Solve Data Sufficiency Questions the Easy Way

Solve Data Sufficiency Questions the Easy Way

Data sufficiency is a challenge that is unique to any competitive exam. In almost every exam there are several questions from data sufficiency, you will need to spend a lot of time getting comfortable with the Data Sufficiency question type.


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Most of you try to solve data-sufficiency questions by guesswork. As every question carries the same marks, questions in this part also deserve some time. Instead of guesswork use a simple strategy as given below to get the correct answer.

Format of data sufficiency Question:

If you are a beginner, it’s necessary to familiarize yourself with the basic format. Here’s what a Data Sufficiency question looks like:

If x is positive, is x a prime number?

(1) x is odd.

(2) x < 8

There are three important components to any DS question:

Information is given in the question. Here, we know that x is positive. That will never change. (There isn’t always information given in the question.)

The question itself. We want to know whether x is prime.

The statements. (1) and (2) give us information that may or may not allow us to answer the question.

 

The process to solve DS Questions:

Step 1: Read the given problem. Don’t assume anything except universal facts.

Step 2: Take the first statement and combine it with the main statement. Try to find the answer.

Step 3: If you are unable to find the answer using the 2nd step, then combine the second statement and combine it with the main statement and try to find the answer.

Step 4: If you are unable to find an answer using the second statement, then add both statements with the main statement and try to find the answer

Step 5: If even now you can’t find the answer, simply tick both statements are insufficient.

 

The process illustrated for the above example:

If x is positive, is x a prime number?

Statement (1) x is odd.

Statement (2) x < 8

Step 1: Evaluate each statement on its own. If there is information given in the question, keep that in mind.

Step 2: 

Statement (1) alone

Look at (1). Using (1) alone, we know that x is positive and that it is odd.

Is that enough information to answer the question?

If x is a positive odd number, it could be prime:

For instance, if x = 3.

However, it might not be prime.

For instance, if x = 9.

Thus, we say that statement (1) is insufficient.

 

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Step 3: 

Statement (2) alone

Look at (2) alone. The tricky part is that you have to temporarily forget what you learned in (1). (It may sound easy, but I absolutely guarantee you that you’ll make this mistake at least once, and probably many more times than that.)

Again, we are also considering the information given in the question.

Here, then, we know that x is positive and that it is less than 8.

If x is greater than 0 and less than 8, is it prime?

Again, we don’t know.

It could be 3, which is prime, but it could be 4, which is not.

Further, we don’t know that x is an integer, which opens up the possibility that x is, say, 2.5.

So, statement (2) is insufficient.

 

Step 4: 

Putting the Statements Together

If both statements are insufficient on their own, we must consider both of them together.

Here, we have all of the information available to us: x is positive, it is odd, and it is less than 8. The only possible values for x are 1, 3, 5, and 7.

Still, however, we do not have enough information.

While 3, 5, and 7 are prime, 1 is not a prime.

The statements, when taken together, are still insufficient.

 

Answer options:

One thing that makes Data Sufficiency easier is that the answer options never change. They are the same on every single DS question. Here they are:

Option (A) Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.

Option (B) Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.

Option (C) BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.

Option (D) EACH statement ALONE is sufficient.

Option (E) Statements (1) and (2) TOGETHER are NOT sufficient.

 

In the question we just worked through, the correct option was (E).



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DS Strategies:

• Never try to reach the final answer as it is not asked. You need to find whether the information provided is enough to solve the given problem or not.

• Never make any assumption. Use only universal rules [example: (a + b)2 = a2 + b2 + 2ab]

• Try to solve questions by using the above strategies

• Solve question step by step. First, try to find an answer using the first statement then second and finally with both. Then mark the answer

• Even if you find an answer with only one statement, try to find an answer with the remaining statement as sometimes there is an option that answer can be found with both statements separately.

 

When you are starting out, DS can seem very scary, but keep practicing. By the time you take the test, you should be handling DS questions faster than any other problem (because you do not have to calculate). For more tricks and practice question, click on the below link for a details course on Logical reasoning.


Solved Examples

In each of the questions below consists of a question and 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. Read both the statements and

Give answer

  • (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 given in both statements I and II together are not sufficient to answer the question and
  • (E) If the data in both statements I and II together are necessary to answer the question.




Q.1.Question: What will be the total weight of 10 poles, each of the same weight ?

Statements:

  1. One-fourth of the weight of each pole is 5 kg.
  2. The total weight of three poles is 20 kilograms more than the total weight of two poles.


Solution: C

From I, we conclude that weight of each pole = (4×5) kg = 20 kg.

So, total weight of 10 poles = (20 x 10) kg = 200 kg.

From II, we conclude that:

Weight of each pole = (weight of 3 poles) – (weight of 2 poles) = 20 kg.

So, total weight of 10 poles = (20 x 10) kg = 200 kg.


Q.2.Question: How much was the total sale of the company ?

Statements:

  1. The company sold 8000 units of product A each costing Rs. 25.
  2. This company has no other product line.


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Solution: E

From I, total sale of product A = Rs. (8000 x 25) = Rs. 200000.

From II, we know that the company deals only in product A.

This implies that sale of product A is the total sale of the company, which is Rs. 200000.


Q.3.Question: How many children are there between P and Q in a row of children ?

Statements:

  1. P is fifteenth from the left in the row.
  2. Q is exactly in the middle and there are ten children towards his right.


Solution: E

From II, Q being in the middle, there are 10 children to his right as well as to his left. So, Q is 11th from the left. From I, P is 15th from the left.

Thus, from both I and II, we conclude that there are 3 children between P and Q.


Q.4.Question: How is J related to P ?

Statements:

  1. M is brother of P and T is sister of P.
  2. P’s mother is married to J’s husband who has one son and two daughters.


Solution: B

From II, we know that P’s mother is married to J’s husband, which means that J is P’s mother.


Q.5.Question: Who is to the immediate right of P among five persons P, Q, R, S and T facing North ?

Statements:

  1. R is third to the left of Q and P is second to the right of R.
  2. Q is to the immediate left of T who is second to the right of P.


Solution: C

From I, we have the order: R, -, P, Q.

From II, we have the order: P, Q, T.

Clearly, each one of the above two orders indicates that Q is to the immediate right of P.


Q.6.Question: How is X related to Y?

Statements:

  1. Y says, “I have only one brother”.
  2. X says, “I have only one sister”.


Solution: D

The statements in I and II do not provide any clue regarding relation between X and Y.


Q.7.Question: B is the brother of A. How is A related to B ?

Statements:

  1. A is the sister of C.
  2. E is the husband of A.


Solution: C

B is A’s brother means A is either brother or sister of B. Now, each one of I and II individually indicates that A is a female, which means that A is B’s sister.


Q.8.Question: How many children are there in the row of children facing North ?

Statements:

  1. Vishakha who is fifth from the left end is eighth to the left of Ashish who is twelfth from the right end.
  2. Rohit is fifth to the left of Nisha who is seventh from the right end and eighteenth from the left end.


Solution: C

Since 8th to the left of 12th from the right is 20th from the right, so from I, we know that Vishakha is 5th from left and 20th from right i.e. there are 4 children to the left and 19 to the right of Vishakha. So, there are (4 + 1 + 19) i.e. 24 children in the row.

From II, Nisha is 7th from right and 18th from left end of the row.

So, there are (6 + 1 + 17) = 24 children in the row.


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Q.9.Question: How is Tanya related to the man in the photograph ?

Statements:

  1. Man in the photograph is the only son of Tanya’s grandfather.
  2. The man in the photograph has no brothers or sisters and his father is Tanya’s grandfather.


Solution: B

From I, we conclude that the man is the only son of Tanya’s grandfather i.e. he is Tanya’s father or Tanya is the man’s daughter.

From II, we conclude that the man’s father is Tanya’s grandfather. Since the man has no brothers or sisters, so he is Tanya’s father or Tanya is the man’s daughter.


Q.10.Question: On which date in August was Kapil born ?

Statements:

  1. Kapil’s mother remembers that Kapil was born before nineteenth but after fifteenth.
  2. Kapil’s brother remembers that Kapil was born before seventeenth but after twelfth.


Solution: E

From I, we conclude that Kapil was born on any one of the dates among 16th, 17th and 18th.

From II, we conclude that Kapil was born on any one of the dates among 13th, 14th, 15th and 16th.

Thus, from both I and II, we conclude that Kapil was born on 16th August.


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