CAT Introduction to Analytical Puzzles - Practice Questions & MCQ

Directions for question: Dr Anand C Burman, the Chairman Emeritus of M/S Dabur India Ltd, had finalized the wedding plans at Kolkata of his only son Mr Aditya Burman. He allotted the responsibility of each department to one family member and kept himself in charge of the food and beverage segment. After much consultation with the whole Burman family, it was decided to incorporate eight different cuisines in the wedding dinner for the employees of Dabur India Ltd. They were namely 1) Bengali cuisine, 2) Bangladeshi cuisine, 3) Awadhi cuisine, 4) Mughlai cuisine, 5) Kolhapuri cuisine, 6) South Indian cuisine, 7) Chinese cuisine and 8) Continental cuisine.

Dr Burman’s affinity and benevolence towards the Dabur India Ltd employees was legendary, and in true cognizance of that, he ordered a survey to find out the first and second preferences of all the employees of Dabur India Ltd amongst the eight cuisines finalized for the wedding.

The survey results submitted at his table were as below:

The numbers represent the number of employees of Dabur India Ltd who prefer the different types of cuisines. The cuisine mentioned in the column is the first preference, while the cuisine mentioned in the row is the second preference. Where both the column and row cuisines are the same, it indicates that those employees have only one preference.

For example, 
Column 1, Row 1 is 2280. It indicates that 2280 employees of Dabur India Ltd prefer only Bengali cuisine.
Column 1, Row 2 is 1575. It indicates that 1575 employees of Dabur India Ltd have Bengali cuisine as their first preference and Bangladeshi cuisine as their second preference.

From the above data please answer the question given below.
Question: The number of employees of M/S Dabur India Ltd whose first preference is either South Indian or Continental and whose second preference is either Awadhi or Chinese is what per cent of the employees whose first preference is Bangladeshi and second preference Bengali cuisine (rounded to the first decimal place)?

Directions for question :

At the Happily Tipsy Bar, the chief bar-tender, after a lot of experimentation found out that Vodka, White Rum, Gin and Tequila if mixed in different concentrations can create four very exciting cocktails which he named as the Teqnical, the Hard Haddock, the Fiery Ginie and the Russian Heat. The respective percentage alcohol concentrations of the cocktails are provided in the chart below. 

He priced them at Rs 160, Rs 400, Rs 320 and Rs 240 per single peg respectively. On specific orders from customers, he was ready to mix two or more drinks in the ratio as fancied by the customer.

Question :

A customer at the Happily Tipsy Bar asks for a peg of a drink with a single portion each of Teqnical, Fiery Ginie and Russian Heat, and a double portion of Hard Haddock. What will be the minimum integral ratio of the percentage contents of Vodka, White Rum, Gin and Tequila in that drink ? 

Directions for question: In 2022, on the occasion of their 450th year of being established, the Order of the Jesuit Missionaries, who founded the chain of St Xavier’s Schools in India, decided to honour the Fathers as well as the Principals of their Indian schools who helped propagate quality education in India. 

For that, they had to choose one of the schools where they would carry out this landmark ceremony. In the final contention were St Xavier’s Collegiate School Kolkata, St Xavier’s School Durgapur, St Xavier’s School Mumbai and St Xavier’s School Ranchi. St Xavier’s Schools in India as per rule had one Principal per school, and all the schools in India were represented by their Principals in the selection. 

The eventual winner was determined through several rounds of voting by all the Principals of all the St Xavier’s Schools. In any round of voting, the school receiving the minimum number of votes in that round was eliminated. The surviving St Xavier’s School after the last round of voting would get the chance to host the ceremony.

Each Principal was allowed to cast votes for at most two schools in all rounds of voting combined. Hence, a Principal would become ineligible to cast a vote in a given round if both the St Xavier Schools he voted for in earlier rounds were out of contention in that round of voting. A Principal was also ineligible to cast a vote in a round if the St Xavier’s School he represented was in contention in that round of voting. As long as the Principal was eligible, he had to vote for only one contesting St Xavier’s School in any round of voting.

The following incomplete table shows the information on St Xavier’s Schools that received the maximum and minimum votes in different rounds of voting, the number of votes cast in their favour, and the total votes that were cast in those rounds.

 The following facts were also known:
a) All the Principals who voted for St Xavier’s School Durgapur and St Xavier’s School Ranchi in round one went on doing so as long they were in contention
b) Three-fourths of those Principals who voted for St Xavier’s School Mumbai in round one voted for St Xavier’s School Mumbai in round two
c) Those Principals who voted for St Xavier’s Collegiate School Kolkata in round one voted for either St Xavier’s School Ranchi or St Xavier’s School Mumbai in round two
d) Half of the Principals who voted for St Xavier’s School Mumbai in round one voted for St Xavier’s School Ranchi in round three
e) The difference in votes between the two contending schools in the last round was 2.

Question: What is the number of votes cast in favour of St Xavier’s School Ranchi in round two?

Directions for question: In 2022, on the occasion of their 450th year of being established, the Order of the Jesuit Missionaries, who founded the chain of St Xavier’s Schools in India, decided to honour the Fathers as well as the Principals of their Indian schools who helped propagate quality education in India. 

For that, they had to choose one of the schools where they would carry out this landmark ceremony. In the final contention were St Xavier’s Collegiate School Kolkata, St Xavier’s School Durgapur, St Xavier’s School Mumbai and St Xavier’s School Ranchi. St Xavier’s Schools in India as per rule had one Principal per school, and all the schools in India were represented by their Principals in the selection. 

The eventual winner was determined through several rounds of voting by all the Principals of all the St Xavier’s Schools. In any round of voting, the school receiving the minimum number of votes in that round was eliminated. The surviving St Xavier’s School after the last round of voting would get the chance to host the ceremony.

Each Principal was allowed to cast votes for at most two schools in all rounds of voting combined. Hence, a Principal would become ineligible to cast a vote in a given round if both the St Xavier Schools he voted for in earlier rounds were out of contention in that round of voting. A Principal was also ineligible to cast a vote in a round if the St Xavier’s School he represented was in contention in that round of voting. As long as the Principal was eligible, he had to vote for only one contesting St Xavier’s School in any round of voting.

The following incomplete table shows the information on St Xavier’s Schools that received the maximum and minimum votes in different rounds of voting, the number of votes cast in their favour, and the total votes that were cast in those rounds.

The following facts were also known:
a) All the Principals who voted for St Xavier’s School Durgapur and St Xavier’s School Ranchi in round one went on doing so as long they were in contention.
b) Three-fourths of those Principals who voted for St Xavier’s School Mumbai in round one voted for St Xavier’s School Mumbai in round two.
c) Those Principals who voted for St Xavier’s Collegiate School Kolkata in round one voted for either St Xavier’s School Ranchi or St Xavier’s School Mumbai in round two.
d) Half of the Principals who voted for St Xavier’s School Mumbai in round one voted for St Xavier’s School Ranchi in round three
e) The difference in votes between the two contending schools in the last round was 2.

Question Assuming that all the Principals of all the St Xavier’s Schools in India had the right to vote to elect one of the schools where the Order of the Jesuit Missionaries in Rome would carry out the landmark ceremony on the 450th year of their establishment, how many St Xavier’s Schools were there in India in 2022?

Directions for question: In 2022, on the occasion of their 450th year of being established, the Order of the Jesuit Missionaries, who founded the chain of St Xavier’s Schools in India, decided to honour the Fathers as well as the Principals of their Indian schools who helped propagate quality education in India. 

For that, they had to choose one of the schools where they would carry out this landmark ceremony. In the final contention were St Xavier’s Collegiate School Kolkata, St Xavier’s School Durgapur, St Xavier’s School Mumbai and St Xavier’s School Ranchi. St Xavier’s Schools in India as per rule had one Principal per school, and all the schools in India were represented by their Principals in the selection. 

The eventual winner was determined through several rounds of voting by all the Principals of all the St Xavier’s Schools. In any round of voting, the school receiving the minimum number of votes in that round was eliminated. The surviving St Xavier’s School after the last round of voting would get the chance to host the ceremony.

Each Principal was allowed to cast votes for at most two schools in all rounds of voting combined. Hence, a Principal would become ineligible to cast a vote in a given round if both the St Xavier Schools he voted for in earlier rounds were out of contention in that round of voting. A Principal was also ineligible to cast a vote in a round if the St Xavier’s School he represented was in contention in that round of voting. As long as the Principal was eligible, he had to vote for only one contesting St Xavier’s School in any round of voting.

The following incomplete table shows the information on St Xavier’s Schools that received the maximum and minimum votes in different rounds of voting, the number of votes cast in their favour, and the total votes that were cast in those rounds.

The following facts were also known:
a) All the Principals who voted for St Xavier’s School Durgapur and St Xavier’s School Ranchi in round one went on doing so as long they were in contention.
b) Three-fourths of those Principals who voted for St Xavier’s School Mumbai in round one voted for St Xavier’s School Mumbai in round two.
c) Those Principals who voted for St Xavier’s Collegiate School Kolkata in round one voted for either St Xavier’s School Ranchi or St Xavier’s School Mumbai in round two.
d) Half of the Principals who voted for St Xavier’s School Mumbai in round one voted for St Xavier’s School Ranchi in round three.
e) The difference in votes between the two contending schools in the last round was 2.

Question: What percentage of Principals who had voted for St Xavier’s School Mumbai in round two and were eligible to vote, voted for St Xavier’s School Durgapur in round three?

Directions for question: Consultancy firm M/S McKinsey & Company was hired by the World Health Organization in 2022 and was given the task of evaluating the total health budgets (in million USD) of five countries namely Ghana, Egypt, Nigeria, Libya and South Africa.                    

Each of the above-mentioned countries allocates its total health budget behind two parameters – healthcare budget and research and development budget. Moreover, the total health budget of each country was different and was a multiple of 50 million USD. 

The report submitted by the firm had the following points: 
i)  Among the five countries, Ghana had the lowest total health budget and also spent the lowest on healthcare. 
ii) South Africa, which had the highest total health budget and Egypt were the only countries to allocate 50% of their total health budget to healthcare. 
iii) Nigeria’s healthcare budget allocation matched that of Egypt. Also, their research and development budget allocation was double that of Ghana's research and development budget allocation. 
iv) Libya was second to only South Africa and ahead of other countries in the total health budget as well as allocation to healthcare budget and research and development budget. 
v) Ghana's healthcare budget allocation was only 10% of the highest healthcare budget allocation amongst all the five countries which was 250 million USD. 
vi) Except Ghana's healthcare budget allocation, all other healthcare budget allocations were a multiple of 50 million USD. 

From the above report, find the answer to the question that follows:
Question: The ratio of the Research and Development Budget allocation to the Healthcare Budget allocation is termed the RPR Index. What was the RPR Index of the five countries taken together as per the report of M/S McKinsey & Company?