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Master Logarithm and Modulus, PYQs for Circular Arrangement Problems for Top Scores- Day 21
Edited By Team Careers360 | Updated on Sep 19, 2024 02:13 PM 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 | DILR | Quant | Chapter-wise Practice MCQs
CAT 2024: CAT'23 Official Question with Solutions (Slot 1, 2, 3)
Test: 20 Free Mock Test | 10 Year PYQs | Most Scoring Concepts
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 Equations
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
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Questions related to CAT
Have a question related to CAT ?
The student cannot join the postgraduate MA program directly in the second year of the MA after completing the MBA.
Universities generally expect students to begin the first year of a masters' program even though they had qualifications at the level of a bachelor's degree. The university's curriculum along with the courses are planned to give an in-depth knowledge of the subjects.
But you could opt for:
Postgraduate Studies:
Research Career: In case research interests you, then you can pursue a Ph.D. in your specific interest.
Specialized Master's Programs: Find any specific master's course that supports the career goal.
Professional Certifications:
Make a professional certification in CFA, CA, or FRM to enhance the professional skills and better opportunities in the career field.
Job Entry via MBA
After gaining an MBA from a renowned institution, it's possible to get entry into the corporate world where the diversity in the career field is assured.
In the end, it would depend on what you would like and what you are particularly interested in. It will be better if you take a suggestion from your academic advisor or career counselor.
Samprikta Mondal 13 November,2024
Hello Pratik,
If your family income exceeds 8 LPA, it will affect your eligibility for the NC-OBC category under the CAT reservation rules. The NC-OBC category requires that the family income should be below 8 LPA to qualify. If you anticipate that your income will exceed this threshold, you should update your status and notify the CAT authorities .
Here's what you can do:
-
Email the CAT authorities : Inform them about the potential change in your income status and request to be considered under the General category, if applicable. You should do this before the examination or any further processing, as your eligibility for the OBC category depends on the income criteria.
-
Documents and Proof : Make sure you have a valid OBC certificate and any relevant documentation regarding your family income, in case they require verification. Also, be aware that if your income exceeds 8 LPA, you might need to apply under the General category, as the OBC-NC reservation is no longer applicable.
-
General Category Consideration : If your application is accepted as General, you will be evaluated based on the General category criteria, including cutoffs and ranking.
To summarize, notifying the CAT authorities is the correct approach to avoid discrepancies later, and if your income is above the threshold, you will be treated as a General candidate for the admissions process.
For more details about CAT exam you can check out an article by Careers360 whose link is given below:
Link: https://bschool.careers360.com/exams/cat
I hope this answer helps you. If you have more queries then feel free to share your questions with us we will be happy to assist you.
Thank you and wishing you all the best for your bright future.
kumardurgesh1802 08 November,2024
Hi Shreya ,
Having a tattoo on your wrist should not create a problem during the CAT exam as long as it does not contain any content that violates exam rules , such as communication-related symbols , unauthorised messages or any text resembling formulas or answers .
For a safe side , it is recommended :
1. Inform the Invigilators : Let them know about your tattoo during the identification check , so there are no misunderstandings .
2. Follow the Guidelines : Ensure you follow all instructions regarding permissible items and dress code on the exam day .
Hope this helps you .
ALL THE BEST .
Mitali Sharma 09 November,2024
To know about this please prefer our college predictor
Sumit Mishra 07 November,2024
Hello,
Yes, you can also join IIMs two years after graduation, depending upon the justification in interviews and your performance in entrance exams. If you are not sure about CAT, try those other management exams less hard:
Common Management Admission Test: Easier than CAT; 4-5 months of continuous preparation will suffice.
MAT : Much easier and takes place thrice a year.
SNAP (Symbiosis National Aptitude Test): A bit easier than CAT, apt for Symbiosis Institutes.
Xavier Aptitude Test or XAT : Hence, easier than CAT but the unique decision-making section.
Use exams like CMAT and MAT as a challenge to be competitively prepared. This can be given about 4-5 months, along with a few rounds of mock tests and smart studying.
Deepti Singh 06 November,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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