Are you prepared for Mathematical Reasoning in DI-LR? In the previous post, we discussed the Dos and Don’ts of representing and structuring data, as well as how to prioritize conditions. In this post, we will focus on the type of reasoning sets that often pose challenges for test-takers. Specifically, we will cover Numerical Reasoning and Algebraic Reasoning.

When test-takers find a DI or LR set to be difficult, it usually means that they are not encountering the following elements in the sets: closed DI sets involving pie charts, graphs, and tables, and LR sets involving simple plugin conditions for arrangements. What tends to stump most people are sets that do not involve direct calculation or arrangement. These sets are typically open sets, which we defined in the previous post, blurring the line between DI and LR and requiring the test-taker to apply numerical and algebraic reasoning.

Numerical Reasoning sets involve testing various numbers that a specific variable can take based on given conditions. To solve these sets, you must list, test, and eliminate possibilities according to the conditions. Solving Numerical Reasoning sets is similar to solving Sudoku puzzles.

On the other hand, Algebraic Reasoning sets require you to assign one unknown value as X and express other values in terms of X using the given conditions. You can use these conditions to determine the precise value of X or the maximum and minimum values it can take. The key to cracking these sets is to be open to using algebra or Sudoku-style reasoning and to understand that the sets may remain open even after solving, with questions potentially involving ranges or inequalities.

Once you adopt this new perspective and embrace non-standard lines of reasoning, along with the use of algebra, you will enhance your DI-LR skills. Let’s take a DI set from a Sim CAT that we classified as a must-solve. To crack this set, you need to use algebra and be comfortable with the set remaining open even after solving. By applying the basic conditions and assigning X to one of the values, your representation should look like this. Once you calculate the value of X and fill in the remaining values, the table should appear as shown. From here on, you should be able to answer all the questions correctly by ensuring that you carefully read the given requirements without rushing through them.

Now, let’s decode my favorite CAT LR set of all time, which is the Erdös Number set from CAT 2006. This set stands out because it introduces a completely novel concept in CAT Logical Reasoning Sets, something unrelated to any previous topics. There is no table, so you must carefully consider how to represent the data. Additionally, every condition requires deductive reasoning rather than simple plugging. It is an open set, not a closed one.

To approach this set logically, we can start by considering F as X since no one has a lower Erdös number than F. When F co-authors papers with A and C on the third day, their Erdös numbers become X+1. This collaboration also reduces the average Erdös number of the group to 3, leading us to calculate the total as 24, given that there are 8 mathematicians in the group. Are you prepared for Mathematical Reasoning in DI-LR- On the fifth day, when E co-authors a paper with F, the average Erdös number decreases by 0.5, indicating a total decrease of 4. Since no other papers were written during the conference, this decrease is solely due to the change in E’s Erdös number after collaborating with F. Before the collaboration, E’s Erdös number must have been X+5. With this information, we can determine various values for each day of the conference.

At the end of Day 3, we know A = X+1, C = X+1, E = X+5, F = X, and the total is 24. After Day 5, A = X+1, C = X+1, E = X+1, F = X, and the total is 20. Additionally, five members have the same Erdös number, leaving four unknown values: B, D, G, and H.

Considering the five equal values, we can conclude that the equal value must be among X, X+1, or X+5. Since there are only four unknown values, there cannot be two X+1’s aside from the five equal values. Therefore, the equal value must be X+1. With this information, at the end of Day 3, we have X, X+1, X+1, X+1, X+1, X+1, X+5, and one unknown value. The total at the end of Day 3 is 24, so we can derive the equation 7X + Unknown Value = 14, or 7X + Unknown Value = 14. Since the unknown value cannot be negative or zero, X must be 1, resulting in the unknown value being 7.

Are you prepared for Mathematical Reasoning in DI-LR- These findings signify the progress we have made in understanding the values involved in the set. By carefully analyzing the information given and applying logical reasoning, we can successfully navigate through this unique set without using pen and paper.

By practicing and refining your skills in Mathematical Reasoning for DI-LR, you can tackle challenging sets with confidence and achieve success in the CAT exam.

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