Test: CAT Logical Reasoning & Data Interpretation- 1 - CAT MCQ

There are 5 ladies whose weights are 50 or above
There ages are 50, 50, 70, 60 and 80
Average = 310/5 = 62

Step 1: Apply Condition II (Mathematics)
The student who missed the Mathematics examination did not miss any other examination.
This means the Mathematics score must equal the average of the best 3 out of 4 exam scores of that student.

• Deep and Esha can be eliminated immediately since their Mathematics score is greater than all their other exam scores.

• Checking the remaining candidates:

  • Carl: Best 3 scores = 80 (Hindi), 90 (Social Science), 100 (Science)
    Average = 270 ÷ 3 = 90, which matches the Mathematics score.
    ∴ Carl missed his Mathematics examination.

Step 2: Apply Condition III (Hindi and Science)
The student who missed Hindi and Science must have similar scores in these two subjects.

• Alva has 75 in both Hindi and Science.

• Deep has 90 in both Hindi and Science.
  Thus, one of Alva and Deep missed both Hindi and Science, while the other missed only Hindi.

Step 3: Identify English candidates
Carl, Alva, and Deep are unlikely to have missed English. So the candidates for missing English must be from Bithi, Esha, and Foni.

• Bithi: Her English score (90) is higher than all her other scores → eliminate her.

• Esha: Best 3 scores = 85 (Hindi), 95 (Maths), 60 (Science)
  Average = 240 ÷ 3 = 80, which matches → ∴ Esha missed English.

• Foni: Best 3 scores = 78 (Maths), 83 (Social Science), 88 (Science)
  Average = 249 ÷ 3 = 83, which matches → ∴ Foni missed English.

Thus, Esha and Foni missed English.

Step 4: Apply Condition I (exactly two candidates missed each subject)

• English: Esha and Foni

• Hindi: Alva and Deep

• Science: One of (Alva or Deep) + another candidate

• Social Science: Two students still to be identified

Step 5: Check Science and Social Science

• Bithi: Her Science and Social Science scores are similar.
  Best 2 out of 3 = 90 (English), 80 (Hindi)
  Average = 170 ÷ 2 = 85, which matches → ∴ Bithi missed Science and Social Science.

• Foni: Her English and Social Science scores are similar.
  Considering best 2 out of 3, the average also equals 83 → ∴ Foni missed Social Science.

Step 6: Final allocation of missed exams

• Mathematics: Carl

• English: Esha and Foni

• Hindi: Alva and Deep

• Science: Bithi and one out of (Alva or Deep)

• Social Science: Foni and Bithi

The students who missed just one exam are:

• Carl (Mathematics)

• Esha (English)

• One out of Alva and Deep (Hindi)

Hence, of the six students, we can correctly determine the missed subjects for four of them (except Alva and Deep).
Therefore, the correct answer is: Option D – Esha and Foni.

Step 1: Apply Condition II (Mathematics)

• The student who missed the Mathematics examination did not miss any other examination.

• This means the Mathematics score must equal the average of the best 3 out of the 4 exam scores.

• Deep and Esha can be eliminated because their Mathematics score is greater than their other exam scores.

• Checking the remaining candidates:

  Carl: Best 3 out of 4 → Hindi (80), Social Science (90), Science (100)
  Average = 270 ÷ 3 = 90, which matches the given Mathematics score.
  ∴ Carl missed his Mathematics examination.

Step 2: Apply Condition III (Hindi and Science)

• The student who missed Hindi and Science should have similar scores in both subjects.

• Alva has 75 in Hindi and Science.

• Deep has 90 in Hindi and Science.
  Thus, one of Alva and Deep missed Hindi and Science, while the other missed only Hindi.

Step 3: Identify English candidates

• Carl, Alva, and Deep are unlikely to have missed English.

• Therefore, the candidate must be among Bithi, Esha, and Foni.

• Bithi’s English score (90) is higher than all her other scores → eliminate her.

• Esha: Best 3 out of 4 → Hindi (85), Mathematics (95), Science (60)
  Average = 240 ÷ 3 = 80, which matches.
  ∴ Esha missed her English examination.

• Foni: Best 3 out of 4 → Mathematics (78), Social Science (83), Science (88)
  Average = 249 ÷ 3 = 83, which matches.
  ∴ Foni missed her English examination.

Thus, the English candidates are Esha and Foni.

Step 4: Apply Condition I (exactly two missed per subject)

• English → Esha and Foni

• Hindi → Alva and Deep

• Science → one among (Alva or Deep) + another candidate

• Social Science → two candidates still to be identified

Step 5: Check Science and Social Science

• Bithi: Has similar scores in Science and Social Science.
  Best 2 out of 3 → English (90), Hindi (80)
  Average = 170 ÷ 2 = 85, which matches.
  ∴ Bithi likely missed Science and Social Science.

• Foni: Has similar scores in English and Social Science.
  Considering best 2 out of 3, the average = 83, which matches.
  ∴ Foni also missed Social Science.

Step 6: Final Allocation

• Mathematics: Carl

• English: Esha and Foni

• Hindi: Alva and Deep

• Science: Bithi and one out of (Alva or Deep)

• Social Science: Foni and Bithi

Step 7: Conclusion

• The students who missed just one exam are:
  Carl (Mathematics), Esha (English), and one out of Alva and Deep (Hindi).

• Of the six students, we can correctly determine the missed subjects for four of them (except Alva and Deep).

Final Answer: Option B – Alva and Deep

• Missed 1 exam → that score equals average of best 3 of the other 4.

• Missed 2 exams → each missed score equals average of best 2 of the other 3.

• Cond. I: There exists a set of four students who took all four core papers (E, H, S, SS).

• Cond. II: If anyone missed Mathematics, they missed no other exam.

• Cond. III: Exactly two missed Hindi: one missed only Hindi; the other missed Hindi and Science.

Step 1: Test “single‑miss Mathematics” (Cond. II restriction)

Compute if Maths equals avg(best3 of the other 4):

• Alva 70 ≠ 76.67

• Bithi 55 ≠ 86.67

• Carl 90 = (100+90+80)/3 → possible

• Deep 100 ≠ 90

• Esha 95 ≠ 68.33

• Foni 78 ≠ 84.67

Only Carl could have missed Maths, and then he missed no other subject. It is also consistent that nobody missed Maths (Cond. II is a restriction, not a must).

Step 2: Identify who can miss Hindi and Science (Cond. III)

Check single‑miss viability for H and S:

• Alva: H=75 equals avg(best3 of {80,70,75,60})=75 → can miss Hindi. S=75 equals avg(best3 of {80,75,70,60})=75 → can miss Science.

• Deep: H=90 equals avg(best3 of {70,100,90,80})=90 → can miss Hindi. S=90 equals avg(best3 of {70,90,100,80})=90 → can miss Science.

• Bithi: S=85 equals avg(best3 of {90,80,55,85})=85 → can miss Science; H cannot.

• Carl, Esha, Foni: cannot miss Science by the rule; none (except Alva/Deep) can miss Hindi.

Therefore, the two Hindi missers must be Alva and Deep, with exactly one of them also missing Science. The only other student who can miss Science is Bithi.

Step 3: Satisfy Cond. I (four students took all four core papers)

Choose assignments that keep four students all‑core and respect Cond. III:

• Let Deep be the “Hindi+Science” student (required by Cond. III).

• Let the other Hindi misser be Alva, missing only Hindi (fits single‑miss rule).

• Among the remaining students, only Bithi can miss Science; assign Bithi as the second Science misser.

• The four all‑core writers can then be chosen as Carl, Esha, Foni, and one of Alva/Bithi depending on whether they actually miss a core. Either way, the Science absentees remain the same.

This meets all conditions simultaneously.

Conclusion

The students who missed the Science examination are Deep and Bithi.

Answer: C) Deep and Bithi.

Based on Condition II, we understand that the student who missed the Mathematics examination did not miss any other examination. This indicates that the Maths score is bound to be the average of the best 3 out of the 4 exam scores obtained by this candidate. Based on this inference, we can proceed with identifying the math score that can be represented as an average of the rest of the scores. We can straightaway eliminate Deep and Esha as potential candidates, given that their Mathematics score is greater than the rest of the exam scores. After estimating the average scores for the rest of the candidates, we observe that only Carl has missed his Mathematics examination.
For Carl: best 3 out of 4 - 80(Hindi), 90(Social Science), 100(Science)
Avg. = 270/3 = 90 which matches the given value
∴  Carl missed his Mathematics examination.
Further, based on Condition III, we can surmise that the student who missed Hindi and Science should have similar average scores in these two subjects. We notice that Alva has the same score of 75 in both Hindi and Science. The same can be said about Deep, who has a score of 90 in both these subjects. Thus, one out of Alva and Deep missed out on Hindi and Science examination, while the second individual missed out only on the Hindi examination.
Since we know that Carl, Alva and Deep are unlikely to have missed out on the English exam, we can divert our attention to determining which individual out of Bithi, Esha and Foni failed to appear for this subject. However, we notice that Bithi's English score is greater than the rest of her scores, thereby helping us eliminate her as the potential candidate.
For Esha: best 3 out of 4 - 85(Hindi), 95(Mathematics), 60(Science)
Avg. = 240/3 = 80 which matches the given value
∴  Esha most likely missed her English examination.
For Foni: best 3 out of 4 - 78(Mathematics), 83(Social Science), 88(Science)
Avg. = 249/3 = 83 which matches the given value
∴  Foni most likely missed her English examination.
Based on Condition I, we know that exactly two candidates missed the examinations for English, Hindi, Science, and Social Science.
For English, we determined these individuals to be Esha and Foni. For Hindi, we determined these individuals to be Alva and Deep. For Science, we know one of the individuals is either Alva or Deep. Given that Carl, Alva and Deep cannot be a part of the group that missed Science or Social Science exam, we can proceed by carefully scrutinizing the rest of the group that includes Bithi, Esha and Foni.We notice that Bithi has a similar score in both Science and Social Science examination. Assuming that she did miss these exams, let us proceed to check if this was actually the case.
For Bithi: Best 2 out 3 - 90(English), 80(Hindi)
Avg = 170/2 = 85 which matches the given value
 ∴  Bithi is likely to have missed her Science and Social Science examinations.
We additionally notice that Foni has a similar score in English and Social Science. On considering the best 2 out of 3 scores, the average value of the score for both the subject holds (equal to 83). Thus, we can conclude that Bithi and Foni missed their Social Science examination.
Thus, the students who missed just one exam were: Carl (Mathematics); Esha (English) and one out of Alva and Deep (Hindi).
Hence of the six students, we can correctly determine the missed subjects for four of them (except Alva and Deep):
Mathematics: Carl ; English: Esha & Foni ; Hindi: Alva & Deep; Science: Bithi & one out of Alva and Deep ; Social Science: Foni & Bithi
Hence, the correct answer to this question is 3. {Carl (Mathematics); Esha (English) and one out of Alva and Deep (Hindi)}

From the given information, we can make the following empty table:

From (ii) and (iii), we get that Q got F grade in match II and match IV.
From (v) and (vi), P got same grade in match II and match III. Now, P could obtain grade B in match II and match III (from (vi)).
Now, in every match, at least one century was scored; thus, R obtained grade A in match II and match IV (from (iv)).
Thus, grade C would be obtained by Q in match I, R in match III and P in match IV (from (iii) and (v)).
Now, remaining rows and columns can be filled giving the final table as follows:

From the given information, we can make the following empty table:

From (ii) and (iii), we get that Q got F grade in match II and match IV.
From (v) and (vi), P got same grade in match II and match III. Now, P could obtain grade B in match II and match III (from (vi)).
Now, in every match, at least one century was scored; thus, R obtained grade A in match II and match IV (from (iv)).
Thus, grade C would be obtained by Q in match I, R in match III and P in match IV (from (iii) and (v)).
Now, remaining rows and columns can be filled giving the final table as follows:

Maximum runs scored by Q in match I = 49
Maximum runs scored by Q in match II = 30
Average of maximum runs scored by Q in match I and match II = (49+30)/2 = 39.5

From the table, we can see that the % decline in the rupee was maximum in the month of July among the options and also the stock index of UK was lowest in July among the given months so the maximum decline in the portfolio was in July.

The percentage increase in the USA market index is the maximum among the three markets in a year.

1. On 1 May 2019

   • IndexMay = 119

   • INR/USD on that date = 69.0

   • RupeeValueMay = UnitsBought × IndexMay
     = (1 013.8889) × 119
     ≈ 120 652.78 ₹

   • USDValueMay = RupeeValueMay ÷ 69.0
     ≈ 120 652.78 ÷ 69.0
     ≈ 1 748.57 USD

2. On 1 June 2019

   • IndexJun = 118

   • INR/USD on that date = 69.0

   • RupeeValueJun = (1 013.8889) × 118
     ≈ 119 638.89 ₹

   • USDValueJun = 119 638.89 ÷ 69.0
     ≈ 1 734.54 USD

3. On 1 October 2019

   • IndexOct = 120

   • INR/USD on that date = 68.0

   • RupeeValueOct = (1 013.8889) × 120
     ≈ 121 666.67 ₹

   • USDValueOct = 121 666.67 ÷ 68.0
     ≈ 1 789.51 USD

4. On 1 December 2019

   • IndexDec = 122

   • INR/USD on that date = 73.0

   • RupeeValueDec = (1 013.8889) × 122
     ≈ 123 694.44 ₹

   • USDValueDec = 123 694.44 ÷ 73.0
     ≈ 1 694.33 USD

Comparing the four USD‐values:

• 1 May 2019 → ≈ 1 748.57 USD

• 1 June 2019 → ≈ 1 734.54 USD

• 1 October 2019 → ≈ 1 789.51 USD

• 1 December 2019 → ≈ 1 694.33 USD

The single largest value in dollar terms is on 1 October 2019, at approximately $1 789.51.

Among the given options since the dollar got weak the most on 1st May 2019 and also the US market index fell below the value of the index on 1st January so therefore the minimum value reaches was in 1st May 2019.

Total C.P of magazines of Week 1 = 54 × 7.5 + 88 × 8 = 1,109
Total C.P of magazines of Week 2 = 34 × 8 + 88 × 6.75 + 2 × 6.5 = 879
Total C.P of magazines of Week 3 = 72 × 6.5 + 36 × 7.75 = 747
Total C.P of magazines of Week 4 = 84 × 7.75 + 30 × 6 = 831
Total C.P of magazines of Week 5 = 66 × 6 + 42 × 6.52 = 669
Total C.P of magazines of Week 6 = 22 × 6.52 + 82 × 8.50 = 840

Total C.P of magazines of Week 1 = 54 × 7.5 + 88 × 8 = 1,109
Total C.P of magazines of Week 2 = 34 × 8 + 88 × 6.75 + 2 × 6.5 = 879
Total C.P of magazines of Week 3 = 72 × 6.5 + 36 × 7.75 = 747
Total C.P of magazines of Week 4 = 84 × 7.75 + 30 × 6 = 831
Total C.P of magazines of Week 5 = 66 × 6 + 42 × 6.52 = 669
Total C.P of magazines of Week 6 = 22 × 6.52 + 82 × 8.50 = 840

Thus, the number of magazines with profit > 20% is 410.

Total C.P of magazines of Week 1 = 54 × 7.5 + 88 × 8 = 1,109
Total C.P of magazines of Week 2 = 34 × 8 + 88 × 6.75 + 2 × 6.5 = 879
Total C.P of magazines of Week 3 = 72 × 6.5 + 36 × 7.75 = 747
Total C.P of magazines of Week 4 = 84 × 7.75 + 30 × 6 = 831
Total C.P of magazines of Week 5 = 66 × 6 + 42 × 6.52 = 669
Total C.P of magazines of Week 6 = 22 × 6.52 + 82 × 8.50 = 840

Lowest profit i.e. $138 was made in week 4.

Total C.P of magazines of Week 1 = 54 × 7.5 + 88 × 8 = 1,109
Total C.P of magazines of Week 2 = 34 × 8 + 88 × 6.75 + 2 × 6.5 = 879
Total C.P of magazines of Week 3 = 72 × 6.5 + 36 × 7.75 = 747
Total C.P of magazines of Week 4 = 84 × 7.75 + 30 × 6 = 831
Total C.P of magazines of Week 5 = 66 × 6 + 42 × 6.52 = 669
Total C.P of magazines of Week 6 = 22 × 6.52 + 82 × 8.50 = 840

Total profit from week 3 to week 6 is $864.72.
Average for the 4 weeks = $216.18

Total C.P of magazines of Week 1 = 54 × 7.5 + 88 × 8 = 1,109
Total C.P of magazines of Week 2 = 34 × 8 + 88 × 6.75 + 2 × 6.5 = 879
Total C.P of magazines of Week 3 = 72 × 6.5 + 36 × 7.75 = 747
Total C.P of magazines of Week 4 = 84 × 7.75 + 30 × 6 = 831
Total C.P of magazines of Week 5 = 66 × 6 + 42 × 6.52 = 669
Total C.P of magazines of Week 6 = 22 × 6.52 + 82 × 8.50 = 840

Difference of profit of week 1 and week 2 = $361 - $240 = $121
Now, 121/361 × 100% = 33.52%

By observing table II, we can see that NP/NW ratio is maximum for ITC.
Hence it is the best performer.

Operating Profit/Sales for Birla
= 324145/1280812 = 0.253.
Operating Profit/Sales for Mafatlal
= 26485/1611263 = 0.016.
Operating profit/Sales for RPG
= 62580/289391 = 0.216.
Operating profit/Sales for ESSAR
= 91092/155391 = 0.586.
Thus ESSAR is the best choice.

The question suggests that dividends are determined by the ratio of net profit to net worth. While a higher Net Profit/Net Worth ratio indicates greater profitability relative to equity, investment decisions should consider additional factors such as:

• Growth potential
• Market position
• Overall financial health

Without specific data comparing these companies' ratios, ITC is selected based on the premise provided. However, investors should conduct a comprehensive analysis beyond this single metric before making a decision.