"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."

A $20 \mathrm{m}$long wire is cut into $3$ pieces. How long is the longest piece?

(I) Two pieces are each $2 \mathrm{m}$ shorter than the longest piece.

(II) Two pieces of the wire are of the same length

(III) The longest piece of the wire is $20\%$ more than the smallest piece

Find the area of an isosceles triangle $\mathrm{ABC}$.

(I) Perimeter of $∆\mathrm{ABC}=56 \mathrm{cm}$.

(II) Base of $∆\mathrm{ABC}=18 \mathrm{cm}$.

(III) Height of $△\mathrm{ABC}=14\sqrt{2} \mathrm{cm}$.

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) $\angle \mathrm{BCD}=180°$

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 $80$

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

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 $9\sqrt{3}$

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 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 $36$