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Master Logarithm and Modulus, PYQs for Circular Arrangement Problems for Top Scores- Day 21
Edited By Team Careers360 | Updated on Aug 05, 2024 08:39 AM IST | #CAT
Hello CAT 2024 aspirants,
The CAT exam for MBA admission in 2024-2026 is scheduled for November 26. In this 60-day CAT preparation guide series by Careers360, we’ll be discussing the strategies for Day 21 to help you prepare effectively and excel in the CAT entrance test 2024.
This article will cover CAT questions on logarithms, modulus, and circular arrangements, as well as VARC questions. Logarithm and modulus problems can be quite challenging, and students sometimes struggle with them. Various difficult logarithm problems can be found online, and it's essential to engage in thorough practice sessions. Additionally, reviewing previous years' logarithm questions can be beneficial for your preparation.
Free Study Material: VARC | Chapter-wise Practice MCQs
Practice Questions: DILR | Quant | Most Scoring Concepts
Test: 20 Free Mock Test | 10 Year PYQs
This Story also Contains
Part 1: CAT 2024 QA Preparation Tips (Quantitative Aptitude)
Topic: Algebra (CAT Logarithm questions and Modulus)
Logarithm is an important part of algebra and is consistently asked in the CAT entrance exam. We will also cover a few Logarithm CAT questions and modulus. Students can also refer to the logarithm questions for the CAT pdf as well for more practice.
In the simplest terms, what a logarithm is:
If ax = N, then x = loga N.
Here ‘a’ is the base of the logarithm.
For Example:
102 = 100; So, 2 = log10100
A modulus is a function which always returns a positive value. The graph of the modulus function is symmetric about the y-axis.
For Example:
If |x| =2, then x can be 2 or -2.
Tips to solve CAT questions on Logarithm and Modulus
(a part of CAT Arithmetic questions) Learn all the properties related to Logarithm.
The following are some of the key characteristics of logarithms:
loga xy=loga x + loga y
loga x/y=loga x - loga y
logaxn = nloga x
logan xm =m/n logax
logax = 1/ logxa (Base Change Operation)
logaa= 1
loga1 = 0
a^(logax) = x
Some CAT common mistakes to avoid:
loga (x+ y) ≠ loga x + loga y.
loga xy ≠ (logax) (logay)
The logarithm to base 1 is not defined.
Questions of modulus can be solved by squaring both sides
For example:
If x =y, then x2 = y2 and we can solve accordingly.
Practice inequality problems based on logarithms.
Candidates preparing for the CAT should dedicate time to practice a wide range of inequality questions to ensure they're well-prepared for any variation that may appear on the exam.
The characteristic of a number is defined as
If log N = 4.73, then the characteristic of N is 4 and Mantissa is .73.
This property is used to find the number of digits in a given number.
i.e. Number of digits = characteristics + 1.
CAT 2024 Most Scoring Concepts- VARC, DILR & QUANT
Start your CAT journey today and download CAT 2024 most scoring concepts PDF, including study materials based on CAT previous year papers, CAT question papers, and CAT exam sample questions.
Download EBookFor example: find the number of digits in 212
log 212 = 12 log 2 = 12 x 0.3010 = 3.612
Therefore, the number of digits in 212 will be (3+1 = 4)
Importance of Logarithm and Modulus
Logarithms are used to solve exponential equations and hence can be used for analysis while designing software or hardware.
The modulus Function gives magnitude only irrespective of the direction of the variable.
In the CAT exam, 1-2 questions are expected from this function.
CAT Previous Year logarithm questions and questions on modulus for CAT:
Q1. For a real number a, if (log15a+log32a)/[(log15a) (log32a)] = 4 then a must lie in the range [CAT 2021, slot-3]
4 < a < 5
3 < a < 4
a > 5
2 < a < 3
Solution: (1)
(log15a + log32a)/[(log15a) (log32a)] = 4
⇒ 1/ log32a + 1/log15a = 4
⇒ loga 32 + loga15 = 4 (Using base change property)
⇒ loga(32x15) = 4
⇒ a4 = 32 x 15 = 480
Doing hit and trial;
24 = 16
34 = 81
44 = 256
54 = 625; clearly a4 lies between 256 and 625.
So, a must lie between 4 and 5.
Q.2
equals ____________ [TITA, CAT 2020]
Solution:
Find the value of the denominator first as follows:
(log2 4)2 = 4
Using properties of logarithm
log4 8 = log28/ log24 = 3/2
So, (Log48)3 = (3/2)3 = 27/8
Similarly,
log816 = log216/ log2 8 = 4/3
So, (Log816)4 = 256/81
Therefore, denominator becomes 4 x (27/8) x (256/81) = 128/3
So,
= (2x 4 x 8 x 16)/(128/3) = 24
Hence, the correct answer is 24.
Prerequisite:
Knowledge of Exponents
Knowledge of some basic functions
Knowledge of Linear and Quadratic Equation
References for Study (Theory):
For Properties go through NCERT class 11.
How to Prepare Quantitative Aptitude by Arun Sharma (7th edition)
Mission CAT (You-Tube)
References to Study (Practice):
https://iim-cat-questions-answers.2iim.com
Previous Year's Question Papers
Part 2: CAT 2024 Preparation Tips: CAT DILR tips (Logical Reasoning and Data Interpretation)
Topic: Circular Arrangement questions for CAT (LR)
Type 1: All Persons facing the same direction (Simple)
Directions: Study the following information carefully and answer the questions given below:
Bhuvan, Mohan, Kartik, Hina, Tina, Ramu, David, and Aastha are sitting around a circle facing the centre. Ramu is third to the right of Bhuvan. Hina is second to the right of Aastha who is second to the right of Ramu. Karthik is third to the right of Tina who is not an immediate neighbour of Hina. David is second to the left of Tina.
Q1: Who is to the immediate left of Mohan?
Ramu
Tina
Bhuvan
Kartik
Q2: Who is the third to the left of Bhuvan?
Bhuvan
Aastha
Kartik
Tina
Q3: Who is the third to the left of Hina?
Astha
Tina
Kartik
Ramu
Solution: From the given information, we can make the following figure.
Tricks: Use the Initials of the name while drawing diagrams.
Draw all possibility diagrams.
Ans 1: (d)
Ans 2: (b)
Ans 3: (b)
Type 2: Half are Males and Half are females
Direction: Study the following information to answer the given questions:
Asha, Binay, Chintu, Daman, Esha, Fatima, Gurmeet and Haresh are sitting around a circular table facing away from the centre where half of them are males and half are females. No two males or two females are immediate neighbours of each other.
Asha is the wife of Haresh. Asha sits third to the left of Esha. Binay sits second to the right of Daman. Daman is not an immediate neighbour of Asha or Esha. Haresh and Chintu are immediate neighbours of each other. Binay is not an immediate neighbour of his wife Fatima.
Q4: Which of the following is true about Gurmeet?
Gurmeet is a male
Gurmeet sits exactly between Fatima and Haresh
Gurmeet sits third to the left of Esha
None is true
Q5: Who sits third to the left of Binay?
Fatima
Haresh
Daman
Asha
Q6: How many people sit between Binay and Fatima when counted in an anti-clockwise direction from Binay?
One
Two
Three
Four
More than four
Solution:
Trick: Notice the important points first
Half are males and Half are females. No two males and no two females are together.
Do not consider a person male or female by their name. Haresh is male (Husband of Asha). Chintu should be female.
All are facing away from the centre:
Left: Anticlockwise
Right: Clockwise
Since Binay sits second to the right of Daman, Daman must be male as Binay is male.
So, male members are Haresh, Binay, Daman, and Esha
And female members are Asha, Fatima, Gurmeet, and Chintu
Since Daman cannot be a neighbour of Esha or Asha, Daman is at position 7, and Binay must be at 5. Haresh will be at 3. So, Chintu will be at 2 and Fatima should be at 8.
Gurmeet will be at 6.
The arrangement will look like
Ans 4: (d)
Ans 5: (a)
Ans 6: (b)
Type 3: Half facing Centre and half facing away from the centre
Direction: Study the following information carefully and answer the questions given below:
Eight persons A, B, C, D, E, F, G and H are sitting around a rectangular table in such a way that two persons sit on each of the four sides of the table. Half of them are facing the centre and the remaining half are facing away from the centre. Persons sitting on opposite sides are exactly opposite to each other.
D faces North (Towards the centre) and sits exactly opposite to H. E is to the immediate left of H. A and G sit on the same side. G is exactly opposite of B who is to the immediate right of C. A is sitting to the left of D.
Q7: From the following, who is facing South?
G
D
H
A
Ans: (C)
Q8: If G is facing centre, who is right of B?
G
C
F
A or F
Ans: (B)
Q9: Which of the following pairs of persons has both the persons sitting on the same side with the first person sitting to the right of the second person?
DF
CB
FC
Cannot be determined
Ans: (D)
Solution:
References for Study (Theory):
Verbal and Non-Verbal Reasoning by R S Aggarwal. (Basic)
CAT entrance test preparation-iQuanta (YouTube Channel)
References to Study (Practice):
Verbal and Non-Verbal Reasoning by R S Aggarwal. (Basic)
LRDI for CAT and GMAT by Nishit K Sinha. (Advance)
Previous Years CAT Question Papers
Part-3: CAT Exam Preparation 2024: CAT exam tips for VARC (Verbal Ability & Reading Comprehension)
Topic: To solve cloze tests based on articles, tenses, prepositions etc.
The Cloze test is a combination of fill-in-the-blank and reading comprehension. In this exercise, incomplete words must be filled in using the available options.
A cloze test can be based on the following:
Parts of Speech
Tenses
Articles
Prepositions etc
CAT Tips and Tricks to Solve Cloze Tests:
Read the passage in the CAT question paper thoroughly to get an idea about the flow of the passage.
Write down the key points as you read slowly.
Connect (link) the next sentence with the previous sentence. Reading articles, novels, or newspapers can help with this. Thus, cultivate a reading habit.
Look at the options to get the best word to fit in and eliminate the most unfit word first.
Check for grammatical mistakes, missing articles or prepositions, and other errors.
Attempt CAT mock tests.
CAT Exam Practice Questions on Cloze test
VARC CAT questions
You can better understand cloze tests by using the example below.
Direction (Q1-Q5)
Before the giant waves slammed into the coast in India and Sri Lanka, wild and domestic animals....(1)....to know what was about to happen.....(2)....fled to safety. According to eyewitnesses....(3)...., elephants screamed and ran for....(4)....grounds, dogs refused to go outdoors, flamingoes abandoned....(5)....low-lying breeding areas and zoo animals rushed into their shelters.
A. Seeming B. Were Seemed C. Seemed D. Seem
A. We B. Them C. Us D. They
A. Statement B. Accounts C. Explanations D. Narrations
A. High B. Higher C. Highest D. More high
A. our B. their C. theirs D. her
Ans:
(B) Were Seemed
(B) them
(D) Narrations is a suitable word.
(B) Comparative degree of high should be taken.
(B), since Flamingoes is plural.
References for Study (Theory):
Advanced English grammar by Wren and Martin
CAT Edurav (YouTube Channel)
References to Study (Practice):
How to Prepare for Verbal Ability & Reading Comprehension for CAT by Meenakshi Upadhyay and Arun Sharma (9th Edition)
https://www.800score.com/gmat-prep/prep-guide/sample-questions/
Practice CAT Sample Papers and CAT Previous Year Question Papers.
Free PDFs for CAT 2024 preparation
Frequently Asked Question (FAQs)
1. How can you approach solving a circular arrangement problem?
The steps to approach a circular arrangement problem are:
Identify any given constraints or conditions.
To simplify counting, fix one object to break the circular symmetry.
Use permutations of the remaining objects to find the number of distinct arrangements.
If there are extra constraints, adjust your arrangements accordingly.
2. What are some tips and tricks to solve cloze test problems?
Some tips and tricks to solve cloze test problems are:
Read the passage in the CAT question paper thoroughly to get an idea about the flow of the passage.
Write down the key points as you read slowly.
Connect (link) the next sentence with the previous sentence. Reading articles, novels, or newspapers can help with this. Thus, cultivate a reading habit.
Look at the options to get the best word to fit in and eliminate the most unfit word first.
Check for grammatical mistakes, missing articles or prepositions, and other errors.
Attempt CAT mock tests.
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Questions related to CAT
Have a question related to CAT ?
The National Academy of Legal Study & Research (NALSAR) University of Law in Hyderabad has 147 seats, with 25% of seats reserved for Telangana state candidates. There is no reservation for this category in central list so you can claim only for your state.so whatever serial no. Is provided in clat guidelines you should follow that only and don't worry this is just a procedure when you get selected you just need to submit the caste certificate only.
sadafreen356 07 September,2024
Hello Student,
Uploading the certificate number instead of the serial number of your category certificate in the CAT application may not immediately nullify your admit card or affect your admission. However, discrepancies in the application form could cause issues later during the verification process, especially at the time of admission.
To avoid potential problems:
Contact CAT authorities: It's best to reach out to CAT helpdesk or authorities via their official helpline or email. Explain the error and ask for guidance on correcting it.
Check for correction windows : CAT sometimes provides a correction window after the application process closes, allowing applicants to fix errors like these.
Document the issue: Keep records of any communications with the authorities regarding this issue, in case it needs to be referenced later.
By addressing it early, you can reduce the risk of complications during the admission process.
Thankyou.
Uploading the certificate number instead of the serial number of your category certificate in the CAT application may not immediately nullify your admit card or affect your admission. However, discrepancies in the application form could cause issues later during the verification process, especially at the time of admission.
To avoid potential problems:
Contact CAT authorities: It's best to reach out to CAT helpdesk or authorities via their official helpline or email. Explain the error and ask for guidance on correcting it.
Check for correction windows : CAT sometimes provides a correction window after the application process closes, allowing applicants to fix errors like these.
Document the issue: Keep records of any communications with the authorities regarding this issue, in case it needs to be referenced later.
By addressing it early, you can reduce the risk of complications during the admission process.
Thankyou.
Hridaya Rao 05 September,2024
Hey there! Welcome to the Careers360 team. That's quite a specific situation you've got there - let me see if I can help break it down for you.
So, you're from Telangana, did your MBBS in AP, and now you're wondering about your status in AP, right? It's a bit of a tricky one, to be honest. The local status and reservation policies can get pretty complicated, especially when you're crossing state lines.
From what I understand, your local status in AP might be a bit dicey since you're originally from Telangana. As for the BC-D reservation, that's even trickier because each state has its own list and criteria.
Here's what I think, but take it with a grain of salt:
1. Your local status in AP: This might depend on how long you've been in AP and if you meet their residency requirements. You'd need to check the specific rules for AP.
2. BC-D status in AP: Even if you get local status, your BC-D certificate from Telangana might not directly apply in AP. Each state has its own backward classes list.
3. Open category: If neither of the above works out, you might indeed have to go for the open category seats in AP.
But listen, don't take my word as gospel. These rules can be super complex and change often. Your best bet would be to check with the AP medical education department or maybe the AP Public Service Commission. They'll have the most up-to-date info.
Also, why not chat with some of the seniors here at Careers360? They might have dealt with similar cases before and could have some insider tips. You can also have a look at our College Predictor for more details.
Let me know if you want to bounce around some ideas on how to get more concrete info on this. We could make it a little project - might be useful for other students too!
Jefferson 04 September,2024
Unfortunately, you cannot change your CGPA after submitting the CAT 2024 form. The information provided in the form is final and cannot be modified.
While some institutions might allow you to update your CGPA during the admission process, this is not always the case. It's best to assume that the information you provided in the CAT form will be the basis for your application.
If your final CGPA is significantly higher than what you initially reported, you might want to consider retaking the CAT exam in the future. This will give you a chance to improve your score and provide a more accurate representation of your academic abilities. However, this is a decision that should be made carefully, as it will require additional time and effort.
It's important to consult with the admissions offices of the institutions you're interested in to determine their specific requirements and policies regarding CGPA updates. They can provide you with the most accurate and up-to-date information.
While some institutions might allow you to update your CGPA during the admission process, this is not always the case. It's best to assume that the information you provided in the CAT form will be the basis for your application.
If your final CGPA is significantly higher than what you initially reported, you might want to consider retaking the CAT exam in the future. This will give you a chance to improve your score and provide a more accurate representation of your academic abilities. However, this is a decision that should be made carefully, as it will require additional time and effort.
It's important to consult with the admissions offices of the institutions you're interested in to determine their specific requirements and policies regarding CGPA updates. They can provide you with the most accurate and up-to-date information.
monag2673 03 September,2024
Hello Student,
For the CAT (Common Admission Test) exam form, when asked about your education status, you typically have two options:
1. Completed Graduation: This option is for students who have completed all requirements of their undergraduate degree, including passing the final exams and completing any mandatory internships or practical training.
2. Pursuing Graduation: This option is for students who are still in the process of completing their degree requirements, including pending internships, final projects, or exams.
Since you have passed your final exams but have not yet completed the mandatory internship, you should choose the option "Pursuing Graduation." This accurately reflects that your degree requirements are still in progress due to the incomplete internship.
Thankyou. I hope this information helped you
For the CAT (Common Admission Test) exam form, when asked about your education status, you typically have two options:
1. Completed Graduation: This option is for students who have completed all requirements of their undergraduate degree, including passing the final exams and completing any mandatory internships or practical training.
2. Pursuing Graduation: This option is for students who are still in the process of completing their degree requirements, including pending internships, final projects, or exams.
Since you have passed your final exams but have not yet completed the mandatory internship, you should choose the option "Pursuing Graduation." This accurately reflects that your degree requirements are still in progress due to the incomplete internship.
Thankyou. I hope this information helped you
Hridaya Rao 03 September,2024
Popular CAT Questions
Directions for question :
M/s Deloitte Touche Tohmatsu Limited, one of the top four audit and accounting firms in the world with headquarters at London, UK, and with an operational presence in 153 countries, hires Management Trainees (MT) from all the premier management institutes of India thrice every year, in the months of January, May and September.
Each new group of Management Trainees (MT) have to go through a four month rigorous training schedule, after which they have to pass through a test consisting of a written assessment and a case-analysis. The top hundred ranked Management Trainees (MT) based on the performance in the test are confirmed as Management Executives (ME). The rest are given the opportunity of undergoing the training for four months one more time along with the next batch of Management Trainees (MT) and then passing through the subsequent test consisting of the written assessment and case-analysis. The Management Trainee (MT) who fails to get confirmed as a Management Executive (ME) the second time is fired.
The scatter-graph below depicts the number of Management Trainees (MT) at Deloitte taking the tests from January 2020 till May 2022, and the vis-à-vis hired Management Trainees (MT) at Deloitte who were fired :
It is also known that for the month of September 2019 at Deloitte, 96 hired Management Trainees (MT) failed to be confirmed as a Management Executive (ME) the first time, and that 36 hired Management Trainees (MT) were fired.
Question :
In which test did the minimum number of Management Trainees (MT) get confirmed as a Management Executive (ME) in the second attempt ?
Option: 1
September 2020
Option: 2
May 2021
Option: 3
January 2021
Option: 4
January 2022
Directions for question:
The bar-graph given below shows the foreign exchange reserves of Nepal (in million Rupees) from 2014 to 2021. Answer the following questions based on the graph :
Question:
What was the percentage increase (rounded to the nearest integer, if deemed necessary) in the foreign exchange reserves in 2020 over 2016 ?
Option: 1 None
Option: 2 None
Option: 3 None
Option: 4 None
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