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CAT 2019 | SLOT - 2 | DILR

CAT 2019 | Slot 2 | Quantitative Ability 

Dive into the 8 sets - question CAT 2019 | Slot 2 DILR paper, designed to test your quantitative skills. Includes solutions and explanations for all questions to help you understand key concepts. Uploaded on MBA Litmus to help aspirants practice and prepare effectively.

Set 1: Languages Spoken

The table below indicates languages spoken by five people: Paula, Quentin, Robert, Sally, and Terence. For example, Paula speaks only Chinese and English. They form three teams (Team 1, Team 2, Team 3). Each team has 2 or 3 members. A team speaks a language if at least one member speaks it.

Additional facts:

  1. Each team speaks exactly four languages and has the same number of members.
  2. English and Chinese are spoken by all three teams, Basque and French by exactly two teams, and the other languages by exactly one team.
  3. None of the teams include both Quentin and Robert.
  4. Paula and Sally are together in exactly two teams.
  5. Robert is in Team 1 and Quentin is in Team 3.

Q1. Who among the following is not a member of Team 2?

  • Sally
  • Paula
  • Quentin
  • Terence

Q2. Who among the following people is a part of exactly two teams?

  • Sally
  • Quentin
  • Robert
  • Paula

Q3. Who among the five people is a member of all teams?

  • No one
  • Terence
  • Sally
  • Paula

Q4. Apart from Chinese and English, which languages are spoken by Team 1?

  • Basque and French
  • Arabic and French
  • Basque and Dutch
  • Arabic and Basque

Set 2: Rainfall

To compare rainfall data, the India Meteorological Department (IMD) calculated the Long Period Average (LPA) of rainfall during June-August for 16 states. The figure shows actual rainfall in June-August 2019 (in mm) and percentage deviations from LPA in 2018.

Q1. If a ‘Heavy Monsoon State’ is defined as a state with actual rainfall of 900 mm or more, what percentage of ‘Heavy Monsoon States’ have a negative deviation from LPA in 2019?

  • 75.00
  • 57.14
  • 42.86
  • 14.29

Q2. If a ‘Low Monsoon State’ is defined as a state with rainfall of 750 mm or less, what is the median ‘deviation from LPA’ of these states?

  • -30%
  • 10%
  • -20%
  • -10%

Q3. What is the average rainfall of all states with rainfall ≤ 600 mm in 2019 and a negative deviation from LPA?

  • 450 mm
  • 367 mm
  • 460 mm
  • 500 mm

Q4. The LPA of a state is the average rainfall in the preceding 10 years (June-August). Given that actual rainfall in Gujarat in 2019 was 20% more than in 2009, the LPA of Gujarat in 2019 is closest to:

  • 475 mm
  • 490 mm
  • 505 mm
  • 525 mm

Set 3: Students & Proposals

Students are discussing two proposals:

  1. A: Dress code on campus.
  2. B: Allow multinational food franchises on campus.
A student may support neither proposal. Two candidates, Sunita and Ragini, are contesting for student union president. Each student prefers one candidate. A survey of 500 students yielded:
  • 250 supported proposal A and 250 supported proposal B.
  • Among 200 who preferred Sunita, 80% supported proposal A.
  • Among those who preferred Ragini, 30% supported proposal A.
  • 20% of those who supported B preferred Sunita.
  • 40% of those who did not support B preferred Ragini.
  • Every student preferring Sunita and supporting B also supported A.
  • Among Ragini supporters, 20% did not support any proposals.

Q1. Among students who supported proposal A, what percentage preferred Sunita? [TITA]

Q2. What percentage of students who did not support proposal A preferred Ragini? [TITA]

Q3. What percentage of students who supported both proposals A and B preferred Sunita?

  • 25
  • 50
  • 40
  • 20

Q4. How many students supported proposal B, did not support proposal A, and preferred Ragini?

  • 40
  • 210
  • 200
  • 150

Set 4: Three Doctors

Three doctors—Dr. Ben, Dr. Kane, and Dr. Wayne—visit a clinic Monday to Saturday to see patients.

  • Dr. Ben: 10 min per patient, charges Rs. 100.
  • Dr. Kane: 15 min per patient, charges Rs. 200.
  • Dr. Wayne: 25 min per patient, charges Rs. 300.
There are three rooms (1, 2, 3) assigned to the doctors. Clinic is open 9 a.m.–11:30 a.m. Each patient receives a numbered token starting from 1 each day. Patients enter the room that becomes free first; if multiple rooms are free, the next patient goes to the room with the smallest number.

Q1. What is the maximum number of patients that the clinic can cater to on any single day?

  • 15
  • 30
  • 31
  • 12

Q2. On a Saturday when the queue is never empty, which doctor earns the maximum consultation charges?

  • Dr. Kane
  • Dr. Wayne
  • Dr. Ben
  • Both Dr. Wayne and Dr. Kane

Q3. Mr. Singh visited the clinic Monday, Wednesday, and Friday at 8:50 a.m. with token number 13. On which day was he at the clinic the longest?

  • Friday
  • Wednesday
  • Same duration on all three days
  • Monday

Q4. On a slow Thursday, with two patients initially at 9 a.m. and subsequent patients arriving every 15 minutes, total duration in minutes when all three doctors are simultaneously free is:

  • 30
  • 10
  • 15
  • 0

Set 5: Three Pouches

Three pouches (each shown as a filled circle) are kept in each of the nine slots of a 3×3 grid. Each pouch has some one-rupee coins. The minimum and maximum amounts in the three pouches of each slot are known. For example, in the second column of the first row, the minimum is Rs. 6 and maximum Rs. 8.
It is known that:

  • Each row and column of nine pouches has an integer average.
  • Total amount in three pouches in the first column of the third row is Rs. 4.

Q1. Total amount in the three pouches in the first column of the second row? [TITA]

Q2. How many pouches contain exactly one coin? [TITA]

Q3. Number of slots where the average amount of its three pouches is an integer? [TITA]

Q4. Number of slots for which the total amount in three pouches strictly exceeds Rs. 10? [TITA]

Set 6: MT & ET

The first-year students in a business school are split into six sections. In 2019, the Business Statistics course was taught in these six sections by Annie, Beti, Chetan, Dave, Esha, and Fakir. All six sections had a common Midterm (MT) and a common Endterm (ET), each worth 100 marks. ET contained more questions than MT. Questions for MT and ET were prepared collectively by all six faculty members, each preparing the same number of questions considering MT and ET together. Both MT and ET had at least four 5-mark questions, at least three 10-mark questions, and at least two 15-mark questions. All 5-mark questions preceded the 10-mark questions, and all 15-mark questions followed the 10-mark questions.
Additional facts:

  • Annie prepared the fifth question for both MT and ET; in MT this question carried 5 marks.
  • Annie prepared only one question for MT; all other faculty prepared more than one question for MT.
  • All questions prepared by a faculty member appeared consecutively in both MT and ET.
  • Chetan prepared the third question in both MT and ET; Esha prepared the eighth question in both.
  • Fakir prepared the first question of MT and the last of ET. Dave prepared the last question of MT and the first of ET.

Q1. The second question in ET was prepared by:

  • Eshan
  • Chetan
  • Dave
  • Beti

Q2. How many 5-mark questions were there in MT and ET combined?

  • Cannot be determined
  • 12
  • 10
  • 13

Q3. Who prepared 15-mark questions for MT and ET?

  • Only Dave, Esha and Fakir
  • Only Beti, Dave, Esha and Fakir
  • Only Esha and Fakir
  • Only Dave and Fakir

Q4. Which of the following questions did Beti prepare in ET?

  • Ninth question
  • Tenth question
  • Fourth question
  • Seventh question

Set 7: Rifle Shooting

Ten players participated in a rifle shooting competition with 10 rounds. Each round had 6 participants. Players 1-6 competed in Round 1, players 2-7 in Round 2, and so on, following a circular pattern.
The top three performances in each round received 7, 3, and 1 points respectively. There were no ties. Total points after Rounds 6 and 10 are provided.
Additional information:

  • Gordon did not score consecutively in any two rounds. Eric and Fatima both scored in a round.
  • For Rounds 7-10, only two players scored in three consecutive rounds, one being Chen. No other player scored in two consecutive rounds. Joshin scored in Round 7; Amita scored in Round 10. No player scored in all four rounds.

Q1. What were the scores of Chen, David, and Eric respectively after Round 3?

  • 3, 0, 3
  • 3, 3, 0
  • 3, 3, 3
  • 3, 6, 3

Q2. Which three players were in the last three positions after Round 4?

  • Hansa, Ikea, Joshin
  • Bala, Chen, Gordon
  • Bala, Ikea, Joshin
  • Bala, Hansa, Ikea

Q3. Which player scored points in maximum number of rounds?

  • Joshin
  • Chen
  • Ikea
  • Amita

Q4. Which players scored points in the last round?

  • Amita, Bala, Chen
  • Amita, Chen, David
  • Amita, Eric, Joshin
  • Amita, Chen, Eric

Set 8: Revenue & Cost

A large store has three departments: Clothing, Produce, and Electronics. Revenue and cost percentages for the years 2016, 2017, and 2018 are given. Profit is calculated as (Revenue – Cost) and Percentage Profit as (Profit/Cost) × 100%.
Known facts:

  • Percentage profit in 2016 was 100%.
  • Revenue doubled from 2016 to 2017; cost doubled from 2016 to 2018.
  • No profit from Electronics in 2017.
  • Revenue from Clothing in 2018 equals the cost in Produce in 2018.

Q1. What was the percentage profit of the store in 2018? [TITA]

Q2. What was the ratio of revenue generated from the Produce department in 2017 to that in 2018?

  • 8 : 5
  • 16 : 9
  • 4 : 3
  • 9 : 16

Q3. What percentage of the total profits for the store in 2016 was from the Electronics department? [TITA]

Q4. What was the approximate difference in profit percentages of the store in 2017 and 2018?

  • 8.3
  • 33.3
  • 25.0
  • 15.5