CAT 2017: Logical Reasoning Question 2 Venkatesan IIMB Alumnus

A study to look at the early teaming of rural kids was carried out in a number of villages spanning three states, chosen from the North East (NE), the West (W) and the South (S). 50 four- year old kids each were sampled from each of the 150 villages from NE, 250 villages from W arid 200 villages from S. It was found that of the 30000 surveyed feds 55% studied in primary schools run by government (G), 37% in private schools (P) white the remaining 8% did not go to school The kids surveyed were further divided into two groups based on whether their mothers dropped out of school before completing primary education or not. The table below gives the number of kids in different types of schools for mothers who dropped out- of school before completing primary education:

4200 4200 5100 13500 300 1200 300 1800 Total 5000 7300 5700 18000 NE 500 1900 300 2700 Total It is also known that: 1. 2. 3. In S, 60% of the surveyed kids were m G. Moreover, in S, all surveyed kids whose mothers had completed primary education were in school In NE, among the O kids, 50% had mothers who had dropped out before completing primary education The number of kids in G in NE was the same as the number of kids in G in W

Question No.:1 What percentage of kids from S were studying in P? A) 37% B) 6% C) 79% D) 56%

Question No.: 2 Among the kids in W whose mothers had completed primary education, how many were not in school? A) 300 B) 1200 C) 1050 D) 1500

Question No.: 3 In a follow up survey of the same kids two years later, it was found that all the kids were now in school. Of the kids who were not in school earlier, in one region, 25% were in G now, whereas the rest were enrolled in P; in the second region, all such kids were in G now; while in the third region, 50% of such kids had now joined G while the rest had joined P. As a result, in all three regions put together, 50% of the kids who were earlier out of school had joined G. It was also seen that no surveyed kid had changed schools. What number of the surveyed kids now were in G in W? A) 6000 B) 5250 C) 6750 D) 6300

Question No.: 4 In a follow up survey of the same kids two years later, it was found that all the kids were now in school. Of the kids who were not in school earlier, in one region, 25% were in G now, whereas the rest were enrolled in P; in the second region, all such kids were in G now; while in the third region, 50% of such kids had now joined G while the rest had joined P. As a result, in all three regions put together, 50% of the kids who were earlier out of school had joined G. It was also seen that no surveyed kid had changed schools. What percentage of the surveyed kids in S, whose mothers had dropped out before completing primary education, were in G now? A) 94.7% B) 89.5% C) 93.4% D) Cannot be determined from the given information

A study to look at the early teaming of rural kids was carried out in a number of villages spanning three states, chosen from the North East (NE), the West (W) and the South (S). 50 four- year old kids each were sampled from each of the 150 villages from NE, 250 villages from W arid 200 villages from S. It was found that of the 30000 surveyed feds 55% studied in primary schools run by government (G), 37% in private schools (P) white the remaining 8% did not go to school Gd 4200 4200 5100 13500 8400 Pd 500 1900 300 2700 Od 300 1200 300 1800 Ts 2500 5200 4300 12000 Td 5000 7300 5700 18000 30000 RegionGs NE 7500 12500 10000 Total 3000 600

It is also known that: I. In S, 60% of the surveyed kids were m G. Moreover, in S, all surveyed kids whose mothers had completed primary education were in school. 2. In NE, among the O kids, 50% had mothers who had dropped out before completing primary education 3. The number of kids in G in NE was the same as the number of kids in G in W Gd 4200 4200 5100 13500 8400 Pd 500 1900 300 2700 Od 300 1200 300 1800 Ts 2500 5200 4300 12000 Td 5000 7300 5700 18000 RegionGs NE 1050 1050 900 3000 1150 3850 3400 300 300 0 600 Total 7500 12500 10000 30000 Total

Question No.:1 What percentage of kids from S were studying in P? A) 37% B) 6% C) 79% D) 56%

Question No.: 1 What percentage of kids from S were studying in P? A) 37% B) 690 C) 79% D) 56% Gd 4200 4200 5100 13500 8400 Pd 500 1900 300 2700 Od 300 1200 300 1800 Ts 2500 5200 4300 12000 Td 5000 7300 5700 18000 RegionGs NE 1050 1050 900 3000 1150 3850 3400 300 300 0 600 Total 7500 12500 10000 30000 Total

Question No.: 2 Among the kids in W whose mothers had completed primary education, how many were not in school? A) 300 B) 1200 C) 1050 D) 1500

Question No.: 3 In a follow up survey of the same kids two years later, it was found that all the kids were now in school. Of the kids who were not in school earlier, in one region, 25% were in G now, whereas the rest were enrolled in P; in the second region, all such kids were in G now; while in the third region, 50% of such kids had now joined G while the rest had joined P. As a result, in all three regions put together, 50% of the kids who were earlier out of school had joined G. It was also seen that no surveyed kid had changed schools. What number of the surveyed kids now were in G in W? A) 6000 B) 5250 C) 6750 D) 6300

Question No.: 4 In a follow up survey of the same kids two years later, it was found that all the kids were now in school. Of the kids who were not in school earlier, in one region, 25% were in G now, whereas the rest were enrolled in P; in the second region, all such kids were in G now; while in the third region, 50% of such kids had now joined G while the rest had joined P. As a result, in all three regions put together, 50% of the kids who were earlier out of school had joined G. It was also seen that no surveyed kid had changed schools. What percentage of the surveyed kids in S, whose mothers had dropped out before completing primary education, were in G now? A) 94.7% B) 89.5% C) 93.4% D) Cannot be determined from the given information

CAT 2017: Logical Reasoning Question 3 Venkatesan IIMB Alumnus

Question No.:17 There are 21 employees working in a division, out of whom 10 are special-skilled employees (SE) and the remaining are regular skilled employees (RE). During the next five months, the division has to complete five projects every month. Out of the 25 projects, 5 projects are "challenging", while the remaining ones are "standard". Each of the challenging projects has to be completed in different months. Every month, five teams - T1, T2, T3, T4 and T5, work on one project each. T1, T2, T3, T4 and T5 are allotted the challenging project in the first, second, third, fourth and fifth month, respectively. The team assigned the challenging project has one more employee than the rest. In the first month, T1 has one more SE than T2, T2 has one more SE than T3, T3 has one more SE than T4, and T4 has one more SE than T5. Between two successive months, the composition of the teams changes as follows: a. The team allotted the challenging project, gets two SE from the team which was allotted the challenging project in the previous month. In exchange, one RE is shifted from the former team to the latter team. b. After the above exchange, if T1 has any SE and T5 has any RE, then one SE is shifted from T1 to T5, and one RE is shifted from T 5 to T1. Also, if T2 has any SE and T4 has any RE, then one SE is shifted from T2 to T4, and one RE is shifted from T 4 to T2

Question No.:1 Each standard project has a total of 100 credit points, while each challenging project has 200 credit points. The credit points are equally shared between the employees included in that team The number of times in which the composition of team T 2 and the number of times in which composition of team T 4 remained unchanged in two successive months are:

Question No.: 2 The number of SE in T1 and T5 for the projects in the third month are, respectively:

Question No.: 17 There are 21 employees working in a division, out of whom 10 are special skilled employees (SE) and the remaining are regular skilled employee (RE). During the next five months, the division has to complete five project every month. Out of the 25 projects, 5 projects are "challenging", while th remaining ones are "standard". Each of the challenging projects has to b completed in different months. Every month, five teams - T1, T2, T3, T4 and Te T5, work on one project each. T1, T2, T3, T4 and T5 are allotted th challenging project in the first, second, third, fourth and fifth month, T1 respectively. The team assigned the challenging project has one more T2 3 employee than the rest. RE Total 5 4 T3 2 24 4 4 In the first month, T1 has one more SE than T2, T2 has one more SE than T4 T3, T3 has one more SE than T4, and T4 has one more SE than T5 3 T5 0 4

Team SE T1 T2 T3 T4 T5 RE Total Question No.: 17 4 4 4 Between two successive months, the composition of the teams changes as follows: 0 a. The team allotted the challenging project, gets two SE from the team which was allotted the challenging project in the previous month. In exchange, one RE is shifted from the former team to the latter team Team SE T1 T2 T3 T4 T5 RE Total 4 b. After the above exchange, if T1 has any SE and T5 has any RE, then one SE is shifted from T1 to T5, and one RE is shifted from T 5 to T1. Also, if T2 has any SE and T4 has any RE, then one SE is shifted from T2 to T4, and one RE is shifted from T 4 to T2 0 4

Month 3 Team SE T1 T2 T3 T4 RE Total 4 4 Question No.: 17 0 4 Between two successive months, the composition of the teams changes as follows: a. The team allotted the challenging project, gets two SE from the team which was allotted the challenging project in the previous month. In exchange, one RE is shifted from the former team to the latter team Month 4 Team SE T1 T2 T3 T4 T5 RE b. After the above exchange, if T1 has any SE and T5 has any RE, then one SE is shifted from T1 to T5, and one RE is shifted from T 5 to T1. Also, if T2 has any SE and T4 has any RE, then one SE is shifted from T2 to T4, and one RE is shifted from T 4 to T2 Total 1 4

Month 4 Team SE T1 RE Total Question No.: 17 0 4 Between two successive months, the composition of the teams changes as follows: T3 T4 T5 0 a. The team allotted the challenging project, gets two SE from the team which was allotted the challenging project in the previous month. In exchange, one RE is shifted from the former team to the latter team 4 Month 5 Team SE T1 T2 T3 T4 T5 RE b. After the above exchange, if T1 has any SE and T5 has any RE, then one SE is shifted from T1 to T5, and one RE is shifted from T 5 to T1. Also, if T2 has any SE and T4 has any RE, then one SE is shifted from T2 to T4, and one RE is shifted from T 4 to T2 Total 4 4

44445 44201 00244 12345 44544 44454 43112 43202 01432 01252 12345 12345 54444 45444 11234 31223 43210 14221 12345 12345

Question No.: 2 The number of SE in T1 and T5 for the projects in the third month are, respectively:

Question No.: 3 Each standard project has a total of 100 credit points, while each challenging project has 200 credit points. The credit points are equally shared between the employees included in that team. Which of the following CANNOT be the total credit points earned by any employee from the projects? A) 140 B) 150 C) 170 D) 200

In a square layout of size 5m x 5m, 25 equal sized square platforms of different heights are built. The heights (in metres) of individual platforms are as shown below: 9 7 4 7 Individuals (all of same height) are seated on these platforms. We say an individual A can reach at individual B if all the three following conditions are met:

(i) A and B are In the same row or column (ii) A is at a lower height than B (ii) If there is/are any individuals (s) between A and B, such individual(s) must be at a height lower than that of A Thus in the table given above, consider the Individual seated at height 8 on 3rd row and 2nd column. He can be reached by four individuals. He can be reached by the individual on his left at height 7, by the two individuals on his right at heights of 4 and 6 and by the individual above at height 5. Rows in the layout are numbered from top to bottom and columns are numbered from left to right.

Question No.:1 How many individuals in this layout can be reached by just one individual? A) 3 B) 5 C) 7 D) 8

(i) A and B are In the same row or column (ii) A is at a lower height than B (ii) If there is/are any individuals (s) between A and B, such individual(s) must be at a height lower than that of A Thus in the table given above, consider the Individual seated at height 8 on 3rd row and 2nd column. He can be reached by four individuals. He can be reached by the individual on his left at height 7, by the two individuals on his right at heights of 4 and 6 and by the individual above at height 5. Rows in the layout are numbered from top to bottom and columns are numbered from left to right.

Question No.: 2 Which of the following is true for any individual at a platform of height 1 m in this layout? A) They can be reached by all the individuals in their own row and column B) They can be reached by at least 4 individuals C) They can be reached by at least one individual D) They cannot be reached by anyone

Question No.: 3 We can find two individuals who cannot be reached by anyone in A) the last row B) the fourth row C) the fourth column D) the middle column

Question No.: 4 Which of the following statements is true about this layout? A) Each row has an individual who can be reached by 5 or more individuals B) Each row has an individual who cannot be reached by anyone C) Each row has at least two individuals who can be reached by an equal number of individuals D) All individuals at the height of 9 m can be reached by at least 5 individuals 6 2 4 4 5 6

Applicants for the doctoral programme of Ambi Institute of Engineering (AIE) and Bambi Institute of Engineering (BIE) have to appear for a Common Entrance Test (CET). The test has three sections: Physics (P), Chemistry (C), and Maths (M). Among those appearing for CET, those at or above the 80th percentile in at least two sections, and at or above the 90th percentile overall, are selected for Advanced Entrance Test (AET) conducted by AIE. AET is used by AlE for final selection. For the 200 candidates who are at or above the 90th percentile overall based on CET, the following are known about their performance in CET: 1. No one is below the 80th percentile in all 3 sections. 2. 150 are at or above the 80th percentile in exactly two sections. 3. The number of candidates at or above the 80th percentile only in P is the same as the number of candidates at or above the 80th percentile only in C. The same is the number of candidates at or above the 80th percentile only in M. 4. Number of candidates below 80th percentile in P: Number of candidates below 80th percentile in C: Number of candidates below 80th percentile in M-4:2:1.

Question No.:1 What best can be concluded about the number of candidates sitting for the separate test for BIE who were at or above the 90th percentile overall in CET? A) 3 or 10 B) 10 C) 5 D) 7 or 10

Question No.: 2 If the number of candidates who are at or above the 90th percentile overall and also at or above the 80th percentile in all three sections in CET is actually a multiple of 5, what is the number of candidates who are at or above the 90th percentile overall and at or above the 80th percentile in both P and M in CET? A) 60 B) C) D)

Question No.: 3 If the number of candidates who are at or above the 90 th percentile overall and also at or above the 80 th percentile in all three sections in CET is actually a multiple of 5, then how many candidates were shortlisted for the AET for AIE? A) 170 B) C) D)

Question No.: 4 If the number of candidates who are at or above the 90th percentile overall and also are at or above the 80th percentile in P in CET, is more than 100, how many candidates had to sit for the separate test for BIE? A) 299 B) 310 C) 321 D) 330

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Venkatesan S

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Upma Jain

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