2015 Bull Mock CAT - 18

2015 Bull Mock CAT - 18 DIRECTIONS for the question: Solve the following question and mark the best possible option. Question No. : 1 Avanti and Avani  start playing a game in which the one who wins gets W points and the loser gets L points (W > L > 0), ties are not possible and all scores are integral. After some games, Avanti scored 30 and Avani 25. If Avani has won exactly two games, the value of W, is A) 5

B) 6

C) 7

D) 8

Explanation:-   As Avanti's + Avani's score is 55, which must be an integral multiple of W+L. The 4 possibilities are W+L = 1, W+L = 5, W+L = 55 or W+L = 11 Possibility 1:W+L = 55; which is impossible, because Avanti and Avani played at least 2 rounds. Possibility 2: W+L = 1, which is impossible, since W and L are positive. Possibility 3 : W+L = 5, then (W,L) is either (4,1) or (3,2), since W > L > 0 and the number of rounds must have been 11.  But with 2 wins, Avani would have a score of either 2(4) + 9(1) = 17 Or 2(3) + 9(2) = 24, which are impossible, since Avani's score is 25. ∴W+L = 11, and the number of rounds was 5 Thus, (W+L) is either (10,1), (9, 2), (8,3) (7,4) or (6,5). The only choice for which 2W + 3L = 25 is (W,L) = (8,3). Therefore, the winner of each round gets 8 points, the loser 3 points and they played 5 rounds.   Question No. : 2 A thief has stolen a credit card and wishes to withdraw some money from ATM. Unfortunately he could not remember the fourdigit PIN number written on a paper slip, which he had seen while stealing the card. He does remember the first two digits and he knows that each of the last two digits is greater than 5. The ATM will allow him three tries before it blocks further access. If he randomly guesses the last two digits, then what is the probability that he will be able to withdraw money from the ATM? A) 

B) 

C) 

D) 

Explanation:-   Randomly guessing either of the last two digits not affecting the choice of the other means that these events are mutually exclusive. Since each of the last two digits is greater than 5, the thief has four digits to choose from: 6,7,8,9. His chance of guessing the first digit correctly is 1/4 and that for the second digit is also 1/4. His chance of guessing both the digits correctly is 

Question No. : 3 ABCDE is a pentagon with A = (0,2), B = (4,0), C = (2π + 1, 0), D = (2π + 1, 4) and E = (0, 4). Point P is selected at random from the interior of this pentagon. What is the probability that ∠APB is obtuse? A) 

B) 

C) 

D) 

Explanation:-   If P is selected on a semi-circle with AB as diameter, then ∠APB = 900. If P is selected from the interior of semi-circle with AB as diameter, then ∠APB will be obtuse. Now, A(ABCDE) = A(OCDE)

Question No. : 4 A truck is to be driven 300km on a highway at a constant speed of x kmph. Speed rules of the highway require that 30 ≤ x ≤ 60. The fuel costs Rs. 10 per litre and is consumed at the rate of most economical speed to drive the truck, in kmph, is A) 30

B) 60

C) 

litres / hour. The wages of the driver are Rs. 200 per hour. The

D) 

Explanation:-   Given: Distance to be, covered by the truck = 300 km. Constant speed = x kmph (where 30 ≤ x ≤ 60). Cost of fuel = Rs. 10 / litre

Wage of driver = Rs. 200 / hour By the above information, we can frame the cost expression for the journey as Traveling time × (cost of fuel + wager of the driver)

Now as cost is least at 60, so option 2. Question No. : 5 Player A has n+1 coins, while player B has n coins (n > 3). Both players throw all of their coins simultaneously and observe the number of heads. If all coins are fair, then what is the probability that A obtains more heads than B? A) 

B) 

C) 

D) 

Explanation:-   Answer will be same whatever the value of n be. Let us assume player A has 3 coins and player B has 2 coins. Now, if A has all 3 heads B will have either 2 heads or 1 head or no heads, if A has 2 heads B will have either 1 head or no head and if A has 1 head then B will have no heads. Hence the probability that A obtains more heads than B. = PA (all 3 heads) [PB (2 heads) + PB(1 head) + PB(no heads)]+PA (2 heads)  [PB (1 head) + PB(no heads)] + PA (1 head) [ PB (no heads)]

Similarly this can be checked for other values of A = n+1 and B = n coins, and the same result will be obtained.   Question No. : 6 The lengths of the sides of a right-angled triangle are in geometric progression. What is the ratio of the sines of its acute angles? A) 1

B) 

C) 

D) 

Explanation:-  

Question No. : 7 For an odd positive integer n, satisfying 51 ≤ n ≤ 99, the quantity n3 – n is always divisible by A) 48

B) 24

C) 18

D) None of these

Explanation:-   n2-n = n(n2- 1) = (n – 1)n (n + 1) We can observe that the given quantity is the product of three consecutive numbers. One of these three numbers (n – 1), n, or (n + 1) will be divisible by 3. Since x is an odd integer, one of (n – 1) or (n + 1) will be divisible by 2 and the other by 4. Therefore n3 – n is always divisible by 2 × 4 × 3, which is 24.   Question No. : 8 For a particular day of the year, it happens that the sum of the date and square root of the month gives the square of the month. What is the date? A) 14th September Explanation:-  

B) 16th April

C) 16th September

D) 14th April

  Hence 4th option is the answer.

Question No. : 9 A series in which any term is equal to the sum of the preceding two terms is called a Fibonacci series. Usually the first two terms are given initially and together they determine the entire series. Now, it is known that the difference of the squares of the ninth and the eighth terms of a Fibonacci series is 840. What is the 12th term of that series? A) 157

B) 142

C) 143

D) Data inadequate

Explanation:-  

  As there are more than 1 cases, the answer is 4th option. Question No. : 10

A) 

B) 

C) 

D) None of these

Explanation:-  

Question No. : 11

A) Ajay and Chandu Explanation:-  

B) Balram

C) Chandu

D) Ajay

Question No. : 12

The total no. of holdings of AP & UP together is what percent more or less than the total no. of holdings of BH & RJ together? A) 14.5 % more Explanation:-  

B) 17% more

C) 14.5% less

D) 17% less

Question No. : 13

If in 1990-91, the total no. of holdings for KR has increased by 12% from the 1980-81 and the area of holding has decreased by 15% from 1980-81, find the approx. average size of holding for KR in 1980-81 ? A) 3.11

B) 1.98

Explanation:-  

Question No. : 14

C) 2.77

D) 3.56

It has been estimated that the total no. of holdings will increase by 25% for MP in 2000-01 from 1990-91 levels. The average size of holding for MP in 2000-01 will be what % of the average size of holding for MP in 1990-91. A) 119.67

B) 127.23

C) 83.56

D) Cannot be determined

Explanation:-   Since the area of operational holding in 2000-01 is not given for MP, we cannot find the answer. Question No. : 15 Each coefficient in the equation ax2 + bx + c = 0 is determined by throwing an ordinary die. Find the probability that the equation will have equal roots. A) 

B) 

Explanation:-  

Question No. : 16

C) 

D) None of these

If (1 – x + x2)n = a0 + a1x + a2x2+---+a2n x2n, then a0 + a2 + a4 + ----+a2n is equal to A) 

B) 

C) 

D) 

Explanation:-   We have (1-x+x2)n = a0+a1 x+a2x2 + ............. a2nx2n put x = 1 and -1, we get, 1 =a0 + a1 +a2 + ...........+a2n   ......... (2)

And 3n = a0 - a1 + a2 - a3 +  .......... + a2n      ....(3) Adding  (2) and (3), we get 1+ 3n = 2(a0 + a2 + an  ....... + a2n) ⇒ a0 + a2 + an + ......+ a2n = 3n + 1/ 2   Question No. : 17 The angle between hour hand and minute hand is exactly 10. The time is an integral number ‘n’ of minutes after noon (0 < n < 720). Find the total possible values of n. A) 12

B) 2

C) 3

D) 4

Explanation:-  

minute hand is one degree ahead of the hour hand. We need to find the integral values of these times. For the first condition, we get k = 7 and n = 458 and for the second condition, we get k = 4 and n = 262. Therefore we have two integral values of n below 720. Question No. : 18 The longer side of a parallelogram is 10 cm and the shorter is 6 cm. If the longer diagonal makes an angle 30° with the longer side, then the length of the longer diagonal is. A)  Explanation:-  

B) 

C) 

D) None of these

Question No. : 19 Ajit can work for three hours nonstop but then needs to rest for half an hour. His sister can work for two hours but rests for 15 minutes after that, while his brother can work for 1 hour before resting for half an hour. If a work takes 50 man hours to get completed and they all start together, then approximately, how long will it take for the three to complete the work? Assume that all of them are equally skilled in their work. A) 14 hours

B) 17 hours

C) 20 hours

D) 25 hours

Explanation:-  

Ajit does 3 man hours in every 3.5 hours (because he takes rest for half an hour on the 4th hour. In 20 hours (3.5 × 5 + 2.5), Ajit completes 3 × 5 + 2.5 = 17.5 man hours. His sister completes 2 man hours every 2.25 hours (because she rests on the 3rd hour). In 20 hours (2.25 × 8 + 2) she completes 2 × 8 + 2 = 18 man hours. His brother completes 1 man hour every 1.5 hour. In 20 hours (1.5 × 13 + 0.5), he completes 1 × 13 + 0.5 = 13.5 man hours. So the total work done = 17.5 + 18 + 13.5 = 49 man hours Hence the work can be completed in approximately 20 hours.

Question No. : 20 India plays two matches each with West Indies and Australia. In any match the probabilities of India getting points 0, 1 and 2 are 0.45, 0.05 and 0.5 respectively. Assuming that the outcomes are independent, the probability of India getting at least 7 points is A) 0.0875

B) 0.06875

C) 0.0625

D) 0.875

Explanation:-   A total of at least seven points can be made as follows (2,2,2,2) or (1,2,2,2) or (2,1,2,2) or (2,2,1,2) or (2,2,2,1). Now P(2 points in all matches) = (0.5)4 and P(2 points in any three matches and 1 point in remaining match) = 4 × (0.5)3 × 0.05. Hence the required probability is (0.5)4 + 4 × (0.5)3 × 0.5 = 0.08750   Question No. : 21 World’s Most Valuable Brand 1-Yr Value Change (%)

Brand Revenue ($b)

Industry

Rank

Brand

Brand Value ($b)

1.

Apple

104.3

22

156.5

Technology

2.

Microsoft

56.7

14

77.8

Technology

3.

Coca-Cola

54.9

9

23.5

Beverages

4.

IBM

50.7

2

104.5

Technology

5.

Google

47.3

26

43.5

Technology

6.

McDonald’s

39.4

5

88.3

Restaurants

7.

General Electric

34.2

2

132.1

Diversified

8.

Intel

30.9

-4

53.5

Technology

9.

Samsung

29.5

-5

200.0

Technology

10.

Louis Vuitton

28.4

16

9.4

Luxury

11.

BMW

27.9

6

77.6

Automotive

12.

Cisco

27.0

3

48.6

Technology

13.

Oracle

26.9

4

37.2

Technology

14.

Toyota

25.6

3

186.6

Automotive

15.

AT&T

24.2

0

126.4

Telecom

Which was the second most valuable company in terms of the brand value, one year before? A) Microsoft

B) Coca Cola

C) Apple

D) IBM

Explanation:-   Brand value of the companies one year before was (i) Microsoft       = 49.73$b (ii) Coco Cola    = 50.37$b (iii) Apple           = 85.49$b (iv) IBM               = 49.70$b So the coca cola was second most valuable company in terms of the brand value.  

Question No. : 22 World’s Most Valuable Brand 1-Yr Value Change (%)

Brand Revenue ($b)

Industry

Rank

Brand

Brand Value ($b)

1.

Apple

104.3

22

156.5

Technology

2.

Microsoft

56.7

14

77.8

Technology

3.

Coca-Cola

54.9

9

23.5

Beverages

4.

IBM

50.7

2

104.5

Technology

5.

Google

47.3

26

43.5

Technology

6.

McDonald’s

39.4

5

88.3

Restaurants

7.

General Electric

34.2

2

132.1

Diversified

8.

Intel

30.9

-4

53.5

Technology

9.

Samsung

29.5

-5

200.0

Technology

10.

Louis Vuitton

28.4

16

9.4

Luxury

11.

BMW

27.9

6

77.6

Automotive

12.

Cisco

27.0

3

48.6

Technology

13.

Oracle

26.9

4

37.2

Technology

14.

Toyota

25.6

3

186.6

Automotive

15.

AT&T

24.2

0

126.4

Telecom

If the % age change in Brand revenue for the next year is same as the % age change in Brand value this year, then which would be the 3rd largest company in terms of Brand Revenue next year? A) Apple

B) Samsung

C) Toyota

D) Coca Cola

Explanation:-   Brand Revenue of Companies after one year will be Apple =156.5×1.22=190.93$b Samsung=200×0.95=190$b Toyota=186.6×1.03=192.2$b Coca Cola=23.5×1.09=25.61$b So the Samsung will be the third largest company in terms of the brand revenue. (If we calculate the brand revenue of other companies then it will not exceed Samsung, Apple or Toyota as their brand revenue is already lesser than Samsung, Apple or Toyota this year)  

Question No. : 23 World’s Most Valuable Brand 1-Yr Value Change (%)

Brand Revenue ($b)

Industry

Rank

Brand

Brand Value ($b)

1.

Apple

104.3

22

156.5

Technology

2.

Microsoft

56.7

14

77.8

Technology

3.

Coca-Cola

54.9

9

23.5

Beverages

4.

IBM

50.7

2

104.5

Technology

5.

Google

47.3

26

43.5

Technology

6.

McDonald’s

39.4

5

88.3

Restaurants

7.

General Electric

34.2

2

132.1

Diversified

8.

Intel

30.9

-4

53.5

Technology

9.

Samsung

29.5

-5

200.0

Technology

10.

Louis Vuitton

28.4

16

9.4

Luxury

11.

BMW

27.9

6

77.6

Automotive

12.

Cisco

27.0

3

48.6

Technology

13.

Oracle

26.9

4

37.2

Technology

14.

Toyota

25.6

3

186.6

Automotive

15.

AT&T

24.2

0

126.4

Telecom

The total Brand value of automotive industry is what percent of total Brand revenue of Technology Sector? A) 7.41%

B) 13.48%

C) 9.23%

D) 14.33%

Explanation:-  

Question No. : 24

A) 

B) 

C) 

D) 

Explanation:-   Factorizing numerator and denominator, we have k3 - 1 = (k-1)(k2+k+1) and k3 + 1 = (k+1)(k2-k+1) Note that, (k + 1)2 - (k+1)+1= k2+k+1, and so k3+1 = (k+1)[(k+1)2 - (k+1) +1] We can now calculate Pn1 the partial product of the first n-1 terms.

As n→ ∞, Pn → 2/3. That is, the infinite product, P, converges to 2/3; P = P∞ = 2/3.   Question No. : 25 Suppose the height of a pyramid with a square base is decreased by p% and the lengths of the sides of its square base increased by p%(where p > 0). If the volume remains the same, then

A) 50 < p