Answer key of THE LAST LAP ANALYTICAL SKILLS-2

THE LAST LAP ANALYTICAL SKILLS-2

An automobile plant contracted to buy shock absorbers from two suppliers X and Y. X supplies 60% and Y supplies 40% of the shock absorbers. All shock absorbers are subjected to a quality test. The ones that pass the quality test are considered reliable. Of X’s shock absorbers, 96% are reliable. Of Y’s shock absorbers, 72% are reliable. The probability that a randomly chosen shock absorber, which is found to be reliable, is made by Y is

A.0.288                       B.0.334                       C. 0.667          D. 0.720

A and B take part in a duel. A can strike with an accuracy of 0.6. B can strike with an accuracy of 0.8. A has the first shot, post which they strike alternately. What is the probability that A wins the duel?
A] 7/10                        B] 15/23          C] 2/3              D] 11/17

Joseph bought two varieties of rice, costing 5 cents per ounce and 6 cents per ounce each, and mixed them in some ratio. Then he sold the mixture at 7 cents per ounce, making a profit of 20 percent. What was the ratio of the mixture?
A. 1:10            B. 1:5                           C. 2:7                           D.3:8

Given A = 2⁶⁵ and B = (2⁶⁴+2⁶³+2⁶²+...+2⁰)
A. B is 264 larger than A
B. A and B are equal
C. B is larger than A by 1
D. A is larger than B by 1

There are two books each of 5 volumes and two books each of two volumes. In how many ways can these books be arranged in a shelf so that the volumes of the same book should remain together?

A. 4! × 5! × 2!              B. 4! × 14!                   C. 14!                          D. 4! × 5! × 5! × 2! × 2!

In the first 1000 natural numbers, how many integers exist such that they leave a remainder 4 when divided by 7, and a remainder 9 when divided by 11?
A. 11               B. 14                C. 16                D. 13

A vessel contain 72 litres of milk and water. The ratio of milk and water is 5:4. If 18 litre of mixture is taken out from the vessel and then 10 litre of water is added to it, what will be the percentage of milk in the final mixture?
A) 46.875%                 B) 44%                                    C) 42.76%                   D) 48.87%

A work is done by 30 workers not all of them have the same capacity to work. Every day exactly 2 workers, do the work with no pair of workers working together twice. Even after all possible pairs have worked once, all the workers together works for two more days to finish the work. Find the number of days in which all the workers together will finish the whole work?
A.31                                       B.29                                       C.41                                       D.48

The number of gift pack bought by Dexter is one more than the price, in rupees, of each gift pack. The amount of Rs 380 which Dexter had, fell short of the required amount. What is the amount by which he might have fallen short.
A.20                                       B.40                                       C.21                                       D.10

Kartik's mother asked him to get the vegetables, milk and butter from the market and gave him the money in the denominator of 1 Rupee, 2 Rupee and 5 Rupee coins. Kartik first goes to the grocery shop to buy vegetables. At the grocery shop he gives half of his 5 Rupee coins in return receives the same number of 1 Rupee coins. Next he goes to the dairy shop to buy milk and butter and gives all 2 Rupee coins and in return get thirty 5 Rupee coins, which increase the number of five rupee coins by 75 more than the original number. If the number of 1 rupee coins now is 50, the number of 1 rupee and 5 rupee coins originally were:
A.10,  60                               B.10,  70                               C.10, 80                D.None of these

A tank is filled by three pipes with uniform flow. The first two pipes operating simultaneously fill the tank in the same time during which the tank is filled by the third pipe alone. The second pipe fills the tank 5 hours faster than the first pipe and 4 hours slower than the third pipe. The time required by the first pipe is:
A. 6 hours            B. 10 hours          C. 15 hours          D. 30 hours

Three athletes A, B and C run a race, B finished 24 meters ahead of C and 36 m ahead of A, while C finished 16 m ahead of A. If each athlete runs the entire distance at their respective constant speeds, what is the length of the race?
A.108 m                                                B.90 m                                  C.80 m                                  D.96 m

A man takes twice as long to row a distance against the stream as to row the same distance in favour of the stream. The ratio of the speed of the boat (in still water) and the stream is:
A. 2 : 1                   B. 3 : 1                   C. 3 : 2                   D. 4 : 3

A boat can travel 4.2 km upstream in 14 min. If the respective ratio of speed of the boat in still water & speed of the stream is 7:1, how much time will the boat take to cover 17.6 km downstream?
A. 44 MIN            B. 41 MIN            C. 38 MIN            D. 52 MIN

Two merchants sell, each an article for Rs.1000. If Merchant A computes his profit on cost price, while Merchant B computes his profit on selling price, they end up making profits of 25% respectively. By how much is the profit made by Merchant B greater than that of Merchant A?
A. Rs.66.67     B. Rs.50                      C. Rs.125                    D. Rs.200

. If the total numbers of terms in the expansion of  (x+y+z)ⁿ is 45. Then value of n is
A] 8                             B] 9                             C] 7                             D] 22

. Three pipes A, B and C can fill a tank in 6 hours. After working at it together for 2 hours, C is closed and A and B can fill the remaining part in 7 hours. The number of hours taken by C alone to fill the tank is:
A. 10                      B. 12                      C. 14                      D. 16

Three boys P,Q and R are to speak at a function along with 5 others. If all of them speak in random order, what is the probability that P speaks before Q and Q speaks before R?
A] 2/9              B] 1/3              C] 1/6              D] 1/9

There is a point in a circle. What is the probability that this point is closer to its circumference than to the centre?
A] 1/3              B] 1/4              C] 2/3              D] ¾

Class photograph has to be taken. The front row consists of 6 girls who are sitting. 20 boys are standing behind. The two corner positions are reserved for the 2 tallest boys. In how many ways can the students be arranged?
A] 6! × 1440                B] 18! × 1440              C] 18! ×2! × 1440        D] None of these

Marie is getting married tomorrow, at an outdoor ceremony in the desert. In recent years, it has rained only 5 days each year. Unfortunately, the weatherman has predicted rain for tomorrow. When it actually rains, the weatherman correctly forecasts rain 90% of the time. When it doesn't rain, he incorrectly forecasts rain 10% of the time. What is the probability that it will rain on the day of Marie's wedding?
A.0.567                       B.0.111                        C.0.332                        D. 0.732

A boatman goes 2 km against the current of the stream in 1 hour and goes 1 km along the current in 10 minutes. How long will it take to go 5 km in stationary water?
A. 40 minutes    B. 1 hour              C. 1 hr 15 min     D. 1 hr 30 min

Set P comprises all multiples of 4 less than 500. Set Q comprises all odd multiples of 7 less than 500, Set R comprises all multiples of 6 less than 500. How many elements are present in P∪Q∪R ?
A] 202             B] 243             C] 228             D] 186

Consider a class of 40 students whose average weight is 40 kgs. m new students join this class whose average weight is n kgs. If it is known that m + n = 50, what is the maximum possible average weight of the class now?
A. 40.18 kgs                B. 40.56 kgs                C. 40.67 kgs                D. 40.49 kgs

A G.P. consists of an even number of terms. If the sum of all the terms is 5 times the sum of the terms occupying odd places, then the common ratio will be
A.2                  B.3                  C. 4                 D. 5

Of 60 students in a class, anyone who has chosen to study maths elects to do physics as well. But no one does maths and chemistry, 16 do physics and chemistry. All the students do at least one of the three subjects and the number of people who do exactly one of the three is more than the number who do more than one of the three. What are the maximum and minimum number of people who could have done Chemistry only?
A] 40, 0           B] 28, 0                       C] 38, 2                       D] 44, 0

Manish, Rahul and Bharti have some stones with each of the. Five times the number of stones with Rahul equals seven times the number of stones with Manish while five times the number of stones with Manish equals seven times the number of stones with Bharti. What is the minimum number of stones that can be there with all three of them put together?
A] 113             B] 109                         C] 97                           D] 93

A´ is defined as the complement of A, as in, set of all elements that are part of the universal set but not in A. How many of the following have to be true?
i. n(A∪B)′=n(A′∩B′)
ii. If A∩B=0, then A′∪B′ is equal to the universal set
iii. If A∪B = universal set, then A′∩B′ should be the null set.
iv. If A⊂B then A′∪B′=(A∩B)′

A] 1                 B] 2                 C] 3                 D] 4

For Rs 600 Mr Karan can buy a max of 24 cups of tea and for Rs 1500 he can buy a maximum of 15 cups of coffee. he has 2200 in his pocket and purchase 8 cups of tea what is the max no of cups of coffee he can purchase with the remaining money?
A.20                B.30                C.40                D.50

Set F_n gives all factors of n. Set M_n gives all multiples of n less than 1000. Which of the following statements is/are true?
i. F₁₀₈∩F₈₄=F₁₂
ii. M₁₂∪M₁₈=M₃₆
iii. M₁₂∩M₁₈=M₃₆
iv. M₁₂⊂(M₆∩M₄)

A] i, ii and iii only                   B] i, iii and iv only                 
C] i and iii only                                   D] All statements are true

Let S_n denote the sum of first n terms of an A.P.. If S_2n = 3S_n, then the ratio S_3n/S_n is equal to
A.6                  B.7                  C.8                  D.9

. In a group, each person has at most two A. No person has less than three C. Considering all the persons in the group there are more A than G, more G than B and more B than persons. Find the minimum number of persons in the groups?
A.4                                         B.5                                          C.3                                          D.2