**Analytical Reasoning **

**Data Arrangements**** Introduction**

These are based on comparison, sequential order, seating/ placing arrangements and classifications. These are clue-based questions and involve an analysis of given information (conditions). You will then be required to condense it in a suitable pattern (with the help of diagrams or tables) and answer the questions asked.

All this requires sharp observation and presence of mind. These questions seem fairly complex but actually have the simplest solutions once you put them in a pattern using abbreviations or matrix tables. Some of the questions may appear straight forward but may have a catch somewhere, while others may look tough at first glance but end up being rather easy when you draw the matrix or the right picture. We will give you examples of both scenarios in this section.

**Q1) Six cricketers from Indian team Sehwag, Tendulkar, Dravid, Yuvraj, Harbhajan and Pathan are doing catching practice in a circle facing the center. Y is standing between P and T. S is second to the left of Y and second to the right of H.**

Who among them is facing Yuvraj?

- Sehwag
- Tendulkar
- Dravid
- Harbhajan
- Pathan

A1) Correct answer is (c), Dravid

Make a diagram, and use abbreviations instead of names – S, T, D, Y, H and P. Make an arrangement according to given information. One of the possible arrangements is (in a circular format)

As you can see, Dravid is facing Yuvraj

**Q2) In the same question, who is facing Sehwag ?**

- a) Tendulkar
- b) Dravid
- c) Pathan
- d) Tendulkar or Pathan
- e) Dravid or Patan

A2) Correct answer is (d).

Remember it is only stated that Y is between P and T. Whether P is to the left or right of Y is not given. So there are two possible diagrams. Read carefully and then draw accordingly.

Answer questions 3-7 based on the information below..

In a college having three disciplines (Science, Arts and Commerce), competitions are to be held for five items (Drama, Music, Debate, Sports and General Knowledge Quiz). Four students are, selected as the in-charges of these five competitions. They are Harish, Smita, Leena and Jatin.

(B) The Science student is in-charge of G.K. Quiz only.

(C) Harish, an Arts student, is in-charge of Music competition.

(D) Leena, a Commerce student, is in-charge of Debate competition.

(E) The Drama competition is neither headed by Harish nor Jatin, while the Arts student heads both Music & Sports competitions.

(F) There are two students of commerce discipline, one of whom heads Drama competition.

**Q3) Who is the in-charge of two competitions?**

- a) Smita
- b) Harish
- c) Leena
- d) Jatin

**Q4) Jatin is the in-charge of which of the following competitions?**

- a) Drama
- b) Music
- c) Sports
- d) G.K. Quiz

**Q5) Which two competitions are headed by lady students?**

- a) Music and Drama
- b) Music and Debate
- c) Sports and Debate
- d) Drama and Debate

**Q6) Which of the following combinations is right?**

- a) Harish – Sports – Science
- b) Music – Arts – Leena
- c) Smita – Commerce – Drama
- d) Commerce – drama – Leena

**Q7) Which of the following combinations is wrong?**

- a) Science – Sports
- b) Harish – Sports
- c) Drama – Smita

d) Jatin – Science

A3) to A7)

The best way to answer these type of questions is by drawing a matrix table as shown below and start filling it based on information provided. In the table below, the information in black is provided in the question and that in the red is deducted from that.

H | S | L | J | ARTS | SCIENCE | COMM | ||

DRAMA | Y | N | N | Y | ||||

MUSIC | Y | Y | ||||||

DEBATE | Y | Y | ||||||

SPORTS | Y | Y | ||||||

GK QUIZ | Y |

A3) Correct answer is (b). As can be seen from the table, Harish, an arts student, heads two competitions

A4) Correct answer is (d). The only slot open for Jatin is GK quiz. This also means that Jatin is the science student and Smita is the other commerce student

A5) Correct answer is (d). The two ladies head Drama and Debate.

A6) Correct answer is ©. Smita is a commerce student who heads Drama

A7) Correct answer is (a). Sports is headed by Harish, an arts student.Too often in real life, we say we will do certain things only if some other things are also done. You will gain entrance to top MBA schools only if you do well in the entrance examination and you will do well in entrance examination only if you study and practice hard. This is what conditionality menas…..(XYZ) will happen only if (ABC) happens or in some cases does not happen. Lets start with an example

Sometimes the questions are designed to approximate the type of reasoning required in the workplace. The questions will often use very specific illustrations, for example the question may present financial data or use information technology jargon. However, an understanding of these areas is not required to answer the question.

**For the next 5 questions, read the following information carefully and answer the questions given below it.**

Mr Ramakant, the Manager of PQR Ltd has to complete four assignments (X, Y, Z &W) from six people (At B, C, D, E & F) working under him. Two of these assignments have the duration of 6 months each while the other two assignments have the durations of 9 months and one year respectively. On the basis of the information below, answer the questions that follow:

(1) The assignments of 6 month duration are to be handled by one person only while the other assignments are to be handled by two persons each

(2) Assignment X has the duration of 12 months while assignment W has the duration of 9 months

(3) A, B & D do not work with each other

(4) E works independently. He has to be allotted assignment Z

(5) A and C cannot work together

(6) F can work either with D or with C only. However, cannot work on the assignment of one year’s duration

(7) C and D cannot work together

**Q1) Who among the following would be handling assignment Y?**

(a) A (b) B (c) C (d) D

**Q2) Who among the following would be handling assignment W?**

(a) B & C together (b) F & D together

(c) F & C together (d) A & F together

**Q3) Who among the following would be handling assignment X?**

(a) A & B together (b ) C & D together

(c) F & D together (d) B & C together

**Q4) Which of the following statements is TRUE?**

(a) Assignment X is of 1 year and assignment Y is of 9 months duration

(b) Both the Assignments Z & W are handled by one person only

(c) Assignment Y would be handled by A alone

(d) Assignment W would be handled by F alone

**Q5) Which of the following pairs cannot be RIGHT with reference to the allotment of the assignments?**

(a) A and F (b) F and D

(c) B and C (d) All are RIGHT

A1) The approach to solving these problems is similar to the matrix approach that was shown in the previous section. Lets start by making a table and putting in all the information that is provided to us. Easier to make a 2×2 table in this case since the information re duration of assignments is clearly provided to us.

Assignment Name | X | Y | Z | W |

Duration | 12 | 6 | 6 | 9 |

# of people needed | 2 | 1 | 1 | 2 |

A | Y | |||

B | Y | |||

C | Y | |||

D | Y | |||

E | Y | |||

F | Y |

A1) Correct answer is (a)

A2) Correct answer is (b)

A3) Correct answer is (d)

A4) Correct answer is ©

A5) Correct answer is (a)

**For questions 6 & 7, read the following information carefully and answer the questions given below it.**

If one were to visit the Ellora caves, one is bound to visit the Aiholi temple clusters which are the confluence of sculpture cultures of the northern and southern parts of ancient India. The northern temples marked by their flat roofs and the southern by their round domes. The amazing part is that there are seven temples in a row, starting from the left with a domed temple, with northern and southern temples alternating with each other, Each temple is dedicated to a single deity and no deity is repeated in this row of nine.

-The Shivaling is five temples before the Vsihnupratishthan.

-The third domed temple is the Ganesh mandir.

-The first northern temple after the Ganesh temple is ‘Shaktisthan’

-The fourth temple in the row is the ‘Krishnamandir’

-The ‘Rammandir’ is a southern temple.

-The ‘ Brhamadarshan’ is between the Ganeshmandir and Shivlinga.

**6) Which of the following is a sequence from right to left ?**

- a) Brhamadarshan, Krishnamandir, Rammandir, Vishnupratishthan.
- b) Shaktisthan, Vishnupratishthan, Brahmadarshan, Shivlinga.
- c) Ganeshmandir, Shaktisthan, Krishnamandir, Brahmadarshan
- d) Vishnupratishtahn, Ganesh mandir, Krishnamandir, Shivlinga.

**7). Which of the following may be said about ‘Brahmadarshan’ ?**

- a) It is a northern temple
- b) It is two temples away the Rammandir.
- c) It is next to the krishnamandir.
- d) It is three temples away from the shaktisthan.

A6) Correct answer is (d)

The position of the temples is as shown below

RAM SHIV BRAHMA KRISHNA GANESH SHAKTI VISHNU

1S 2N 3S 4N 5S 6N 7S

A7) Correct answer is ©

The position of the temples is as shown below

RAM SHIV BRAHMA KRISHNA GANESH SHAKTI VISHNU

1S 2N 3S 4N 5S 6N 7S

**LR ****Practice Test**

**(based on sections 10 & 11)**

**1) Read the information given below and answer the questions that follow.**

Five friends (Avinash, Vijay, Alok, Vivek and Rajiv) went to a hotel and ordered five different soups (Tomato, Chicken, Vegetable, Corn and Mutton), followed by lunch. After lunch, they ordered five different desserts. (Mango, Pista, Vanilla, Tutti-Fruti and Casatta).

(i) Avinash ordered for vegetable soup and Mango ice-cream

(ii) Vivek didn’t order mutton soup but ordered Vanilla ice-cream

(iii) Vijay is a vegetarian who ordered Tutti-Fruti ice-cream

(iv) The person who ordered corn-soup also ordered Pista ice-cream while Rajiv ordered Casatta ice-cream

**Who among the following ordered Tomato soup?**

(a) Avinash (b) Vijay (c) Alok (d) Vivek

**Which among the following soups was ordered by Vivek?**

(a) Vegetable (b) Corn (c) Chicken (d) Mutton

**Which of the following combinations is FALSE?**

(a) Rajiv – Chicken soup

(b) Tomato soup – Tutti Fruti ice-cream

(c) Chicken soup – Vivek

(c) Alok – Corn soup

**Which of the following ice-creams was ordered by Alok?**

(a) Vanilla (b) Tutti-Fruti (c) Mango (d) Pista

**Which of the following combinations is TRUE?**

(a) Avinash – Tomato soup – Tutti-Fruti ice-cream

(b) Vijay – Corn soup – Mango ice-cream

(c) Alok – Mutton soup – Pista ice-cream

(d) Vivek – Chicken soup – Vanilla ice-cream

A1) As mentioned in the instructional material, the best way to answer questions of these type is by making a matrix table

Tom | Chick | Veg | Corn | Mutton | Mango | Pista | Vanilla | Tutti | Cass | ||

Av | Y | Y | |||||||||

Viv | Y | N | Y | ||||||||

Al | Y | Y | |||||||||

Vj | Y | Y | |||||||||

R | Y | Y |

For Q1, correct answer is (b)

A2) Correct answer is ©

A3) Correct answer is (a)

A4) Correct answer is (d)

A5) Correct answer is (d)

**For question 6 – 10, read the following information carefully and answer the questions given below it.**

Mr Krishnamurthy, Director of ATN International, has decided to open 5 new branches in five cities (P, Q, R, S & T). He has selected 5 candidates (Amit, Bala, Charu, Dev and John) to handle the branches. The candidates have completed their MBA with specialisations in 5 different fields (Marketing, Finance, Production, Purchasing and Systems).

(1) Amit will handle the branch in city S only

(2) Dev has completed MBA in Purchasing. He would not handle the branch in city P

(3) The person handling the branch in city Q has done specialisation in Marketing

(4) Bala will be handling the branch in city R. She has specialised in Finance

(5) John has specialised in Systems

**6) In which of the following fields has Amit done his specialisation?**

(a) Marketing (b) Purchasing (c) Finance (d) Production

**7) Which of the following branches would be handled by Dev?**

(a) City S (b) City T (c) City R (d) City P

**8) Who among the following has done specialisation in Marketing?**

(a) Charu (b) Amit (c) John (d) Dev

**9) Which of the following combinations is RIGHT?**

(a) Dev – Purchase – City R

(b) Marketing – Charu – City T

(c) Bala – City Q – Finance

(d) John – City P – Systems

**10) Which of the following combinations is WRONG?**

(a) Charu – Marketing – City Q

(b) City P – Systems – John

(c) Amit – City S – Purchase

(d) Finance – Bala – City R

A5) Lets start with making a matrix table

P | Q | R | S | T | Mktg | Fin | Prod | Pur | Sys | ||

Amit | Y | Y | |||||||||

Bala | Y | Y | |||||||||

Charu | Y | Y | |||||||||

Dev | N | Y | Y | ||||||||

John | Y | Y |

A6) Correct answer is (d)

A7) Correct answer is (b)

A8) Correct answer is (a)

A9) Correct answer is (d)

A10) Correct answer is ©

**For questions 11 – 15, Read the following information and answer the questions given below.**

There is a group of six students M, N, O, P, Q and R in a class. Each of the six students opt for two subjects, one compulsory and the other optional subject. P’s optional subject was Geography while three others have it as a compulsory subject. Q and R have Chemistry as one of their subjects. R’s compulsory subject is Physics which is an optional subject of both O and Q. Geography and English are M’s subjects, as compulsory and optional respectively. Biology is an optional subject of only one of them. The only female student in the group is the one who has Geography as the optional subject and English as the compulsory one

**Who is the female student in the group?**

(a) M (b) N

(c) 0 (d) P

**What is the compulsory subject of ‘0’?**

(a) Geography (b) Chemistry

(c) Physics (d) English

**Which of the following have the same “compulsory/optional” set as that of R?**

(a) M (b) N

(c) O (d) None of the above

**Disregarding which is the compulsory and which is the optional Subject, who has the same combination as that of R?**

(a) M (b) Q

(c) 0 (d) P

**Which of the following groups of students have Geography as their compulsory subject?**

(a) M, 0 & P (b) 0, N & P

(c) O, P & R (d) M, N & 0

A11)

The distribution of subjects based on information given is as follows:

Student | Compulsory Subject | Optional Subject |

M | Geography | English |

N | Geography | Biology |

O | Geography | Physics |

P | English | Geography |

Q | Chemistry | Physics |

R | Physics | Chemistry |

A11) Correct answer is (d). The only female student is P.

A12) Correct answer is (a)

A13) Correct answer is (d)

A14) Correct answer is (b)

A15) Correct answer is (d)

**SAMPLE QUESTIONS AND EXPLANATIONS:**

**Directions:**

Each group of questions in this section is based on a set of conditions. In answering some of the questions, it may be useful to draw a rough diagram. Choose the response that most accurately and completely answers the question and blacken the corresponding space on your answer sheet.

**Passage for Question 1**

A university library budget committee must reduce exactly five of eight areas of expenditure — G, L, M, N, P, R, S, and W — in accordance with the following conditions:

- If both G and S are reduced, W is also reduced.
- If N is reduced, neither R nor S is reduced.
- If P is reduced, L is not reduced.
- Of the three areas L, M, and R, exactly two are reduced.

**Question 1**

If both M and R are reduced, which one of the following is a pair of areas neither of which could be reduced?

- G, L
- G, N
- L, N
- L, P
- P, S

**Explanation for Question 1**

This question concerns a committee’s decision about which five of eight areas of expenditure to reduce. The question requires you to suppose that M and R are among the areas that are to be reduced, and then to determine which pair of areas could not also be among the five areas that are reduced.

The fourth condition given in the passage on which this question is based requires that exactly two of M, R, and L are reduced. Since the question asks us to suppose that both M and R are reduced, we know that L must not be reduced:

- Reduced: M, R
- Not reduced: L

The second condition requires that if N is reduced, neither R nor S is reduced. So N and R cannot both be reduced. Here, since R is reduced, we know that N cannot be. Thus, adding this to what we’ve determined so far, we know that L and N are a pair of areas that cannot both be reduced if both M and R are reduced:

- Reduced: M, R
- Not reduced: L, N

Answer choice (C) is therefore the correct answer, and you are done.

When you are taking the test, if you have determined the correct answer, there is no need to rule out the other answer choices. However, for our purposes in this section, it might be instructive to go over the incorrect answer choices. For this question, each of the incorrect answer choices can be ruled out by finding a possible outcome in which at least one of the two areas listed in that answer choice are reduced. Consider answer choice (A), which lists the pair G and L. We already know that for this question L must be one of the areas that is not reduced, so all we need to consider is whether G can be one of the areas that is reduced. Here’s one such possible outcome:

- Reduced: M, R, G, S, W

**If areas M, R, G, S, W are reduced, then the supposition for the question holds and all of the conditions in the passage are met:**

- M and R are both reduced, as supposed for this question.
- Both G and S are reduced, and W is also reduced, so the first condition is satisfied.
- N is not reduced, so the second condition is not relevant.
- P is not reduced, so the third condition is not relevant.
- Exactly two of L, M, and R are reduced, so the fourth condition is satisfied.

Thus, since G could be reduced without violating the conditions, answer choice (A) can be ruled out. Furthermore, since G appears in the pair listed in answer choice (B), we can also see that (B) is incorrect.

Now let’s consider answer choice (D), which lists the pair L and P. We already know that for this question L must be one of the areas that is not reduced, so all we need to consider is whether P can be one of the areas that is reduced. Here’s one such possible outcome:

- Reduced: M, R, P, S, W

**If areas M, R, P, S, and W are reduced, then the supposition for the question holds and all of the conditions in the passage are met:**

- M and R are both reduced, as supposed for this question.
- G is not reduced, so the first condition is not relevant.
- N is not reduced, so the second condition is not relevant.
- P is reduced and L is not reduced, so the third condition is satisfied.
- Exactly two of L, M, and R are reduced, so the fourth condition is satisfied.

Thus, since P could be reduced without violating the conditions, answer choice (D) can be ruled out. Furthermore, since P appears in the pair listed in answer choice (E), we can also see that answer choice (E) is incorrect.

**Passage for Questions 2 and 3**

Seven piano students — T, U, V, W, X, Y, and Z — are to give a recital, and their instructor is deciding the order in which they will perform. Each student will play exactly one piece, a piano solo. In deciding the order of performance, the instructor must observe the following restrictions:

- X cannot play first or second.
- W cannot play until X has played.
- Neither T nor Y can play seventh.
- Either Y or Z must play immediately after W plays.
- V must play either immediately after or immediately before U plays.

**Question 2**

If V plays first, which one of the following must be true?

- T plays sixth.
- X plays third.
- Z plays seventh.
- T plays immediately after Y.
- W plays immediately after X.

**Explanation for Question 2**

This question deals with an ordering relationship defined by a set of conditions concerning when seven piano students will perform. As an aid in visualizing this problem you can draw a simple diagram that shows the seven recital slots arranged in order from left to right. Student V is shown in the first slot, as specified by the supposition that “V plays first”:

1 |
2 |
3 |
4 |
5 |
6 |
7 |

V |

We can immediately fill in one of the empty slots in the diagram. The condition that “V must play either immediately after or immediately before U plays” tells us that U must occupy the second slot in the recital schedule. This is shown below:

1 |
2 |
3 |
4 |
5 |
6 |
7 |

V | U |

Since the question asks us what must be true, we can eliminate incorrect responses by showing that they could be false. Response (A) is incorrect because the statement that “T plays sixth” is not necessarily true — we can place T in one of the slots other than sixth and still meet all the conditions of the problem. One such recital schedule, with T playing third, is shown in the diagram below:

1 |
2 |
3 |
4 |
5 |
6 |
7 |

V | U | T | X | W | Y | Z |

This schedule can be derived as follows:

- With V, U, and T in the first three positions, there are four positions left for W, X, Y, and Z.
- W must come after X — because of the condition that “W cannot play until X has played” — so if X is fourth and W is fifth, this condition will be met.
- This leaves two possible slots for Y and Z. Y cannot play seventh because of the condition that “Neither T nor Y can play seventh.” Suppose, then, that Y is sixth and Z is seventh.

A check will verify that this schedule meets the conditions of the problem, including the one that “Either Y or Z must play immediately after W plays.”

The schedule shown in the diagram also demonstrates that response (B)is incorrect. In it, X plays fourth, so it is not correct that the statement, “X plays third,” must be true.

Response (C), “Z plays seventh,” is the credited response. We can show Z must be seventh by demonstrating that:

- all the conditions can be met with Z in the seventh slot, and
- some of the conditions would be violated with Z in any slot other than seventh.

To demonstrate that Z can play seventh, you can refer to the schedule that was developed for the discussion of response (A), above. In it, Z plays seventh, and the supposition given in the question and all the conditions in the passage are met.

To demonstrate that Z cannot play in a slot other than seventh, we can attempt to find another student to play seventh. We already know that neither U nor V can play seventh. Hence, there are four remaining players: T, W, X, and Y. However, a review of the conditions shows that none of those players can play seventh:

- The third condition states that “Neither T nor Y can play seventh.”
- W can’t play seventh, because there must be a slot following W’s in order to meet the condition, “Either Y or Z must play immediately after W plays.” If W plays seventh, then there is no such slot left for Y or Z.
- For a similar reason X can’t play seventh, because there must be a slot following X’s in order to meet the condition, “W cannot play until X has played.”

Since Z can play seventh and no other player can, then the statement that Z must play seventh is correct and (C) is the credited response.

Response (D) is incorrect because it is not necessarily true that “T plays immediately after Y.” In our discussion of response (A), we developed a schedule in which T plays third and Y plays sixth, yet all conditions are satisfied.

Response (E) is incorrect because, as shown in the diagram below, it is not necessarily true that “W plays immediately after X.” This schedule is obtained by simply reversing the order of players W and Y in the schedule we developed in the analysis of response (A).

A review will show that all of the suppositions given in the question and all the conditions in the passage are met by this schedule:

1 |
2 |
3 |
4 |
5 |
6 |
7 |

V | U | T | X | W | Y | Z |

**Logical Reasoning**

**LR 8 – Analytical Reasoning or Logic Games**

Questions that involve analytical reasoning tend to inspire fear in most test takers, especially those who haven’t developed a specific method for solving these problems. The recommended plan to solving problems in this set is to make a diagram outlining all the give information and

- Know the rules of the logic game and what each rule means
- Draw up an easy-to-reference diagram that includes all the game’s information
- Look for common elements in the rules; you can combine these to make deductions
- Read the questions carefully; be sure to know what is being asked before you try to answer the question

Now, let us try this approach on a few problems.

Answer the next two questions based on the basis of the information below. (Q1 and Q2)

A weekly television show routinely stars six actors – J, K, L, M, N and O. Since the show has been on the air for a long time, some of the actors are good friends and some do not get along at all. In an effort to keep peace, the director sees to it that friends work together and enemies do not. Also, as the actors have become more popular, some of them need time off to do other projects. To keep the schedule working, the director has a few things he must be aware of –

- J will only work on episodes on which M is working
- N will not work with K under any circumstances
- M can only work every other week, in order to be free to film a movie
- At least three of the actors must appear in every weekly episode

**Q1 ) In a show about L getting a job at the same company J already works for and K used to work for, all three actors will appear. Which of the following is true about the other actors who may appear ?**

- M, N and O must all appear
- M may appear and N must appear
- M must appear and O may appear
- O may appear and N may appear
- Only O may appear

A1) Correct answer is ©

J will only work in episodes in which M is working and there are no restrictions on O’s schedule.

**Q2) Next week, the show involves N’s new car and O’s new refrigerator. Which of the following is true about the actors who may appear ?**

- M, J, L and K all may appear
- J, L and K mist appear
- Only K may appear
- Only L may appear
- L and K must appear

A2) Correct answer is (d)

K will not work with N, so choices ‘c’ and ‘e’ are incorrect. M can only work every other week, so choice ‘a’ is incorrect. Since M is not working, J will not work, so choice ‘b’ is incorrect too.

*Answer the next two questions based on the information provided*

Q, R, S, T and U were guest at a party where people were asked to dress as an object that represents their profession. R and S are women while the other 3 are men. The costumes included a flower, a pencil, a spoon, a camera and a thermometer. The professions included a photographer, a florist, a doctor, an accountant and a chef,

- Q is an accountant
- Neither of R and S were dressed as a spoon
- None of the men is a doctor
- T is dressed as a camera
- S is a florist

**3) Which person is dressed as a thermometer ?**

- a) Q
- b) R
- c) S
- d) T
- e) U

A3) Correct answer is (b)

Thermometer represents a doctor and since none of the men are doctors and S is a florist, R must be the doctor in the group

**4) What is U’s profession ?**

- a) photographer
- b) florist
- c) doctor
- d) accountant
- e) chef

A4) Correct answer is (e)

Q is an accountant, R is a doctor, S is a florist, T is a photographer, so U must be a chef

**For questions 3 to 5: Read the following information and answer the questions that follow.**

Two shopkeepers go to buy newly designed weights from the trade fair. In a particular shop the salesman asks their limits of weighing at a time. Both of them tell their limit as 120 kg at a time. The salesman shows them the price list as:

Any weight less than 10 kg ? Rs. 10 per piece

More than 11 kg but less than 50 kg ? Rs. 20 per piece

More than 51 kg but less than 100 kg ? Rs. 30 per piece.

More than 100 kg ? Rs. 50 per piece.

The salesman gave them two options:

In the 1st option, the shopkeepers might have to put the weights on both sides. He gave them an example:

Suppose you want to weigh 7 kg, so put 10 kg on weight side and put 3 kg on the goods side.

In the second option, the shopkeeper did not need to put the weights on goods side.

**3) If the 1st shopkeeper opts for the 1st option, what is the minimum number of weights he would need to buy at the lowest cost?**

- a) 8 b ) 10 c) 5 d) None of these4). The 2nd shopkeeper opts for the 2nd option. What is the min. no. of weights he would need to buy at the lowest cost?

a) 5 b)7 c) 10 d) None of these5) One of them needed as much more amount as the other has left after purchase. Suppose both of them left their home with the same amount. Who borrowed and what amount was borrowed?

a) First shopkeeper borrowed Rs. 30 - b) Second shopkeeper borrowed Rs. 30

c) Second shopkeeper borrowed Rs. 15 - d) First shopkeeper borrowed Rs. 15

A3) Correct answer is ©.

The minimum number of weights needed are 5 – 1 kg, 3 kg, 9 kg, 27 kg and 81 kg

A4) Correct answer is (b)

The minimum number of weights needed are 7 – 1 kg, 2 kg, 4 kg, 8 kg, 16 kg, 32kg and 64 kg

A5) Correct answer is ©

First shopkeeper needs Rs 80 (3 x 10 + 1 x 20 + 1 x 30)

Second shopkeeper needs Rs 110 ( 4 x 10 + 2 x 20 + 1 x 30)

So second shopkeeper needs to borrow Rs 15 (Rs 110 –Rs 80 divided by 2)

**For questions 6, 7 & 8 refer to the following data to answer the questions that follow.**

An old woman died recently. Unaware to all, she was quite rich. As she had no children, she left most of her estate to her favourite charities; she willed Rs 50,00,000 to three couples who had shown her kindness in the later years of her life. Kareena received Rs 50,000 more than Krishna and Mandira received Rs 50,000 more than Kareena. The three women received a total of Rs 19,80,000. The rest was left to their husbands. Balwant was given as such much as his wife, Raju received 3/2 as much as his wife and Jaswant was granted twice as much as his wife.

**6) The wife of Jaswant is:**

(a) Mandira (b) Kareena (c) Krishna (d) Can’t be determined

**7) The husband of Krishna is:**

(a) Balwant (b) Jaswant (c) Raju (d) Can’t say

**8) Which of the following is the correct pair?**

(a) Krishna and Jaswant (b) Kareena and Raju

(c) Raju and Mandira (4d) Raju and Krishna

A6) Correct answer is (a)

A7) Correct answer is (a)

A8) Correct answer is (b)

Let Rs k be the amount that Krishna received.

So, Kareena received 50,000 +k

Mandira received a total of 50,000+(50,000 + k) = 1,00,000 + k

The 3 women received a total of Rs 19,80,000

So, k+ (50,000 + k) + (1,00,000 + k) = 19,80,000; 3k + 1,50,000 = 19,80,000 or k = 6,10,000

So Krishna received Rs 6,10,000

Kareena received 6,10,000 + 50,000 = Rs 6,60,000

Mandira received 6,10,000+1,00,000 = Rs 7,10,000.

Now, husbands share 50,00,000 – 19,80,000 = 30,20,000. F

If Raju is Kareena’s husband, he gets 1.5 her amount or 9,90,000 which given a 0 in the thousandth digit. If Raju is Krishna’s husband, he gets Rs 915,000; or if he is Mandira’s husband, he will Rs 10,65,000. Both of these amounts give a 5 in the thousandth digit and the amounts of the husbands will not add up to a 0 in the thousandth digit as in Rs 30,20,000. So Raju is Kareena’s husband.

Now, Balwant and Jaswant are leftg with 30,20,000 – 9,90,000 = 20,30,000. A quick calculation will show that is also the sum of 2 x 7,10,000 + 6,10,000. So, Raju is Kareena’s husband, Balwant is Krishna’s husband and Jaswant is Mandira’s husband.

*Answer questions 9 & 10 based on the information below*

Three friends are playing with a set of red, yellow and green marbles. When it is time to go home, the first friend takes half the marbles, second one takes half of the remaining, third one half of the remaining. They are still left with a few and they decide to equally divide the left over amongst themselves. At the end of all this, the third friend has 20

**9) The number of total balls is**

- a) 1200 b) 1600
- c) 800 d) 2400

**10) The difference between the marbles that the first friend has and the second friend has is**

- a) 10 b) 20
- c) 30 d) 40

A9) Correct answer is (a)

If ‘x ‘ is the total number of balls, friend one gets x/2 in the beginning, friend two gets x/4 and friend 3 gets x/8. They divide the remaining amongst themselves so they get additional x/24. So the third friend has

x/8+ x /24= 20,or x= 120

A10) Correct answer is ©

First friend has x/2 + x/ 24 = 60 + 5= 65

Second friend has x/4 + x/24 = 30 + 5=35

The difference between the two is 30

*For questions 11 – 15, answer the questions based on the information below*

An inventor is trying to develop a new machine for casinos. A player would enter a coin, the wheel would start turning, the lights would start blinking and they would either stop blinking (no winning) or there would be bright lights with loud noise (winner). The logic behind differentiating between a winner and looser is calculation done in the machine based on three numbers A, B & C.

The machine randomly starts with two single digit values for A & B and a multiple of 10 for C. It updates them such that A= AB and B=B+1 for every rotation of the circle. The machine stops when A >= C. The winning happens when the machine stops in number of circle rotations that are multiple of 4. When the machine stops for other number of circle rotations, the player doesn’t win.

**11) When Radhesh starts playing, the machine uses these numbers as starting point A = 3, B= 2 and C= 100. The ending scenario for him is**

- a) winner with 8 rotations
- b) looser with 6 rotations
- c) winner with 4 rotations
- d) looser with 2 rotation

A11) Correct answer is ©

Lets make a table and see how many rotations does the circle make before the machine stops with the condition A >= C (100)

A | B | |

Starting | 3 | 2 |

After Rotation 1 | 6 | 3 |

After Rotation 2 | 18 | 4 |

After Rotation 3 | 72 | 5 |

After Rotation 4 | 360 | 6 |

After rotation 4, A is 360 or > 100, so the machine stops and Radesh wins

**12) In the above scenario, what is the final value of A**

- a) 36 b) 360
- c) 48 d) 480

A12) Correct answer is (b), as can be seen from the table

**13) If value of C is changed to 2000, what would be the final value of A ?**

- a) 2160 b) 15120
- c) 2042 d) 14480

A13) Correct answer is (a)

Add another rotation to the table above and the next values for A and B are 2160 and 7 resp. Since 2160 is > 2000 (A>C), the machine will stop.

**14) If starting values for A and B are 7 and 5, what is the minimum value for C so that the final value of B is 8**

- a) 1260 b) 1400
- c) 1470 d) 1600

A14) Correct answer is ©

The machine would stop after the third rotation when the value of B is 8 and A is 1470. For the machine to stop, C should be atleast 1470

A | B | |

Starting | 7 | 5 |

After Rotation 1 | 35 | 6 |

After Rotation 2 | 210 | 7 |

After Rotation 3 | 1470 | 8 |

**For question 15 – 18, read the information below and then answer the questions that follow**

Pallavi, Rekha and Geeta are playing a game staring with Rs 20000, Rs 16000 and Rs 10000 resp. The person who has the maximum money gives to other two an amount equal to half the difference between her amount and the respective person’s amount. The game finishes when the difference between any two of them is less than Rs 500

**15) At the end of the game, the person with the highest money is**

- a) Pallavi b) Rekha c) Geeta d) All have equal amount

A15) Correct answer is (b)

Lets do the calculation in 000s

Pallavi | Rekha | Geeta | |

Starting Point | 20 | 16 | 10 |

Round 1 | 20 – 2 – 5 = 13 | 16 + 2 = 18 | 10 + 5= 15 |

Round 2 | 13 + 2.5 = 15.5 | 18 – 2.5 – 1.5 = 14 | 15 + 1.5 = 16.5 |

Round 3 | 15.5 + 0.5 = 16 | 14 + 1.25 = 15.25 | 16.5 – 0.5 – 1.25 = 14.75 |

Round 4 | 16 – 0.375 – 0.625 = 15 | 15.25 + 0.375 = 15.625 | 14.75 + 0.625 = 15.375 |

At the end of Round 4, Pallavi has 15,000, Rekha has 15,625 and Geeta has 15,375.

**16) At the end of the game, Pallavi has**

- a) Rs 10,000 b) Rs 12,000
- c) Rs 15,000 d) Rs 18,000

A16) Correct answer is ©

**17) The number of times the lead changes in terms of a different person being the one with the highest money is**

- a) 1 b) 2 c) 3 d) 4

A17) Correct answer is (d). The lead changes in every round

**18) The biggest gain was**

- a) 0% – 25% b) 25% – 50%
- c) 50% – 75% d) 75% – 100%

A18) Correct answer is ©.

Geeta had the maximum gain of 50% +

Answer questions 19 and 20 based on the information below

In order to gain the benefit from the booming real estate market, the planning team at a real estate company has put together a proposal for a housing estate. They are targeting sales coverage such that by the end of year 2, 1/6th of the buyers will own a villa and 3/4th will own a flat. 1/8th of those that will own a villa would not own a flat

**19) What percentage of the buyers would end up owning both a villa and a flat ?**

- a) 3/32 b) 21/32
- c) 3/16 d) 21/ 64

A19) Correct answer is (b)

Since 1/8th of those that own a villa would not own a flat, the remaining 7/8th would own a flat. So percentage that would own both is 7/8 x ¾ = 21/32

**20) The overall sales coverage (% of houses that are sold) by end of year 2 is**

- a) 0% – 25% b) 25% – 50%
- c) 50% – 75 % d) 75% – 100%

A20) Correct answer is ©

1/6 + ¾ – 21/32 = 67/96 or 70%

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