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Data Sufficiency questions appeared when IDBI Assistant Manager exam was conducted last time and it won’t be surprising if you face them this year as well. Questions on Data Sufficiency are scoring in nature provided you have done enough practice beforehand and are careful enough while answering the questions. These questions are a little bit tricky in the sense that you don’t have to solve the complete question but you just have to ascertain if the given data is sufficient to answer the question or not. In this article, we will be covering data sufficiency concepts, tips, solved examples and questions for practice which will definitely help you improve your score in the upcoming IDBI Asst Manager exam.

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**Data Sufficiency Concept**

Here you are given a problem which could relate to any topic of quantitative aptitude (ranging from time & work to profit & loss to averages etc.). You are also given 2 statements and then you are asked which combination of the given statements is just sufficient to answer the question. So if a question has been asked and there are 2 statements labelled I & II. You have to ascertain:

- Whether the answer can be obtained from Statement I alone, but statement II alone is not sufficient to mark the answer.
- Whether the answer can be obtained from both statements I and II together, but neither of the statement alone is sufficient to answer the question
- Whether the answer can be obtained from statement II alone but statement I alone is not sufficient to answer the question
- Whether we can answer the asked question from either statement I or statement II.
- Last but not least, whether we can not answer the question asked from Statement I and II together, and if any additional information is required to answer the question.

Also, an important point to note is that the definition of ‘sufficient information’ is if from that information 1 numerical value can be determined.

There isn’t any doubt that you have to know the topic properly which is asked in the question (for example, in the below example, the topic is simple interest). So if a simple interest problem is asked in a data sufficiency question and you don’t know the concept & formulas of simple interest, you can’t answer that question correctly. You need to be very cautious when answering data sufficiency questions as aspirants are prone to make mistakes while answering these questions. Sometimes, the answer can be just found out by the first option and aspirants don’t care to check if the second option alone is sufficient to answer the question and therefore answering the question incorrectly. We’ll be mentioning this and other tips below. Let’s first understand the concept of data sufficiency better with the help of an example:

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**Data Sufficiency Example**

Directions: The question consists of two statements numbered “I and II” given below it. You have to decide whether the data provided in the statements are sufficient to answer the question.

A man deposited different amounts in two different banks i.e. A and B. The simple interest offered by bank A and bank B is 15% and 30%, respectively. Find the amount deposited in bank B.

Statement I: The total simple interest earned from both banks together in 2 years is 4800.

Statement II: The total simple interest earned from both banks together in 3 years is 7200.

a) 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) 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) The data either in statement I alone or in statement II alone are sufficient to answer the question.

d) The data given in both statements I and II together are not sufficient to answer the question.

e) The data in both statements I and II together are necessary to answer the question.

Answer: d

Solution:

Let the amount deposited in bank A and bank B be Rs. ‘x’ and Rs. ‘y’, respectively.

Statement I:

(x × 15 × 2)/100 + (y × 30 × 2)/100 = 4800

0.3x + 0.6y = 4800

So, data in statement I alone is not sufficient to answer the question.

Statement II:

(x × 15 × 3)/100 + (y × 30 × 3)/100 = 7200

0.45x + 0.9y = 7200

So, data in statement II alone is not sufficient to answer the question.

Combining statement I and statement II:

0.3x + 0.6y = 4800 ———(1)

0.45x + 0.9y = 7200 ———-(2)

Multiplying eq. (1) by 1.5, we get eq. (2).

So, both equations cannot be solved.

Therefore, the data given in both statements I and II together are not sufficient to answer the question.

Hence, option d.

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**Are Data Sufficiency Questions Easy?**

Some aspirants have the misconception that data sufficiency questions are easy because you don’t have actually to solve the question. Data Sufficiency questions are not easy when compared with other questions because you have to be extra careful while ascertaining which combination of the given statement is just sufficient to answer the question. This combination should not provide even an iota of less/more information than what is required to answer the question.

**Data Sufficiency Tips**

**Checking Statement II is important**

If you get the answer just from the first statement, you might get overjoyed and tick the option which says: only statement 1 is sufficient to answer the question. This will lead you to an incorrect answer. Please note that in all scenarios, you should check the Statement II as well.

**Check the Options in all the Questions**

New things are always expected in banking exams. Although generally the format and placement of all the 5 options are as given below, there can be slight variations in different data sufficiency questions.

- If the data given in statement I alone is sufficient to answer the question.
- If the data given in statement II alone is sufficient to answer the question.
- If the data given in either statement I or statement II alone is sufficient to answer the question.
- If the data given in both statement I and statement II are sufficient to answer the question.
- If the data given in both statement I and statement II are not sufficient to answer the question.

So, for each and every question, check the options carefully before marking th e answer.

**Focus on what the Question is asking**

Since you don’t have to calculate the answer, but you just have to ascertain what information is required to answer the question, this step becomes extremely important. Sometimes the question asks an exact numerical value, sometimes it only asks the ratio and at times it asks yes or no. We suggest solving a lot of data sufficiency questions and analyze the ones which you answered incorrectly.

**Revise the fundamentals of all the topics**

Since any data sufficiency question will include one or the other topic, it’s important that you revise all the concepts of quantitative aptitude. Even if you know all the tricks of data sufficiency, you will not be able to answer the question correctly if you are not aware of the concept asked in the DS question.

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**Data Sufficiency Questions for Practice**

1. The question consists of two statements numbered “I and II” given below it. You have to decide whether the data provided in the statements are sufficient to answer the question.

If perimeter of a rectangle is 188 cm, then find its area.

Statement I: Length is 35% more than breadth.

Statement II: Breadth is 14 cm less than length.

a.) 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.) 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.) The data either in statement I alone or in statement II alone are sufficient to answer the question.

d.) The data given in both statements I and II together are not sufficient to answer the question.

e.) The data in both statements I and II together are necessary to answer the question.

Answer: c)

Solution:

Statement I:

Let, breadth be ‘x’ cm

Length = ‘1.35x’ cm

So, 2 × 2.35x= 188

x = 40

Area of rectangle = 1.35x × x = 2160 cm^{2}

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

Statement II:

Let, breadth be ‘x’ cm

Length = ‘x + 14’ cm

So, 2 × (2x + 14) = 188

4x = 160

x = 40

Area of rectangle = 40 × 54 = 2160 cm^{2}

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

Hence, option c.

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2. The question consists of two statements numbered “I and II” given below it. You have to decide whether the data provided in the statements are sufficient to answer the question.

An article was sold at 20% profit. Find its cost price.

Statement I: Marked price was Rs. 1000 and discount was 28%.

Statement II: Marked price was Rs. 400 more than cost price.

a.) 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.) 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.) The data either in statement I alone or in statement II alone are sufficient to answer the question.

d.) The data given in both statements I and II together are not sufficient to answer the question.

e.) The data in both statements I and II together are necessary to answer the question.

Answer: a)

Solution:

Statement I:

Selling price = 0.72 × 1000 = Rs. 720

Cost price = 720/1.2 = Rs. 600

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

Statement II:

Nothing can be concluded from this statement.

So, data in statement II alone is not sufficient to answer the question.

Hence, option a.

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3. The question consists of two statements numbered “I and II*”* given below it. You have to decide whether the data provided in the statements are sufficient to answer the question.

If an item is sold at 25% discount, then it gives a profit of 25%. Find the selling price (in Rs.) of the item.

Statement-I: If it is sold for Rs. 45 more, then profit percentage is 40%.

Statement-II:If marked up price of item is increased by 10%, and discount rate remains the same, then profit percentage is 37.5%.

a.) 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.) 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.) The data either in statement I alone or in statement II alone are sufficient to answer the question.

d.) The data given in both statements I and II together are not sufficient to answer the question.

e.) The data in both statements I and II together are necessary to answer the question.

Answer: a)

Solution:

Let, cost price of item be Rs. x.

So, selling price = Rs. 1.25x

So, mark-up price = 1.25x/0.75 = Rs. (5/3)x

Statement-I:

According to question,

(1.25x + 45) = 1.4x

1.4x – 1.25x = 45

0.15x = 45

x = 45/0.15

x = Rs. 300

So, selling price = Rs. 1.25x = Rs. 375

Therefore, question can be solved using statement-I.

Statement-II:

Marked up price = (5/3)x × 1.1 = Rs. (5.5/3)x

According to question,

(5.5/3)x × 0.75 = 1.375x

1.375x = 1.375x

Therefore, question can’t be solved using statement-II.

Hence, option a.

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4. The question consists of two statements numbered “I and II*”* given below it. You have to decide whether the data provided in the statements are sufficient to answer the question.

The ratio of the population of males to the population of females is 15:13, respectively. What is the population of the city?

Statement-I: The difference between population of males and the population of females is 1000.

Statement-II: The population of females is 6500.

d.) The data given in both statements I and II together are not sufficient to answer the question.

e.) The data in both statements I and II together are necessary to answer the question.

Answer: c)

Solution:

The ratio of the population of males to the population of females is 15x, and 13x, respectively.

Population of city = 15x + 13x = 28x

Statement-I:

According to question,

15x – 13x = 1000

2x = 1000, x = 500

Therefore, population of city = 28 × 500 = 14000

Therefore, question can be solved using statement-I alone.

Statement-II:

According to question,

13x = 6500

x = 6500/13, x = 500

Therefore, population of city = (15 + 13) × 500 = 14000

Therefore, question can be solved using statement-II alone.

Hence, option c.

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5. The question consists of two statements numbered “I and II” given below it. You have to decide whether the data provided in the statements are sufficient to answer the question.

Find the average of the five consecutive natural numbers.

Statement I: Largest natural number is 4 more than the smallest natural number.

Statement II: Largest natural number is 50% more than the smallest natural number.

d.) The data given in both statements I and II together are not sufficient to answer the question.

e.) The data in both statements I and II together are necessary to answer the question.

Answer: b)

Solution:

Statement I:

Let the numbers are x, x + 1, x + 2, x + 3 and x + 4, respectively.

According to question: x + 4 – x = 4

4 = 4

Here ‘x’ is eliminated, so the numbers can’t be determined.

So, data in statement I alone is not sufficient to answer the question.

Statement II:

Let the numbers are x, x + 1, x + 2, x + 3 and x + 4 respectively.

According to question: 1.5x = x + 4

0.5x = 4, x = 8

So, the numbers are 8, 9, 10, 11 and 12

Average of the numbers = (8 + 12)/2 = 10

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

Hence, option b.

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6. The question consists of two statements numbered “I and II*”* given below it. You have to decide whether the data provided in the statements are sufficient to answer the question.

A person invests Rs. 4200 for four years at simple interest. Find the final amount he would get after the stipulated time.

Statement-I: The interest earned in the third year is Rs. 504.

Statement-II: The rate of simple interest is 12% p.a.

d.) The data given in both statements I and II together are not sufficient to answer the question.

e.) The data in both statements I and II together are necessary to answer the question.

Answer: c)

Solution:

Statement-I:

Simple interest earned in 4 years = 504 × 4 = Rs. 2016

Amount he would get after 4 years = 4200 + 2016 = Rs. 6216

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

Statement-II:

Amount he would get after 4 years = 4200 + (4200 × 12 × 4)/100 = Rs. 6216

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

Hence, option c.

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7. The question consists of two statements numbered “I and II*”* given below it. You have to decide whether the data provided in the statements are sufficient to answer the question.

Find the length of train A which travels with the same speed whenever it travels from one place to another.

Statement-I: Train A can cross a platform of length (x + 60) m in 20 seconds with the speed of 30 m/s.

Statement-II: Train A can cross a pole in 12 seconds.

d.) The data given in both statements I and II together are not sufficient to answer the question.

e.) The data in both statements I and II together are necessary to answer the question.

Answer: e)

Solution:

Let, the length and speed of train A be ‘l’ m and ‘s’ m respectively.

Statement-I:

According to question,

[l + (x + 60)] = 30 × 20

(l + x) = 600 – 60 = 540 … (i)

Therefore, question can’t be solved using statement-I.

Statement-II:

l = 12 × s

Therefore, question can’t be solved using statement-II.

Combining statement-I and statement-II, we get,

l = 12 × 30 = 360 m

Therefore, question can be solved by combining statement-I and statement-II

Hence, option e.

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8. The question consists of two statements numbered “I and II*”* given below it. You have to decide whether the data provided in the statements are sufficient to answer the question.

A man deposited some amount of money in scheme A and scheme B in the ratio of 8:11, respectively. Find the interest earned from scheme A after 5 years.

Statement I: The difference between the amount deposited in scheme A and scheme B is Rs. 3000.

Statement II: The rate of simple interest offered by scheme A is 8% p.a.

d.) The data given in both statements I and II together are not sufficient to answer the question.

e.) The data in both statements I and II together are necessary to answer the question.

Answer: e)

Solution:

Let the amount deposited in scheme A and scheme B be Rs. 8x and Rs. 11x, respectively.

Statement I:

11x – 8x = 3000

3x = 3000

x = 1000

Amount deposited in scheme A = 8x = Rs. 8000

Since, we don’t know the rate of interest offered by scheme A.

So, statement I alone is not sufficient to answer the question.

Statement II:

Statement II alone is not sufficient to answer the question.

Combining statements, I and statement II:

11x – 8x = 3000

3x = 3000, x = 1000

Amount deposited in scheme A = 8x = Rs. 8000

Interest earned from scheme A after 5 years = (8000 × 8 × 5)/100 = Rs. 3200

Hence, option e.

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9. The question consists of two statements numbered “I and II*”* given below it. You have to decide whether the data provided in the statements are sufficient to answer the question.

Find the time taken by boatman to travel 480 km in still water.

Statement-I: The upstream speed of the boatman is 4 km/hour less than the downstream speed, and speed of boatman in still water is 20% less than downstream speed of boatman.

Statement-II: The speed of boatman downstream and upstream is 10 km/hour and 6 km/hour, respectively.

d.) The data given in both statements I and II together are not sufficient to answer the question.

e.) The data in both statements I and II together are necessary to answer the question.

Answer: c)

Solution:

Let, speed of boatman and stream be B km/hour and s km/hour, respectively.

Statement-I:

(B + s) = (B – s) + 4

2s = 4

s = 4/2 = 2 km/hour…… (i)

Also, B = 0.8(B + s)

Using equation (i), we get,

B = 0.8B + 0.8 × 2

B = 1.6/0.2 = 8 km/hour

Therefore, required time = 480/8 = 60 hours

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

Statement-II:

(B + s) = 10 … (i)

And, (B – s) = 6 … (ii)

Solving both equations, we get,

B = 8 km/hour and s = 2 km/hour

Therefore, required time = 480/8 = 60 hours

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

Hence, option c.

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10. The question consists of two statements numbered “I and II*”* given below it. You have to decide whether the data provided in the statements are sufficient to answer the question.

A, B and C are hired to do a certain piece of work for Rs. 4,200. All of them started working together and finished the work in 20 days. In how many days B alone can complete the work?

Statement-I: A received Rs. 1400 for his work. C alone can complete the work in 50 days.

Statement-II: A is 25% more efficient than B. C received Rs. 1,680 for his work.

d.) The data given in both statements I and II together are not sufficient to answer the question.

e.) The data in both statements I and II together are necessary to answer the question.

Answer: c)

Solution:

Statement-I:

Time taken by A alone to complete the work = (4200/1400) × 20 = 60 days

Let the total work = 300 units (LCM of 50, 60 and 20)

Amount of work done by A alone in one day = 300/60 = 5 units

Amount of work done by C alone in one day = 300/50 = 6 units

Amount of work done by A, B and C together in one day = 300/20 = 15 units

Amount of work done by B alone in one day = 15 – 6 – 5 = 4 units

Time taken by B alone to complete the work = 300/4 = 75 days

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

Statement-II:

Time taken by C alone to complete the work = (4200/1680) × 20 = 50 days

Let the time taken by A alone to complete the work = x days

Time taken by B alone to complete the work = 1.25x days

According to question: 1/x + 1/1.25x + 1/50 = 1/20

2.25/1.25x = 3/100

9/5x = 3/100

x = 60

So, the time taken by B alone to complete the work = 1.25 × 60 = 75 days

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

Hence, option c.

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