# How to crack the DI-LR section of the CAT – II

In the previous post, we took up 6 of the 8 sets from the DI-LR section CAT 2017 Slot 2 and took a call on which ones solve and also looked at the best way of solving the same. In this post, we will look at the remaining two sets and also what is making the DI-LR sections on recent CATs unique.

## It’s no longer DI-LR but Math-LR!

One of the things I like to do when I teach is to show students the inner workings of the machine that is a question or a set. As the old adage goes, one should teach people to fish rather than give them fish. To do that one should first know more about fish than about fishing!

So I took a lot of time looking at these DI-LR sets, trying to figure out why they are creating problems for test-takers.

In cricket, we often have mystery bowlers springing up on to the scene who in a short span of time wreak havoc on batsmen of all stripes, most of them also disappear suddenly — the Lankan spinner Ajantha Mendis epitomized this phenomenon.

Why do they cause so much destruction? Because they defy expectation and test a different kind of skill or mindset that most batsmen take time to figure out.

The DI-LR sets have been defying the two expectations that test-takers have come to expect when they hear the word DI-LR — calculation and reasoning.

All of you know by now that calculation in the classical sense of breaking numbers down has come down. But what most test-takers haven’t seen is that reasoning in the classical sense has also disappeared.

When we think reasoning we think of it in terms of solving puzzles.

But if we take a look at all the sets, barring The Pizza Set, on the DI-LR section of CAT 2017  Slot 2, they have moved to a new area — Mathematical Reasoning or reasoning in a Math context.

What do I mean by this?

If we can think of an LR set as an equation where the variables are on the LHS and the conditions are on the RHS, earlier the RHS was pure logical constraint, now the RHS is a number!

The LHS has always been the various possibilities and using the RHS we eliminated possibilities.

When the RHS becomes a number, the LHS also becomes a series of numerical possibilities!

Let us look at the sets, which we discussed in detail in the previous post, to get a fair idea:

The Old Woman and her Wealth

The amount of 210 lakhs had to be divided equally and hence the RHS becomes 70 each. Now you have to try out different number combinations, eliminate the ones that contradict conditions and arrive at the answer. This is how we solved the first two questions in the set, we eliminated numbers.

What about questions 3 and 4 in that set?

Q.11) The value of the assets distributed among Neeta, Seeta and Geeta was in the ratio of 1:2:3, while the gold coins were distributed among them in the ratio of 2:3:4. One child got all three flats and she did not get the house. One child, other than Geeta, got Rs. 30 lakh in bank deposits. How many gold coins did the old woman have?

1. 72
2. 90
3. 180
4. 216

Q.12) The value of the assets distributed among Neeta, Seeta and Geeta was in the ratio of 1:2:3, while the gold coins were distributed among them in the ratio of 2:3:4. One child got all three flats and she did not get the house. One child, other than Geeta, got Rs. 30 lakh in bank deposits. How much did Geeta get in bank deposits (in lakhs of rupees)?

Ans. 20

It is so obvious that they are purely Arithmetic questions!

There is no way anyone can argue that the two questions cannot be part of the QA section. Just because a question is long does not mean that it becomes an LR question.

The Dormitory Set

The first two questions were pure LR questions but what about the next two?

1. 4 of the 10 dorms needing repair are women’s dorms and need a total of Rs. 20 Crores for repair.
2. Only one of Dorms 1 to 5 is a women’s dorm.

Q 15) What is the cost for repairing Dorm 9 (in Rs. Crores)?

Ans. 3

Q 16) Which of the following is a women’s dorm?

1. Dorm 2
2. Dorm 5
3. Dorm 8
4. Dorm 10

20 Crores has to be divided into 4 dorms and the numbers available are 1, 2, 3, 4, 5 and 6.

Only those with a good grasp of averages can see that since the maximum number you have is 6, you have to first give as many 5s and 6s as possible.

This again pushes the set into the realm of Math LR.

The Cup of Tea

This is a simple set but the anchor condition gives you a set of 5 pairs of numbers of which you have to eliminate 4 using other numerical conditions.

None of these sets were pure LR sets that did not involve numbers.

The two sets that are left will illustrate even more clearly the concept of Math-LR set.

## The Airplane Seating

Eight friends: Ajit, Byomkesh, Gargi, Jayanta, Kikira, Manik, Prodosh and Tapesh are going to Delhi from Kolkata by a flight operated by Cheap Air. In the flight, sitting is arranged in 30 rows, numbered 1 to 30, each consisting of 6 seats, marked by letters A to F from left to right, respectively. Seats A to C, are to the left of the aisle (the passage running from the front of the aircraft to the back), and seats D to F, are to the right of the aisle. Seats A and F are by the windows and referred to as Window seats, C and D are by the aisle and are referred to as Aisle seats while B and E are referred to as Middle seats. Seats marked by consecutive letters are called consecutive seats (or seats next to each other). A seat number is a combination of the row number, followed by the letter indicating the position in the row; e.g., 1A is the left window seat in the first row, while 12E is the right middle seat in the 12th row.

Cheap Air charges Rs. 1000 extra for any seats in Rows 1, 12 and 13 as those have extra legroom. For Rows 2-10, it charges Rs. 300 extra for Window seats and Rs. 500 extra for Aisle seats. For Rows 11 and 14 to 20, it charges Rs. 200 extra for Window seats and Rs. 400 extra for Aisle seats. All other seats are available at no extra charge.

The following are known:

1. The eight friends were seated in six different rows.
2. They occupied 3 Window seats, 4 Aisle seats, and 1 Middle seat.
3. Seven of them had to pay extra amounts, totaling to Rs. 4600, for their choices of seats. One of them did not pay any additional amount for his/her choice of seat.
4. Jayanta, Ajit, and Byomkesh were sitting in seats marked by the same letter, in consecutive rows in increasing order of row numbers; but all of them paid different amounts for their choices of seats. One of these amounts may be zero.
5. Gargi was sitting next to Kikira, and Manik was sitting next to Jayanta.
6. Prodosh and Tapesh were sitting in seats marked by the same letter, in consecutive rows in increasing order of row numbers; but they paid different amounts for their choices of seats. One of these amounts may be zero.

Q.25) In which row was Manik sitting?

1. 10
2. 11
3. 12
4. 13

Q.26) How much extra did Jayanta pay for his choice of seat?

1. Rs. 300
2. Rs. 400
3. Rs. 500
4. Rs. 1000

Q.27) How much extra did Gargi pay for her choice of seat?

1. 0
2. Rs. 300
3. Rs. 400
4. Rs. 1000

Q.28) Who among the following did not pay any extra amount for his/her choice of seat?

1. Kikira
2. Manik
3. Gargi
4. Tapesh

Look at the anchor condition — it’s purely a mathematical condition — condition 3.

Why is this the anchor condition — an anchor condition is a boundary condition that puts constraint on all the stakeholders, it does not pertain to one specific stakeholders.

You might ask why then are conditions 1 and 2 not the anchor conditions. Well, they do not bring in a specific constraint that will result in deductive breakthroughs — for example, the total score in R2 and twice that of the total score in R1 — they are very general like conditions 1 and 2 — conditions that you have to keep in mind but will lead to any additional breakthroughs.

Just like 210 lakhs, and 20 crores in the previous sets, in this one, it is 4600.

You have to divide 4600 among 7 people using the numbers, 1000, 500, 400, 300 and 200.

The biggest mistake that test-takers can make while solving this set is to start by trying to arrange people into seats and then try to fit the Math into it. Nothing can lead you to waste more time and get stuck than this. And if this set came right at the beginning for you then you have had it.

What you need to do is to start by changing your mindset — put the Math before the LR. The way Aravinda De Silva, for example, was very successful against Anil Kumble because he did not treat him like a spinner but like a medium-pacer.

How do you go about putting the Math first?

4600 divided by 7 means an average of around 650. Since the average is closer to 500 than to 1000 there will be more 500s and under than 1000s. So more 500s than 1000s out of 7 means the division can be 4-3 or 5-2. It is always best to test the extreme cases, 5-2 instead of 4-3.

Can you have two 1000s? If you have two 1000s then the balance is 2600 over 5 people making the average over 500. If the maximum value available is 500 then you cannot have an average of over 500!

So it has to be three 1000s, and the rest of the 1600 over 4 people.

The next big condition says

Jayanta, Ajit, and Byomkesh were sitting in seats marked by the same letter, in consecutive rows in increasing order of row numbers; but all of them paid different amounts for their choices of seats. One of these amounts may be zero.

This is how the pricing looks.

 R A M W 1 1000 1000 1000 2-10 J – 500 J – 300 11 A – 400 A – 200 12 B – 1000 1000 B – 1000 13 1000 1000 1000 14-20 400 200 21-30

From this we know that the only possible option for three consecutive rows for Jayant, Ajit, Byomkesh with different pricing are 10, 11 and 12 aisle or window.

The next condition:

Gargi was sitting next to Kikira, and Manik was sitting next to Jayanta.

The first question asks, in which row was Manik sitting?

Since Jayanta is sitting in row 10 and Manik is sitting next to him it has to be in row 10, so we have the answer to one question in the bag. (Note that next to him need not mean in the middle seat. It can be that they are sitting on two aisle seats in row 10)

We now go back to the numbers and know that we have to use three 1000s.

Jayanta, Ajit and Byomkesh, 10, 11, 12  be it aisle or window, use up only one 1000.

The two 1000s are there in rows 1 and 13, and we know that Gargi and Kikiri are the only two other people next to each other so they have to use the two 1000s either in row 1 or row 13.

The third question asks how much extra did Gargi pay for her seat, we have the answer now, Rs.1000.

The next condition:

Prodosh and Tapesh were sitting in seats marked by the same letter, in consecutive rows in increasing order of row numbers; but they paid different amounts for their choices of seats. One of these amounts may be zero.

If we go back to the pricing table, we can see that the only two consecutive row with different pricing left are rows 20 and 21, aisle or window. So the only options left for Prodosh and Tapesh are 20 and 21 in that order. So Tapesh is the one who did not pay for his seat, which is exactly what the last question is asking.

Manik is sitting next to Jayanta in row 10, but it cannot be in the middle seat since the middle seat is free and, the only free seat has been used by Tapesh.

So the only way Manik and Jayant can sit next to each other are by sitting in two aisles in  row 10.

This means that J, A and B are in aisles of 10, 11, and 12 in that order.

The only question left is how much Jayanta pay for the seat, aisle in row 10 costs Rs.500.

Since we have come this far, we can complete the set as much as we can since they could have also asked other questions as well based on the same information — how much did Prodosh pay extra?

• Jayanta — 500 (A) Manik — 500 (A)
• Ajit — 400 (A)
• Byomkesh — 1000 (A)
• Gargi — 1000 (W/M) Kikira — 1000 (W/M)

Prodosh is in row 20 aisle or window.

The total is now 4400, we have 200 left, so Prodosh has to be in the window seat in row 20, with Tapesh behind him in a window seat in row 21.

## The Fingerprint Set

A high-security research lab requires the researchers to set a passkey sequence based 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.

Q.29) 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?

Enter your response (as an integer) using the virtual keyboard.

For any given key if two letters can be out of place then how many ways can we choose those two letters out of 5 letters? 5C2 or 10 pairs can be out of place and still be valid. So including the original combination, one can have 11 valid passkeys.

This entire set is built on the bedrock of P&C. It is no surprise that my colleague VK, whom most of you would have seen during the LMTC sessions or know from his website vkpedia, found this set very easy since he is a champ at P&C.

On such a DI-LR section, those who are naturally good at QA, especially the Number Systems experts should have cleared the cut-offs without much trouble. Those who are primarily good at VA-RC, Arithmetic, and LR, would have struggled or just fallen short of the cut-off.

## There are no closed sets

Another feature of these sets is that none of them are closed.

• The Pizza Set — With the given information you still do not know anything about EC or DD
• The Dormitory Set — You do not know where rooms 2 and 10 fit in or the specific costs of rooms, 1, 3, 5 & 9
• The Old Woman and her Wealth — everything is open
• The Chess Set — everything is open
• A Cup of Tea — the places of 4 cups are unknown
• The Airplane Seating — the rows of Gargi and Kikira or the specific seat numbers of the aisle people.
• The Fingerprint Set — everything is open

It is now easy to see why these sets are causing trouble or taking a lot of time — they are Open Sets based on Math and this is the exact opposite of what test-takers like and want — Closed sets based on Arrangement.

## Developing the fast-twitch muscle in the brain

One of the key requirements to be good at solving LR sets such as The Dormitory Set or even The Airplane Set is to be able to quickly list alternatives, keep moving from one condition to the other and keep eliminating options.

This is very different from LR sets where you do not have to list alternatives but only work the conditions.

I find the former skill very similar to solving Sudoku. One has to keep moving very dynamically across cells and keep arriving at the number by the process of elimination.

Even before I began solving all of these sets, I felt that I needed to get my brain warmed up and supple. I felt that I since I haven’t solved LR sets in a while I would need to get the blood pumping through the gray cells. So I did what works best for me a few Sudoku sets on my phone till I knew that I was moving absolutely smoothly without getting stuck.

My favourite batsman, Brian Lara, was known to have a net or play some TT during the breaks between innings, especially if he was in good nick and scoring fast, he just didn’t want to let go of the rhythm and quick reflexes.

I would strongly advise solving 3 medium-level Sudoku sets a day targeting an average time of 4 mins per set. On every third day, you should take up a difficult set so that you push yourself a bit harder.

## Don’t expect sets to yield with you on auto-pilot

The brain like the body wants to be on auto-pilot mode. This means that it is traversing familiar territory and hence will execute the motions it has perfected already with considerable ease. Think of this as playing on an ODI or T20I pitch where the ball and the bowler cannot surprise you because the pitch does give them any purchase.

And what is tough is usually so because it is unique. And unique means that you cannot be on autopilot. Think of this as batting on a worsening pitch in the fourth innings — the same limited overs heroes struggle to chase down 250 in a day (it’s not the format but the skill sets that have become limited, which why our Indian team manager’s talk on recent international test tours about intent is doesn’t translate into runs).

If you make this change in your head then you know what you are up against.

## The ability to think deeply and with clarity

Chasing down a total, not just surviving, on a fourth innings pitch means that you have to concentrate hard.

The ability to think deeply means that when you read a set you are figuring out the complexity of the set and really understanding it in terms of how to represent it.

The core skill would be the ability of your brain to focus deeply and for long without getting tired or distracted.

The best way to do this by ensuring that all your prep sessions are for 3 hours with your phone switched off. If you are prepping with your phone on then I am afraid that you are doing yourself a great disservice.

I always know how likely I am to do a set correctly and in good time based on how fresh and relaxed my brain is feeling.

So one of the things that you should ensure over the next two months when you will be taking a lot of tests is that you conserve your mental energy.

While you might think that watching your favorite TV show or browsing social media for an hour or so is relaxing, it is taxing your eyes with light from the screen. I would rather suggest a nap or a walk as the ideal rest or break.

Also, do not forget to do some form of exercise regularly since it increases the oxygen supply in the system. I know of a few people for whom none of this will matter but as I said I know only a few and I am not one of them.

There is no point in looking for exactly these kind of sets to solve since you will never get mirror replicas. I would rather suggest that you resolve all the sets from the SimCATs keeping in mind the following things:

• rate the set before solving
• figure out the best way of representing instead of blindly jumping to draw something
• identify the anchor conditions and learn to work with them
• keep moving between conditions and eliminating instead of getting stuck in your table
• identify the Math-LR sets and execute putting the Math first

Becoming good at something is always about doing 10 small things right. Most of the time people think it is one big thing that they lack and that couldn’t be farther from the truth.

1. Shubham Jain says

Sir why didn’t we consider the possibility of 400, 400, 500, 300 in the first set?

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• You are right Shubham we have to list that option and eliminate it since two 400s are separate by the two 1000 rows.

Thanks for pointing it out.

All the best!

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2. Akhil k says

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• Nothing to comment on except that the number of questions will come down, which anyone can tell.

No point wasting time and mental energy speculating about the possible changes, which is a news channel/anchor’s job, since they will release more details this weekend, we can utilise our time to get better at one of the sections.

All the best!

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Hi sir,
Your analysis on how to approach DI-LR-MR questions is very useful.
Thanks a lot.
Sir my doubt is that in the above old woman question why didnt you consider the gold coins for the 1st 2 questions because since the number of gold coins are not mentioned the woman could have adjusted the defficiency in wealth for her daughters with any number of gold coins ?
This question has been disturbing me a lot lately.

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Whenever things disturb you a lot it means only one thing — there is a piece of information that you have forgotten and are you are then going around in circles trying to solve without this piece of information.

Read the second sentence of the question again.

Question
Among the three, Neeta received the least amount in bank deposits, while Geeta received the highest. The value of the assets was distributed equally among the children, as were the gold coins. How much did Seeta receive in bank deposits (in lakhs of rupees)?

All the best!

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4. Akshat says

Sir will LMTC round 2 will be held differently with change in cat pattern. So those who attended first round should attend 2 one also?

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Yeah, we will incorporate the implications fo the full changes, which will be announced this weekend, into the next edition of the LMTC.

The bulk of the content in terms of methods of selecting will remain the same, the time management portion will have to be tweaked.

So yeah, no harm in attending again or just watch the recording for the relevant portion.

All the best!

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5. Aswini S. Kamath says

sir, can you please provide the answers of the questions you have given in the article? I approached the question very differently, and i am finding it difficult to compare the answers.

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• These are CAT 2017 Slot II questions, you can find all sets and answers online.

I have added the options(where applicable) and answers to the questions in the post.

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6. Aman Agarwal says

Sir firstly thanks a lot for all your articles they’ve been really helpful.
I am extremely anxious and want to know if I can get the SP Jain profile based call for 2021-23.

My profile is as follows –

Xth – 97 (Stood 3rd in school)

XIIth – 93.4 (Topper of Commerce Stream, Best Scholar of Commerce Stream, awarded for the highest marks in Economics subject and for General Proficiency)

Bcom from Pune University- 59.3% (Still in final year of graduation. Low marks because of focus on CA and college switch due to which I missed internals)

Cleared first two levels of CA in the first attempt and interned in the Audit department for 4 months at Kirloskar Oil Engines Ltd. But now I have left CA and I want to pursue MBA in Marketing as I’m interested in it. I’ve completed the Google Digital Marketing Course. I’m an extrovert and love communicating with people. I’m also creative and hence want to pursue a career in Marketing.

ECA –

1. Started a dance academy and managed it on weekends with my CA internship.
2. Completed German A-1 level.
3. I have a YouTube Channel where I post dance videos and it has a reach of almost 20k. I also shoot and edit videos on my own.
4. Won a Dance competition which had 100 participants.
5. Taught children Maths and English at an NGO.
6. Certified in Information Technology (including MsExcel, Ms Word etc) and Soft skills as a part of CA curriculum.

I still have a month or two left for the form to be filled. Due to covid I lost my chance of having a better graduation score because exams haven’t been conducted yet. Hopefully if they’re conducted in October and result is out in November I’ll have a better profile before form filling ends.

But as of now what are my chances of getting a call for Marketing sir? If not should I mention Finance as first preference and later will I be allowed to switch to Marketing?

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• Hi Aman,

You have a decent profile as far as X, XII and ECAs go.

You have to apply to the specialization you are interested in, you cannot switch later.

The profile-based call requires that you score only an 85 percentile on the CAT, this means that your academic profile needs to be exceptionally good so that they know that you will be on par with those who get score-based calls at 95 percentile.

You have a slim chance of getting a call for Marketing, the only hitch being the low Grad Marks.

Go ahead and make a great application, you lose nothing and can still get a score-based call later (not getting profile-based call does not mean that your application is rejected).

Hope this clarifies,

All the best!

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• Cat aspirant says

Thank you so much for the reply. Sir, my mental health is deteriorating by overthinking and self degradation since a year. I was in Symbiosis for Bcom and due to attendance issue I had to leave it and take up a normal Bcom college for CA but I ended up leaving CA now and I feel I neither have a good college nor marks. On top of this exam postponement due to covid and me leaving CA with only final left are the things that are stopping me from studying peacefully to my best potential. Given this career switch I feel I just need to stabilize by getting into a decent B school for Marketing and I’m giving up by accepting my poor performance in mocks often thinking that Top B-schools won’t accept me due to incomplete CA and low grad scores. Sir what can be my realistic Target Bschool so that I have a clear goal and I’m able to perform better?

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• Hi Aman,

Given your profile, you need to look at what is the best post-MBA scenario since MBA always offers a 2.5 jump on your current earning capacity and role.

So I feel a salary of 10 LPA post-MBA is a decent proposition. Apply to schools that have average salaries in this range.

You can lose your sleep over your choices or let mistakes be forgotten memories and go ahead with what you can control.

Trust me if you can turn this phase around, it will hold you in good stead for the future, it is better that you face these tough challenges early in life and not later.

Hope this helps,

All the best!

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7. Ankit Debnath says

Hi sir ,
In the airplane set how can we mathematically negate the possibility of two window seats being occupied are 1000 and 200 ?

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8. thegoodfornothingguy says

Hi Sir ,
In the airplane set how could you negate the possibility of two window seats being occupied are 1000 and 200?

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9. Shubhangi says

Hello Sir,

I have been reading your blogs and following most of the strategies you suggested. I am facing a problem that I miss out or misread some crucial information in the DILR sets and also in quant questions sometimes and keep on spiraling around because I have rated the set 10 and yet I am stuck. I know that this set is quite easy still miss that one information which unlocks the set. No matter how many times I read it again, I’ll only interpret what my brain has captured in the first go. Please give some suggestions on how to improve on that.

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• Hi Shubangi,

A simple way of enforcing this can be to put your pen/pencil down while reading the question and only picking it up after.

The hurry to solve and jumping into it with partial information results in your continually going around in circles with the approach you started with using the partial information.

Slow down.

Hope this clarifies,

All the best!

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10. Vignesh T says

hello sir . can you make a session for LRDI Time planning according to the new pattern?

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11. SHITIJ MAHAJAN says

In the airplane set, it says “For Rows 11 and 14 to 20, it charges Rs. 200 extra for Window seats and Rs. 400 extra for Aisle seats. All other seats are available at no extra charge.”
So shouldn’t Prodosh and Tapesh be in rows 20 and 21 respectively? (Window seat in row 20 costing Rs. 200 and that in row 21 free of charge)

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• Hi Shitij,

Yep, thanks for pointing it out. I missed the “to 20” bit.

One of those lucky edges that that landed safely :-).

All the best!

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12. harshit nigam says

sir i m not able to attend any of the DI SETS
i can give a time to LR SETS but not in di and i m facing problem in cut off
how to attend di questions sir
even in my past 10 sim cats i was very much week in di

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• Hi Harshit,

I am covering all of this in today’s Last Mile To CAT DI-LR session, all IMS students, including Test Series students, can attend the session.

All the best!

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13. Ayushi Sharma says

Hello Sir,
Would LMTC-2 be uploaded on the portal ?

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14. A JYOTHEESWAR REDDY says

hi sir,
A lot many possibilities for a set, how it an be eliminated sir?

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15. Prakash says

Hello sir, could you please provide me the link of LMTC-2 session here?

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• Hi Prakash,

All the LMTC-2 sessions are available on the CHANNEL Tab of myIMS.

All the best!

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