the letter ‘A’ form Group 2. Each person from Group 1 forms a team each person from Group 2 to produce a certain number of handicraft items of a particular type, the details of which are given in the tables below.

Table 1 gives details of the type of handicraft item produced by each team.

Table 2 gives details of the number of handicraft items produced by each team.

Table 3 gives the cost price and selling price of one item of each type

The money (Cost Price and Profit) is shared according to the number of items each one has worked on. For example, if Rahul and Arvind made 175 pots, the total cost price and the profit made by selling those pots would be shared equally.

...view full instructions

Which of the following statement(s) is/are true?

I. The total profit earned by Atul is Rs. 6,000

II. The total selling price of all the items that Ramesh has worked on is Rs. 32,125

III. The team of Raju and Arjun had the lowest total selling price of the items they had produced.

A
I and II

B
II and III

C
Only II

D
I, II and III

Solution

Statement III can be directly verified from the solutions to one of the earlier questions.

The team of Ramesh-Atul has the lowest selling price.

Hence, statement III is false.

Hence, options 2 and 4 can be eliminated.

Since II is present in both the remaining options, you can directly assume it to be true.

Hence, just verify I.

The total profit earned by Atul = (50/2) * 30 + (100/2) x 30 + (25/2 x 20) + (175/2 x 40) = Rs. 6,000 Thus, statement I is true.

Hence, option 1.
Question 4
4 / -1

Directions For Questions

Answer the following question based on the information given below.

Eight friends Raju, Ravi, Ramesh, Rahul, Arjun, Arvind, Anish and Atul are skilled at making Handicraft items. In order to make money using their skills, they decide to make a certain number of handicraft items and sell them at a Handicraft Expo. They decided to minimize time and maximize their productivity by forming two groups. The people whose names start with the letter ‘R’ form Group 1 and the people whose names start with the letter ‘A’ form Group 2. Each person from Group 1 forms a team each person from Group 2 to produce a certain number of handicraft items of a particular type, the details of which are given in the tables below.

Table 1 gives details of the type of handicraft item produced by each team.

Table 2 gives details of the number of handicraft items produced by each team.

Table 3 gives the cost price and selling price of one item of each type

The money (Cost Price and Profit) is shared according to the number of items each one has worked on. For example, if Rahul and Arvind made 175 pots, the total cost price and the profit made by selling those pots would be shared equally.

...view full instructions

Q. For which type of handicraft was the total number of items produced the highest?

A
Basket

B
Shoe

C
Pot

D
Lantern

Solution

The total number of items for each type of handicraft is: Baskets = 125 + 200 + 50 + 50 = 425 Shoes = 75 + 100 + 75 + 100 + 250 = 600 Pots = 25 + 175 + 50 + 100 = 350 Lanterns = 100 + 175 = 275 Hence, option 2
Question 5
4 / -1

Directions For Questions

Owing to a global economic slowdown the company Testa Ltd. has decided to review its employee compensation structure in order to cut costs. In the existing structure all 100 employees are paid a Fixed Salary (FS) equal to 10000 and a Variable Salary (VS), where the Variable Salary depends upon the performance of the company and is decided as a percentage of the Fixed Salary.

Employee salary = FS + VS The company is thinking of changing it into a variable pay structure where different groups of employees are paid as shown in the table below.

Where the Variable Salary depends on the company performance and is calculated as a percentage of Fixed salary.

...view full instructions

Q. The company does not perform satisfactorily and decides on a variable salary = 10% of fixed salary. What is the percentage gain/loss of the company if it uses the new structure with respect to the existing compensation structure?

A
Gain of 11%

B
Loss of 10%

C
Gain of 10%

D
Loss of 11%

Solution

As there are 100 employees and VS = 10% of FS In the existing structure, the total salary would be = 100 x (10000 + 10% of 10000) = Rs. 1100000

In the proposed new structure, total salary = 60 x (8000 + 10% of 8000) + 30 x (10000 + 10% of 10000) + 10 x (12000 + 10% of 12000)

= Rs. 990000 Difference in total salary = 1100000 - 990000 = Rs. 110000. The company saves Rs. 110000 if it uses the new compensation structure. Percentage gain = (110000/1100000) x 100 = 10%

Hence, option 3.
Question 6
4 / -1

Directions For Questions

Owing to a global economic slowdown the company Testa Ltd. has decided to review its employee compensation structure in order to cut costs. In the existing structure all 100 employees are paid a Fixed Salary (FS) equal to 10000 and a Variable Salary (VS), where the Variable Salary depends upon the performance of the company and is decided as a percentage of the Fixed Salary.

Employee salary = FS + VS The company is thinking of changing it into a variable pay structure where different groups of employees are paid as shown in the table below.

Where the Variable Salary depends on the company performance and is calculated as a percentage of Fixed salary.

...view full instructions

If the variable salary is decided as 15% of the fixed salary in the existing compensation structure, what should be the percentage variable pay in the new compensation structure such that there is no difference in total employee compensation between both the structures?

A
18.67%

B
25%

C
15%

D
27.78%

Solution

YS = 15% of FS Total employee salary in the existing compensation structure = 100 x (10000 + 15% of 10000) = Rs. 1150000

Let the variable salary be x% of the fixed salary in the new compensation structure. Total salary in the new compensation structure = 60 x (8000 + x% of 8000) + 30 x (10000 + x% of 10000) + 10 x (12000 + x% of 12000)

= Rs. (900000 + 9000x)

For there to be no difference between the two compensation structures, 1150000 = 900000 + 9000x.

x = (250/9) % = 27.78% Hence, option 4.
Question 7
4 / -1

Directions For Questions

Owing to a global economic slowdown the company Testa Ltd. has decided to review its employee compensation structure in order to cut costs. In the existing structure all 100 employees are paid a Fixed Salary (FS) equal to 10000 and a Variable Salary (VS), where the Variable Salary depends upon the performance of the company and is decided as a percentage of the Fixed Salary.

Employee salary = FS + VS The company is thinking of changing it into a variable pay structure where different groups of employees are paid as shown in the table below.

Where the Variable Salary depends on the company performance and is calculated as a percentage of Fixed salary.

...view full instructions

The company is not satisfied with the cost savings from the new compensation structure and decides to retrench 9 employees from employee categories of A and B such that employees retrenched from category A is twice those retrenched from category B. The variable pay for the new compensation is declared to be 10%. What should be the percentage variable pay in the old compensation structure such that there is no difference between the two?

A
3.33%

B
5%

C
6.67%

D
None of these

Solution

As the company retrenches 9 employees the total employees now left are 91.

Let the employees retrenched from category B be y.

Employees retrenched from category A = 2y

y + 2y = 9.

y = 3. The employees in category A, B and C are 54, 27 and 10 respectively.

Total employee compensation in the new structure = 54 x (8000 + 10% of 8000) + 27 x (10000 + 10% of 10000) + 10 x (12000 + 10% of 12000).

Let the variable salary in the old compensation structure be z% of the fixed salary Total employee compensation in the old structure = 91 x (10000 + z% of 10000) = Rs. (910000 + 9100z) For there to be no difference in the two compensation structures, 904200 = 910000 + 9100z, which is not possible So, the total compensation of both the structures can never be same.

Hence, option 4.
Question 8
4 / -1

Directions For Questions

Owing to a global economic slowdown the company Testa Ltd. has decided to review its employee compensation structure in order to cut costs. In the existing structure all 100 employees are paid a Fixed Salary (FS) equal to 10000 and a Variable Salary (VS), where the Variable Salary depends upon the performance of the company and is decided as a percentage of the Fixed Salary.

Employee salary = FS + VS The company is thinking of changing it into a variable pay structure where different groups of employees are paid as shown in the table below.

Where the Variable Salary depends on the company performance and is calculated as a percentage of Fixed salary.

...view full instructions

If the total variable salary component of category A employees is equal to the total salary of category C employees, in the new system, then what percentage of the fixed salary is the variable salary?

A
33.33

B
25

C
35

D
None of these

Solution

Let the variable salary be x% of the fixed salary. Then, 60 * x% of 8000 = 10 *(12000 + x% of 12000). Therefore 4800x= 12000 + 1200x.

x= 33.33%

Hence, option 1
Question 9
4 / -1

In a group of 132 children, 50, 60, 70 children like three different games – Cricket, Football, Tennis, respectively. The number of children who play all the three games is half the number of children who play exactly two games. The number of children who play exactly any two out of the three games is the same as those who play exactly any other two of the three games. The number of children who play the three games:

A
12

B
6

C
8

D
10

Solution

SOLUTION:

Let, \(a=a+b+c\)

\(\beta=x+y+z y=k\)

Here,

Again, \(x=y=z=p\) \(\beta=3 p\)

\(\Upsilon=\frac{3}{2} p\)

Now, \(a+2 \beta+3 y=50+60+70=180\)

\(a+4 y+3 y=180\)

\(a+7 y=180-\)

Again, \(a+\beta+\gamma=132\)

\(a+2 y+y=132\)

\(a+3 y=132\)

from (i) and (ii), we get \(y=12\) Hence, 12 children play all 3 games. Hence, Option A is correct.
Question 10
4 / -1

The total number of factors of a number is 24 and the product of the prime factors of the same number is 30. The ratio of such a smallest and the greatest possible numbers in minimum terms is:

A
32/725

B
28/525

C
16/625

D
28/625

Solution

The product of prime factors = 30 = 2 ×3×5

Now, the total number of prime factors = 24

= 2×2×6 = (1+1) (1+1) (5+1)

So, the least possible number = 2⁵×3¹×5¹ = 480

And the greatest possible number = 21×31×55 = 18750

So, the ratio of 480 / 18750=24 / 54 = 16 / 625

Option (c) is correct.