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 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?
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)?
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?
- 4 of the 10 dorms needing repair are women’s dorms and need a total of Rs. 20 Crores for repair.
- 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)?
Q 16) Which of the following is a women’s dorm?
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:
- The eight friends were seated in six different rows.
- They occupied 3 Window seats, 4 Aisle seats, and 1 Middle seat.
- 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.
- 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.
- Gargi was sitting next to Kikira, and Manik was sitting next to Jayanta.
- 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.
Look at the anchor condition — it’s purely a mathematical condition.
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.
As in if you start with the arrangement 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 boundary conditions, that is the lower side first.
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 is 500 then you cannot have an average of over 500!
So it has to be three 1000s.
Once you have three 1000s how can you make the remaining 1600 using 4 numbers?
- Option 1 — 500, 500, 400, 200
- Option 2 — 500, 500, 300, 300
- Option 3 — 400, 400, 400, 400
The next big condition says that you have three people in consecutive seats with 3 different prices, so they are either 3 different aisles or three different windows.
So the only combinations can be 1000, 500, 400 or 1000, 300, 200.
This straightway eliminates options 2 and 3.
Once you do this the rest of the set opens up easily.
- 4 Aisle, 3 Windows and 1 middle
- You need 3 seats with same letters and 2 seats with same letters with different numbers
- You have 1000 (A/W), 1000 (1000A/W), 1000 (A/W), 500 (A), 500 (A), 400 (A) and 200(W)
- Since you have only two different values for Windows — 1000 and 200 — it has to be 3 consecutive Aisles and 2 Consecutive Windows.
- If you have 2 consecutive windows but only one value of 200, then it means that one guy paid and the other had a seat that
- wasn’t chargeable and was immediately after the paid 200 seat.
- 200s are from 14 to 20, so the two consecutive seats have to be 20W and 21W, Prodosh and Tapesh
- The three consecutive aisle seats with different rates have to be 500, 400 and 1000 the only possible combination is 10A, 11A & 12A — Jayant (500), Ajit (400) & Byomkesh (1000) (I have used ‘A’ to represent an aisle and not the letter of the seat).
- Out of the 7 numbers you have assigned 4
- The three left are 1000, 1000 and 500.
- Two more people are next to each other and they have to be the two 1000s
- Manik is next to Jayanta but if he takes the middle he will be not paying anything but we already have one person who is not paying anything.
- So he is sitting next to Jayanta but on the aisle next to him by paying 500
- All 4 Aisles are done, and 2 out of 3 Windows are done and 1 middle is left.
- So, Gargi and Kikira occupy a Window and a Middle that cost 1000 each, in either row 1 or row 13
Q.25) In which row was Manik sitting?
Q.26) How much extra did Jayanta pay for his choice of seat?
- Rs. 300
- Rs. 400
- Rs. 500
- Rs. 1000
Q.27) How much extra did Gargi pay for her choice of seat?
- Rs. 300
- Rs. 400
- Rs. 1000
Q.28) Who among the following did not pay any extra amount for his/her choice of seat?
You have all the answers and you are only left wondering who came up with the names Prodosh and Kimura!
If you see, unlike a typical LR set you can solve all the questions without drawing (This is what makes it a classic Math-LR Set.
Some of you might have cracked this set using drawing. I am not saying you should not draw but I am saying is that you should add the skill of putting Math before LR to your repertoire.
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.