Introduction

In such type of problems, a question is followed by two or more statements. We are required to decide whether the data provided in the statements are sufficient to answer the question or not.

Practice Exercise 1: Among A, B, C, D, E and F, who is the heaviest?

Statements:

I. A and D are heavier than B, E, and F but none of them is the heaviest.

II. A is heavier than D but lighter than C.

(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.

> From Statement I, we know that none of A, B, D, E, and F are the heaviest. Therefore, C is the heaviest. So, statement 1 alone is sufficient to answer the question.

> Statement II does not provide any information regarding the weight of B, E and F. So, statement II alone is not sufficient.

Therefore, option (1) is correct.

Practice Exercise 2: What will be the weight of 10 poles, each of the same weight?

Statements:

I. One-fourth of the weight of each pole is 10 kg.

II. The total weight of the three poles is 40 kg more than the total weight of two poles. 

(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.

It is given in the question that each pole has the same weight.

> Statement I: 

Clearly, the weight of each pole is 40 kg. Since there are 10 poles, therefore, the total weight of the poles is 400 Kg.

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

> Statement II:

Weight of each pole = Weight of 3 poles – Weight of 2 poles = 40 kg.

Therefore, the total weight of the poles = 400kg. So, statement II alone is also sufficient to answer the question.

Therefore, option (3) is correct.

Practice Exercise 3: How many children does W have?

Statements:

I. K is the only son of D who is the husband of W.

II. M and N are brothers of W. 

(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.

> From Statement I, we can conclude that W has 1 son, but it does not tell about the number of daughters W has.

> The information provided in Statement II is irrelevant.

So, the information provided in neither statement I nor statement II is sufficient to answer the question. Therefore, option (4) is correct.

Practice Exercise 4: In which year was Senorita born?

Statements:

I. Senorita at present is 25 years younger than her mother.

II. Senorita’s brother, who was born in 1970, is 35 years younger than his mother.

(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.

From Statement II, we can see that Senorita’s mother was born in 1935.

From Statement I, we know that Senorita is 25 years younger than her mother. Therefore, she was born in 1960.

So, both Statement I and II are necessary and sufficient to answer the question. Therefore, option (5) is correct.

Another Approach:

From both the statements, we can see that Senorita is 10 years older than his brother. Since her brother was born in 1970, therefore, she was born in 1960.

Practice Exercise 5: Among X, Y and Z who is the most intelligent?

Statements:

I. X is more intelligent than Y. 

II. Z is more intelligent than M.

III. M is more intelligent than N.

IV. X is more intelligent than N.

(1) I alone is sufficient.

(2) I and IV are sufficient.

(3) I, II and IV are sufficient.

(4) I, III and IV are sufficient.

(5) More information is needed.

From Statement I, we have X > Y.

From Statement II, we have Z > M

From Statement III, we have M > N

From Statement IV, we have X > N

Clearly, with the information provided, we can’t conclude who among X and Z is more intelligent. So, more information is required to answer the question. Therefore, option (5) is correct.

Practice Exercise 6: Who among Pikachu, Bulbasaur, Doraemon, Charmander, and Squirtle is shortest?

Statements:

I. Charmander is taller than Doraemon and Bulbasaur but not as tall as Squirtle.

II. Squirtle is taller than Pikachu

(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.

From both the statements, we can infer that Squirtle is tallest but we can’t figure out who among Doraemon, Bulbasaur, and Pikachu is the shortest. So, the information provided in both statements is not sufficient to answer the question. Therefore, option(4) is correct.