Coded Inequalities
Directions (1-5):
‘P $ Q’ means ‘P is not smaller than Q’ ‘P @ Q’ means ‘P is neither smaller than nor equal to Q’ ‘P # Q’ means ‘P is neither greater than nor equal to Q’ ‘P & Q’ means ‘P is neither greater than nor smaller than Q’ ‘P * Q’ means ‘P is not greater than Q’
1. statements: H @ T, T # F, F& E, E * V
Conclusions: I. V $ F II. E @ T III. H @ V IV. T # V

A. Only I, II, and III are true B. Only I, II, and IV are true C. Only II, III, and IV are true D. Only I, III, and IV are true E. All I, II, III, and IV are true

Answer: Option (B)
2. statements: D # R, R * K, K @ F, F $ J
Conclusions: I. J # R II. J # K III. R # F IV. K @ D

A. Only I, II, and III are true B. Only II, III, and IV are true C. Only I, III, and IV are true D. All I, II, III, and IV are true E. None of these

Answer: Option (E)
3. statements: N & B, B $ W, W # H, H * M
Conclusions: I. M @ W II. H @ N III. W & N IV. W # N

A. Only I is true B. Only III is true C. Only IV is true D. Only either III or IV are true E. Only either III or IV and I are true

Answer: Option (E)
4. statements: R * D, D $ J, J # M, M @ K
Conclusions: I. K # J II. D @ M III. R # M IV. D @ K

A. None is true B. Only I is true C. Only II is true D. Only III is true E. Only IV is true

Answer: Option (A)
5. statements: M $ K, K @ N, N * R, R # W
Conclusions: I. W @ K II. M $ R III. K @ W IV. M @ N

A. Only I and II are true B. Only III and IV are true C. Only III or IV are true D. Only II, III, and IV are true E. None of these

Answer: Option (E)
Blood Relations
Direction (1-3): B is grandson of E, who is not mother of P. D is wife of P, who is father of B. C is mother of S, who is brother of P.
1. How is E related to S?

A. Father B. Grand Father C. Mother D. Can’t be determined E. None of these

Answer: Option (A)
2. How is B related to C?

A. Son B. Grandson C. Daughter D. Granddaughter E. None of these

Answer: Option (B)
3. How is S related to D?

A. Brother B. Son-in-law C. Son D. Brother-in-law E. None of these

Answer: Option (D)
Direction (4 - 5): A, B, C, I, J and K are six family members. J is the son of I, who is not the mother of J. B is the brother of I. K and I are a married couple. C is the daughter of K, who is the sister of A.
4. How is J related to C?

A. Father B. Brother C. Sister D. Mother E. None of these

Answer: Option (B)
5. How many female members are there in the family?

A. Two B. Three C. Four D. Can’t be determined

Answer: Option (D)
Verbal Reasoning
1. REASON: SFBTPO:: THINK:?

A. SGHMJ B. UIJOL C. UHNKI D. UJKPM

Answer: Option (B)
2. Carbon: Diamond:: Corundum:?

A. Garnet B. Ruby C. Pukhraj D. Pearl

Answer: Option (B)
Explanation: As Diamond is made of Carbon similarly Ruby is made of Corundum.
3. Architect: Building:: Sculptor:?

A. Museum B. Stone C. Chisel D. Statue

Answer: Option (D)
Explanation: As 'Architect' makes 'Building' similarly 'Sculptor' makes 'Statue'.
4. Eye: Myopia:: Teeth:?

A. Pyorrhoea B. Cataract C. Trachoma D. Eczema

Answer: Option (A)
Explanation: As Myopia is the disease of eye similarly pyorrhoea is a disease of teeth.
5. Conference: Chairman:: Newspaper:?

A. Reporter B. Distributor C. Printer D. Editor

Answer: Option (D)
Explanation: As Chairman is the highest authority in a conference similarly Editor is in Newspaper.
Coding and Decoding
1. In a certain code language if the word PANCREAS is coded as SAERCNAP, then how is the word STADIUM coded in that language?

A. MUDIATS B. MUDIAST C. MUIDATS D. MIUDATS E. ATSDMUI

Answer: Option (C)
Explanation: Word: PANCREAS Pattern: Letters in the word are reversed. Code: SAERCNAP Similarly, the code for STADIUM is MUIDATS.
2. In a certain code language, if the word CIRCUMSTANCE is coded as CRUSACICMTNE, then how is the word HAPPINESS coded in that language?

A. HPEISAPNS B. HPISEAPNS C. HPIESPANS D. HPIESAPNS E. APNSSEIPH

Answer: Option (D)
Explanation: Word: CIRCUMSTANCE Pattern: Alternate letters are written as a group. Code: CRUSACICMTNE Similarly, the code for HAPPINESS is HPIESAPNS.
3. In a certain code language, if the word REGISTRATION is coded as TSIGERNOITAR, then how is the word ACCURATE coded in that language?

A. UCCAETAR B. UACCETAR C. UCACETAR D. UCCATEAR E. UCAAECTR

Answer: Option (A)
Explanation: Word: REGISTRATION Pattern: The word is divided into two equal halves and the letters in each half are reversed. Code: T S I G E R N O I T A R Similarly, the code for ACCURATE is UCCAETAR.
4. In a certain code language 'allow children to play on the ground' is written as 'play allow on children the to ground' then how will 'the do open not electric tough wires' be declared from that language?

A. Not the electric do touch open wires B. Do not touch the electric open wires C. Do not touch the open electric wires D. Not the do electric touch open wires E. None of these

Answer: Option (C)
5. In a certain coded language, the word DISPLAY is written as BLQSJDW. How will the word PROJECT be written in that language?

A. NUMMCER B. NUNMCER C. NTNMCFR D. NTMMCFR E. None of these

Answer: Option (E)
Explanation: The odd-number-positioned letters move two letters backward and the even-number-positioned ones move three letters forward. Thus, PROJECT will become NUMMCFR.
Data Sufficiency
Direction (1-5): In each of the following problems, there is one question and three statements I, II and III given below the question. You have to decide whether the data given in the statements are sufficient to answer the question. Read all the statements carefully and find which of the statements is/are sufficient to answer the given question. Choose the correct alternative in each question.
1. Question: What is Suman's rank from the top in a class of forty students? Statements: I. Suman is 3 ranks below Deepak from the top. II. Deepak's rank from the bottom is 23. III. Suman is 3 ranks above Deepak from the bottom.

A. Any two of the three B. Only I and II C. Only II and III D. All I, II and III E. Only II and either I or III

Answer: Option (E)
Explanation: From II, we conclude that in a class of 40, Deepak ranks 23rd from the bottom i.e. 18th from the top. From I and II, we find that Suman is 3 ranks below 18th rank from the top i.e. she ranks 21st from the top. From II and III, we find that Suman is 3 ranks above 23rd rank from the bottom i.e. she ranks 20th from the bottom or 21st from the top.
2. Question: Five persons - A, B, C, D, and E are sitting in a row. Who is sitting in the middle? Statements: I. B is between E and C. II. B is to the right of E. III. D is between A and E.

A. Only I and II B. Only II and III C. Only I and III D. All I, II and III E. None of these

Answer: Option (D)
Explanation: From I, the order is E, B, C or C, B, E. From II, the order is E, B. From III, the order is A, D, E. Combining the above three, we get the order as A, D, E, B, C. Clearly, E is sitting in the middle.
3. Question: How is 'DATE' written in the code language? Statements: I. DEAR is written as $#@? in that code. II. TREAT is written as %?#@% in that code. III. TEAR is written as %#@? in that code,

A. Only I and II B. Only II and III C. All I, II and III D. Only I and either II or III E. None of these

Answer: Option (D)
Explanation: Observing I, II and III, we find that similar letters have similar code symbols at the corresponding places in the code. So, this is direct-coding. Thus, to find the code for DATE, we need the code for D which can be obtained from I only (i.e. $.) and the codes for A, T, and E which can be obtained either from II or III (@, # and % respectively).
4. Question: In which year was Sanjay born? Statements: I. Sanjay is six years older than Gopal. II. Gopal's brother was born in 1982. III. Sanjay's brother is two years younger than Gopal's brother who was eight years younger than Gopal.

A. Only I and II B. Only II and III C. Only I and III D. All I, II and III E. None of these

Answer: Option (D)
Explanation: From II, we know that Copal's brother was born in 1982. From III, we find that Gopal's brother was 8 years younger to him i.e. Gopal was born in 1974. From I, we find that Sanjay is 6 years older than Gopal. Thus, Sanjay was born in 1968.
5. Question: Who among Siddhartha, Nikunj, Vipul and Mukul is the youngest? Statements: I. Vipul is younger than Mukul but older than Siddhartha and Nikunj. II. Mukul is the oldest. III. Siddhartha is older than Nikunj.

A. Only I B. Only I and II C. Only II and III D. Only I and III E. None of these

Answer: Option (D)
Explanation: From I, we have: M > V, V > S, V > N ...(i) From II, we have: Mukul is the oldest ...(ii) From III, we have: S > N ...(iii) Combining (i) and (iii), we get :M > V, V >S > N or M>V > S > N. Clearly, Nikunj is the youngest.

Input and Output
Directions (1-5): Study the following information carefully to answer the given questions.
A word and number arrangement machine when given an input line of words and numbers rearranges them following a particular rule in each step. The following is an illustration of input and rearrangement.
Input: Prone nine 36 49 angles 66 crows 64 ideate Choose 54 51 Step I: Choose 1 Pronenine 49angle 66crow 64 ideate 54 51 Step II: Choose 1 ideate 29 Prone nine angle 66 crow 64 54 51 Step III: Choose 1 ideate 29 Prone31 nine angle 66 crow 64 54 Step IV: Choose 1 ideate 29 Prone 31 Crow 39 nine angle 66 64 Step V: Choose 1 ideate 29 Prone 31 Crow 39 nine 50 angles 66 Step VI: Choose 1 ideate 29 Prone 31 Crow 39 nine 50 angles 60 Step VI is the last step, find out in each of the rules followed in the above steps, find out in each of the following questions the appropriate step for the given input
Input: Ware 33 watch 38gonenook 5132 cast feat 50 64.
1. After how many steps no further rearrangement of words is possible?

A. Six B. Four C. Five D. Seven E. Eight

Answer: Option (A)
2. Which word/number would be the fourth from the left end in Step IV?

A. Ware B. 44 C. 32 D. 50 E. None of these

Answer: Option (E)
3. What will be the position of ‘63’ in the last but one step?

A. Eleventh from the left B. Second from the right C. Tenth from the left D. First from the left E. None of these

Answer: Option (E)
4. Which of the following will be the penultimate step of the above input and which word/number will be the fourth from the right end in the same step?

A. Step V, ware B. Step V, cast C. Step IV, ware D. Step IV, cast E. None of these

Answer: Option (B)
5. What will be the position of the cast in step III?

A. Sixth from right B. Seventh from right C. Seventh from left D. Third from right E. None of these

Answer: Option (D)
Circular Seating Arrangement
Direction (1-5): Study the following information carefully and answer the given questions:
1. A, B, C, D, E, F, G, and H are sitting around a circle facing the center but not necessarily in the same order. 2. B sits second to the left of H’s husband.No female is an immediate neighbor of B. 3. D’s daughter sits second to the right of F. F is the sister of G. F is not an immediate neighbor of H’s husband. 4. Only one person sits between A and F. A is the father of G. H’s brother Diets to the immediate left of H’s mother. Only one person sits between H’s mother and E. 5. Only one person sits between H and G. G is the mother of C. G is not an immediate neighbor of E.
1. What is the position of A with respect to his mother-in-law?

A. Immediate left B. Third to the right C. Third to the left D. Second to the right E. Fourth to the left

Answer: Option (A)
2. Who amongst the following is D’s daughter?

A. B B. C C. E D. G E. H

Answer: Option (C)
3. What is the position of A with respect to his grandchild?

A. Immediate right B. Third to the right C. Third to the left D. Second to the left E. Fourth to the left

Answer: Option (D)
4. How many people sit between G and her uncle?

A. One B. Two C. Three D. Four E. More than four

Answer: Option (C)
5. Four of the following five are alike in a certain was based on the given information and so form a group. Which is the one that does not belong to that group?

A. F B. C C. E D. H E. G

Answer: Option (B)
Directions and Distances
1. Ram walks 10 m South from his house, turns left and walks 25 m, again turns left and walks 40 m, then turns right and walks 5 m to reach the school. In which direction is the school from his house?

A. North-East B. West C. South D. East

Answer: Option (A)
2. From his house, Rahul went 25 km to north. Then he turned towards the west and covered 15 km. Then he turned south and covered 10 km. Finally, turning to the east, he covered 15 km. In which direction is he from his house?

A. North B. West C. South D. East

Answer: Option (A)
3. Satish starts from his house and takes two right turns and then one left turn. Now he is moving towards the south. In which direction Satish started from his house?

A. North B. West C. South D. East

Answer: Option (D)
4. After walking 10 m, Shankar turned left and covered a distance of 6 m, then turned right and covered a distance of 20 m. In the end, he was moving towards the south. From which direction did Shankar start his journey?

A. North B. West C. South D. East

Answer: Option (A)
5. Sumi ran a distance of 40 m towards South. She then turned to the right and ran for about 15 m, turned right again and ran 50 m. Turning to right then ran for 15 m. Finally she turned to the left an angle of 45° and ran. In which direction was she running finally?

A. South-East B. South-West C. North-East D. North-West

Answer: Option (D)
Double Line Up
Directions (1 - 5): Study the following information carefully and answer the questions follows:
There are eight different restaurants A, B, C, D, E, F, G, and H. Each restaurant has its own special dish: D1, D2, D3, D4, D5, D6, D7 and D8 not necessarily in the same order. These restaurants are at a distance of 4, 6, 7, 9, 11, 12, 13 and 15 km, but not necessarily in the same order.
Dish D6 is served in the restaurant which is the farthest. The restaurant E serves the dish D3 and it is 3 km more far than the restaurant F. The restaurant B serves D8 dish and it is at the half distance as compared to the restaurant which serves D1 dish. Dish D4 is served in the restaurant G and it is 4 km less far than the restaurant D. The distance of restaurant D is the multiple of 3. The restaurant A neither serves the dish D5 nor it is 12 km far. Restaurant H serves the dish D7 and it is 4 km farther than restaurant A.
1. Which dish is served in Restaurant A?

A. D1 B. D6 C. D2 D. D3 E. None of these

Answer: Option (C)
2. What is the distance of Restaurant C?

A. 11 km B. 13 km C. 7 km D. 12 km E. 9 km

Answer: Option (D)
3. Which of the following combinations is correct?

A. A – D8 – 6 km B. F – D2 – 4 km C. B – D8 – 7 km D. H – D7 – 13 km E. None of these

Answer: Option (D)
4. Which of the following is not true?

A. Restaurant D is 15 km away B. Dish D5 is served in Restaurant F C. Restaurant H is 11 km away D. Restaurant B is 6 km away E. All are true

Answer: Option (C)
5. How far is the restaurant in which Dish D5 is served?

A. 7 km B. 4 km C. 9 km D. 11 km E. 13 km

Answer: Option (B)
Ordering and Ranking
1. Vandana ranked eighteenth from the top and thirty sixths from the bottom among those who passed an examination. Four boys did not participate in the competition and six failed in it. How many boys were there in the class?

A. 62 B. 63 C. 64 D. 60 E. None of these

Answer: Option (B)
Explanation: Number of boys who passed = 17+1+35 = 53 Total Number of boys in class = 53+4+6 = 63
2. Niranjan is eighth from the left end and Arjun is Eleventh from the right end in a row of boys. If there are seven boys between Niranjan and Arjun, how many boys are there in the row?

A. 26 B. 27 C. 28 D. 25 E. None of these

Answer: Option (A)
Explanation: Clearly, the number of boys in row = 8+7+11 = 26
3. In a row of girls, Damini and Karishma occupy the tenth place from the right end and eleventh place from the left end, respectively. If they interchange their places, then Damini and Karishma occupy the eighteenth place from the right and fifteenth place from the left respectively. How many girls are there in the row?

A. 25 B. 30 C. 28 D. 20 E. None of these

Answer: Option (C)
Explanation: Damini and Karishma interchange their positions. So after interchanging, Damini got position 18th from the right end and 11th from the left end. Therefore total number of girls in the row = 17+1+10 = 28
4. In the parade, seven persons are standing in a row. Kuldeep is standing left to Anirudh but the right to Brijesh. Jasdeep is standing right to Gunjesh and left to Brijesh. Similarly, Karan is standing right to Anirudh and left to Randhir. Find out who is standing in the middle.

A. Anirudh B. Karan C. Kuldeep D. Gunjesh E. None of these

Answer: Option (C)
5. Five boys are sitting in a row. Ashish is not adjacent to Sandeep or Aditya. Deepak is not adjacent to Sandeep. Ashish is adjacent to Lalit. Lalit is at the middle in the row. Then, Deepak is adjacent to whom out of the following?

A. Lalit B. Aditya C. Sandeep D. Ashish E. None of these

Answer: Option (D)

Linear Seating Arrangement
Directions (1 - 5): Read the given information carefully and answer the questions given beside:
Nine persons – Chaya, Dimple, Beena, Ajit, Jaya, Fatima, Gagan, Hemant and Kaushal – are sitting in a straight line facing north, but not necessarily in the same order.
Beena is fourth to the left of Gagan; Fatima is fourth to the right of Chaya and second to the left of Kaushal, who is fifth to the right of Ajit. Dimple is not an immediate neighbor of either Kaushal or Beena. There are only three persons between Jaya and Ajit. Gagan is second to the right of Chaya.
1. In which of the following combinations is the third person sitting between the first and the second person?

A. Jaya, Kaushal, Beena B. Chaya, Hemant, Beena C. Ajit, Gagan, Chaya D. Fatima, Gagan, Dimple E. None of these

Answer: Option (D)
2. Who among the following sits third to the right of Hemant?

A. Gagan B. Dimple C. Jaya D. Beena E. None of these

Answer: Option (A)
3. Who among the following sits third to the left of Jaya?

A. Kaushal B. Gagan C. Dimple D. Beena E. None of these

Answer: Option (B)
4. Who among the following sit at the extreme ends of the line?

A. Ajit, Dimple B. Hemant, Jaya C. Kaushal, Beena D. Chaya, Kaushal E. None of these

Answer: Option (C)
5. If Kaushal and Hemant exchange their places, then who among the following sits on the immediate right of Kaushal?

A. Chaya B. Jaya C. Beena D. Ajit E. None of these

Answer: Option (A)
Puzzles
1. Which one will replace the question mark?

A. 46 B. 60 C. 75 D. 86

Answer: Option (D)
Explanation: (30 - 24) x 8 = 48 and (23 - 12) x 8 = 88 Therefore, (92 - 86) x 8 = 48.
2. Which one will replace the question mark?

A. 5 B. 6 C. 8 D. 9

Answer: Option (D)
Explanation: 93 - (27 + 3) = 63 79 - (38 + 4) = 37 Therefore, 67 - (16 + X) = 42 X = 9
3. Which one will replace the question mark?

A. 2 B. 3 C. 6 D. 7

Answer: Option (A)
Explanation: Putting the position of the letters in reverse order P = 11, S = 8, V = 5 and Y = 2.
4. Which one will replace the question mark?

A. 3 B. 5 C. 7 D. 9

Answer: Option (D)
Explanation: 5 x 8 x 10 = 400 and 6 x 9 x 7 = 378 Therefore 5 x 7 x ? = 315 ? = 9.
5. Which one will replace the question mark?

A. 4 B. 8 C. 16 D. 32

Answer: Option (A)
Explanation: (16)[latex]^{2}[/latex] = 256 Therefore, (2)[latex]^{2}[/latex] = 4.
Syllogism
Direction (1 - 5): In each of the following questions two statements are given and these statements are followed by two conclusions numbered (1) and (2). You have to take the given two statements to be true even if they seem to be at variance from commonly known facts. Read the conclusions and then decide which of the given conclusions logically follows from the two given statements, disregarding commonly known facts.
Give answer:
(A) If only (1) conclusion follows (B) If only (2) conclusion follows (C) If either (1) or (2) follows (D) If neither (1) nor (2) follows and (E) If both (1) and (2) follow.
1. Statements: Some dogs are bats. Some bats are cats. Conclusions: 1. Some dogs are cats. 2. Some cats are dogs.

A. Only (1) conclusion follows B. Only (2) conclusion follows C. Either (1) or (2) follows D. Neither (1) nor (2) follows E. Both (1) and (2) follow

Answer: Option (D)
Explanation:

2. Statements: All the trucks are flies. Some scooters are flies. Conclusions: 1. All the trucks are scooters. 2. Some scooters are trucks.

A. Only (1) conclusion follows B. Only (2) conclusion follows C. Either (1) or (2) follows D. Neither (1) nor (2) follows E. Both (1) and (2) follow

Answer: Option (D)
Explanation:

3. Statements: All buildings are chalks. No chalk is toffee. Conclusions: 1. No building is toffee 2. All chalks are buildings.

A. Only (1) conclusion follows B. Only (2) conclusion follows C. Either (1) or (2) follows D. Neither (1) nor (2) follows E. Both (1) and (2) follow

Answer: Option (A)
Explanation:

4. Statements: All cars are cats. All fans are cats. Conclusions: 1. All cars are fans. 2. Some fans are cars.

A. Only (1) conclusion follows B. Only (2) conclusion follows C. Either (1) or (2) follows D. Neither (1) nor (2) follows E. Both (1) and (2) follow

Answer: Option (D)
Explanation:

5. Statements: All the actors are girls. All the girls are beautiful. Conclusions: 1. All the actors are beautiful. 2. Some girls are actors.

A. Only (1) conclusion follows B. Only (2) conclusion follows C. Either (1) or (2) follows D. Neither (1) nor (2) follows E. Both (1) and (2) follow

Answer: Option (E)
Explanation:

Scheduling
Directions (1-5): Study the following information carefully and answer the questions that follow:
There is some unknown number of flights have taken off starting from 06:00 am during the course of the day at the interval of 60 minutes from Mumbai Airport. All flights are of different Airlines companies and to different cities. Further, it is given that
1. The flight for Guwahati is not the last among them and the flight for Surat is not the first among them. 2. The flight for Surat is 3 hours before the flight for Delhi. 3. The flight of GoAir airlines is 2 hours after the flight for Bangalore but the flight of GoAir did not go to Delhi. 4. The flight at 08:00 am is of Jet Airways and there are not more than five flights after that. 5. At the middle of all these flights, there is a flight for Bangalore. 6. The flight for Pune is immediately before the flight of Air India. 7. The flight of Vistara airlines is after the flight for Delhi and there is a gap of three flights between flight for Delhi and flight of Spice Jet. 8. The flight of Air India is after the flight of Indigo but before the flight for Guwahati.
1. Which airline is available if you want to travel from Mumbai to Surat?

A. Jet Airways B. Indigo C. Air India D. Spice Jet E. Can't be determined

Answer: Option (B)
2. At what time the flight for Guwahati has taken off?

A. 09:00 am B. 01:00 pm C. 11:00 am D. 12:00 am E. 07:00 am

Answer: Option (C)
3. How many flights have taken off between the flight of Vistara and the flight for Pune?

A. Two B. Four C. Five D. Three E. None of the above

Answer: Option (D)
4. Which flight has taken off immediately after the flight for Guwahati?

A. Flight of Air India B. Flight for Surat C. Flight for Delhi D. Flight of Vistara E. Can't be determine

Answer: Option (D)
5. If the flight for Kolkata is scheduled before the flight for Pune then which airlines would be providing the flight for Kolkata?

A. Indigo B. Spice Jet C. Go Air D. Vistara E. Jet Airways

Answer: Option (B)
Data Analysis and Interpretation
Direction (1-5): The following table gives the percentage of marks obtained by seven students in six different subjects in an examination.

1. What are the average marks obtained by all the seven students in Physics? (rounded off to two digits after the decimal)

A. 77.26 B. 89.14 C. 91.37 D. 96.11

Answer: Option (B)
Explanation: Average marks obtained in Physics by all the seven students = [latex]\frac {1}{7}[/latex] x [ (90% of 120) + (80% of 120) + (70% of 120) + (80% of 120) + (85% of 120) + (65% of 120) + (50% of 120) ] = [latex]\frac {1}{7}[/latex] x [ (90 + 80 + 70 + 80 + 85 + 65 + 50)% of 120 ] = [latex]\frac {1}{7}[/latex] x [ 520% of 120 ] = [latex]\frac {624}{7}[/latex] = 89.14.
2. The number of students who obtained 60% and above marks in all subjects is?

A. 1 B. 2 C. 3 D. None

Answer: Option (B)
Explanation: From the table, it is clear that Sajal and Rohit have 60% or more marks in each of the six subjects.
3. What was the aggregate of marks obtained by Sajal in all the six subjects?

A. 409 B. 419 C. 429 D. 449

Answer: Option (D)
Explanation: Aggregate marks obtained by Sajal = [(90% of 150) + (60% of 130) + (70% of 120) + (70% of 100) + (90% of 60) + (70% of 40)] = [135 + 78 + 84 + 70 + 54 + 28] = 449.
4. What is the overall percentage of Tarun?

A. 52.5% B. 55% C. 60% D. 63%

Answer: Option (C)
Explanation: Aggregate marks obtained by Tarun = [(65% of 150) + (35% of 130) + (50% of 120) + ((77% of 100) + (80% of 60) + (80% of 40)] = [97.5 + 45.5 + 60 + 77 + 48 + 32] = 360. The maximum marks (of all the six subjects) = (150 + 130 + 120 + 100 + 60 + 40) = 600. Therefore Overall percentage of Tarun = ([latex]\frac {360}{600}[/latex] X 100)% = 60%.
5. In which subject is the overall percentage the best?

A. Maths B. Chemistry C. Physics D. History

Answer: Option (A)
Explanation: We shall find the overall percentage (for all the seven students) with respect to each subject. The overall percentage for any subject is equal to the average of percentages obtained by all the seven students since the maximum marks for any subject is the same for all the students. Therefore, overall percentage for:
(i) Maths = ([latex]\frac {1}{7}[/latex] x (90 + 100 + 90 + 80 + 80 + 70 + 65))% = ([latex]\frac {1}{7}[/latex] x (575))% = 82.14%.
(ii) Chemistry = ([latex]\frac {1}{7}[/latex] x (50 + 80 + 60 + 65 + 65 + 75 + 35))% = ([latex]\frac {1}{7}[/latex] x (430))% = 61.43%.
(iii) Physics = ([latex]\frac {1}{7}[/latex] x (90 + 80 + 70 + 80 + 85 + 65 + 50))% = ([latex]\frac {1}{7}[/latex] x (520))% = 74.29%.
(iv) Geography = ([latex]\frac {1}{7}[/latex] x (60 + 40 + 70 + 80 + 95 + 85 + 77))% = ([latex]\frac {1}{7}[/latex] x (507))% = 72.43%.
(v) History = ([latex]\frac {1}{7}[/latex] x (70 + 80 + 90 + 60 + 50 + 40 + 80))% = ([latex]\frac {1}{7}[/latex] x (470))% = 67.14%.
(vi) Comp. Science = ([latex]\frac {1}{7}[/latex] x (80 + 70 + 70 + 60 + 90 + 60 + 80))% = ([latex]\frac {1}{7}[/latex] x (510))% = 72.86%. Clearly, this percentage is highest for Maths.