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 the Teqnical, 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 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: 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 the Teqnical, 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 fancied by the customer.

Question: If the most economical drink which contains 25% of Gin is to be prepared at the Happily Tipsy Bar, then what will be the concentration of White Rum (in percentage, rounded to the nearest integral value) in a peg of 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: In this fictitious tale, the two legendary mathematicians and astronomers Aryabhatta and Varahamihira met at a dinner party hosted by King Chandragupta Vikramaditya at his palace in Pataliputra. 

Aryabhatta, the senior and moodier among the two, being slightly inebriated with the excellent ‘somras’ served by the king, and in a very good mood, suddenly said to Varahamihira -- ‘If distinct alphabets of the English language stand for distinct digits, then SATURN plus URANUS will be equal to JUPITER’!! 

Though initially puzzled by this sudden statement from Aryabhatta, Varahamihira quickly regained composure and solved the challenge thrown by Aryabhatta.

Question: In sync with the thought process of Aryabhatta, what would be the summation of the letters of ‘PARASITE’?

Directions for question:
On 1st February 2022, Ms Dipali Goenka, MD & CEO of Christy’s, a subsidiary of Gujarat based M/s Welspun India, received a large order for supplying handmade players’ towels for the centenary Wimbledon Tennis tournament in July 2022, and the ICC Men’s T-20 World Cup in October 2022, both to be delivered by the last date of June 2022.
Christy’s have
a) Twenty cutters whose job is to cut the towel fabric supplied by M/s Welspun India.
b) Fifty printers who do the dyeing and screen printing on the towels
c) Twenty stitchers whose job is to do the border stitching and monogramming on the towels
d) Five packers who fold, pack and seal the towels
Each of the hundred employees mentioned above works for ten hours per day.
Each of the Wimbledon towels requires forty minutes for cutting the towel fabric, two hours for dyeing and screen printing, forty minutes for border stitching and monogramming, and ten minutes for folding, packing and sealing. Whereas the ICC World Cup towels require one hour, two hours, eighty minutes and fifteen minutes respectively for the same above mentioned activities.
At Christy’s, the following steps are followed in order, after the arrival of the towel fabric, till the final packed product is obtained:
Step I: Cutting of towel fabric by the cutters.
Step II: Dyeing and screen printing on the towels by the printers.
Step III: Stitching and monogramming on the towels by the stitchers.
Step IV: Folding, packing and sealing of towels by the packers.
Question: What is the maximum number of Wimbledon towels that Christy’s can complete in a day?

Directions for question:
On 1st February 2022, Ms Dipali Goenka, MD & CEO of Christy’s, a subsidiary of Gujarat based M/s Welspun India, received a large order for supplying handmade players’ towels for the centenary Wimbledon Tennis tournament in July 2022, and the ICC Men’s T-20 World Cup in October 2022, both to be delivered by the last date of June 2022. 

Christy’s have 

a) Twenty cutters whose job is to cut the towel fabric supplied from M/s Welspun India 

b) Fifty printers who do the dyeing and screen printing on the towels 

c) Twenty stitchers whose job is to do the border stitching and monogramming on the towels 

d) Five packers who fold, pack and seal the towels 

Each of the hundred employees mentioned above work for ten hours per day. 

Each of the Wimbledon towels require forty minutes for cutting the towel fabric, two hours for dyeing and screen printing, forty minutes for border stitching and monogramming, and ten minutes for folding, packing and sealing. Whereas the ICC World Cup towels require one hour, two hours, eighty minutes and fifteen minutes respectively for the same above-mentioned activities. 

At Christy’s, the following steps are followed in order, after the arrival of the towel fabric, till the final packed product is obtained :

Step I: Cutting of towel fabric by the cutters

Step II: Dyeing and screen printing on the towels by the printers

Step III: Stitching and monogramming on the towels by the stitchers

Step IV: Folding, packing and sealing of towels by the packers 

Question: On a particular day Christy’s decided to complete a hundred ICC World Cup towels. How many Wimbledon towels can be completed on that day?

Directions for question: 
On 1st February 2022, Ms Dipali Goenka, MD & CEO of Christy’s, a subsidiary of Gujarat-based M/s Welspun India, received a large order for supplying handmade players’ towels for the centenary Wimbledon Tennis tournament in July 2022, and the ICC Men’s T-20 World Cup in October 2022, both to be delivered by the last date of June 2022. 

Christy’s have 

a) Twenty cutters whose job is to cut the towel fabric supplied by M/s Welspun India 

b) Fifty printers who do the dyeing and screen printing on the towels 

c) Twenty stitchers whose job is to do the border stitching and monogramming on the towels 

d) Five packers who fold, pack and seal the towels 

Each of the hundred employees mentioned above works for ten hours per day. 

Each of the Wimbledon towels requires forty minutes for cutting the towel fabric, two hours for dyeing and screen printing, forty minutes for border stitching and monogramming, and ten minutes for folding, packing and sealing. Whereas the ICC World Cup towels require one hour, two hours, eighty minutes and fifteen minutes respectively for the same above-mentioned activities. 

At Christy’s, the following steps are followed in order, after the arrival of the towel fabric, till the final packed product is obtained :

Step I: Cutting of towel fabric by the cutters

Step II: Dyeing and screen printing on the towels by the printers

Step III: Stitching and monogramming on the towels by the stitchers

Step IV: Folding, packing and sealing of towels by the packers 

Question: If Christy’s decides to make two hundred Wimbledon towels only and no other towels on a particular day, how many total man-hours will remain unutilized on that day? (Man – hours for a task = number of men who can do the task * number of hours for the task.)