DI/LR/DS - Part 2: Illustrations of strategies with some solved examples

DI:

Here I illustrate with some previous years' CAT questions.

Example: There are six companies, 1 through 6. All of these companies use six operations, A through F. The following graph shows the distribution of efforts put in by each company in these operations. Right click on the graph to open in a separate window.

Q1.  Suppose effort allocation is interchanged between operations B and C, then C and D, and then D and E and if companies are then ranked in ascending order of effort in E, what will be the rank of company 3?

1. 2            2. 3            3. 4            4. 5

Q2. A new technology is introduced in company 4 such that the total effort for operations B through F gets evenly distributed among these. What is the change in the percentage of effort in operation E?

1. Reduction of 12.3                2. Increase of 12.3
3. Reduction of 5.6                4. Increase of 5.6

Q3. Suppose the companies find that they can remove operations B, C and D and re-distribute the effort released equally among the remaining operations. Then, which operation will show the maximum effort across all companies and all operations?

1. Operation E in company 1            2. Operation E in company 4
3. Operation F in company 5            4. Operation E in company 5

Here after first effort interchange, B moves to C - 2nd interchange B moves to D, third interchange B to moves to E. So, rankings of the company at the end of 3 interchanges is on B - hence answer = 3. This is a purely logical reasoning question. Don't get caught up in unnecessary details of the graphs.

An example of a question where you use common sense and not calculations. E has the highest efforts. Hence redistribution will reduce E. So, options 2 & 4 eliminated. Now, if the reduction is by 5.6%, then each option B to F will be 23% which is impossible. Hence, option 1 is the correct one. Did you use calculations here at all?

This is also a question of elimination where you'll need hardly any calculations. Company 5 has two options - start with company 5. Now for company 5, efforts on E > F and even after equal distribution, it will be so. Hence, option 3 eliminated.

Between options 2 and 4, visual results show that B+C+D for company 5 >those of company 4. Hence, option 2 eliminated.

Between options 1 & 4, already E in company 5 is greater than company 1 by 5%. Visually we can see that E in company 1 can't make it up - it needs B+C+D in company 1 to be 15% greater than (B+C+D) in company 5 - which is not the case here... hence, correct answer option 4. See did you need calculations here?

DI: Second example

Chart-1 shows the distribution by value of top 6 suppliers of MFA Textiles in 1995. Chart-2 shows the distribution by quantity of top 6 suppliers of MFA textiles in 1995. The total value is 5760 million Euros (the European currency). The total quantity is 1.055 million tonnes.

Q1. The country, which has the highest average price, is
1. USA 2. Switzerland 3. Turkey     4. India

Q2. The average price in Euro/ kg for Turkey is roughly
1. 6.20            2. 5.60                3. 4.20            4. 4.80

Conventional way is to go through the calculations

USA = (0.17*5760)/(0.15*1.055)

Switz = (0.2*5760)/(0.11*1.055)

Turkey = (0.16*5760)/(0.15*1.055)

India = (0.2*5760)/(0.26*1.055)

Can we simplify it a lot without going into calculations? Yes we can - here 5760/1.055 is common for all. Now, the problem is reduced to 17/15, 20/11, 16/15, 20/26. We can eliminate option 3 & 4 - Turkey and India. 20/11 > 17/15 obviously. Hence, correct answer is option 2.

Do you need to calculate here?

It's in kg hence 1055 kg. 5760/1055 > 5 clearly. Here for Turkey the ratio is 0.16/0.15 = 16/15, just above 1. Hence, 5 point something into 1 = 5 point something.... so it should be 5+. Now our choice is restricted between options 1 and 2. Can it be 6? No! Since  5760/1055 = 58/11 = 5.3. Hence multiplied by 1.07 can't be > 5.6. Hence, 5.6 is the accurate answer. How long did it take? Less than 30 seconds? Then it's ok!

Logical Reasoning

Question 1:

The table below provides certain demographic details of 30 respondents who were part of a survey. The demography characteristics are: gender, number of children, and age of respondents. The first number is each cell is the number of respondents in that group. The minimum and maximum age of respondents in each group is given in brackets. For example, there are 5 female respondents with no children and among these five, the youngest is 34 years old, while the oldest is 49.

 No of Children Male Female Total 0 1 (38, 38) 5 (34, 49) 6 1 1 (32, 32) 8 (35, 57) 9 2 8 (21, 65) 3 (37, 63) 11 3 2 (32, 33) 2 (27, 40) 4 Total 12 18 30

Q1. The percentage of respondents aged less than 40 years is at least.
1. 10%            2. 16.67%         3. 20.0%        4. 30%

Q2. Given the information above, the percentage of respondents older than 35 can be at most.
1. 30%            2. 73.33%        3. 76.67%        4. 90%

Q3. The percentage of respondents that fall into the 35 to 40 years age group (both inclusive) is at least
1. 6.67%        2. 10%            3. 13.33%        4. 26.67%

To answer these questions you need to grasp and build up a structure of the questions first.

Take Q 1 for example. "Respondents aged < 40 years" means

• if min and max ages of a group < 40, then all respondents meet the criteria
• if min is <40 and max >40, then at least 1 respondent meets the criteria
• if both min and max ages are >40, then none meets the criteria.

Hence, we get:

• (For No of children = 0), 1 M and 1 F
• (For No of children = 1), 1 M and 1 F
• (For No of children = 2),1 M  and 1 F
• (For No of children = 3), 2 M and 1 F = total 9.

9/30 = 30%. Did you need a calculator here?

For Q2: similarly build up a structure

• If minimum and maximum age <= 35, then no respondent meets the condition
• If minimum <= 35 and maximum > 35, then one less than the number of respondents in the group meet the condition
• If minimum and maximum > 35 then, all respondents meet the condition

Hence, we get:

• (For No of children = 0), 1 M and 4 F
• (For No of children = 1), 0 M and 7 F
• (For No of children = 2), 7 M  and 3 F
• (For No of children = 3), 0 M and 1 F = total 23. 23/30 = 76.67%

For Q3, again build up a structure

• If both minimum and maximum ages are < 35 or > 40 then no respondent meets the condition
• If both minimum and maximum ages are 35 to 40 then all respondents meet the condition
• If minimum < 35 and maximum between 35 to 40 then at least 1 respondent meets the condition
• If minimum is between 35 to 40 and maximum > 40 then at least 1 respondent meets the condition

Hence, we get:

• (For No of children = 0), 1 M and 0 F
• (For No of children = 1), 0 M and 1 F
• (For No of children = 2), 0 M  and 1 F
• (For No of children = 3), 0 M and 1 F = total 4. 4/30 = 13.33%

This is what I meant in earlier discussion by structure - in all LR questions you need to build up a structure first to solve the question. Don't attempt to answer without logically building up a structure. Thinking clarity will be particularly important for the structure to take an accurate shape.

Data sufficiency

In a Decathlon, the events are 100m, 400m, 100m hurdles, 1500m, High jump, Pole-vault, Long jump, Discus, Shot put and Javelin. The performance in the first four of these events is consolidated into Score-1, the next three into Score-2, and the last three into Score-3. Each such consolidation is obtained by giving appropriate positive weights to individual events. The final score is simply the total of these three scores. The athletes with the highest, second highest and the third highest final scores receive the gold, silver and bronze medals, respectively. The table below gives the scores and performances of nineteen top athletes in this event.

Q1. What is the least that Daley Thompson must get in Score-2 that ensures him bronze medal?
1. 5309        2. 5296        3. 5271        4. 5270

Q2. At least how many competitors (excluding Daley Thompson) must Michael Smith have out-jumped in the long jump event?
1. 1            2. 2            3. 3             4. 4

Don't get frightened by the table size. I told you, CAT questions are like snakes - the bigger the questions - more likelihood of it being harmless one. In fact, this question is a sitter!

For Q1, look at the final score column, the third highest score is 8880, so Thompson needs equal to or more than 8880, hence he should get 5296 (8881 – 582 – 3003) in Score-2. How long did it take you?Even for the last one you need not to calculate. Just work out the last digits of the numbers, you get that the last digit of the answer will be 6! Hence, even without calculation you can surely and correctly answer it to be 5296.

Q2, again you need a structure here! Here we don't have any data on long jump, but we have data on Score-2, high jump and pole vault. It's a minimum question - hence, the structure to answer would be

min. no. of competitors Smith outjumped in long jump = athletes with score in high jump and pole vault >or = Smith; but Score-2 < Smith.

Only 4 athletes qualify, Torsten Voss, Jurgen Hingsen, Grigory Degtyarov and Steve Fritz. Hence, correct answer is 4.