Practice Exercise 1: At what position will Nobita speak?

Statements:

I. There are five speakers before Nobita.

II. There are three speakers after Nobita.

III. There are nine speakers in all.

(1) II and III are sufficient.

(2) Either I or II is sufficient.

(3) Either I or II and III are sufficient.

(4) Only III is sufficient.

(5) None of these

> From Statement I, we know that there are five speakers before Nobita, therefore, he will speak at 6th position. So, this statement alone is sufficient.  

> From Statement II, we know that there are 3 speakers after Nobita. To figure out his position from this information, we must also know the total number of candidates which is given in Statement III. Therefore, the position of Nobita is 9 – 3 = 6. So, Statements II and III together are also sufficient.

Therefore, option (3) is correct. 

Practice Exercise 2: What is the age of Shizuka?

Statements:

I. Shizuka is half as old as her mother.

II. 8 years ago Shizuka was one-third as old as her mother.

III. Shizuka is 16 years younger than her mother.

IV. 12 years ago her mother was five times as old as Shizuka.

(1) I and II are sufficient.

(2) I and either II or III is sufficient.

(3) Either I or II and either III or IV is sufficient.

(4) Any two out of I, II, III, and IV are sufficient.

(5) None of these.

Observe that in each of the statement, Shizuka’s age is given in relation to her mother’s age. Therefore, we have two unknowns: Shizuka’s age and her mother’s age. To calculate two unknowns, we need two different relations. Each of the statement gives us a different relation between Shizuka’s and her mother’s age. Therefore, using any 2 of these statements, we will be able to determine Shizuka’s age. So, option (4) is correct.

Practice Exercise 3: In a school, what percent of students plays cricket, if each student plays exactly one out of three sports (Football, Hockey and Cricket) and all students play any one sport?

Statements:

I. The ratio of students playing Hockey and Cricket is 4 : 5

II. Out of total students in the school, only 19% of students play Football.

(1) I alone is sufficient while II alone is not sufficient.

(2) II alone is sufficient while I alone is not sufficient.

(3) Either I or II is sufficient.

(4) Neither I nor II is sufficient.

(5) Both I and II are sufficient.

Obviously, both the statements are sufficient to answer the question. 

From Statement II, we know that 81% of the students play Hockey and Cricket. The ratio of students playing hockey and cricket is given in statement I, which is 4 : 5. Using this, the percentage of students playing cricket is [5/(4 + 5)] × 81% = 45%.

Therefore, option (5) is correct.

Practice Exercise 4: A certain company has only two types of employees executive and nonexecutive. The company paid $125 bonuses to each of its executive employees and $75 to each of its non-executive employees. If 100 of the employees were non-executives, how many of the employees were executives?

Statements:

I. The company has a total of 120 employees.

II. The total amount that the company paid in bonuses to its employees was $10,000.

(1) I alone is sufficient while II alone is not sufficient.

(2) II alone is sufficient while I alone is not sufficient.

(3) Either I or II is sufficient.

(4) Neither I nor II is sufficient.

(5) Both I and II are sufficient.

> Statement I:

Since it is given that the number of non-executive employees is 100, therefore, the number of executives is 120 – 100 = 20.

So, this statement alone is sufficient to answer the question.

> Statement II:

The total amount paid by the company in bonuses to its employees = $10,000.

The total amount paid by the company in bonuses to its non-executive employees = $75 × 100 = $7500

Therefore, the total amount paid by the company in bonuses to its executive employees = $10,000 – $7500 = $2500

The amount received by each executive employee = $125

Therefore, the number of executive employees = $2500 / $125 = 20

So, this statement alone is also sufficient to answer the question.

Therefore, option (3) is correct.

Practice Exercise 5: In a school, 60% of boys and 40% of girls participated in sports. How many boys are there in the school?

Statements:

I. More than 300 boys are there. 120 girls participated in sports.

II. The number of girls in school is 25% more than the number of boys who participated in sports.

(1) I alone is sufficient while II alone is not sufficient.

(2) II alone is sufficient while I alone is not sufficient.

(3) Either I or II is sufficient.

(4) Neither I nor II is sufficient.

(5) Both I and II are sufficient.

Using Statement I, we can calculate the total number of girls in the school.

The number of girls who participated in sports = 120. These are 40% of the total number of girls in the school.

Therefore, total number of girls in the school = 120 (100/40) = 300

In statement II it is given that,

Total number of girls in the school = 125% of the number of boys  who participated in sports

Therefore, the number of boys who participated in sports = 300 (100/125) = 240. These are 60% of the total number of boys in the school.

Therefore, the total number of boys in school = 240 (100/60) = 400

Thus, both the statements are sufficient to answer the question. Therefore, option (5) is correct.

Practice Exercise 6: What is the code of ‘good’?

Statements:

I. ‘energy is good’ is written as ‘763’ and ‘earth is round’ is written as ‘579’.

II. ‘mistakes are good’ is written as ‘164’ and ‘mistakes are necessary’ is written as ‘421’.

(1) I alone is sufficient while II alone is not sufficient.

(2) II alone is sufficient while I alone is not sufficient.

(3) Either I or II is sufficient.

(4) Neither I nor II is sufficient.

(5) Both I and II are sufficient.

> In statement I, the code of ‘is’ is ‘7’. This implies that the code of good is either ‘6’ or ‘3’. So, the statement I alone is not sufficient.

> In statement II, the code of “mistakes are” is ’14’. This implies the code of good is ‘6’. So, statement II alone is sufficient.

Therefore, the correct option is (2).