CAT Introduction to Binary Logic - Practice Questions & MCQ

You are given an n×n square matrix to be filled with numerals so that no two adjacent cells have the same numeral. Two cells are called adjacent if they touch each other horizontally, vertically or diagonally. So a cell in one of the four corners has three cells adjacent to it, and a cell in the first or last row or column which is not in the corner has five cells adjacent to it. Any other cell has eight cells adjacent to it.

Question:

Suppose you are allowed to make one mistake, that is, one pair of adjacent cells can have the same numeral. What is the minimum number of different numerals required to fill a 5×5 matrix?

Fuel contamination levels at each of 20 petrol pumps P1, P2, …, P20 were recorded as either high, medium, or low. 

1. Contamination levels at three pumps among P1 – P5 were recorded as high. 

2. P6 was the only pump among P1 – P10 where the contamination level was recorded as low. 

3. P7 and P8 were the only two consecutively numbered pumps where the same levels of contamination were recorded. 

4. High contamination levels were not recorded at any of the pumps P16 – P20. 

5. The number of pumps where high contamination levels were recorded was twice the number of pumps where low contamination levels were recorded.

Question:

Which of the following MUST be true? 

Fuel contamination levels at each of 20 petrol pumps P1, P2, …, P20 were recorded as either high, medium, or low. 

1. Contamination levels at three pumps among P1 – P5 were recorded as high. 

2. P6 was the only pump among P1 – P10 where the contamination level was recorded as low. 

3. P7 and P8 were the only two consecutively numbered pumps where the same levels of contamination were recorded. 

4. High contamination levels were not recorded at any of the pumps P16 – P20. 

5. The number of pumps where high contamination levels were recorded was twice the number of pumps where low contamination levels were recorded.

Question:

 If the contamination level at P11 was recorded as low, then which of the following MUST be true? 

Applicants for the doctoral Programmes 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 CM). 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 ATE. AET is used by ATE for final selection.
For the 200 candidates who are at or above the 9oth 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 V Number of candidates below 8oth percentile in C:
Number of candidates below 80th percentile in M = 4 : 2 : 1.
 

BIE uses a different Process for selection. If any candidate is appearing in the AET by ATE, BIE considers their AET score for final selection provided the candidate is at or above the 80th percentile in P. Any other candidate at or above the 80th percentile in P in CET, but who is not eligible for the AET, is required to appear in a separate test to be conducted by STE for being considered for final selection. Altogether, there are 400 candidates this year who are at or above the 80th percentile in P. 

Question :  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? 

Simple Happiness index (SHI) of a country is computed on the basis of three parameters: social support (S), freedom to life choices (F) and corruption perception (C). Each of these three parameters is measured on a scale of 0 to 8 (integers only). A country is then categorised based on the total score obtained by summing the scores of all the three parameters, as shown in the following table:

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: 

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?