Abhijit Guha Solutions for Chapter: Data Sufficiency, Exercise 1: Regular Problems

In each of the following questions, a question is asked followed by three statements. You have to study the questions and the statements given and decide whether any information provided in the statement(s) are redundant and can be dispensed with while answering the questions.

Is $\angle \mathrm{ACD}$ an obtuse?

(I) $\angle \mathrm{ACB}$ is acute

(II) $\angle \mathrm{ACD}$ is formed externally if $\mathrm{BC}$ is extended to $\mathrm{D}$

(III) $\angle \mathrm{BCD}=180°$

"In each of the following questions, a question is asked followed by three statements. You have to study the questions and the statements given and decide whether any information provided in the statement(s) are redundant and can be dispensed with while answering the questions."

Find the sum of all the natural numbers lying between $1$and $\mathrm{n}$. (inclusive of $\mathrm{n}$)

(I) $\frac{\mathrm{n}}{2}=3\mathrm{n}-20$

(II) $\mathrm{n}$ is even, and its cube root is a prime

(III) ${\mathrm{n}}^2$ is greater than $60$, but less than $80$

"In the following questions, a question is asked followed by three statements. You have to study the questions and the statements given and decide whether any information provided in the statement(s) are redundant and can be dispensed with while answering the questions."

Is $\frac{\mathrm{p}}{\mathrm{q}}$  is said to be the lowest form?

(I) Both p and q are satisfying two distinct linear equations

(II) HCF of$\mathrm{p}$ and $\mathrm{q}$ is $1$

(III) $\mathrm{p}$and $\mathrm{q}$are prime numbers

"In each of the following questions, a question is asked followed by three statements. You have to study the questions and the statements given and decide whether any information provided in the statement(s) are redundant and can be dispensed with while answering the questions."

What is the perimeter of an equilateral triangle?

(I) Its area lies between $2.25\sqrt{3}$ and $6.25\sqrt{3}$

(II) Its side is an integer

(III) Its side if increased by $50\%$, then its area becomes $9\sqrt{3}$

"In each of the following questions, a question is asked followed by three statements. You have to study the questions and the statements given and decide whether any information provided in the statement(s) are redundant and can be dispensed with while answering the questions."

What is the average speed of the car during its journey from $\mathrm{A}$to $\mathrm{B}$?

(I) Its speed is $45 \mathrm{km}/\mathrm{h}$during journey from $\mathrm{A}$ to $\mathrm{P}$ and its speed is $60 \mathrm{km}/\mathrm{h}$ while going from $\mathrm{P}$ to $\mathrm{B}$

(II) Distance $\mathrm{AB} = 170 \mathrm{km}$, time to cover $\mathrm{AB} = 3 \mathrm{hours}$

(III) Time to cover$\mathrm{AP}= 4$hours, time to cover $\mathrm{PB}= 2$hours

In the following questions, a question is asked followed by two to four statements. While answering the question, you may or may not require the data provided in all the statements. You have to read the question and the two to four statements and then decide upon the data given that how many statements are required to answer the question. The answer number bearing the statements which are required to answer the question is your answer.

A number is $63$more than its $\frac{4}{7}\mathrm{th}$. What is the number?

(I) Let the unknown number be $\mathrm{X}$

(II) Make the equation on the basis of known facts

(III) Add $63$with $\frac{4}{7}\mathrm{th}$ of the number

(IV) Solve the equation which is formed in II

In the following questions, a question is asked followed by two to four statements. While answering the question, you may or may not require the data provided in all the statements. You have to read the question and the two to four statements and then decide upon the data given that how many statements are required to answer the question. The answer number bearing the statements which are required to answer the question is your answer.

In an examination, if a candidate gets $37$marks and fails by $17$marks, what is the maximum marks?

(I) Pass marks percentage is $36$

(II) Divide the difference of $37$ and $17$by $\frac{36}{100}$

(III) Add $37$and $17$

(IV) Multiply the result of III by $100$and divide it by $36$

In each of the following questions, a question is asked followed by two to four statements. While answering the question, you may or may not require the data provided in all the statements. You have to read the question and the two to four statements and then decide upon the data given that how many statements are required to answer the question. The answer number bearing the statements which are required to answer the question is your answer.

If the average score in first six innings is$\text{'}\mathrm{p}\text{'},$find the score in the sixth inning out of $11$innings played.

(I) The average score in last six innings is $\mathrm{q}$.

(II) The total runs scored in $11$innings is $\mathrm{r}$.

(III) Multiply the sum of $\mathrm{p}$ and $\mathrm{q}$ by $6$and subtract $\mathrm{r}$from it.

(IV) Subtract the score of first six innings from $(\mathrm{r} + 6\mathrm{q})$.