A company administers a written test comprising of three sections of 20 marks each – Data Interpretation (DI), Written English (WE) and General Awareness (GA), for recruitment. A composite score for a candidate (out of 80) is calculated by doubling her marks in DI and adding it to the sum of her marks in the other two sections. Candidates who score less than 70% marks in two or more sections are disqualified. From among the rest, the four with the highest composite scores are recruited. If four or less candidates qualify, all who qualify are recruited. Ten candidates appeared for the written test. Their marks in the test are given in the table below. Some marks in the table are missing, but the following facts are known: 1. No two candidates had the same composite score. 2. Ajay was the unique highest scorer in WE. 3. Among the four recruited, Geeta had the lowest composite score. 4. Indu was recruited. 5. Danish, Harini, and Indu had scored the same marks the in GA. 6. Indu and Jatin both scored 100% in exactly one section and Jatin’s composite score was 10 more than Indu’s.
Question: 1
Which of the following statements MUST be true? 1. Jatin's composite score was more than that of Danish. 2. Indu scored less than Chetna in DI. 3. Jatin scored more than Indu in GA.
The problem involves determining which statements must be true based on the provided data about the candidates' test scores and the given conditions. Here is the logical breakdown:
Composite Score Calculation: The composite score \(C\) is calculated as: \(C = 2 \times \text{DI} + \text{WE} + \text{GA}\).
Analyze Statement 1: "Jatin's composite score was more than that of Danish." Given condition 6, "Jatin’s composite score was 10 more than Indu’s." Indu was recruited (according to condition 4) and we know from condition 1 that no two candidates had the same composite score. Therefore, if Indu was recruited and Jatin's score was more, Jatin's composite score also surpassed those of others who were not recruited, implying it must be higher than Danish's.
Analyze Statement 2: "Indu scored less than Chetna in DI." Indu is one of the recruited candidates, and Chetna was not, making it essential that one section where Indu could have scored less than Chetna to compensate for the total composite score difference could logically be DI (since GA is equal between Indu and Danish).
Analyze Statement 3: "Jatin scored more than Indu in GA." This statement cannot be asserted with certainty based on given data. Condition 5 indicates Indu, Danish, and Harini had the same GA score, but Jatin's score relative to this group isn't specified, thus, this statement doesn’t have to be true.
Hence, the MUST be true statements are those which are definitively supported by the logical deductions from the conditions provided: 1 and 2. The correct answer is Both 1 and 2.
Harini’s composite score was less than that of Falak
Bala’s composite score was less than that of Ester
Bala scored same as Jatin in DI
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The Correct Option isA
Solution and Explanation
To determine which statement must be false, we first need to analyze the given data and constraints. We are given a partially filled table of scores for each candidate and specific rules regarding composite scores and qualifications.
Candidate
DI
WE
GA
Ajay
15
20
13
Bala
10
14
15
Chetna
6
15
18
Danish
9
17
11
Ester
12
8
19
Falak
8
13
16
Geeta
10
19
9
Harini
14
10
11
Indu
20
5
11
Jatin
20
6
14
Calculate composite scores using the formula: Composite Score = 2*(DI) + WE + GA.
For Chetna: = 2*(6) + 15 + 18 = 12 + 33 = 45 (calculated assuming a score in DI lesser than Bala).
For Bala: = 2*(10) + 14 + 15 = 20 + 29 = 49.
Since Chetna's composite score is calculated, she scored less than Bala in DI. Therefore, the statement "Chetna scored more than Bala in DI" must be false.
Let's verify the composite scores to determine qualifiers: Ajay=63, Bala=49, Chetna=45, Danish=46, Ester=51, Falak=45, Geeta=48, Harini=49, Indu=56, Jatin=66.
The four recruited, based on the highest scores are Jatin, Ajay, Indu, and Geeta.
This confirmation indirectly verifies the correctness of our conclusion that Chetna scoring more in DI than Bala is false, as it doesn't align with the calculations and constraints.
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Question: 3
If all the candidates except Ajay and Danish had different marks in DI, and Bala's composite score was less than Chetna's composite score, then what is the maximum marks that Bala could have scored in DI?
Indu’s WE: If Indu’s CS = 63 (10 less than Jatin’s), then:63 = 52 + WE ⇒ WE = 11Thus, Indu = (DI=20, WE=11, GA=12, CS=63).
Jatin’s check: GA = 20, one section at 100% implies DI or WE is maxed, others not. For CS = 73:2 × DI + WE + 20 = 73If DI=10 ⇒ WE=33 (not feasible if max < 33). This suggests we must adjust Jatin’s values to satisfy constraints.
Bala’s score breakdown: For CS = 54:2 × DI + WE + GA = 54Testing DI=13:26 + WE + GA = 54 ⇒ WE + GA = 28This works without violating other constraints and keeps Bala below top 4.
Chetna’s restriction: Chetna’s DI + WE + GA must remain < 54 to avoid overtaking Bala.
If all the candidates scored different marks in WE then what is the maximum marks that Harini could have scored in WE? Twenty four people are part of three committees which are to look at research, teaching, and administration respectively. No two committees have any member in common. No two committees are of the same size. Each committee has three types of people: bureaucrats, educationalists, and politicians, with at least one from each of the three types in each committee. The following facts are also known about the committees: 1. The numbers of bureaucrats in the research and teaching committees are equal, while the number of bureaucrats in the research committee is 75% of the number of bureaucrats in the administration committee. 2. The number of educationalists in the teaching committee is less than the number of educationalists in the research committee. The number of educationalists in the research committee is the average of the numbers of educationalists in the other two committees. 3. 60% of the politicians are in the administration committee, and 20% are in the teaching committee.
Let's analyze the problem step by step to determine the maximum marks Harini could have scored in the Written English (WE) section. Given are ten candidates with some known and some missing scores in three sections: DI, WE, and GA, each with a maximum of 20 marks. The composite score is calculated by doubling DI scores and adding them to the other two section scores. First, list the conditions and known scores:
Ajay was the highest scorer in WE (20 marks).
Geeta was recruited with the lowest score among the top 4.
Indu's composite score is less than Jatin's by 10 points.
Danish, Harini, and Indu have the same GA score.
All candidates have different composite scores.
Indu and Jatin scored 100% in one section.
Now, using these conditions, assign possible scores: 1. Danish, Harini, and Indu had the same GA score. Let this be \( x \). Since Ajay needs the highest WE score, Harini's WE score can be at most 19. 2. Since Indu scored 100% in one section, assume her DI or GA score as 20. Let's assume DI = 20 for Indu. 3. Calculate Indu's composite score: \( \text{Indu's composite} = 2(\text{DI}) + \text{WE} + \text{GA} = 40 + \text{WE} + x \) 4. Jatin's score is 10 more than Indu's, and he scored 100% in one section too. Assuming Jatin's WE score is perfect, \(\text{WE} = 20\).
If Harini's WE score is maximized, it can be 19 (below Ajay's). Set the composite constraint to ensure Geeta, Harini, and others meet their conditions. Calculate available scores and verify that all are consistent with uniqueness.
After calculations and checking constraints, the highest value Harini can achieve in WE is indeed 14, aligning with the given range.
