Embibe Experts Solutions for Chapter: Data Sufficiency, Exercise 1: Data Sufficiency

The question given below consists of a question and three statements numbered I, II and III given below it. You have to decide whether the data provided in the statements are sufficient to answer the question.

What is the cost of milk in the completely filled up cylindrical tank?

I. Area of the base of the tank is $2464$ cm² 

II. Area of the square with side equal to one-third of the tank's height is $841$ cm²

III. Cost of milk per litre is Rs. $45$

How many of the boys in a group of $350$children have brown hair (if children have only two types of hair black and brown)?
I. The ratio between boys and girls is $4:3$ and the ratio between the numbers of girls who have brown and black hair is $7:8$.
II. The number of boys who have black hair is $20\%$ more than the number of girls having brown hair.

The given question below consists of a question and two statements numbered I and II given below it. You have to decide whether the data provided in the statements are sufficient to answer the question. Read both the statements and give the answer:
Mark (a) if statement I alone is sufficient, but statement II alone is not sufficient.
Mark (b) if statement II alone is sufficient, but statement I alone is not sufficient.
Mark (c) if both statements I and II together are sufficient but neither statement alone is sufficient. 
Mark (d) if each statement alone is sufficient

Anil, Sunil and Vimal are three brothers. What is the order of their ages?
I. The sum of Anil's and Sunil's age is twice that of Vimal's age.
II. Five years ago, Sunil was twice as old as Vimal.

The given question below consists of a question and two statements numbered I and II given below it. You have to decide whether the data provided in the statements are sufficient to answer the question. Read both the statements and give the answer:
Mark (a) if statement I alone is sufficient but statement II alone is not sufficient.
Mark (b) if statement II alone is sufficient but statement I alone is not sufficient.
Mark (c) if both statements I and II together are sufficient but neither statement alone is sufficient. 
Mark (d) if each statement alone is sufficient

If $a>1$. Is $M>N$ where $M, N$ being positive numbers?
I. $M=(a-1)(a^2+a-1)$ and $N=(a+1)(a^2-a+1)$
II. $M=a.N$

The given question below consists of a question and two statements numbered I and II given below it. You have to decide whether the data provided in the statements are sufficient to answer the question. Read both the statements and give the answer:
Mark (a) if statement I alone is sufficient, but statement II alone is not sufficient.
Mark (b) if statement II alone is sufficient but statement I alone is not sufficient.
Mark (c) if both statements I and II together are sufficient but neither statement alone is sufficient. 
Mark (d) if each statement alone is sufficient.

What is the value of '$a$', if '$a$' and '$b$' are real numbers?
I. $a+b=6$
II. $a^2-b^2=12$

A question and three statements labelled (I), (II) and (III) are given. You have to decide which statement(s) is /are sufficient to answer the question.
Question: Find the present age of $Y$.
Statements:

I. At present, X is $3$ times as old as $Y$.
II. $X$ and $Y$ started schooling in the same year.
III. After $5$ years, the age of $X$ will be  $2\frac{1}{2}$ times that of $Y$.

The given question is followed by two statements I and II. Answer each question using the following instructions.

Mark option (a) if the question can be answered by using one of the statements alone, but cannot be answered using the other statement alone.

Mark option (b) if the question can be answered by using either statement alone.

Mark option (c) if the question can be answered by using both statements together, but cannot be answered using either statement alone.

Mark option (d) if the question cannot be answered even by using both statements together.

How many families in the village have both a radio and a TV?

I. The villages has $2500$ families.

II. $580$ families have TVs and $275$ families have radios.

The given question is followed by two statements $\mathrm{I}$ and $\mathrm{II}$. Answer each question using the following instructions.

Mark option (a) if the question can be answered by using one of the statements alone, but cannot be answered using the other statement alone.
Mark option (b) if the question can be answered by using either statement alone.
Mark option (c) if the question can be answered by using both statements together, but cannot be answered using either statement alone.
Mark option (d) if the question cannot be answered even by using both statements together.

Find the height to which each end of a seesaw can rise.
$\mathrm{I}.$ The see-saw is $14$ feet long.
$\mathrm{II}.$ The board is supported at the centre by a block $5$ feet high.