Great Lakes - PGPM & PGDM 2025
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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
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.
(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
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.
For 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)
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.
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.
Knowledge of Exponents
Knowledge of some basic functions
Knowledge of Linear and Quadratic Equation
For Properties go through NCERT class 11.
How to Prepare Quantitative Aptitude by Arun Sharma (7th edition)
Mission CAT (You-Tube)
https://iim-cat-questions-answers.2iim.com
Previous Year's Question Papers
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)
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)
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:
Verbal and Non-Verbal Reasoning by R S Aggarwal. (Basic)
CAT entrance test preparation-iQuanta (YouTube Channel)
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
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
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.
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.
Advanced English grammar by Wren and Martin
CAT Edurav (YouTube Channel)
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.
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.
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.
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.
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!
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