CAT Introduction to Binary Logic - Practice Questions & MCQ

Directions: Twenty-four people are part of three committees which are to look at research, teaching, and administration respectively. No two committees have any members in common. No two committees are of the same size. Each committee has three types of people: bureaucrats, educationalists, and politicians, with at least one from each of the three types in each committee. The following facts are also known about the committees:
1. The number of bureaucrats in the research and teaching committees is equal, while the number of bureaucrats in the research committee is 75% of the number of bureaucrats in the administration committee. 
2. The number of educationalists in the teaching committee is less than the number of educationalists in the research committee. The number of educationalists in the research committee is the average of the number of educationalists in the other two committees. 
3. 60% of the politicians are in the administration committee, and 20% are in the teaching committee. 
Question: Based on the given information, which of the following statements MUST be FALSE? 

Directions for question:
Healthy Bites is a fast food joint serving three items: burgers, fries and ice cream. It has two employees Anish and Bani who prepare the items ordered by the clients. Preparation time is 10 minutes for a burger and 2 minutes for an order of ice cream. An employee can prepare only one of these items at a time. The fries are prepared in an automatic fryer which can prepare up to 3 portions of fries at a time, and takes 5 minutes irrespective of the number of portions. The fryer does not need an employee to constantly attend to it, and we can ignore the time taken by an employee to start and stop the fryer; thus, an employee can be engaged in preparing other items while the frying is on. However, fries cannot be prepared in anticipation of future orders.
Healthy Bites wishes to serve the orders as early as possible. The individual items in any order are served as and when ready; however, the order is considered to be completely served only when all the items of that order are served.
The table below gives the orders of three clients and the times at which they placed their orders:
 

Question: Assume that only one client’s order can be processed at any given point in time. So, Anish or Bani cannot start preparing a new order while a previous order is being prepared.
At what time is the order placed by Client 1 completely served?

Directions for question: A study to look at the early learning of rural kids was carried out in several villages spanning three states, chosen from the North East (NE), the West (W) and the South (5). 50 four-year-old kids each were sampled from each of the 150 villages from NE, 250 villages from W and 200 villages from S It was found that of the 30000 surveyed kids 55% studied in primary schools run by the government (G), 37% In private schools (P) while the remaining 8% did not go to school (0).
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:

It Is also known that:
1. In S, 60% of the surveyed kids were in G. Moreover, in S, all surveyed kids whose mothers had completed primary education were in school.
2. In NE, among the 0 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. 
Question: What percentage of kids from S were studying in P?

Directions for question: A study to look at the early learning 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 (5). 50 four-year-old kids each were sampled from each of the 150 villages from NE, 250 villages from W and 200 villages from S It was found that of the 30000 surveyed kids 55% studied in primary schools run by the government (G), 37% In private schools (P) while the remaining 8% did not go to school (0).
 

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:

It Is also known that:
1. In S, 60% of the surveyed kids were in G. Moreover, in S, all surveyed kids whose mothers had completed primary education were in school.
2. In NE, among the 0 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. 
Question: 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 0 now, whereas the rest were enrolled in F, in the second region, all such kids were in 0 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 0. 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, was in G now?

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 months, respectively. The team assigned to 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 TS. Between two successive months, the composition of the teams changes as follows:

a. The team allotted the challenging project, gets two SEs 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 TB has any RE, then one SE is shifted from T1 to T5, and one RE is shifted from TB 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 T4 to T2.

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. 

Question:  Which of the following CANNOT be the total credit points earned by any employee from the projects?

In a square layout of size 5m × 5m, 25 equal-sized platforms of different heights are built. The heights (in metres) of individual platforms are as shown below:

Individuals (all of the same height) are seated on these platforms. We say an individual A can reach an 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

(iii) If there is/are any individual (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 the 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.

Row in the layout are numbered from top to bottom and columns are numbered from left to right.

Question: How many individuals in this layout can be reached by just one individual?

A new airlines company is planning to start operations in a country. The company has identified ten different cities which they plan to connect through their network to start with The flight duration between any pair of cities will be less than one hour To start operations, the company has to decide on a daily schedule.

The underlying principle that they are working on is the following:

Any person staying in any of these 10 cities should be able to make a trip to any other city in the morning and should be able to return by the evening of the same day

Question : If the underlying principle is to be satisfied in such a way that the journey between any two cities can be performed using only direct (non-stop) flights, then the minimum number of direct flights to be scheduled is: 

Funky Pizzana was required to supply pizzas to three different parties. The total number of pizzas it had to deliver was 800, 70% of which were to be delivered to Party 3 and the rest equally divided between Party 1 and Party 2. Pizzas could be of Thin Crust (T) or Deep Dish (0) variety and come in either Normal Cheese (NC) or Extra Cheese (EC) versions. Hence, there are four types of pizzas: T-NC, T-EC, D-NC and D-EC. Partial information about the proportions of T and NC pizzas ordered by the three parties is given below:

Question: How many Thin Crust pizzas were to be delivered to Party 3?

There were seven elective courses - E1 to E7 - running in a specific term in a college. Each of the 300 students enrolled had chosen just one elective from among these seven. However, before the start of the term, E7 was withdrawn as the instructor concerned had left the college. The students who had opted for E7 were allowed to join any of the remaining electives. Also, the students who had chosen other electives were given one chance to change their choice. The table below captures the movement of the students from one elective to another during this process. Movement from one elective to the same elective simply means no movement. Some numbers in the table got accidentally erased; however, it is known that these were either 0 or 1.

Further, the following are known:
1. Before the change process there were 6 more students in El than in E4, but after the reshuffle, the number of students in E4 was 3 more than that in El.
2. The number of students in E2 increased by 30 after the change process.
3. Before the change process, E4 had 2 more students than E6, while E2 had 10 more students than E3. 

Question: After the change process, which of the following is the correct sequence of the number of students in the six electives E1 to E6?

A tea taster was assigned to rate teas from six different locations - Munnar, Wayanad, Ooty, Darjeeling,
Assam and Himachal, These teas were placed in six cups, numbered 1 to 6, not necessarily in the same order
The tea taster was asked to rate these teas on the strength of their flavour on a scale of 1 to 10 He gave a
unique integer rating to each tea. Some other information is given below 

1. Cup 6 contained tea from Himachal.
2. Tea from Ooty got the highest rating, but it was not in Cup 3.
3. The rating of tea in Cup 3 was double the rating of the tea in Cup 5.
4 Only two cups got ratings in even numbers.
5. Cup 2 got the minimum rating and this rating was an even number.
6. Tea in Cup 3 got a higher rating than that in Cup 1.
7. The rating of tea from Wayanad was more than the rating of tea from Munnar, but less than that from
Assam.

Question:

 If the tea from Munnar did not get the minimum rating, what was the rating of the tea from Wayanadl?