Data Sufficiency (DS): A Bonus or a Trap
By Ankur Agarwal
Data Sufficiency continues to be one of the trickiest yet scoring segments of various MBA entrance exams. It can trick the smartest of the brains by the simplicity of its logic. There are many different approaches which can be applied to solving a DS question but the simplest of them seems to be the flowchart method.
The Basic Direction for any Data Sufficiency questions are on the following lines:
Choose A: if the question can be answered by using statement 1 alone but not by using 2 alone.
Choose B: if the question can be answered by using statement 2 alone but not by using 1 alone.
Choose C: if the question can be answered by using both the statements together but not by either statement.
Choose D: if the question can be answered by using either statement alone.
Choose E: if the question cannot be answered by using the given statements.
To relate a flowchart with the directions would be easier with an example. Let us look at a few questions and identify probable traps and way out of them.
Example 1:
Three clubs A, B and C are taking part in three competitions. 3 marks are awarded to the winner, 2 marks to the 2nd ranker and 1 mark to the 3rd ranker in each competition.
- Club B does not win any competition.
- Club A wins exactly one competition.
How many points does club C earn?
Statement I: Overall, club B gets more points than club A.
Statement II: Club B gets 2 marks each in two of the 3 competitions.
Solution: Normally any one would have marked either of the statements is sufficient but that is the trap. After reading the Statement I we can make the following table.
| Competition |
1 |
2 |
3 |
| A |
3 |
1 |
1 |
| B |
2 |
2 |
2 |
| C |
1 |
3 |
3 |
In this case if B gets more points that A then B maximizes at 2+2+2 = 6 points and only then A will get 3+1+1 =5 points.
Moving ahead and using Statement II we get following two scenarios:
| Competition |
1 |
2 |
3 |
| A |
3 |
1 |
2 |
| B |
2 |
2 |
1 |
| C |
1 |
3 |
3 |
| Competition |
1 |
2 |
3 |
| A |
3 |
1 |
1 |
| B |
1 |
2 |
2 |
| C |
2 |
3 |
3 |
Hence statement II is not sufficient and we can conclude that only statement I can help us reach a conclusion.
Example 2:
What is Geeta's relationship with the person in the photograph?
Statement I: Geeta says, "The person in the photograph is the father of my brother's brother-in-law."
Statement II: Geeta has two brothers and the person in the photograph has two sisters.
Solution: The immediate answer would be Statement I, but the trap here is that there are multiple solutions possible. While Statement II is not useful. So we cannot get a conclusion.
Example 3:
Is x2 equal to xy?
Statement I: x2 – y2 = (x + 5)(y - 5)
Statement II: x = y
Solution: Statement I traps you here. Many students will get confused by reading “(x + 5)(y - 5)” as “(x + 5)(x - 5)”and mark either statement is sufficient. But actually only Statement II is sufficient.
Example 4:
Is 3x-7 odd?
Statement I: x is a prime number
Statement II: x is not a multiple of 2
The Catch: Read the question carefully, it does not ask you what is written but asks you something else. The question is: Is x even? (odd subtracted from even will be odd, 3x will be even only if x is even), It is this that you have to understand and then work towards it.
Solution: The first statement would trap you as all prime nos. are odd except 2 which would result in this statement be insufficient. Looking at the second statement we would get that x is not even. Hence the answer is that 3x-7 is an even no. Here comes the second trap, A good number of aspirants will mark is insufficient as the answer to the question asked is NO, BUT we are getting a clear answer, hence the statement II alone is sufficient.
Some more questions in order to solve and get your thought process right:
- In a cricket match, the ‘man of the match’ award is given to the player scoring the highest number of runs. In case of a tie, the player (out of those locked in the tie) who has taken the higher number of catches is chosen. Even thereafter if there is a tie, the player (out of those locked in the tie) who has dropped fewer catches is selected. Aakash, Biplab and Chirag who were contenders for the award dropped at least one catch each. Biplab dropped 2 catches more than Aakash did, scored 50, and took 2 catches. Chirag got two chances to catch and dropped both. Who was the ‘man of the match’?
A. Chirag made 15 runs less than both Aakash and Biplab.
B. The catches dropped by Biplab are 1 more than the catches taken by Aakash. - Four friends, A, B, C and D got the top four ranks in a competitive examination, but A did not get the first, B did not get the second, C did not get the third, and D did not get the fourth rank. Who secured which rank?
A. Neither A nor D were among the first 2.
B. Neither B nor C was third or fourth. - The members of a local club contributed equally to pay Rs.600 towards a donation. How much did each one pay?
A. If there had been five fewer members, each one would have paid an additional Rs 10.
B. There were at least 20 members in the club, and each one paid no more than Rs 30. - A family has only one kid. The father says “after ‘n’ years, my age will be 4 times the age of my kid.” The mother says “after ‘n’ years, my age will be 3 times that of my kid.” What will be the combined ages of the parents after ‘n’ years?
A. The age difference between the parents is 10 years.
B. After ‘n’ years, the kid is going to be twice as old as she is now. - How many among the four students A, B, C and D have passed the exam?
A. This is a true statement: A and B passed the exam.
B. This is a false statement: at least one among C and D has passed the exam.
DS Mantras!
- Determine the exact requirement of the question: Identify the data requirement to solve the given question
- What to assume and what not to? There is lot of confusion among students as to what should be assumed while handling DS questions in CAT. One can assume the knowledge of commonly known facts or facts of life and derive some conclusion from it. A candidate has to consider all the mathematical concepts, rules and theorems as given. Even if not given mathematical theorems can be proved and the desired conclusion be derived from the basic concepts. Anything which can be logically derived from the given data i.e. if all A are B and all B are C then it can be logically derived that all A are C, such a conclusion can be assumed.
- Check if multiple solutions are possible: If the question is asking for a unique solution than the most common trap is that the solution set will have multiple solutions.
- Do not use your general knowledge.
All the Best!
About the author:
Ankur Agarwal heads the IT and Publishing verticals of Endeavor Careers and Catgurus - a leading online Testing portal for CAT Aspirants.
