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1.

Each family in a locality has at most two adults, and no family has fewer than 3 children. Considering all the families together, there are more adults than boys, more boys than girls, and more girls than families. Then the minimum possible number of families in the locality is
(1) 4
(2) 5
(3) 2
(4) 3

last reply by CpjJwWHV • 13 years ago • asked in CAT

The year was 2006. All six teams in Pool A of World Cup hockey, play each other exactly once. Each win earns a team three points, a draw earns one point and a loss earns zero points. The two teams with the highest points qualify for the semi-finals. In case of a tie, the team with the highest goal difference (Goal For – Goals Against) qualifies.
In the opening match, Spain lost to Germany. After the second round (after each team played two matches), the pool table looked as shown below.

POOL A :

Teams Games played
Won
Drawn
Lost
Goal for
Goal against
Points

Germany 2 2 0 0 3 1 6

Argentina 2 2 0 0 2 0 6

Spain 2 1 0 1 5 2 3

Pakistan 2 1 0 1 2 1 3

New Zealand 2 0 0 2 1 6 0

South Africa
2 0 0 2 1 4 0

In the third round, Spain played Pakistan, Argentina played Germany, and New Zealand played South Africa. All the third round matches were drawn. The following are some results from the fourth and fifth round matches.
(a) Spain won both the fourth and fifth round matches.
(b) Both Argentina and Germany won their fifth round matches by 3 goals to 0.
(c) Pakistan won both the fourth and fifth round matches by 1 goal to 0.

[1]	Which one of the following statements is true about matches played in the first two rounds? (1) Pakistan beat South Africa by 2 goals to 1. (2) Argentina beat Pakistan by 1 goal to 0. (3) Germany beat Pakistan by 2 goals to 1. (4) Germany beat Spain by 2 goals to 1.

[2]	Which one of the following statements is true about matches played in the first two rounds? (1) Germany beat New Zealand by 1 goal to 0. (2) Spain beat New Zealand by 4 goals to 0. (3) Spain beat South Africa by 2 goals to 0. (4) Germany beat South Africa by 2 goals to 1.

[3]	If Pakistan qualified as one of the two teams from Pool A, which was the other team that qualified? (1) Argentina (2) Germany (3) Spain (4) Cannot be determined

[4]	Which team finished at the top of the pool after five rounds of matches? (1) Argentina (2) Germany (3) Spain (4) Cannot be determined

asked in CAT

Twenty one participants from four continents (Africa, Americas, Australasia, and Europe) attended a United Nations conference. Each participant was an expert in one of four fields, labour, health, population studies, and refugee relocation. The following five facts about the participants are given.
(a) The number of labour experts in the camp was exactly half the number of experts in each of the three other categories.
(b) Africa did not send any labour expert. Otherwise, every continent, including Africa, sent at least one expert for each category.
(c) None of the continents sent more than three experts in any category.
(d) If there had been one less Australasian expert, then the Americas would have had twice as many experts as each of the other continents.
(e) Mike and Alfanso are leading experts of population studies who attended the conference. They are from Australasia.

[1]	Which of the following numbers cannot be determined from the information given? (1) Number of labour experts from the Americas. (2) Number of health experts from Europe. (3) Number of health experts from Australasia. (4) Number of experts in refugee relocation from Africa.

[2]

Which of the following combinations is NOT possible?
(1) 2 experts in population studies from the Americas and 2 health experts from Africa attended the conference.
(2) 2 experts in population studies from the Americas and 1 health expert from Africa attended the conference.
(3) 3 experts in refugee relocation from the Americas and 1 health expert from Africa attended the conference.
(4) Africa and America each had 1 expert in population studies attending the conference.

[3]

If Ramos is the lone American expert in population studies, which of the following is NOT true about the numbers of experts in the conference from the four continents?
(1) There is one expert in health from Africa.
(2) There is one expert in refugee relocation from Africa.
(3) There are two experts in health from the Americas.
(4) There are three experts in refugee relocation from the Americas.

[4]

Alex, an American expert in refugee relocation, was the first keynote speaker in the conference. What can be inferred about the number of American experts in refugee relocation in the conference, excluding Alex?
i. At least one
ii At most two

(1) Only i and not ii
(2) Only ii and not i
(3) Both i and ii
(4) Neither i nor ii

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4.

Coach John sat with the score cards of Indian players from the 3 games in a one-day cricket tournament where the same set of players played for India and all the major batsmen got out. John summarized the batting performance through three diagrams, one for each game. In each diagram, the three outer triangles communicate the number of runs scored by the three top scorers from India, where K, R, S, V, and Y represent Kaif, Rahul, Saurav, Virender, and Yuvraj respectively. The middle triangle in each diagram denotes the percentage of total score that was scored by the top three Indian scorers in that game. No two players score the same number of runs in the same game. John also calculated two batting indices for each player based on his scores in the tournament; the R-index of a batsman is the difference between his highest and lowest scores in the 3 games while the M-index is the middle number, if his scores are arranged in a non-increasing order.

[1]	Which of the players had the best M-index from the tournament? (1) Rahul (2) Saurav (3) Virender (4) Yuvraj

[2]	Among the players mentioned, who can have the lowest R-index from the tournament? (1) Only Kaif, Rahul or Yuvraj (2) Only Kaif or Rahul (3) Only Kaif or Yuvraj (4) Only Kaif

[3]	For how many Indian players is it possible to calculate the exact M-index? (1) 0 (2) 1 (3) 2 (4) More than 2

[4]	How many players among those listed definitely scored less than Yuvraj in the tournament? (1) 0 (2) 1 (3) 2 (4) More than 2

last reply by CpjJwWHV • 14 years ago • asked in CAT

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5.

Help Distress (HD) is an NGO involved in providing assistance to people suffering from natural disasters. Currently, it has 37 volunteers. They are involved in three projects: Tsunami Relief (TR) in Tamil Nadu, FloodRelief (FR) in Maharashtra, and Earthquake Relief (ER) in Gujarat. Each volunteer working with Help Distress has to be involved in at least one relief work project.
> A Maximum number of volunteers are involved in the FR project. Among them, the number of volunteers involved in FR project alone is equal to the volunteers having additional involvement in the ER project.
> The number of volunteers involved in the ER project alone is double the number of volunteers involved in all the three projects.
> 17 volunteers are involved in the TR project.
> The number of volunteers involved in the TR project alone is one less than the number of volunteers involved in ER Project alone.
> Ten volunteers involved in the TR project are also involved in at least one more project.

[1]	Based on the information given above, the minimum number of volunteers involved in both FR and TR projects, but not in the ER project is: (1) 1 (2) 3 (3) 4 (4) 5

[2]

Which of the following additional information would enable to find the exact number of volunteers involved in various projects?
(1) Twenty volunteers are involved in FR.
(2) Four volunteers are involved in all the three projects.
(3) Twenty three volunteers are involved in exactly one project.
(4) No need for any additional information.

[3]

After some time, the volunteers who were involved in all the three projects were asked to withdraw from one project. As a result, one of the volunteers opted out of the TR project, and one opted out of the ER project, while the remaining ones involved in all the three projects opted out of the FR project.
Which of the following statements, then, necessarily follows?
(1) The lowest number of volunteers is now in TR project.
(2) More volunteers are now in FR project as compared to ER project.
(3) More volunteers are now in TR project as compared to ER project.
(4) None of the above

[4]

After the withdrawal of volunteers, as indicated in Question 89, some new volunteers joined the NGO. Each one of them was allotted only one project in a manner such that, the number of volunteers working in one project alone for each of the three projects became identical. At that point, it was also found that the number of volunteers involved in FR and ER projects was the same as the number of volunteers involved in TR and ER projects. Which of the projects now has the highest number of volunteers?
(1) ER
(2) FR
(3) TR
(4) Cannot be determined

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6.

Venkat, a stockbroker, invested a part of his money in the stock of four companies - A, B, C and D. Each of these companies belonged to different industries, viz., Cement, Information Technology (IT), Auto, and Steel, in no particular order. At the time of investment, the price of each stock was Rs.100. Venkat purchased only one stock of each of these companies. He was expecting returns of 20%, 10%, 30%, and 40% from the stock of companies A, B, C and D, respectively. Returns arc defined as the change in the value of the stock after one year, expressed as a percentage of the initial value. During the year, two of these companies announced extraordinarily good results. One of these two companies belonged to the Cement or the IT industry, while the other one belonged to either the Steel or the Auto industry. As a result, the returns on the stocks of these two companies were higher than the initially expected returns. For the company belonging to the Cement or the IT industry with extraordinarily good results, the returns were twice that of the initially expected returns. For the company belonging to the Steel or the Auto industry, the returns on announcement of extraordinarily good results were only one and a half times that of the initially expected returns. For the remaining two companies, which did not announce extraordinarily good results, the returns realized during the year were the same as initially expected.

[1]	What is the minimum average return Venkat would have earned during the year? (1) 30% (2) 31.25% (3) 32.5% (4) Cannot be determined

[2]

If Venkat earned a 35% return on average during the year, then which of these statements would necessarily be true?
I. Company A belonged either to Auto or to Steel Industry.
II. Company B did not announce extraordinarily good results.
III. Company A announced extraordinarily good results.
IV. Company D did not announce extraordinarily good results.
(1) I and II only
(2) II and III only
(3) I and IV only
(4) II and IV only

[3]

If Venkat earned a 38.75% return on average during the year, then which of these statement(s) would necessarily be true?
I. Company C belonged either to Auto or to Steel Industry.
II. Company D belonged either to Auto or to Steel Industry.
III. Company A announced extraordinarily good results.
IV. Company B did not announce extraordinarily good results.
(1) I and II only
(2) II and III only
(3) I and IV only
(4) II and IV only

[4]

If Company C belonged to the Cement or the IT industry and did announce extraordinarily good results, then which of these statement(s) would necessarily be true?
I. Venkat earned not more than 36.25% return on average.
II. Venkat earned not less than 33.75% return on average.
III. If Venkat earned 33.75% return on average, Company A announced extraordinarily good results.
IV. If Venkat earned 33.75% return on average, Company B belonged either to Auto or to Steel Industry.
(1) I and II only
(2) II and IV only
(3) II and III only
(4) III and IV only

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