Data Sufficiency - Introduction and Shortcuts

Data Sufficiency is one of the hardest part of the Logical Reasoning section which involve very simple calculations. Of course, many of you may not agree with me with this point. But its fact, because in many of the cases negligence or over thinking makes you ending up losing marks. With little concentration and practice you can easily score good marks in this section. After all you don't even need to do complete calculations to get answer. Most of the times, with a simple glance on given options you can choose the correct answer. 

What is Data Sufficiency ?

Of course there is no technical definition for this, but simply you can say that "its a process of checking whether the given data is sufficient to get the answer or not".

What to Prepare for Data Sufficiency?

Unfortunately there is no specific area, they can ask questions from any area like Reasoning, Arithmetic, Pure Maths, Time and Work, Time and Distance, Geometry, Menstruation, Percentages, Simple and Compound Interests etc.... So its better to prepare all areas (knowing basic formulas and procedures is enough. No need to be expertise. Now lets have a look at some example problems so that you will get a brief idea on Data Sufficiency problems and solutions.

Practice Problems on Data Sufficiency with Solutions :

Directions for questions 1 to 10 : Each problem contains a question and two statements which give certain data. You have to select the correct answer from (1) to (4) depending on the sufficiency of the data given in the statements to answer the question.

Mark 1 : If statement I alone is sufficient to answer the question and statement II alone is not sufficient to answer the question.

Mark 2 : If statement II alone sufficient to answer the question and statement I alone is not sufficient to answer the question.

Mark 3 : If statements I and II together are sufficient to answer the question, but neither statement alone is sufficient.

Mark 4 : If statements I and II together are not sufficient to answer the question adn additional data specific to the problem are needed. 

1. Which day of the week is 13th March of the year X ?

1. 25th December of the previous year is a Tuesday.
2. The previous year is a non-leap year.

Solution :

From Statement I alone, 25th December of the year preceding X is a Tuesday. But we do not know whether year X is a leap year or not. Hence, I alone is not sufficient.

From Statement II alone, we don not know whether X is a leap year or a non-leap year. This information is not sufficient to answer the question. Hence II alone is not sufficient. From I and II together also we cannot know whether year X is a leap year or not.

so you should choose option 4.

2. Is 2nd October of year Y a holiday ?

1. The third Sunday of July of year Y falls on 15th Day.
2. Only Sunday's are holidays.

Solution :

From statement I alone, 15th July is a Sunday. Hence it can be found out which day of the week is 2nd October. But that does not answer the question. 

Hence, I alone is not sufficient.

From statement II alone, only Sunday's are holidays. But it cannot be determined whether 2nd October is a Sunday or not. 

From I and II together, it can be found out whether 2nd October is a Sunday or not and hence the question can be answered.             So Option 3

3. Among five persons A, B, C, D, and E, sitting in a row (not necessarily in the same order) who is at the middle of the row ?

1. A and E are at the extreme ends and C is to the right of A.
2. B is between C and D, neither of whom are at extreme ends.

Solution :

From I alone, A is at the extreme left and E is at the extreme right. C is at the 2nd, 3rd or 4th place from left. But, who occupies the 3rd place is not known. Hence I alone is not sufficient.

From II alone, B is between C and D. Neither C nor D are at extreme ends. Hence C and D are in 2nd and 4th places in any order and B is in 3rd place.

Hence II alone is sufficient.  So option 2

4. Six persons P, Q, R, S, T and U are sitting around a circular table (not necessarily in the same order). Is P sitting opposite to T?

1. S is to the left of R and U is to the left of Q.
2. Q is sitting opposite to R.

Solution :

From I alone, if S, R, U and Q are sitting adjacent to each other, then P and T are not opposite to each other. If Q and R are opposite to each other then P and T will be opposite to each other. Hence, I alone is not sufficient.

From II alone, Q and R are opposite to each other. This information is not sufficient to answer the question . Hence II alone is not sufficient.

From I and II together, Only one arrangement is possible. From this we can conclude that P is not sitting opposite to T.             So option 3

5. What is the angle between the two hands of a clock ?

1. One hour ago, the angle between the two hands was 75 Degrees and the minute hand was ahead of the hours hand.
2. The hour hand is between 9 and 10.

Solution :

From I alone, in 60 minutes the minute hand reaches the same place and the hour hand moves forward by 30 Degrees. Hence, the angle reduces to 45 degrees. Hence I alone is sufficient.   Option I

6. What is the time indicated by the clock ?

1. The minute hand is at 4.
2. The hour hand is past 9.

Solution :

From I alone, the position of the hour hand is not known. Hence, I alone is not sufficient.

From II alone, we don not know whether the hour hand is past 10 or not and the position of minutes hand is not known.

From I and II together, the exact position of hour hand is not known. The time could be 9:20, 10:20 or 11:20.                    So option 4

7. Is A brother of C ?

1. A's father's only sibling, X, is C' paternal aunt.
2. A is the daughter of B.

Solution :

From I alone, A's father's sibling 'X' is female. She is the aunt of both A and C. It is not know whether A is a male of Female. Hence, I alone is not sufficient.

From II alone, A is female. Hence A is not the brother of C. Hence II alone is sufficient.   

So option 2

8. How is P related to T ?

1. T is the father of P. 
2. T's son-in-law is P's brother-in-law.

Solution :

From I alone, P is either the son or the daughter of T. Hence, I alone is not sufficient.

From II alone, it is not know whether P is a male or a female. II alone is not sufficient.

From I and II together, we cannot conclude whether P is a male or female. 

So option 4

9. Is C the tallest among A, B, C and D ?

1. A is as tall as B and D, but shorter than C.
2. B and D are shorter than C.

Solution :

From I alone, C is the tallest among A, B, C and D.   So option 1

10. Is P the richest among L, M, N, O and P ?

1. M is the poorest. N and O are poorer than L.
2. No one is richer than L

Solution :

From I alone, L is the richest among L, M, N and O. No information regarding P is available. Hence I alone is not sufficient.

From II alone, no one is richer than L. Hence, L is the richest.           So option 2

That's all for now friends. In our next post we shall discuss more problems on Data Sufficiency. All the Best and Happy Reading :)

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