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This is the third set under the CAT 2016 Sprint Preparation Series – LRDI 3. During these last 5 days, we will be covering around 300 questions that we expect to come across in CAT 2016. The answers to LRDI Sprint CAT 2016 – Day 3 will be posted at the end of the day and will include the solution, possible traps and things to keep in mind come similar question types in CAT 2016. You may go through the entire series here: CAT 2016 Sprint Preparation Series by Learningroots

# CAT 2016 Sprint Preparation Series – LRDI 3

## Set 1

Coach John sat with the score cards of Indian players from the 3 games in a one-day cricket tournament where the same set of players played for India and all the major batsmen got out. John summarized the batting performance through three diagrams, one for each game. In each diagram, the three outer triangles communicate the number of runs scored by the three top scores from India, where K, R, S, V, and Y represent Kaif, Rahul, Saurav, Virender, and Yuvraj respectively. The middle triangle in each diagram denotes the percentage of the total score that was scored by the top three Indian scorers in that game. No two players score the same number of runs in the same game. John also calculated two batting indices for each player based on his scores in the tournaments; the R-index of a batsman is the difference between his highest and lowest scores in the 3 games while the M-index is the middle number, if his scores are arranged in a non-increasing order.

1. For how many Indian players is it possible to calculate the exact M-index?

a. 0

b. 1

c. 2

d. More than 2

2. Among the players mentioned, who can have the lowest R-index from the tournament?

a. Only Kaif, Rahul or Yuvraj

b. Only Kaif or Rahul

c. Only Kaif or Yuvraj

d. Only Kaif

3. How many players among those listed definitely scored less than Yuvraj in the tournament?

a. 0

b. 1

c. 2

d. More than 2

4. Which of the players had the best M-index from the tournament?

a. Rahul

b. Saurav

c. Virender

d. Yuvraj

## Set 2

The year was 2006. All six teams in Pool A of World Cup hockey, play each other exactly once. Each win earns a team three points, a draw earns one point and a loss earns zero points. The two teams with the highest points qualify for the semifinals. In case of a tie, the team with the highest goal difference (Goal For – Goals Against) qualifies.

In the opening match, Spain lost to Germany. After the second round (after each team played two matches), the pool table looked as shown below.

In the third round, Spain played Pakistan, Argentina played Germany, and New Zealand played South Africa. All the third round matches were drawn. The following are some results from the fourth and fifth round matches

(a) Spain won both the fourth and fifth round matches.

(b) Both Argentina and Germany won their fifth round matches by 3 goals to 0.

(c) Pakistan won both the fourth and fifth round matches by 1 goal to 0.

5. Which one of the following statements is true about matches played in the first two rounds?

a. Germany beat New Zealand by 1 goal to 0.

b. Spain beat New Zealand by 4 goals to 0.

c. Spain beat South Africa by 2 goals to 0.

d. Germany beat South Africa by 2 goals to 1.

6. Which one of the following statements is true about matches played in the first two rounds?

a. Pakistan beat South Africa by 2 goals to 1.

b. Argentina beat Pakistan by 1 goal to 0.

c. Germany beat Pakistan by 2 goals to 1.

d. Germany beat Spain by 2 goals to 1.

7. If Pakistan qualified as one of the two teams from Pool A, which was the other team that qualified?

a. Argentina

b. Germany

c. Spain

d. Cannot be determined

8. Which team finished at the top of the pool after five rounds of matches?

a. Argentina

b. Germany

c. Spain

d. Cannot be determined

## Set 3

The Table below shows the comparative costs, in US Dollars, of major surgeries in USA and a select few Asian countries.

A consulting firm found that the quality of the health services were not the same in all the countries above. A poor quality of a surgery may have significant repercussions in future, resulting in more cost in correcting mistakes. The cost of poor quality of surgery is given in the table below:

9. A US citizen is hurt in an accident and requires an angioplasty, hip replacement and a knee replacement. Cost of foreign travel and stay is not a consideration since the government will take care of it. Which country will result in the cheapest package, taking cost of poor quality into account?

a. India

b. Thailand

c. Malaysia

d. Singapore

e. USA

10. Taking the cost of poor quality into account, which country/countries will be the most expensive for knee replacement?

a. India

b. Thailand

c. Malaysia

d. Singapore

e. India and Singapore

11. Approximately, what difference in amount in Bahts will it make to a Thai citizen if she were to get a hysterectomy done in India instead of in her native country, taking into account the cost of poor quality? (It costs 7500 Bahts for one-way travel between Thailand and India).

a. 23500

b. 40500

c. 57500

d. 67500

e. 75000

12. The rupee value increases to Rs.35 for a US Dollar, and all other things including quality, remain the same. What is the approximate difference in cost, in US Dollars, between Singapore and India for a Spinal Fusion, taking this change into account?

a. 700

b. 2500

c. 4500

d. 8000

e. No difference

## Set 4

Seven faculty members at a management institute frequent a lounge for strong coffee and stimulating conversation. On being asked about their visit to the lounge last Friday we got the following responses.

JC: I came in first, and the next two persons to enter were SS and SM. When I left the lounge, JP and

VR were present in the lounge. DG left with me.

JP: When I entered the lounge with VR, JC was sitting there. There was someone else, but I cannot remember who it was.

SM: I went to the lounge for a short while, and met JC, SS and DG in the lounge that day.

SS: I left immediately after SM left.

DG: I met JC, SS, SM, JP and VR during my first visit to the lounge, I went back to my office with JC. When I went to the lounge the second time, JP and VR were there.

PK: I had some urgent work, so I did not sit in the lounge that day, but just collected my coffee and left.

JP and DG were the only people in the lounge while I was there.

13. Based on the responses, which of the two, JP or DG, entered the lounge first?

a. JP

b. DG

c. Both entered together

d. Cannot be determined

14 . Who was sitting with JC when JP entered the lounge?

a. SS

b. SM

c. DG

d. PK

15. How many of the seven members did VR meet on Friday in the lounge?

a. 2

b. 3

c. 4

d. 5

16. Who were the last two faculty members to leave the lounge?

a. JC and DG

b. PK and DG

c. JP and PK

d. JP and DG

Solutions

Set 1

1. This looks extremely complicated especially with the long back story and the unusual representation but in reality it is pretty straightforward.

Against Pakistan, the total score would have been 220, as 90% of the total score was 198.

Against South Africa, the total score would have been 250, as 70% of the total score was 175.

Against Australia, the total score would have been 240, as 80% of the total score was 192.

Now, let’s form a table with a few variables and see what we get:

Fair enough? The second thing to know is that, the last two scores will be least scores and so, there is an upper limit to them.

Now, we know that in the first game, both x and 22 – x have to be less than 28. So, R and S would have score anywhere from 0 to 22 depending on what the other person scored. Let’s make a note of it.

Similarly in the second game, V and Y would have scored less than 49 each. So, the maximum that either of them can score is 48 and so, the range will lie from 27 to 48 in this case.

And in the third game, both K and V would have scored less than 50 and so, we have anything possible from 0 to 48.

Let’s plug these values now and check:

Now, for how many people can we say for sure where their least score came? For K, it could be either against Pakistan or Australia, for R it would be against Pakistan for sure, for S it would again be against Pakistan for sure. For V, we cannot say with certainty and for Y too, we cannot say with certainty.

Similarly, we cannot say for sure what the middle score will be for K, V and Y.

So, M-index can be found out for R and S and so, option c is correct.

2. The highest scores for each batsman is given by:

K – 51, R – 55, S – 75, V – 130, Y – 87.

The least score could be:

K – 0 to 28, R – 0 to 22, S – 0 to 22, V – 0 to 48, Y – 27 to 40.

So, the R-index will be 23 to 51, 33 to 55, 53 to 75, 82 to 130 and 47 to 60 respectively.

So, we can see that, it could be minimum for everybody except S and V.

Option a.

3. The total scores would be:

K – 79 to 127

R – 104 to 126

S – 125 to 147

V – 157 to 226

Y – 154 to 175

So, K, R and S definitely scored less than Y in the tournament.

4. The M scores for the 5 players would be:

K – 28 to 48

R – 49

S – 50

V – 27 to 48

Y – 40 to 48

So, S will have the best M index for sure. Option b.

Set 2

5. Spain lost to Germany in the first round, and so, Spain would have won its second match. As Spain played Pakistan in the third round, it would have played either New Zealand or South Africa in the second round. Argentina did not play Germany or Spain in the first two rounds. Also, New Zealand and South Africa did not play each other in the first two rounds (as they have lost both matches).

Germany would have won its matches by margins of 1-0 and 2-1. Argentina would have won by margins of 1-0 in each of its matches.

The possible scorecards would look like this:

Spain played either New Zealand or South Africa in the second round. As none of the score lines of Spain (either 5 – 1 or 4 – 0) matches with that of South Africa, the second round match was between Spain and New Zealand and the result was either 5 – 1 or 4 – 0 in favour of Spain.

As Pakistan won one of its first two matches, it would have come against either New Zealand or South Africa by a margin of 2 – 0. As, New Zealand has not lost any match with 2 – 0 (a couple of cases have been eliminated post the New Zealand game was fixed), it can be said that Pakistan won 2 – 0 against South Africa.

So, Pakistan lost the other game by a 0 – 1 margin. Germany has already used up its 1 – 0 win against Spain. So, Argentina would have won 1 – 0 against Pakistan.

Also, as South Africa has lost its other match by a margin of 1 – 2, we can say that Germany won the game against South Africa.

Subsequently, Argentina won against New Zealand.

So, the first couple of rounds would look like this:

Option d is correct.

6. Option b is correct.

7. The final table will look like this:

So, Germany is at 10 points, Argentina is at 10 points, Spain is at 10 points, Pakistan is at 10 points, New Zealand is at 1 point and South Africa is at 1 point.

So, cannot be determined.

8. The worst case scenario would mean that Spain has a positive goal difference of 5 at the very least, Germany will have a positive difference of 4, Argentina can have a maximum positive difference of 4 and Pakistan will have a gol difference of 3. So, Spain tops the tournament irrespective of what happens in the rest of the matches.

Set 3

9. This was an extremely irritating and calculation intensive set and a lot of people would have let go of this after seeing the multiple tables and conversions. At its heart though, this was an easy set and given sufficient time (~ 10 minutes), one could have cracked this.

Angioplasty, hip replacement and knee replacement is required. If we look at the first table, we can see that, it costs \$28500 in India and \$29000 in Malaysia. As the costs for poor quality are \$21000 and \$18000 in India and Malaysia respectively, it is better to get done with the procedures in Malaysia. I haven’t considered the other countries as the surgery costs are visibly higher compared to that of India and Malaysia.

10. Of course the answer has to be USA. But as it has not been given in the options, the assumption is that, we are talking outside of the US. So, simple calculation will tell us that India has the highest cost associated with the knee replacement procedure.

11. Hysterectomy in Thailand would cost \$10500 and that in India would cost \$8000. So, it creates a difference of \$2500 which is 2500*32.89 ~ 82500 Bahts. As the travel expense would be 15000 Bahts, the difference would be approximately 67500 Bahts. Option d.

12. Spinal fusion cost in Singapore is \$14000 and that in India is \$10500. But this was when \$10500 corresponded to 10500 * 40.928 Rs. So now, the equivalent value will be given by: 10500 * 40.928 / 35 = \$12278.4. So, it should be around \$1778. But it has not been mentioned in the options. So, what they mean to say is that, the quality costs need not be calculated and so, we have to compare \$9000 vs. \$5500*40.928/35 which gives us \$2568 approximately. Option b.

Set 4

13. Another tough set. Similar to what appeared a couple of years ago in CAT.

We have to simply plug in the data and hope it makes sense. This is what a simple representation would look like:

Option b

14. Option c (as DG had not left by then)

15. Option b (JC, DG and JP)

16. JP and DG are left at the end. Option d.

You may go through the entire series here: CAT 2016 Sprint Preparation Series by Learningroots

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