**2. ****DATA**** SUFFICIENCY **

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**2.1 Introduction**

A data sufficiency question has a question followed by two statements. You are expected to answer if the information provided in the statements is sufficient for answering the questions.

The following are the choices asked in these types of questions:

**Give answer (1)** if the data in statement I alone is sufficient to answer the question, while the data in statement II is not sufficient to answer the question.

**Give answer (2)** if the data in statement II alone is sufficient to answer the question, while the data in statement I alone is not sufficient to answer the question.

**Give answer (3)** if the data either in statement I alone or in statement II alone is sufficient to answer the question.

**Give answer (4)** if the data in both the statements I and II together is not sufficient to answer the question.

**Give answer (5)** if the data in both the statements I and II together is necessary to answer the question.

** 2.2 Tips and strategies**

1. For answering data sufficiency questions one should have basic knowledge of maths.

2. Some questions are designed to test the ability to think conceptually, not to solve the exact math problems. It is testing your reasoning ability and quantitative concepts and not the calculation skills.

3. Study the question carefully. One should know what the question is asking. Determine what is needed to solve the question. Use the information that is given in the question not outside of it.

4. Lookout for the statements that tell the same thing in different words.

*Example: *

Statement I: A is 75% of B

Statement II: the ratio of B: A is 4:3

5. Look at the statements individually. Use the process of elimination:

· If statement I is insufficient, then choices 1 and 3 can immediately be eliminated.

· Similarly, if statement II is insufficient, then choices 2 and 3 can immediately be eliminated.

· If either statement I or II is sufficient on its own, then choices 5 and 4 can be eliminated.

6. Select the right alternative.

In Bank PO examination easy questions based on numbers, blood relations, codes, profit & loss, percentages, ages, averages, areas and volumes, directions etc. are asked.

The moderate type of questions is based on trigonometry, Geometry, Quadratic equation etc...

**Note:** In data sufficiency problems that ask for the numerical value of a quantity, the data given in the statements are sufficient only when it is possible to determine exactly one numerical value but not the range of values.

**2.3 Solved Examples**

*Example:*** **Based on Blood relation** **

How many daughters does M have?

Statement I: N and P are sisters of K.

Statement II: M is father of K.

*Answer:*** (4)**

*Explanation:*

From statement I, it can be derived that K has two sisters. But are they related to M is not known. Hence choices 1 and 3 can be eliminated.

From statement II, M is father of K.

By combining both the statements, we have that N, P, K as children of M. but the sex of K is not known. Hence choice 2 can be eliminated.

Even from both the statement we can’t find the exact number daughters of M. hence choice 5 can be eliminated.

Hence the answer is 4.

*Example:*

Among M, N, T, P and R each has different weights, who is the heaviest?

Statement I: T is heavier than P and M but lighter than N who is not heaviest.

Statement II: M is lighter than P.

*Answer:*** (1)**

*Explanation:*

From statement I, N >T>P, M but N is not heaviest. Hence R is the heaviest.

Hence it is alone sufficient

From statement II, P>M but the heaviest can’t be found from this.

Hence statement I alone is sufficient but statement II is insufficient.

Option 1 is correct choice.

*Example:*** **Based on Integers

What is the value of X, if X and Y are two distinct integers and their product is 30?

Statement I: X is an odd integer

Statement II: X > Y.

*Answer:*** (4)**

*Explanation:*

From the question, both X and Y are distinct integers and their product is 30.

30 can be obtained as a product of two distinct integers in the following manner

1 × 30 or -1 × -30

2 × 15 or -2 × -15

3 × 10 or -3 × -10

5 × 6 or -5 × -6

From statement I, we know that the value of X is odd. Therefore, X can be one of the following values: 1, -1, 3, -3, 5, -5, 15, -15. So, using the information in statement 1 we will not be able to conclusively decide the value of X. Hence, statement 1 alone is not sufficient to answer the question.

From statement II, we know that the value of X > Y. From the given combinations, X can take more than one value. Hence, using the information in statement 2, we will not be able to find the value of X.

Combining the two statements, we know that X is odd and that the value of

X > Y. Values of X and Y that satisfy both the conditions include X taking values of -1, -3 and -5.

As the information provided in the two statements independently or together is not sufficient to answer the question, the correct Choice is 4.

*Example:*** **Based on averages

Is the average (arithmetic mean) of the two numbers x and y less than y?

Statement I: x and y are both positive integers.

Statement II: x > y.

*Answer:*** (2)**

*Explanation:*

The average of two numbers x and y is .

The average of two numbers lies between the two numbers. So, the average will be greater than the smaller number and smaller than the greater of the two.

From I we have x and y as positive. But which among them is greater is not known. Hence, statement I is not sufficient.

From II: x > y. The average will be greater than y and smaller than x i.e., the average is not less than y. Hence, II alone is sufficient.

Hence correct choice is 2.

*Example:*** **Based on code language

How is ‘go’ written in a code language?

Statement I: ‘you may go’ is written as ‘pit ja ho’ in that code language

Statement II: ‘He may come’ is written as ‘ja da na’ in that language.

*Answer:*** (4)**

*Explanation:*

We don’t know whether the codes of the given word are in the same order as the order of the words.

Hence statement I alone is not sufficient.

Again statement II doesn’t contain the word ‘go’. Hence statement II alone is not sufficient.

*Example:*** **Based on Directions

A person is walking from Mali to Pali, which lies to its north-east. What is the distance between Mali and Pali?

Statement I: When the person has covered 1/3 the distance, he is 3 km east and 1 km North of Mali.

Statement II: When the person has covered 2/3 the distance, he is 6 km east and 2 km North of Mali.

*Answer:*** (3)**

*Explanation:*

These types of questions can be easily solved by diagrammatic representation.

OX is the distance between Mali and Pali.

From statement I, OP=1/3 OX and OP=

Hence OX=3

Therefore, distance between them can be calculated using (I) alone.

Even statement (II) alone can be used to calculate the distance between Mali and Pali.

Hence either of the statements can be used independently. Thus the choice 3 is the answer.

*Example:*** **Based on Ages

What is Nidhi’s age?

Statement I: Nidhi is 3 times younger to Rani.

Statement II: Surekha is twice the age of Rani and the sum of their ages is 72 years.

*Answer:*** (5)**

*Explanation:*

Let Rani’s age be x years

Then from statement I,** **Nidhi age = x-3 years. Statement I alone is not sufficient. Hence choice 1 and 3 is eliminated.

From statement II, Surekha’s age = 2x years

x + 2x= 72

x= Rani’s age=24 years

But the age of Nidhi can’t be found with statement II alone. Thus, choice 2 is eliminated.

By combining both the statements we have,

The age of Nidhi = Rani’s age -3 years=24-3=21 years.

Thus, choice 5 is apt.

*Example:*** **Based on Ratio

A certain 4-litre solution contains only vinegar and water. It consists of x litres of vinegar and y liters of water. How many litres of vinegar does the solution contain?

Statement I:

Statement II:

*Answer:*** (3)**

*Explanation:*

Vinegar + Water= 4 litre

From statement 1, the quantity of vinegar, x=

Thus statement I alone is sufficient to answer.

From statement II, the quantity of water, y=

Quantity of vinegar= (4-2.5) litre=1.5 litre

Thus statement II alone is sufficient.

As each of the two statements is independently sufficient to answer the question, choice (3) is the best answer.

*Example:*** **Based on profit and loss

By selling a product at 20% profit, how much profit was earned?

Statement I: The difference between cost and selling price is Rs.40.

Statement II: The selling price is 120 percent of the cost price.

*Answer:*** (1)**

*Explanation:*

To answer such types of questions we need one of the following:

a. Cost price of the product

b. Selling price of the product

c. Difference of the selling price and the cost price.

From statement I, we get the required profit as Rs. 40 (profit = selling price – cost price).

Statement II is restatement of question because when profit earned is 20% then obviously selling price will be 120% of the cost price. Choice 2 and 3 can be eliminated.

Thus, statement I alone is sufficient to answer the question.

*Example:*

If a salesman received a commission of 3% of the sales that he has booked in a month, what was the sale booked by the salesman in the month of November 2003?

Statement I: The sale booked by the salesman in the month of November 2003 minus Salesman’s commission was Rs.2, 45,000.

Statement II: The selling price of the sales booked by the salesman in the month of November 2003 was 125 percent of the original purchase price of Rs.2, 25,000.

*Answer:*** (3)**

*Explanation:*

From question, we know that the sales value after the salesman’s commission. If his commission is 3% of the sales booked, then the net sales value is 100–3=97% of the sales booked.

From statement (I), we know that 97% of sales booked = Rs.2, 45,000. So we can find out the sales booked. Statement (I) alone is sufficient.

From statement (II), we know that the original cost of the products is Rs.2, 25,000. We know the sales booked = 1.25 × 225,000. Hence, statement (2) is also sufficient.

As each of the two statements is independently sufficient to answer the question, choice (3) is the best answer.

*Example:*

In a class of 80 students, how many students passed in only English?

Statement I: In the class, 60 students passed in English, Hindi or both.

Statement II: In the class, 40 students passed in Hindi.

*Answer:*** (5)**

*Explanation:*

Total number of students in the class = 80.

From I: number of students failing in both the subjects can be calculated. But, the number of students passing in only English cannot be found out. Hence, statement I alone is not sufficient.

From II: 40 pass in Hindi. This means 40 fail in Hindi. But these 40 may or may not have passed in English. Moreover, out of 40, who passed in Hindi, a few may or may not have passed in English.

Hence, statement II alone is not sufficient.

Combining both the statements, we get the following Venn diagram:

The shaded region represents the number of students passed in English.

The number of students passing only in English = 60 – 40 = 20.

Hence, both statements together are sufficient to answer the question. Hence, choice [5] is best answer.

*Example:*** **Based on areas and volumes

What would be the area of triangle A, if triangle A and triangle B are similar?

Statement I: Area of triangle B is 48sq.cm.

Statement II: The ratio of corresponding sides or median or heights of triangle A to triangle B is 1: 2.

*Answer:*** (5)**

*Explanation:*

When two triangles are similar, then the ratio of their areas is the square of the ratio of their corresponding linear parameters.

Statement I give the area of triangle ‘B’ which in itself is not sufficient to find the area of triangle ‘A’ as we only know that they are similar. Hence, statement I alone is not sufficient to answer the question.

Statement II gives the ratio of corresponding sides or median or heights of triangle A to triangle B is 1: 2.

From statement I we have area of B as 48.

Area of DA is 12.

Hence by using both the statements we can find the area of the DA.

Therefore, the option 5 is correct.

*Example: *

A small storage tank is spherical in shape. What is the storage volume of the tank?

Statement I: The wall thickness of the tank is 1cm.

Statement II: When an empty spherical tank is immersed in a large tank filled with water, 20L of water overflows from the large tank.

*Answer:*** (2)**

*Explanation:*

Statement I: Thickness of the wall cannot be of use to calculate the volume of the tank. Thus this is insufficient. Hence choice 1 and 3 can be eliminated.

Statement II: We know that volume of water displaced is equal to the volume of the sphere displacing the water.

Hence from statement II alone we can find the volume of the tank. Thus choice 2 is apt.