CAT 2006 Question Paper(Available):Download Solutions with Answer Key

Question 1:

Who cannot be a member of a team of size 3?

• (1) L
• (2) M
• (3) N
• (4) P
• (5) Q

Who can be a member of a team of size 5?

• (1) K
• (2) L
• (3) M
• (4) P
• (5) R

What would be the size of the largest possible team?

• (1) 8
• (2) 7
• (3) 6
• (4) 5
• (5) Cannot be determined

What could be the size of a team that includes K?

• (1) 2 or 3
• (2) 2 or 4
• (3) 3 or 4
• (4) Only 2
• (5) Only 4

In how many ways can a team be constituted so that the team includes N?

• (1) 2
• (2) 3
• (3) 4
• (4) 5
• (5) 6

How much did Dipan get in English Paper II?

• (1) 94
• (2) 96.5
• (3) 97
• (4) 98
• (5) 99

Among the top ten students, how many boys scored at least 95 in at least one paper from each of the groups?

• (1) 1
• (2) 2
• (3) 3
• (4) 4
• (5) 5

Had Joseph, Agni, Pritam and Tirna each obtained Group Score of 100 in the Social Science Group, their standing in decreasing order of final score would be:

• (1) Pritam, Joseph, Tirna, Agni
• (2) Joseph, Tirna, Agni, Pritam
• (3) Pritam, Agni, Tirna, Joseph
• (4) Joseph, Tirna, Pritam, Agni
• (5) Pritam, Tirna, Agni, Joseph

Students who obtained Group Scores of at least 95 in every group are eligible for a prize. Among those eligible, the student obtaining the highest Group Score in Social Science Group is awarded this prize. The prize was awarded to:

• (1) Shreya
• (2) Ram
• (3) Ayesha
• (4) Dipan
• (5) No one from the top ten

Each student was allowed to improve his/her score in exactly one paper of choice to 100. After that, the topper among the ten students was:

• (1) Ram
• (2) Agni
• (3) Pritam
• (4) Ayesha
• (5) Dipan

How many participants in the conference did not change their Erd\H{os number during the conference?

• (1) 2
• (2) 3
• (3) 4
• (4) 5
• (5) Cannot be determined

The person having the largest Erd\H{o}s number at the end of the conference must have had Erd\H{o}s number (at that time):

• (1) 5
• (2) 7
• (3) 9
• (4) 14
• (5) 15

How many participants had the same Erd\H{o}s number at the beginning of the conference?

• (1) 2
• (2) 3
• (3) 4
• (4) 5
• (5) Cannot be determined

The Erd\H{o}s number of C at the end of the conference was:

• (1) 1
• (2) 2
• (3) 3
• (4) 4
• (5) 5

The Erd\H{o}s number of E at the beginning of the conference was:

• (1) 2
• (2) 5
• (3) 6
• (4) 7
• (5) 8

If Chetan sold 10 shares of MCS on three consecutive days, while Michael sold 10 shares only once during the five days, what was the price of MCS at the end of day 3?

• (1) Rs 90
• (2) Rs 100
• (3) Rs 110
• (4) Rs 120
• (5) Rs 130

If Chetan ended up with Rs 1300 more cash than Michael at the end of day 5, what was the price of MCS share at the end of day 4?

• (1) Rs 90
• (2) Rs 100
• (3) Rs 110
• (4) Rs 120
• (5) Not uniquely determinable

If Michael ended up with 20 more shares than Chetan at the end of day 5, what was the price of MCS share at the end of day 3?

• (1) Rs 90
• (2) Rs 100
• (3) Rs 110
• (4) Rs 120
• (5) Rs 130

If Michael ended up with Rs 100 less cash than Chetan at the end of day 5, what was the difference in the number of shares possessed by Michael and Chetan at the end of day 5?

• (1) Michael had 10 less shares than Chetan.
• (2) Michael had 10 more shares than Chetan.
• (3) Chetan had 10 more shares than Michael.
• (4) Chetan had 20 more shares than Michael.
• (5) Both had the same number of shares.

What could have been the maximum possible increase in combined cash balance of Chetan and Michael at the end of the fifth day?

• (1) Rs 3700
• (2) Rs 4000
• (3) Rs 4700
• (4) Rs 5000
• (5) Rs 6000

If the government wants to ensure that no traffic flows on the street from D to T, while equal amount of traffic flows through junctions A and C, then a feasible set of toll charged (in rupees) at junctions A, B, C, and D respectively to achieve this goal is:

• (1) 1,5,3,3
• (2) 1,4,4,3
• (3) 1,5,4,2
• (4) 0,5,2,3
• (5) 0,5,2,2

If the government wants to ensure that all motorists travelling from S to T pay the same amount (fuel costs and toll combined) regardless of the route they choose and the street from B to C is under repairs (and hence unusable), then a feasible set of toll charged (in rupees) at junctions A, B, C, and D respectively to achieve this goal is:

• (1) 2,5,3,2
• (2) 0,5,3,1
• (3) 1,5,3,2
• (4) 2,3,5,1
• (5) 1,3,5,1

If the government wants to ensure that the traffic at S gets evenly distributed along streets from S to A, from S to B, and from S to D, then a feasible set of toll charged (in rupees) at junctions A, B, C, and D respectively to achieve this goal is:

• (1) 0,5,4,1
• (2) 0,5,2,2
• (3) 1,5,3,3
• (4) 1,5,3,2
• (5) 0,4,3,2

If the government wants to ensure that all routes from S to T get the same amount of traffic, then a feasible set of toll charged (in rupees) at junctions A, B, C, and D respectively to achieve this goal is:

• (1) 0,5,2,2
• (2) 0,5,4,1
• (3) 1,5,3,3
• (4) 1,5,3,2
• (5) 1,5,4,2

The government wants to devise a toll policy such that the total cost to the commuters per trip is minimized. The policy should also ensure that not more than 70% of the total traffic passes through junction B. The cost incurred by the commuter travelling from point S to point T under this policy will be:

• (1) Rs 7
• (2) Rs 9
• (3) Rs 10
• (4) Rs 13
• (5) Rs 14

Relations between the factory and the dealer are distant and usually strained as the factory tries to force cars on the dealers to smooth out production. Relations between the dealer and the customer are equally strained because dealers continuously adjust prices — make deals — to adjust demand with supply while maximizing profits. This becomes a system marked by a lack of long-term commitment on either side, which maximizes feelings of mistrust. In order to maximize their bargaining positions, everyone holds back information — the dealer about the product and the consumer about his true desires.

• (A) As a result, ‘deal making’ becomes rampant, without concern for customer satisfaction.
• (B) As a result, inefficiencies creep into the supply chain.
• (C) As a result, everyone treats the other as an adversary, rather than as an ally.
• (D) As a result, fundamental innovations are becoming scarce in the automobile industry.
• (E) As a result, everyone loses in the long run.

We can usefully think of theoretical models as maps, which help us navigate unfamiliar territory. The most accurate map that it is possible to construct would be of no practical use whatsoever, for it would be an exact replica, on exactly the same scale, of the place where we were. Good maps pull out the most important features and throw away a huge amount of much less valuable information. Of course, maps can be bad as well as good — witness the attempts by medieval Europe to produce a map of the world. In the same way, a bad theory, no matter how impressive it may seem in principle, does little or nothing to help us understand a problem.

• (1) But good theories, just like good maps, are invaluable, even if they are simplified.
• (2) But good theories, just like good maps, will never represent unfamiliar concepts in detail.
• (3) But good theories, just like good maps, need to balance detail and feasibility of representation.
• (4) But good theories, just like good maps, are accurate only at a certain level of abstraction.
• (5) But good theories, just like good maps, are useful in the hands of a user who knows their limitations.

In the evolving world order, the comparative advantage of the United States lies in its military force. Diplomacy and international law have always been regarded as annoying encumbrances, unless they can be used to advantage against an enemy. Every active player in world affairs professes to seek only peace and to prefer negotiation to violence and coercion.

• (1) However, diplomacy has often been used as a mask by nations which intended to use force.
• (2) However, when the veil is lifted, we commonly see that diplomacy is understood as a disguise for the rule of force.
• (3) However, history has shown that many of these nations do not practice what they profess.
• (4) However, history tells us that peace is professed by those who intend to use violence.
• (5) However, when unmasked, such nations reveal a penchant for the use of force.

I am sometimes attacked for imposing ‘rules’. Nothing could be further from the truth. I hate rules. All I do is report on how consumers react to different stimuli. I may say to a copywriter, “Research shows that commercials with celebrities are below average in persuading people to buy products. Are you sure you want to use a celebrity?” Call that a rule? Or I may say to an art director, “Research suggests that if you set the copy in black type on a white background, more people will read it than if you set it in white type on a black background.”

• (1) Guidance based on applied research can hardly qualify as ‘rules’.
• (2) Thus, all my so-called ‘rules’ are rooted in applied research.
• (3) A suggestion perhaps, but scarcely a rule.
• (4) Such principles are unavoidable if one wants to be systematic about consumer behaviour.
• (5) Fundamentally it is about consumer behaviour — not about celebrities or type settings.

Age has a curvilinear relationship with the exploitation of opportunity. Initially, age will increase the likelihood that a person will exploit an entrepreneurial opportunity because people gather much of the knowledge necessary to exploit opportunities over the course of their lives, and because age provides credibility in transmitting that information to others. However, as people become older, their willingness to bear risks declines, their opportunity costs rise, and they become less receptive to new information.

• (1) As a result, people transmit more information rather than experiment with new ideas as they reach an advanced age.
• (2) As a result, people are reluctant to experiment with new ideas as they reach an advanced age.
• (3) As a result, only people with lower opportunity costs exploit opportunity when they reach an advanced age.
• (4) As a result, people become reluctant to exploit entrepreneurial opportunities when they reach an advanced age.
• (5) As a result, people depend on credibility rather than on novelty as they reach an advanced age.

In the context of science, according to the passage, the interaction of dogmatic beliefs and critical attitude can be best described as:

• (1) A duel between two warriors in which one has to die.
• (2) The effect of a chisel on a marble stone while making a sculpture.
• (3) The feedshare (natural gas) in fertilizer industry being transformed into fertilizers.
• (4) A predator killing its prey.
• (5) The effect of fertilizers on a sapling.

According to the passage, the role of a dogmatic attitude or dogmatic behaviour in the development of science is:

• (1) Critical and important, as, without it, initial hypotheses or conjectures can never be made.
• (2) Positive, as conjectures arising out of our dogmatic attitude become science.
• (3) Negative, as it leads to pseudo-science.
• (4) Neutral, as the development of science is essentially because of our critical attitude.
• (5) Inferior to critical attitude, as a critical attitude leads to the attitude of reasonableness and rationality.

Dogmatic behaviour, in this passage, has been associated with primitives and children. Which of the following best describes the reason why the author compares primitives with children?

• (1) Primitives are people who are not educated, and hence can be compared with children, who have not yet been through school.
• (2) Primitives are people who, though not modern, are as innocent as children.
• (3) Primitives are people without a critical attitude, just as children are.
• (4) Primitives are people in the early stages of human evolution; similarly, children are in the early stages of their lives.
• (5) Primitives are people who are not civilized enough, just as children are not.

Which of the following statements best supports the argument in the passage that a critical attitude leads to a weaker belief than a dogmatic attitude does?

• (1) A critical attitude implies endless questioning, and, therefore, it cannot lead to strong beliefs.
• (2) A critical attitude, by definition, is centred on an analysis of anomalies and “noise”.
• (3) A critical attitude leads to questioning everything, and in the process generates “noise” without any conviction.
• (4) A critical attitude is antithetical to conviction, which is required for strong beliefs.
• (5) A critical attitude leads to questioning and to tentative hypotheses.

According to the passage, which of the following statements best describes the difference between science and pseudo-science?

• (1) Scientific theories or hypotheses are tentatively true whereas pseudo-sciences are always true.
• (2) Scientific laws and theories are permanent and immutable whereas pseudo-sciences are contingent on the prevalent mode of thinking in a society.
• (3) Science always allows the possibility of rejecting a theory or hypothesis, whereas pseudo-sciences seek to validate their ideas or theories.
• (4) Science focuses on anomalies and exceptions so that fundamental truths can be uncovered, whereas pseudo-sciences focus mainly on general truths.
• (5) Science progresses by collection of observations or by experimentation, whereas pseudo-sciences do not worry about observations and experiments.

Among all the apprehensions that Mr. Goran Lindblad expresses against communism, which one gets admitted, although indirectly, by the author?

• (1) There is nostalgia for communist ideology even if communism has been abandoned by most European nations.
• (2) Notions of social justice inherent in communist ideology appeal to critics of existing systems.
• (3) Communist regimes were totalitarian and marked by brutalities and large scale violence.
• (4) The existing economic order is wrongly viewed as imperialistic by proponents of communism.
• (5) Communist ideology is faulted because communist regimes resulted in economic failures.

What, according to the author, is the real reason for a renewed attack against communism?

• (1) Disguising the unintended consequences of the current economic order such as social injustice and environmental crisis.
• (2) Idealising the existing ideology of global capitalism.
• (3) Making communism a generic representative of all historical atrocities, especially those perpetrated by the European imperialists.
• (4) Communism still survives, in bits and pieces, in the minds and hearts of people.
• (5) Renewal of some communist regimes has led to the apprehension that communist nations might overtake the capitalists.

The author cites examples of atrocities perpetrated by European colonial regimes in order to:

• (1) Compare the atrocities committed by colonial regimes with those of communist regimes.
• (2) Prove that the atrocities committed by colonial regimes were more than those of communist regimes.
• (3) Prove that, ideologically, communism was much better than colonialism and Nazism.
• (4) Neutralise the arguments of Mr. Lindblad and to point out that the atrocities committed by colonial regimes were more than those of communist regimes.
• (5) Neutralise the arguments of Mr. Lindblad and to argue that one needs to go beyond and look at the motives of these regimes.

Why, according to the author, is Nazism closer to colonialism than it is to communism?

• (1) Both colonialism and Nazism were examples of tyranny of one race over another.
• (2) The genocides committed by the colonial and the Nazi regimes were of similar magnitude.
• (3) Several ideas of the Nazi regime were directly imported from colonial regimes.
• (4) Both colonialism and Nazism are based on the principles of imperialism.
• (5) While communism was never limited to Europe, both the Nazis and the colonialists originated in Europe.

Which of the following cannot be inferred as a compelling reason for the silence of the Council of Europe on colonial atrocities?

• (1) The Council of Europe being dominated by erstwhile colonialists.
• (2) Generating support for condemning communist ideology.
• (3) Unwillingness to antagonise allies by raking up an embarrassing past.
• (4) Greater value seemingly placed on European lives.
• (5) Portraying both communism and Nazism as ideologies to be condemned.

A just society, as conceptualized in the passage, can be best described as:

• (1) A Utopia in which everyone is equal and no one enjoys any privilege based on their existing positions and powers.
• (2) A hypothetical society in which people agree upon principles of justice which are fair.
• (3) A society in which principles of justice are not based on the existing positions and powers of the individuals.
• (4) A society in which principles of justice are fair to all.
• (5) A hypothetical society in which principles of justice are not based on the existing positions and powers of the individuals.

The original agreement or original position in the passage has been used by the author as:

• (1) A hypothetical situation conceived to derive principles of justice which are not influenced by position, status and condition of individuals in the society.
• (2) A hypothetical situation in which every individual is equal and no individual enjoys any privilege based on the existing positions and powers.
• (3) A hypothetical situation to ensure fairness of agreements among individuals in society.
• (4) An imagined situation in which principles of justice would have to be fair.
• (5) An imagined situation in which fairness is the objective of the principles of justice to ensure that no individual enjoys any privilege based on the existing positions and powers.

Which of the following best illustrates the situation that is equivalent to choosing ‘the principles of justice’ behind a ‘veil of ignorance’?

• (1) The principles of justice are chosen by businessmen, who are marooned on an uninhabited island after a shipwreck, but have some possibility of returning.
• (2) The principles of justice are chosen by a group of school children whose capabilities are yet to develop.
• (3) The principles of justice are chosen by businessmen, who are marooned on an uninhabited island after a shipwreck and have no possibility of returning.
• (4) The principles of justice are chosen assuming that such principles will govern the lives of the rule makers only in their next birth if the rule makers agree that they will be born again.
• (5) The principles of justice are chosen by potential immigrants who are unaware of the resources necessary to succeed in a foreign country.

Why, according to the passage, do principles of justice need to be based on an original agreement?

• (1) Social institutions and laws can be considered fair only if they conform to principles of justice.
• (2) Social institutions and laws can be fair only if they are consistent with the principles of justice as initially agreed upon.
• (3) Social institutions and laws need to be fair in order to be just.
• (4) Social institutions and laws evolve fairly only if they are consistent with the principles of justice as initially agreed upon.
• (5) Social institutions and laws conform to the principles of justice as initially agreed upon.

Which of the following situations best represents the idea of justice as fairness, as argued in the passage?

• (1) All individuals are paid equally for the work they do.
• (2) Everyone is assigned some work for his or her livelihood.
• (3) All acts of theft are penalized equally.
• (4) All children are provided free education in similar schools.
• (5) All individuals are provided a fixed sum of money to take care of their health.

1. According to all statistical indications, the Sarva Shiksha Abhiyan has managed to keep pace with its ambitious goals.

2. The Mid-day Meal Scheme has been a significant incentive for the poor to send their little ones to school, thus establishing the vital link between healthy bodies and healthy minds.

3. Only about 13 million children in the age group of 6 to 14 years are out of school.

4. The goal of universalisation of elementary education has to be a pre-requisite for the evolution and development of our country.

• (1) IIFJ
• (2) JIIJ
• (3) IFJ
• (4) JIFI
• (5) JIFI

1. We should not be hopelessly addicted to an erroneous belief that corruption in India is caused by the crookedness of Indians.

2. The truth is that we have more red tape — we take eighty-nine days to start a small business, Australians take two.

3. Red tape leads to corruption and distorts a people's character.

4. Every red tape procedure is a point of contact with an official, and such contacts have the potential to become opportunities for money to change hands.

• (1) JFIF
• (2) JFJJ
• (3) JIJF
• (4) IFJF
• (5) JFJI

1. So much of our day-to-day focus seems to be on getting things done, trudging our way through the tasks of living — it can feel like a treadmill that gets you nowhere; where is the childlike joy?

2. We are not doing the things that make us happy; that which brings us joy; the things that we cannot wait to do because we enjoy them so much.

3. This is the stuff that joyful living is made of — identifying your calling and committing yourself wholeheartedly to it.

4. When this happens, each moment becomes a celebration of you; there is a rush of energy that comes with feeling completely immersed in doing what you love most.

• (1) IILJ
• (2) IFIJ
• (3) JFJJ
• (4) JJJJ
• (5) JFJII

1. Inequitable distribution of all kinds of resources is certainly one of the strongest and most sinister sources of conflict.

2. Even without war, we know that conflicts continue to trouble us — they only change in character.

3. Extensive disarmament is the only insurance for our future; imagine the amount of resources that can be released and redeployed.

4. The economies of the industrialized western world derive 20% of their income from the sale of all kinds of arms.

• (1) IJJI
• (2) JIJF
• (3) IJJF
• (4) JIIF
• (5) IJIF

1. Given the poor quality of service in the public sector, the HIV/AIDS affected should be switching to private initiatives that supply anti-retroviral drugs (ARVs) at a low cost.

2. The government has been supplying free drugs since 2004, and 35,000 have benefited up to now — though the size of the affected population is 150 times this number.

3. The recent initiatives of networks and companies like AIDSCare Network, Emcure, Reliance-Cipla-Cil, would lead to availability of much-needed drugs to a larger number of affected people.

4. But how ironic it is that we should face a perennial shortage of drugs when India is one of the world’s largest suppliers of generic drugs to the developing world.

• (1) JFIJ
• (2) JIIJ
• (3) IFIJ
• (4) IFJ
• (5) JFII

If \(\frac{a}{b} = \frac{1}{3}\), \(\frac{b}{c} = 2\), \(\frac{c}{d} = \frac{1}{2}\), \(\frac{d}{e} = 3\) and \(\frac{e}{f} = \frac{1}{4}\), then what is the value of \(\frac{abc}{def}\)?

• (1) \(\frac{3}{8}\)
• (2) \(\frac{27}{8}\)
• (3) \(\frac{3}{4}\)
• (4) \(\frac{27}{4}\)
• (5) \(\frac{1}{4}\)

If \(x = -0.5\), then which of the following has the smallest value?

• (1) \(\frac{1}{2^x}\)
• (2) \(\frac{1}{x}\)
• (3) \(\frac{1}{x^2}\)
• (4) \(2^x\)
• (5) \(\frac{1}{\sqrt{-x}}\)

Consider a sequence where the \(n\)th term \(t_n = \frac{n}{n+2}\), \(n = 1, 2, \dots\)

The value of \(t_3 \times t_4 \times t_5 \times \dots \times t_{53}\) equals:

• (1) \(\frac{2}{495}\)
• (2) \(\frac{2}{477}\)
• (3) \(\frac{12}{55}\)
• (4) \(\frac{1}{1485}\)
• (5) \(\frac{1}{2970}\)

Which among \(2^{1/2}\), \(3^{1/3}\), \(4^{1/4}\), \(6^{1/6}\), and \(12^{1/12}\) is the largest?

• (1) \(2^{1/2}\)
• (2) \(3^{1/3}\)
• (3) \(4^{1/4}\)
• (4) \(6^{1/6}\)
• (5) \(12^{1/12}\)

The length, breadth, and height of a room are in the ratio \(3 : 2 : 1\). If the breadth and height are halved while the length is doubled, then the total area of the four walls of the room will:

• (1) Remain the same
• (2) Decrease by 13.64%
• (3) Decrease by 15%
• (4) Decrease by 18.75%
• (5) Decrease by 30%

A survey of 100 people was conducted to find out whether they had read recent issues of Golmal magazine in July, August, and September. Data:


Only September: 18; September but not August: 23; September and July: 8; September: 28; July: 48; July and August: 10; None: 24.


Find the number who read exactly two consecutive issues out of the three months.

• (1) 7
• (2) 9
• (3) 12
• (4) 14
• (5) 17

A semi-circle is drawn with \(AB\) as its diameter. From \(C\), a point on \(AB\), a line perpendicular to \(AB\) is drawn meeting the circumference of the semi-circle at \(D\). Given that \(AC = 2 \ cm\) and \(CD = 6 \ cm\), the area of the semi-circle (in sq. cm) will be:

• (1) \(32\pi\)
• (2) \(50\pi\)
• (3) \(40.5\pi\)
• (4) \(81\pi\)
• (5) undeterminable

What is the weight of Praja's luggage?

• (1) 20 kg
• (2) 25 kg
• (3) 30 kg
• (4) 35 kg
• (5) 40 kg

Using the same data as Q58, what is the free luggage allowance?

• (1) 10 kg
• (2) 15 kg
• (3) 20 kg
• (4) 25 kg
• (5) 30 kg

A group of 630 children is arranged in rows for a group photograph. Each row contains three fewer children than the row in front of it. Which number of rows is not possible?

• (1) 3
• (2) 4
• (3) 5
• (4) 6
• (5) 7

The proportion of the sheet area that remains after punching is:

• (1) \(\frac{\pi + 2}{8}\)
• (2) \(\frac{6 - \pi}{8}\)
• (3) \(\frac{4 - \pi}{4}\)
• (4) \(\frac{\pi - 2}{4}\)
• (5) \(\frac{14 - 3\pi}{6}\)

Find the area of the part of the circle (round punch) falling outside the square sheet.

• (1) \(\frac{\pi}{4}\)
• (2) \(\frac{\pi - 1}{2}\)
• (3) \(\frac{\pi - 1}{4}\)
• (4) \(\frac{\pi - 2}{2}\)
• (5) \(\frac{\pi - 2}{4}\)

What values of \(x\) satisfy \(\sqrt[3]{x} + x^{1/3} - 2 \leq 0\) (\(x\) is a real number)?

• (1) \(-8 \leq x \leq 1\)
• (2) \(-1 \leq x \leq 8\)
• (3) \(1 < x < 8\)
• (4) \(1 \leq x \leq 8\)
• (5) \(-8 \leq x \leq 8\)

Consider the set \(S = \{1, 2, 3, \dots, 1000\}\). How many arithmetic progressions can be formed from the elements of \(S\) that start with \(1\) and end with \(1000\) and have at least \(3\) elements?

• (1) 3
• (2) 4
• (3) 6
• (4) 7
• (5) 8

The graph of \(y - x\) against \(y + x\) is as shown (straight line with slope > 0 through origin). Which of the given five graphs shows \(y\) against \(x\)?

The sum of four consecutive two-digit odd numbers, when divided by 10, becomes a perfect square. Which of the following can possibly be one of these four numbers?

• (1) 21
• (2) 25
• (3) 41
• (4) 67
• (5) 73

The number of solutions of the equation \(2x + y = 40\) where both \(x\) and \(y\) are positive integers and \(x \leq y\) is:

• (1) 7
• (2) 13
• (3) 14
• (4) 18
• (5) 20

The number of employees in Obelix Menhir Co. is a prime number less than 300. The ratio of graduates and above to non-graduates can possibly be:

• (1) 101:88
• (2) 87:100
• (3) 110:111
• (4) 85:98
• (5) 97:84

There are 6 tasks and 6 persons. Task 1 cannot be assigned to person 1 or 2; Task 2 must be assigned to either person 3 or person 4. Every person is assigned one task. How many ways can this assignment be done?

• (1) 144
• (2) 180
• (3) 192
• (4) 360
• (5) 716

If \(\log_x(a \cdot \log_y) = (b \cdot \log_z) = ab\), then which of the following pairs of values for \((a,b)\) is not possible?

• (1) \(\left(-2, \frac{1}{2}\right)\)
• (2) \((1,1)\)
• (3) \((0.4, 2.5)\)
• (4) \(\left(\pi, \frac{1}{\pi}\right)\)
• (5) \((2, 2)\)

What are the values of \(x\) and \(y\) that satisfy both the equations?


\(2^{0.7x} \cdot 3^{-1.25y} = \frac{8\sqrt{6}}{27}\)
\(4^{0.3x} \cdot 9^{0.2y} = 8 \cdot (81)^{\frac{1}{5}}\)

• (1) \(x = 2, y = 5\)
• (2) \(x = 2.5, y = 6\)
• (3) \(x = 3, y = 5\)
• (4) \(x = 3, y = 4\)
• (5) \(x = 5, y = 2\)

Let \(f(x) = \max(2x + 1, 3 - 4x)\), where \(x\) is any real number. Then the minimum possible value of \(f(x)\) is:

• (1) \(\frac{1}{3}\)
• (2) \(\frac{1}{2}\)
• (3) \(\frac{2}{3}\)
• (4) \(\frac{4}{3}\)
• (5) \(\frac{5}{3}\)

When you reverse the digits of the number 13, the number increases by 18. How many other two-digit numbers increase by 18 when their digits are reversed?

• (1) 5
• (2) 6
• (3) 7
• (4) 8
• (5) 10

An equilateral triangle \(BPC\) is drawn inside a square \(ABCD\). What is the value of \(\angle APD\) in degrees?

• (1) 75
• (2) 90
• (3) 120
• (4) 135
• (5) 150

Arun, Barun, and Kiranmala start from the same place and travel in the same direction at speeds of 30, 40, and 60 km/h respectively. Barun starts two hours after Arun. If Barun and Kiranmala overtake Arun at the same instant, how many hours after Arun did Kiranmala start?

• (1) 3
• (2) 3.5
• (3) 4
• (4) 4.5
• (5) 5