  # Concepts & Examples of Data Sufficiency (Quantitative Aptitude) for Bank Exams

By BYJU'S Exam Prep

Updated on: September 25th, 2023 In quantitative aptitude, Data Sufficiency is an important topic that is widely asked about in IBPS Clerk, IBPS RRB Clerk/PO, SBI Clerk/PO, and other bank exams. It just requires your understanding of the various arithmetic topics.

The best part of this topic is “you do not have to solve to complete question”. As the name suggests, you just have to figure out what statements is/are required to answer the given question. Now, let’s have a look at the approach you should follow while solving these questions.

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Table of content ## What is Data Sufficiency?

You cannot take the chance of neglecting Data Sufficiency because it is an important component of practically all competitive tests. Data Sufficiency makes use of both direct and indirect mathematical concept understanding. In this article, we’ll talk about the strategy to use while answering Data Sufficiency questions. The part on data interpretation is typically when questions about data sufficiency are raised. Learn the theory and procedure for answering Data Sufficiency problems.

## Know Concepts of Data Sufficiency

• The first and foremost thing to do is to go through the complete question properly first. This way, you will know, what data is required to arrive at the answer to the given question. After that, proceed to the statements that have been provided.
• Don’t forget, you don’t have to solve the question completely.
• All you need to do is figure out if the data that has been provided to you is sufficient to answer the question. This saves the time that is spent on calculations or the complete solution.
• The step must be: Analyze each statement separately first. There can be two or three statements
• If all the statements aren’t providing sufficient information to answer the question, then take the details provided in any two or all the statements and check if the information together is sufficient to answer the question.
• Understand the language of the question properly. Don’t make assumptions.
• Do not mark the answer after testing just one statement. For instance, even if you conclude that the data in statement 1 is sufficient to answer the question, do not forget to check for the other states.
• Use the process of elimination of options to narrow down the possible answers. For instance, if data in statement 1 is sufficient to answer the question, you only need to check for the second statement. Combining the information of the two statements and checking if it would be sufficient to answer the question won’t be required here.
• Make sure that you don’t spend too much time on these problems.
• Practice these types of questions thoroughly.

Simple calculations are frequently required to answer Data Sufficiency problems. This does not imply that the inquiries are straightforward. It simply indicates that the likelihood of making conceptual errors and/or foolish errors is a little higher than usual. Such questions require that you pay close attention to the small print. Types of the set of instructions you will get in data sufficiency questions. To solve such questions, have a deep knowledge of all miscellaneous topics like Percentage, Profit and loss, Ages, Averages, S.I and C.I, Mensuration, Time & Work, Time, Speed and Distance, etc.

Now to have a clear picture of the above tips, let us consider the following example –

Direction: The question given below is followed by some statements. Read the question carefully and determine which of the given statements is/are necessary/required to answer the question.

1. What is the two-digit number?

i) The digit in tens place is 4 more than the digit in the units place
ii) The difference between the two digits is 4
iii) The difference between the original number and the number obtained by interchanging the digits is 36.

A. Only I and iii
B. Only I and ii
C. Only ii and iii
D. All statements together
E. None of the above

Ans. E.

Let’s one’s and ten’s digit of the 2-digit number x and y respectively.
From statement I, y = x + 4
=> y – x = 4
From statement ii, y – x = 4
From statement iii, (10y + x) – (10x + y) = 36
Y – x = 4
If we see each of the statements separately, we find that we get only the difference between the two digits of the number.
Hence, we can’t find the answer even by using all three statements together.

Direction: In each of the following questions, a question is followed by information given in three Statements I, II, and III. You have to study the question along with the statements and decide the information given in which of the statement(s) is necessary to answer the question.

2. What is the present age of Sanjay?

I. The present age of Sanjay is half of his father’s age.
II. After ﬁve years, the ratio of ages of Sanjay and his father is 6:11.
III. Sanjay is younger than his brother by ﬁve years.

A. I and II
B. I and III
C. II and III
D. All of these
E. Cannot be determined

Ans. A.

From I and II
Sanjay’s age can be obtained.
From I and II
Sanjay’s age can be obtained.

From the statement I:
Let the father’s age be 2x then Sanjay’s age will be x

from statement II:

X+5/2X+5 =6/11
X=25

From statement III we cannot create any relation

Direction: The question given below has a few statements along with it. You have to determine which of the statement/s is/are sufficient/necessary for answering the question and mark your answer accordingly:

3. What is the cost of flooring the rectangular hall?

I. Length and the breadth of the hall are in the ratio of 3:2.
II. Length of the hall is 96 m and the cost of flooring is Rs. 1700 per sqm.
III. Perimeter of the hall is 320 m and the cost of ﬂooring is Rs. 1700 per sqm.

A. I and II
B. I and III
C. Only III
D. I and either II or III
E. Any two of the three

Ans. E.

From Statement I :
Let the length and breadth be in the ratio of 3x and 2x

From statement II:
Length of hall = 96
i.e. 3x=96
x=32 so breath =64
Cost of flooring= 32*96*1700=5222400

From statement III:
2(3x+2x)=320
x=32
Hence length =96 and breath = 64
so cost = 5222400

Hence it is clear that we can find the cost by using any two of the given statements.

Direction: The following question is accompanied by two statements I and II. You have to determine which statement is/is sufficient to answer the question.

4. What is the average speed of a car?
I. Average speed of the car is double the average speed of a truck whereas the average speed of a bus is 30 km/hr.
II. Average speed of the truck is thrice the average speed of the bus whose speed is 30 km/hr.

A. statement I alone is sufficient to answer the question but statement II alone is not sufficient to answer the question.
B. statement II alone is sufficient to answer the question but statement I alone is not sufficient to answer the question.
C. either statement I or II is independently sufficient to answer the question.
D. neither statement I nor II is sufficient to answer the question.
E. both statements I and II are together sufficient to answer the question.

Ans. E.

The answer cannot be obtained from any statement alone.
Using both statements together.
From statement II, we can find that the speed of the truck is 90 km/hr and then by using statement I, we can say that the average speed of the car is 180 km/hr.

Direction: Below question is followed by three statements. You have to study the question and all the three statements given to decide which of the given statement(s) is/ are required/sufficient for answering the given question:

5. Each question given below is followed by two statements I and II. You have to determine whether the data given in the statements are sufficient to answer the question. You have to choose the best possible answer.

1. Find the cost price of the product.

Statement I: The marked price of the product is 25% more than the cost price. After giving some discount, the profit earned is 12.5%.

Statement II: The selling price of the product is Rs. 450 after giving a 10% discount on the marked price.

A. If the data in statement I alone is sufficient to answer the question, while the data in statement II alone is not sufficient to answer the question.
B. If the data in statement II alone are sufficient to answer the question, while the data in statement I alone is not sufficient to answer the question.
C. If the data either in statement I alone or in statement II alone is sufficient to answer the question.
D. If the data in both statements I and II together are not sufficient to answer the question.
E. If the data in both statements I and II together are necessary to answer the question.

Solution:

Statement I:

Let the cost price of the product be Rs. 100x

The marked price of the product = Rs. 125x

The selling price of the product = Rs. 112.5x

Statement I alone is not sufficient to answer the question.

Statement II:

The selling price of the product = Rs. 450

Marked price of the product = (450/90)x100 = Rs. 500

Statement II alone is not sufficient to answer the question.

Statement I and II together:

The marked price of the product = Rs. 500

Cost price of the product = (500/125)X100 = Rs. 400

6. What is the simple interest accrued on a principal of Rs. 25000 in six years?

I. The rate of the simple interest for the first three years is 4 p.c.p.a.?
II. The rate of simple interest for the next three years is 6 p.c.p.a.?

A. statement I alone is sufficient to answer the question but statement II alone is not sufficient to answer the question.
B. statement II alone is sufficient to answer the question but statement I alone is not sufficient to answer the question.
C. either statement I or II is independently sufficient to answer the question.
D. neither statement I nor II is sufficient to answer the question.
E. both statements I and II are together sufficient to answer the question.

Ans. E.

The answer cannot be obtained from any statement alone.
Using both statements together.
SI in first three years = 3 x 4 = 12% of 25000
SI in next three years = 3 x 6 = 18% of 25000
Total SI in six years = 30 % of 25000 = 7500

Direction: The question given below is followed by some statements. Read the question carefully and determine which of the given statements is/are necessary/required to answer the question.

7. ₹ 310 is divided among three persons Aman, Bharat, and Chandu. Find Aman’s share.

I. Bharat gets Rs 16 more than Chandu
II. Aman gets Rs 3 more than Chandu.
III. Aman gets Rs 13 less than Bharat.

A. Only I and III
B. Only II and III
C. All three
D. III and either I or II
E. Any two of the three statements

Ans. E.

Aman + Bharat + Chandu = 310
From I
Bharat = Chandu + 16
From II
Aman = 3 + Chandu
From III
Aman = Bharat – 13
So from any two of statements I, II, and III the share of any person can be obtained. It will convert into two variables and a 2 equation model.
Hence, option E is correct.

Direction: The question given below has a few statements along with it. You have to determine which of the statement/s is/are sufficient/necessary for answering the question and mark your answer accordingly:

The weights of A, B, and C are in the ratio of 8: 7: 5. A’s weight is 60% more than C’s. Find the weight of B.
I. Total weight of A, B, and C is 300 kg.
II. Difference between A’s and C’s weight is 45 kg.

A. If the data in statement I alone are sufficient to answer the question, while the data in statement II alone are not sufficient to answer the question.
B. If the data in statement II alone are sufficient to answer the question, while the data in statement I alone are not sufficient to answer the question.
C. If the data either in statement I alone or in statement II alone are sufficient to answer the question.
D. If the data even in both statements I and II together are not sufficient to answer the question.
E. If the data in both statements I and II together are necessary to answer the question.

Ans. C.

From -(I)
Weight of B = (300*7)/20 = 105
From -(II)
Weight of B = (45*7)/3 = 105

Direction: The following question is accompanied by two statements I and II. You have to determine which statement is sufficient to answer the question.

9. What is the ratio of investment of Ram, Shyam, and Mahesh?
I. Total investment is Rs.6000 of which Ram’s contributions are Rs. 3000
II. Ratio of investment of Ram to Shyam is 3:2 and that of Shyam to Mahesh is 2:1.

A. Statements I are sufficient to answer the question, but statement II by itself is not sufficient to answer the question.
B. Statements II by itself is sufficient to answer the question, but statement I alone is not sufficient to answer the question.
C. Statements either I or II are sufficient to answer the question.
D. Both the statements I and II taken together are not sufficient to answer the question.
E. Both the statements I and II taken together are sufficient to answer the question.

Ans. B.

Statements II by itself is sufficient to answer the question, by Joint Ratio

10. Direction: Each question below is followed by two statements I and II. You have to determine whether the data given in the statement is sufficient for answering the question. You should use the data and your knowledge of Mathematics to choose the best possible answer. ###DONE###

1. Vikram, Rajneesh, and Himanshu are three friends. The present average age of Vikram, Rajneesh, and Himanshu is 26 years. Find the present age of Himanshu.

Statement I: Present average age of Rajneesh and Himanshu is 29 years. The present age of Rajneesh is 20% more than the present age of Vikram.

Statement II: Present average age of Vikram and Rajneesh is 22 years.

A. If the data in Statement I alone are sufficient to answer the question, while the data in Statement II alone are not sufficient to answer the question.
B. If the data in Statement II alone are sufficient to answer the question, while the data in Statement I alone are not sufficient to answer the question.
C. If the data either in Statement I or in Statement II alone are sufficient to answer the question.
D. If the data in both Statements I and II together are necessary to answer the question.
E. If the data even in both Statements I and II together are not sufficient to answer the question.

Solution: Statement I:

Sum of the present ages of Vikram, Rajneesh, and Himanshu = 26 x 3 = 78 years

Sum of the present ages of Rajneesh and Himanshu = 29 x 2 = 58 years

Present age of Vikram = 78 – 58 = 20 years

Present age of Rajneesh = 1.20 x 20 = 24 years

So, the present age of Himanshu = is 58 – 24 = 34 years

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

Statement II:

Sum of the present ages of Vikram, Rajneesh, and Himanshu = 26 x 3 = 78 years

Sum of the present ages of Vikram and Rajneesh = 22 x 2 = 44 years

So, the present age of Himanshu = is 78 – 44 = 34 years

So, statement II alone is sufficient to answer the question.

Thus, the data either in Statement I or in Statement II alone are sufficient to answer the question.

So option (C) is the correct answer.

Key Takeaways of Data Sufficiency Problems

• Understand what is given in the question, reading the statements properly will provide you with some clues and strategies which you should write down as soon as it strikes you.
• Organize the strategies identified based on data points given in the main statement.
• The questions may be based on various topics, For instance, blood relation, ranking, or direction-based problems. Remember, it’s just the topics you already know, presented in a different form.
• You may be more than 2 statements in the question. Don’t let the size of the question scare you, the approach to solving the question remains the same. So practice well.
• You must first carefully read the instructions for each Data Sufficiency question because the examiner may change them even after you have answered all the questions properly and marked the incorrect ones.

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