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Q.No: 1
Test Name : CAT Paper 1993
Q86 to 88 : The following functions have been defined for three numbers A, B and C :
@ (A, B) = average of A and B
*(A, B) = product of A and B
/(A, B) = A divided by B
Answer these questions with the above data.

If A = 2 and B = 4, the value of @(/(*(A, B), B), A) would be

A
2
B
4
C
6
D
16
Answer key/Solution
Solution:
Q.No: 2
Test Name : CAT 2017 Actual Paper Slot 1
Question Numbers : (35 to 38) 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 oan. 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 ttiear orders:

Assume that only one client's order can be processed at any given point of 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?

A
10:17
B
10:10
C
10:15
D
10:20
Answer key/Solution
Solution:
Items ordered by client 1 at 10:00 are 1 burger, 3 portion of flies and 1 ice cream, out of which preparation time of burger is maximum. So, while one of the employees is preparing burger starting at 10:00, the other one can start preparing ice-cream which will take only 2 minutes and also the fries will get prepared in the meantime in fryer.

Hence maximum time required to completely serve client 1’s order is 10 minutes.

Therefore, the order placed by client 1 can be served completely at 10:10.
Q.No: 3
Test Name : CAT 2017 Actual Paper Slot 1
Question Numbers : (35 to 38) 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 oan. 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 ttiear orders:

Assume that only one client's order can be processed at any given point of 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 3 completely served?

A
10:35
B
10:22
C
10:25
D
10:17
Answer key/Solution
Solution:
Following the same process as we have done in above question, client 1 will be served completely at 10:10.

After that, both the employers will start working on client 2’s order and get it prepared by 10:15 as the fries will take 5 minutes in the fryer and they can’t work for two different clients at the same time. Hence, preparation of client 3’s order will get started at 10:15 and as he/she has ordered for 1 burger along with fries it will take 10 minutes for preparation.

Therefore, client 3 will be served completely at 10:25.
Q.No: 4
Test Name : CAT 2017 Actual Paper Slot 1
Question Numbers : (35 to 38) 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 oan. 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 ttiear orders:

Suppose the employees are allowed to process multiple orders at a time, but the preference would be to finish orders of clients who placed their orders earlier.

At what time is the order placed by Client 2 completely served?

A
10:10
B
10:12
C
10:15
D
10:17
Answer key/Solution
Solution:
Since the employees are allowed to process multiple orders, the one who is preparing ice-cream for order placed by client 1, will be free before 10:05, the time at which client 2 placed his order.

Now as per his order, preparation of fries will take more time than that of ice-cream. So, time taken by fryer of 5 minutes for fries and simultaneously 2 minutes by an employee for ice-cream. Order of client 2 will be served completely at 10:10.
Q.No: 5
Test Name : CAT 2017 Actual Paper Slot 1
Question Numbers : (35 to 38) 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 oan. 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 ttiear orders:

Suppose the employees are allowed to process multiple orders at a time, but the preference would be to finish orders of clients who placed their orders earlier.

Also assume that the fourth client came in only at 10:35. Between 10:00 and 10:30, for how many minutes is exactly one of the employees idle?

A
7
B
10
C
15
D
23
Answer key/Solution
Solution:
Since the employees are allowed to process multiple orders at a time, the following table shows the idle time for employees before client 4 ordered at 10:35.
Q.No: 6
Test Name : CAT 2017 Actual Paper Slot 2
Question Numbers : (63 to 66) : A high security research lab requires the researchers to set a pass key sequence Passed on the scan of the five fingers of their left hands. When an employee first joins the lab, her fingers are scanned in an order of her choice, and then when she wants to re-enter the facility, she has to scan the five fingers in the same sequence.
The lab authorities are considering some relaxations of the scan order requirements, since it is observed that some employees often get locked-out because they forget the sequence.

The lab has decided to allow a variation in the sequence of scans of the five fingers so that at most two scans (out of five) are out of place. For example, if the original sequence is Thumb (T), index finger (I), middle finger (M), ring finger (R) and little finger (L) then TLMRI is also allowed, but TMRLI is not.
How many different sequences of scans are allowed for any given person’s original scan?

Answer key/Solution
Solution:
Q.No: 7
Test Name : CAT 2017 Actual Paper Slot 2
Question Numbers : (63 to 66) : A high security research lab requires the researchers to set a pass key sequence Passed on the scan of the five fingers of their left hands. When an employee first joins the lab, her fingers are scanned in an order of her choice, and then when she wants to re-enter the facility, she has to scan the five fingers in the same sequence.
The lab authorities are considering some relaxations of the scan order requirements, since it is observed that some employees often get locked-out because they forget the sequence.

The lab has decided to allow a variations in the original sequence so that the input of the scanned sequence of five fingers is allowed to vary from the original sequence by one place for any of the fingers. Thus, for example, if the original sequence is TIMRL then ITRML is also allowed but LIMRT is not.
How many different sequences are allowed for any given person's original scans?

A
7
B
5
C
8
D
13
Answer key/Solution
Solution:
Q.No: 8
Test Name : CAT 2017 Actual Paper Slot 2
Question Numbers : (63 to 66) : A high security research lab requires the researchers to set a pass key sequence Passed on the scan of the five fingers of their left hands. When an employee first joins the lab, her fingers are scanned in an order of her choice, and then when she wants to re-enter the facility, she has to scan the five fingers in the same sequence.
The lab authorities are considering some relaxations of the scan order requirements, since it is observed that some employees often get locked-out because they forget the sequence.

The lab has now decided to require six scans in the pass key sequence, where exactly one finger is scanned twice, and the other fingers are scanned exactly once, which can be done in any order. For example, a possible sequence is TIMTRL.
Suppose the lab allows a variation of the original sequence (of six inputs) where at most two scans (out of six) are out of place, as long as the finger originally scanned twice is scanned twice and other fingers are scanned once.
How many different sequences of scans are allowed for any given person’s original scan?

Answer key/Solution
Solution:
Q.No: 9
Test Name : CAT 2017 Actual Paper Slot 2
Question Numbers : (63 to 66) : A high security research lab requires the researchers to set a pass key sequence Passed on the scan of the five fingers of their left hands. When an employee first joins the lab, her fingers are scanned in an order of her choice, and then when she wants to re-enter the facility, she has to scan the five fingers in the same sequence.
The lab authorities are considering some relaxations of the scan order requirements, since it is observed that some employees often get locked-out because they forget the sequence.

The lab has now decided to require six scans in the pass key sequence, where exactly one finger is scanned twice, and the other fingers are scanned exactly once, which can be done in any order. For example, a possible sequence is TIMTRL.
Suppose the lab allows a variation of the original sequence (of six inputs) so that input in the form of scanned sequence of six fingers is allowed to vary from the original sequence by one place for any of the fingers, as long as the finger originally scanned twice is scanned twice and other fingers are scanned once.
How many different sequences of scans are allowed if the original scan sequence is LRLTIM?

A
8
B
11
C
13
D
14
Answer key/Solution
Solution:
Q.No: 10
Test Name : CAT 2019 Actual Paper Slot 1

If the population of a town is p in the beginning of any year then it becomes 3 + 2p in the beginning of the next year. If the population in the beginning of 2019 is 1000, then the population in the beginning of 2034 will be

A
(1003)215 – 3
B
(997)214 + 3
C
(997)15 – 3
D
(1003)15 + 6
Answer key/Solution
Solution:
Q.No: 11
Test Name : CAT Actual Paper 2022 Slot-3

The arithmetic mean of all the distinct numbers that can be obtained by rearranging the digits in 1421, including itself, is

A
2222
B
2442
C
3333
D
2592
Answer key/Solution
Solution:
The number of possible rearrangements of the
number 1421 = 4!/2! = 12
Now, consider only the units place.
1 occurs 6 times in the unit’s place.
2 occurs 3 times in the unit’s place.
4 occurs 3 times in the unit’s place.
The total sum of digits of the units place in all the 12 arrangements combined
= 1 × 6 + 2 × 3 + 4 × 3 = 24
Similarly, the sum of digits in ten’s, hundred’s or thousand’s place will also be 24.
So the sum of all the 12 rearrangements = 24 × 1111
Hence, the average of all these rearrangements = 24 × 1111/12 = 2222.
Q.No: 12
Test Name : CAT Actual Paper 2023 Slot 1


A
√x, √z and √y are in arithmetic progression
B
x, y and z are in arithmetic progression
C
√x, √y and √z are in arithmetic progression
D
y, x and z are in arithmetic progression
Answer key/Solution
Solution:
Q.No: 13
Test Name : CAT Actual Paper 2023 Slot 2

Let both the series a1, a2, a3, ... and b1, b2, b3 ... be in arithmetic progression such that the common differences of both the series are prime numbers. If a5 = b9, a19 = b19 and b2 = 0, then a11 equals

A
83
B
79
C
84
D
86
Answer key/Solution
Solution:
Solution:

Solution:
Items ordered by client 1 at 10:00 are 1 burger, 3 portion of flies and 1 ice cream, out of which preparation time of burger is maximum. So, while one of the employees is preparing burger starting at 10:00, the other one can start preparing ice-cream which will take only 2 minutes and also the fries will get prepared in the meantime in fryer.

Hence maximum time required to completely serve client 1’s order is 10 minutes.

Therefore, the order placed by client 1 can be served completely at 10:10.

Solution:
Following the same process as we have done in above question, client 1 will be served completely at 10:10.

After that, both the employers will start working on client 2’s order and get it prepared by 10:15 as the fries will take 5 minutes in the fryer and they can’t work for two different clients at the same time. Hence, preparation of client 3’s order will get started at 10:15 and as he/she has ordered for 1 burger along with fries it will take 10 minutes for preparation.

Therefore, client 3 will be served completely at 10:25.

Solution:
Since the employees are allowed to process multiple orders, the one who is preparing ice-cream for order placed by client 1, will be free before 10:05, the time at which client 2 placed his order.

Now as per his order, preparation of fries will take more time than that of ice-cream. So, time taken by fryer of 5 minutes for fries and simultaneously 2 minutes by an employee for ice-cream. Order of client 2 will be served completely at 10:10.

Solution:
Since the employees are allowed to process multiple orders at a time, the following table shows the idle time for employees before client 4 ordered at 10:35.

Solution:

Solution:

Solution:

Solution:

Solution:

Solution:
The number of possible rearrangements of the
number 1421 = 4!/2! = 12
Now, consider only the units place.
1 occurs 6 times in the unit’s place.
2 occurs 3 times in the unit’s place.
4 occurs 3 times in the unit’s place.
The total sum of digits of the units place in all the 12 arrangements combined
= 1 × 6 + 2 × 3 + 4 × 3 = 24
Similarly, the sum of digits in ten’s, hundred’s or thousand’s place will also be 24.
So the sum of all the 12 rearrangements = 24 × 1111
Hence, the average of all these rearrangements = 24 × 1111/12 = 2222.

Solution:

Solution:

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