# Logical Reasoning

This is a new kind of question and is gaining in CAT. Either a large table is given or else some facts in the form of a riddle where some facts are not given. One has to figure out how to attempt such questions.

Set III

Examples

DIRECTIONS: Answer the questions on the basis of the information given below.

The table below provides certain demographics details of 40 respondents who were part of a survey. The demographic characteristics are: Education, number of children and age of respondents. The first number in 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 6 non-educated persons who have 4 children, out of that the minimum is aged 25 and the maximum is aged 57 years.

 No. of children Educated Non-educated Total 0 8 (25, 41) 2 (32, 42) 10 1 7 (27, 64) 5 (31, 47) 12 2 6 (30, 49) 10 (23, 65) 16 3 3 (22, 52) 11 (21, 46) 14 4 2 (46, 56) 6 (25, 29) 8 Total 25 35 60

1. At least what percentage of the educated persons are more than 40 years old?
1. 20%
2. 16.67%
3. 25%
4. 43.33%

2. At the most what percentage of the total are non-educated persons with more than 30 years of age?
1. 41.66%
2. 58.33%
3. 51.66%
4. 50%

3. At the most what percentage of the total persons surveyed were < 25 years of age?
1. 5%
2. 25%
3. 35%
4. 15%

4. At least what percentage of the persons surveyed were than 46 years old?
1. 11.66%
2. 90%
3. 15%
4. 10%

Solution

This question just requires understanding the facts given. Then it is merely counting off the desired elements from the table. These questions make utterly useless the concepts like Vedic Maths and other shortcuts that students like to learn.

1. 1 Educated persons above 40 least can be 1 in every age group. Hence 5/25 = 20%.

2. 4 Non educated persons more than 30 years (at most) = 2 + 5 + 9 + 10 = 26. Reqd percentage = 26/60 = 43%

3. 3 Less than 25 years (at most) = 9 + 2 + 10 = 21/60 = 35%.

4. 4 Less than 46 years = 6/60 = 10%.

# Games and Puzzles

Questions on games and puzzles are becoming common. In this type, information about some game is given and the student has to figure out the order of winners, and so on. The following question set is from CAT 2006.

Set IV

Examples

The year was 2006. All six teams in Pool A of World Cup hockey play each other exactly once. Each win earns a team three points, a draw earns one point and a loss earns zero points. The two teams with the highest points qualify for the semifinals. In case of a tie, the team with the highest goal difference (Goals For - Goals Against) qualifies.

In the opening match, Spain lost to Germany. After the second round (after each team played two matches), the pool table looked as shown below.

 Teams Games Played Won Drawn Lost Goals for Goals against Points Germany 2 2 0 0 3 1 6 Argentina 2 2 0 0 2 0 6 Spain 2 1 0 1 5 2 3 Pakistan 2 1 0 1 2 1 3 New Zealand 2 0 0 2 1 4 0 South Africa 2 0 0 2 1 4 0

In the third round, Spain played Pakistan, Argentina played Germany, and New Zealand played South Africa. All the third round matches were drawn. The following are some results from the fourth and fifth round matches

(a) Spain won both the fourth and fifth round matches.
(b) Both Argentina and Germany won their fifth round matches by 3 goals to 0.
(c) Pakistan won both the fourth and fifth round matches by 1 goal to 0.

1. Which one of the following statements is true about matches played in the first two rounds?
1. Germany beat New Zealand by 1 goal to 0.
2. Spain beat New Zealand by 4 goals to 0.
3. Spain beat South Africa by 2 goals to 0.
4. Germany beat South Africa by 2 goals to 1

2. Which one of the following statements is true about matches played in the first two rounds?
1. Pakistan beat South Africa by 2 goals to 1
2. Argentina beat Pakistan by 1 goal to 0.
3. Germany beat Pakistan by 2 goals to 1
4. Germany beat Spain by 2 goals to 1.

3. Which team finished at the top of the pool after five rounds of matches?
1. Argentina
2. Germany
3. Spain
4. Cannot be determined from the data.

4. If Pakistan qualified as one of the two teams from Pool A, which was the other team that qualified?
1. Argentina
2. Germany
3. Spain
4. Cannot be determined from the data.

Solution

1. 4 Best done by elimination.

(1): If true, then NZ lost the second game by 5-1, which does not match.

(2): If Spain beats NZ by 4-0, then in the next game it should lose by 1-2.

(3): If Spain beats SA by 2-0, then it should win the next game by 3-2, but it lost the other game.

Only (4) is possible.

2. 2 As above, (1): If Pakistan has 2-1, it should draw the next game 0-0, which is not true.

(2) is possible.

(3): same as in the first choice.

3. 4 We can say nothing about the winner.

4. 4 The question is inconsistent.

If Pakistan wins the last two rounds, and we are also told in (a) to (c) that Spain, Argentina, Germany and Pakistan won their fifth round matches.

This is not possible, since there can be only theree winners.

# Miscellaneous Reasoning

Stand Alone Questions on Reasoning

CAT has often used stand alone questions in reasoning. These questions are fairly large and have certain clues on which the student is required to answer the question. They are time consuming questions and sometimes guess work helps. However, if one uses a slow and steady approach, then the questions can be solved.

# Stand Alone Questions on Reasoning

CAT has often used stand alone questions in reasoning. These questions are fairly large and have certain clues on which the student is required to answer the question. They are time consuming questions and sometimes guess work helps. However, if one uses a slow and steady approach, then the questions can be solved.