Steps to resolve the clues
Steps to resolve the clues:
1. Read the given information and decide how best the information can be arranged.
2. Arrange the information in tables, charts or maps.
3. Look for the more crucial statements first that give the maximum information.
4. Use arrows, crosses and other notations for different elements.
5. Do not proceed sequentially.
6. Tackle one or two variables at a time, completely ignoring the other variables.
We illustrate by explaining step by step how some questions can be done. The following question is taken from CAT paper held in November, 2008:
Directions: Answer the following questions based on the statements given below:
(i) There are three houses on each side of the road.
(ii) These six houses are labeled as P, Q, R, S, T, and U.
(iii) The houses are of different colours, namely Red, Blue, Green, Orange, Yellow and White.
(iv) The houses are of different heights.
(v) T, the tallest house, is exactly opposite the Red coloured house.
(vi) The shortest house is exactly opposite the Green coloured house.
(vii) U, the Orange coloured house, is located between P and S.
(viii) R, the Yellow coloured house, is exactly opposite P.
(ix) Q, the Green coloured house, is exactly opposite U.
(x) P, the White coloured house, is taller than R, but shorter than S and Q.
1. What is the colour of the tallest house?
5. None of these
2. What is the colour of the house diagonally opposite the Yellow coloured house?
5. None of these
3. Which is the second tallest house?
5. None of these
At first glance, the question looks difficult: ten statements have to be read and arranged. There are three variables: colour, height, order. If you start doing all the variables at once, you will no doubt be confused. The second trap is to process the information sequentially, that is, reading each statement and writing it down in an arrangement. We will see that by the time we reach half-way, the information becomes a mess. Instead, scan all the statements quickly and see which statement gives the maximum information. It is easy to see that this crucial statement is (vii). Immediately we know that the three houses on one side are P, U, and S. Combining it with statements (viii) and (ix) and we have the order of the houses as follows:
Note that the above diagram is obtained just by three statements and has given a lot of clarity to us. Also note that we are, at this stage, totally ignoring the third variable, height.
Now we can use the information from the other statements. From (v) we see that T is the tallest house. From (x) we see that P is white. Since the tallest house is opposite the Red coloured house, the only colour left for T is blue, and that is the answer to the first question.
For the second question, we see that R, the yellow coloured house, is opposite S. We are already given the colour of S, that is, red. So we are able to answer two of the three questions simply by using the colour information.
For the third question, we will have to use the third variable, height. The crucial statement for the height is (x). From this we get: S, Q > P > R. Since T is the tallest, we can write:
T > S, Q > P > R.
To find the second tallest house, we need to know the heights of U, S and T. Scan the ten statements again, and we see that no such information is given, so the answer to the third question is (5).
By following this technique, we will find that even difficult sums, having more variables, can also be attempted. The trick is to maintain clarity and not get bogged down by excess information. Always take one or two variables at a time, never more than that.
We can illustrate this by solving another question. This set is from CAT 2006.
DIRECTIONS: Answer on the basis of the information given below.
K., L, M, N, P, Q, R, S, U and W are the only ten members in a department. There is a proposal to form a team from within the members of the department, subject to the following conditions:
A team must include exactly one among P, R, and S.
- A team must include either M or Q, but not both.
- If a team includes K, then it must also include L, and vice versa.
- If a team includes one among S, U, and W, then it must also include the other two.
- L and N cannot be members of the same team.
- L and U cannot be members of the same team.
The size of a team is defined as the number of members in the team.
1. Who cannot be a member of a team of size 3?
2. Who can be a member of a team of size 5?
3. What would be the size of the largest possible team?
5. Cannot be determined
4. What could be the size of a team that includes K?
1. 2 or 3
2. 2 or 4
3. 3 or 4
4. Only 2
5. Only 4.
5. In how many ways a team can be constituted so that the team includes N?
The method used to solve this sum is different from the first set, because an order is not required. Moreover, different teams are possible so we cannot make a table. So each question has to be done separately using the clues that are given.
The crucial statements are the first two, which tell us that one member must be chosen from each of PRS and MQ. Approaching the first question, we have to make a team of 3, with 2 members already from these groups. So these are the crucial statements that will determine how the teams are formed. Now we are ready to do the questions. Starting with the options, we see that L cannot be there because if L is selected then K has to be selected. This creates a problem, since we will then have 4 members. Hence, L cannot be part of any 3-member team.
For the second question, we try to make teams with each option. Starting with the first, we have to choose K and L, M/Q, P/R/S. So we have 4 members. The problem is finding the fifth member. N is ruled out because of the second last statement, and U cannot come because of the fourth statement. By this logic, the first two choices are ruled out as they cannot form any 5-member team. Taking M, we can take the other members as SUW and one of P/R/S. Hence (3) is the correct answer.
Approaching the third question, we know that a 5-member team is possible from the previous question. So letâ€™s try to make a 6-member team. From the previous question, we see that if we take K or L, we can make a 4-member team. So a team larger than 5 members cannot include K or L. A 5-member team can be made with SUWN and one of M/Q. There is no other member that can be added. So the maximum team size is five members.
Question no. 4 can be answered by using the previous information. If KL are chosen, then the maximum team size is only four members.
The fifth question also uses the information we processed in the previous questions. It also involves counting the number of teams by taking different members. If N is taken, L cannot be taken. Hence U may be taken or not. If U is taken, then we have SUWNM or SUWNQ. If U is not taken then we have NMP/NMR and NQP/NQR. Adding up all the different teams, we see there are 6 ways.
Conclusion: We see that questions in analytical reasoning can be done quite easily if we are able to spot the crucial statements. Also, we must decide which statements are the most important ones in a set. The ability to pinpoint these statements will be developed after a lot of practice. We suggest that students solve a large number of questions to develop this ability.
We have also learnt some important tricks. First, we should not solve the questions sequentially. Second, concentrate on one or two variable at a time, ignoring the others. Third, make a small graph or chart to tabulate the information.
The above strategy works wonders in solving difficult questions. The challenge before the student is to process large amount of information, sometimes 10 or even more statements. This looks daunting but if it is broken up into parts, the questions become more manageable. This technique must be learnt, because the Reasoning section is becoming important by the say. In CAT and other management entrance exams, there is less emphasis on data interpretation but most of the questions combine data analysis with reasoning ability.