Data Sufficiency

Which of the following statements are true?

(I) All natural numbers are also whole numbers.

(II) One is the smallest natural number.

If D is the brother of B, how B is related to C? To answer this question which of the statements is/are necessary?

1. The son of D is the grandson of C.
2. B is the sister of D.

The question given below contains two statements giving certain data. You have to decide whether the data given in the statements are sufficient for answering the question. Read both statements and mark the correct answer from the given options:

Who among the five friends Suraj, Taj, Mehmood, Vikramand, Bhairav is the youngest?

I. Bhairav is older than three of them, but Suraj is younger than Mehmood.

II. Taj is older than Vikram and Bhairav.

Directions for questions : Each item is followed by two statements, A and B. Answer each question using the following instructions.

What is the difference between two numbers?

A. First number is $60\%$ of the other number.

B. $50\%$of the sum of first and second number is $24$.

Directions for questions : Each item is followed by two statements, A and B. Answer each question using the following instructions.

What are the ages of two individuals, $\mathrm{x}$ and $\mathrm{y}$ ?

A. The age difference between them is $6$ years.

B. The product of their ages is divisible by $6$ ..

Find the length of the train A?

Statement $\mathrm{I}$ – train A cross a platform with double of his length in $12$ sec and cross a man standing in that platform in $4$ sec.

Statement $\mathrm{II}$ – train B with same length cross train A in $6$ sec while moving opposite direction.

What is the sum of age of father and son?

Statement $\mathrm{I}$ – mother’s present age is double of son’s age two years ago. Mother’s age is $5$ years less than the age of father.

Statement $\mathrm{II}$ – ratio of age of daughter and son is$5: 6$. Age of mother is twice of age of daughter after two years?

Find the area of square?

Statement $\mathrm{I}$ – Side of square is same as the length of a rectangle, whose perimeter is same as the perimeter of a circle. Radius of circle is $7 \mathrm{cm}$.

Statement $\mathrm{II}$ – Side of square is same as the length of rectangle whose perimeter is$88$. Breath of rectangle is half of the side of the square.

Find $50\%$ of sum of A and B :

Statement $\mathrm{I}.$LCM of A and B is $4400\%$ more than their HCF.

Statement $\mathrm{II}.$ Sum of LCM and HCF of both A and B is $1104$.

Find the time taken by train to cross a platform of length $630 \mathrm{meters}$ :

Statement $\mathrm{I}.$ Train can cross a man running at $6 \mathrm{km}/\mathrm{h}$in opposite direction of train in $47$ seconds.

Statement $\mathrm{II}.$Train crosses another train of length $230 \mathrm{meters}$ running at $15 \mathrm{km}/\mathrm{h}$ in opposite direction in $56$ seconds

Pranav and Pankaj started working together. after a few days, Prashant joined them and they were able to finish the work in $10 \mathrm{days}$. All of them together were paid a total of $₹800$. Find the share of Prashant.

Statement $\mathrm{I}:$ Pranav can do the work in $20 \mathrm{days}$, while Pankaj can do the same work in $25 \mathrm{days}$.

Statement $\mathrm{II}:$ Pranav can do the work in $60 \mathrm{days}$, while Pankaj can do the same work in $15 \mathrm{days}$.

Each question given below is followed by two statements

A number is a product of three successive prime numbers. What is the number?

(I) The number is less than $200$

(II) The difference between the first two numbers in the ascending order is $1$.

Two partners, $P$ and $Q$ entered a business, what profit will $Q$ get at the end of $2 \mathrm{years}$?

Statement $\mathrm{I}:$ $P$ and $Q$ started the business by investing in the ratio $4:7$ and After $2 \mathrm{years}$, $P’s$ share is $₹95000$.

Statement $\mathrm{II}:$ $P$ joined the business with an amount of $₹500000$.

$A.$ If the data in statement $\mathrm{I}$ alone is sufficient to answer the question, while the data in statement $\mathrm{II}$ alone is not sufficient to answer the question.

$B.$ If the data in statement $\mathrm{II}$ alone is sufficient to answer the question, while the data in statement $\mathrm{I}$ alone is not sufficient to answer the question.

$C.$ If the data either in statement $\mathrm{I}$ alone or in statement $\mathrm{II}$ alone is sufficient to answer the question.

$D.$ If the data in both statements $\mathrm{I}$ and $\mathrm{II}$ together are necessary to answer the question.

How much time will Ram take to cover a distance of $100 \mathrm{km}$ at a uniform speed?

Statement $\mathrm{I}:$ The speed of Mohan is $10 \mathrm{km} \mathrm{per} \mathrm{hour}$ more than that of Ram.

Statement $\mathrm{II}:$ If Mohan increases his speed by $25\%$ then he takes $3 \mathrm{hours} 20 \mathrm{minutes}$ less to cover a distance of $500 \mathrm{km}$.

$A.$ If the data in statement $\mathrm{I}$ alone is sufficient to answer the question, while the data in statement $\mathrm{II}$ alone is not sufficient to answer the question.

$B.$ If the data in statement $\mathrm{II}$ alone is sufficient to answer the question, while the data in statement $\mathrm{I}$ alone is not sufficient to answer the question.

$C.$ If the data either in statement $\mathrm{I}$ alone or in statement $\mathrm{II}$ alone is sufficient to answer the question.

$D.$ If the data in both statements $\mathrm{I}$ and $\mathrm{II}$ together are necessary to answer the question.

Rahul invested a certain amount in a scheme that offered a certain rate of interest. Find the rate of interest per annum.

$\mathrm{I}).$ The simple interest earned by Rahul in a year is $₹10000$.

$\mathrm{II}).$ The difference between the simple interest and compound interest on a certain sum at the given rate of interest is $₹2000$ at the end of $2 \mathrm{years}$.

$\mathrm{III}).$ The amount becomes $10$ times itself in $45 \mathrm{years}$ at simple interest at the same rate of interest.

How long will $12$ women and $3$ men take to do the work?

$\mathrm{I}).$ $8$ women and $9$ men can do a work in $12 \mathrm{days}$.

$\mathrm{II}).$ $10$ women and $15$ men can do the same work in $8 \mathrm{days}$.

$\mathrm{III}).$ $4$ women and $10$ men can do the same work in $16 \mathrm{days}$.

In a family there are $6$ members, $P, Q, R, S, T$ and $U$. Find the present age of $U$.

$\mathrm{I})$ The average age of six family members is $32 \mathrm{years}$.

$\mathrm{II})$ The total age of $P, Q, R$ and $S$ is $110 \mathrm{years}$.

$\mathrm{III})$ The present age of $T$ is $16 \mathrm{years}$ less than the age of $U$.

Find the loss percentage?

$\mathrm{I})$ The discount offered in the article is $10\%$ of the selling price.

$\mathrm{II})$ The marked price of the article is $20\%$ more than the selling price of the article and the selling price of an article is $₹16$ less than the marked price of the article.

$\mathrm{III})$ The cost price of the article is $₹100$.

In the following question, a question is followed by three statements $\mathrm{I}, \mathrm{II} \text{and} \mathrm{III}$. Read all the statements to find the answer to given question and then answer accordingly that which statement/s can give the answer alone/together.

Ratio of the ages of Vikash and Rana before four years was $14:13$ respectively. Find the present average age of Vikash, Atul and Vinay:

Statement$\mathrm{I}$: Ratio of the present ages of Vikash and Atul is $4: 3$ respectively. After four years, ratio of their ages will be $9: 7$respectively.

Statement $\mathrm{II}$: Average of the present ages of Rana and Vinay is $33 \mathrm{years}$.

Statement $\mathrm{III}$: Ratio of the present ages of Atul and Vinay is $2: 3$ respectively.

Direction Each of the following questions is followed by two statements: 

$\mathrm{C}1$ and $\mathrm{C}2$ are the circumferences of the outer and inner circles, respectively. What is$\mathrm{C}1:\mathrm{C}2$?

$\left(\mathrm{I}\right)$ The two circles are concentric.

$\left(\mathrm{II}\right)$ The area of the ring is $\frac{2}{3}$ the area of greater circle.