M. Tyra Solutions for Chapter: Data Sufficiency, Exercise 3: Exercises

The question given below is followed by three statements. Study the question and the statements. Identify which option is necessary to answer the question.

The mean temperature from Thursday to Saturday was $42°\mathrm{C}$ and that on Friday was $41°\mathrm{C}$. What was the temperature on Sunday?

I. The temperature on Sunday was $\frac{6}{7}$ that on Thursday.

II. The mean temperature of Thursday and Sunday was $39°\mathrm{C}$.

III. The difference between the temperature on Thursday and that on Sunday was $6°\mathrm{C}$.

The question given below is followed by three statements. Study the question and the statements. Identify which option is necessary to answer the question.

$8$men and $4$ women can complete a piece of work in $6$ days. How many days will it take for $13$men and $2$ women to complete the same piece of work?

I. $9$ men can complete the work in $12$days.

II. $15$ women can complete the work in $16$days.

III. The amount of work done by a woman is three-fourths of the work done by a man in one day.

The question given below is followed by three statements. Study the question and the statements. Identify which option is necessary to answer the question.

Find the area of a quadrilateral whose all sides are equal and whose diagonals bisect at right angles.

I. The product of the diagonals is $240{ \mathrm{m}}^2$.

II. The length of a side of the quadrilateral is $13 \mathrm{m}$.

III. The difference between the squares of the diagonals of the quadrilateral is $476 \mathrm{m}$.

The question given below is followed by three statements. Study the question and the statements. Identify which option is necessary to answer the question.

Arun and Bhadra are brothers. In how many years from now will Bhadra's age be $50$years?

I. The ratio of the present ages of Arun and Bhadra is $5: 7$ respectively.

II. Bhadra was born $10$years before Arun.

III. $5$years hence, Arun's age would be three-fourths of Bhadra's age at that time.

The question given below is followed by three statements. Study the question and the statements. Identify which option is necessary to answer the question.

A right-angled triangle is inscribed in a given circle. What is the area of the given circle$($ in $\left.{\mathrm{cm}}^2\right)$ ?

I. The base and the height of the triangle (in $\mathrm{cm}$ ) are both the roots of the equation .

II. The sum of the base and the height of the triangle is $23 \mathrm{cm}$.

III. The height of the right-angled triangle is greater than the base of the same.

The question given below is followed by three statements. Study the question and the statements. Identify which option is necessary to answer the question.

What is the ratio of the marked price of two identical items, A and B, which had been purchased at the same price?

I. Item A was sold at a profit of $20\%$, while item B was sold at a loss of $10\%$.

II. Item A was sold at a discount of $16\frac{2}{3}\%$. The percentage by which item B's cost price had been marked up is the same as the profit $\%$earned on selling item A.

III. The overall profit earned on selling items A and B was ₹ $576$.

The question given below is followed by three statements. Study the question and the statements. Identify which option is necessary to answer the question.

Three workers A, B and C complete a given piece of work within different time spans, while working individually. What is the ratio of efficiency of C to that of B?

I. A takes $100\%$ more time than C to complete the given piece of work.

II. B completes the given piece of work in $8$ days.

III. B takes $2$ days less than A to complete the given piece of work.

The question given below is followed by three statements. Study the question and the statements. Identify which option is necessary to answer the question.

What is a three-digit number having each digit different from the other?

I. Each of the digits of the given number is a multiple of $3$

II. The digit in the unit's place is $50 \%$ less than that in the hundred's place.

III. Sum of digits is $18$.