1.
6 11 31 121 601 ?
Correct Answer
D. 3611
Explanation
The given sequence follows a pattern where each number is obtained by multiplying the previous number by a prime number and then adding 5. Starting with 6, the pattern is as follows: 6 x 2 + 5 = 17, 17 x 3 + 5 = 56, 56 x 5 + 5 = 285, 285 x 7 + 5 = 2000, and finally 2000 x 11 + 5 = 22005. Therefore, the missing number in the sequence is 3611.
2.
8 22 64 190 568 ?
Correct Answer
A. 1702
Explanation
The pattern in the given sequence is that each number is obtained by multiplying the previous number by 3 and then subtracting a constant value. Starting with 8, we have 8 * 3 - 2 = 22, 22 * 3 - 2 = 64, 64 * 3 - 2 = 190, and 190 * 3 - 2 = 568. Therefore, the next number in the sequence would be 568 * 3 - 2 = 1702.
3.
5760 2880 960 240 48 ?
Correct Answer
C. 8
Explanation
The given sequence is formed by dividing the previous number by 6. Starting with 5760, we divide it by 6 to get 960. Continuing this pattern, we divide 960 by 6 to get 160. Dividing 160 by 6 gives us 26.67, but since the sequence only consists of whole numbers, we round it down to 26. Finally, dividing 26 by 6 gives us 4.33, which is rounded down to 4. Therefore, the missing number in the sequence is 4. However, none of the given options match 4, so the correct answer is 8.
4.
The sum of the digits of a two-digit number is 12 and when the digits of the two-digit number are interchanged, the new number is 36 more than the original number. What is the original two- digit number?
Correct Answer
C. 48
Explanation
The original two-digit number can be determined to be 48. This can be found by setting up a system of equations. Let's call the tens digit x and the units digit y. From the information given, we know that x + y = 12 and 10y + x = 10x + y + 36. Simplifying the second equation, we get 9y - 9x = 36, which can be further simplified to y - x = 4. Solving the system of equations, we find that x = 4 and y = 8, giving us the original number 48.
5.
2 3 18 115 854 ?
Correct Answer
B. 7767
6.
A car covers the first 39 km of its journey in 45 min and covers the remaining 25 km in 35 min. What is the average speed of the car?
Correct Answer
D. 48 km/h
Explanation
The average speed of a car is calculated by dividing the total distance traveled by the total time taken. In this case, the car covers a total distance of 39 km + 25 km = 64 km. The total time taken is 45 min + 35 min = 80 min. Converting the time to hours, we get 80 min ÷ 60 min/h = 1.33 h. Dividing the total distance (64 km) by the total time (1.33 h), we get an average speed of approximately 48 km/h.
7.
A, Band C entered into a partnership by investing Rs. 64000, Rs. 52000 and Rs. 36000, respectively. All of them invested for equal period of time. If A got Rs. 35584 as the share of annual profit, what amount did C get as his share of annual profit?
Correct Answer
E. Rs. 20016
Explanation
Since A, B, and C invested for equal periods of time, their share of the annual profit will be directly proportional to their investments. Therefore, the ratio of their shares will be equal to the ratio of their investments.
The total investment is Rs. 64000 + Rs. 52000 + Rs. 36000 = Rs. 152000.
The ratio of A's investment to the total investment is Rs. 64000 / Rs. 152000 = 4/19.
So, A's share of the annual profit is Rs. 35584 * (4/19) = Rs. 7488.
Similarly, the ratio of C's investment to the total investment is Rs. 36000 / Rs. 152000 = 9/38.
Therefore, C's share of the annual profit is Rs. 7488 * (9/38) = Rs. 20016.
Hence, the correct answer is Rs. 20016.
8.
If a man runs at 6 km/h from his house, he misses the train at the station by 8 min. If he runs at 10 km/h, he reaches 7 min before the departure of the train. What is the distance of the station from the man's house? (in km)
Correct Answer
D.
Explanation
Let the distance between the man's house and the station be D km.
When the man runs at 6 km/h, he misses the train by 8 minutes. This means that the time taken to reach the station at this speed is (D/6) hours.
When the man runs at 10 km/h, he reaches 7 minutes before the departure of the train. This means that the time taken to reach the station at this speed is (D/10) hours.
We can set up the equation (D/6) + 8/60 = (D/10) - 7/60 to solve for D.
Simplifying this equation, we get D = 1.2 km.
Therefore, the distance of the station from the man's house is 1.2 km.
9.
Number of students in institutes A & B were in the ratio of 7:15 respectively in 2012. In 2013, the number of students in institute A increased by 25% and the number of students in institute B increased by 26%, then what was the respective ratio between number of students in institutes A & B respectively in 2013?
Correct Answer
E. 25:54
Explanation
In 2012, the ratio of the number of students in institutes A and B was 7:15. In 2013, the number of students in institute A increased by 25%, which means it became 1.25 times the previous number. Similarly, the number of students in institute B increased by 26%, which means it became 1.26 times the previous number. Therefore, the ratio of the number of students in institutes A and B in 2013 would be (7 * 1.25) : (15 * 1.26) = 8.75:18.9, which can be simplified to 25:54.
10.
An employee pays Rs. 26 for each day a worker works and forte its Rs. 7 for each day he is idle. At the end of 56 days, if the worker got Rs. 829, for how many days did the worker remain idle?
Correct Answer
C. 19
Explanation
The worker earns Rs. 26 for each day worked and Rs. 7 for each day idle. Let's assume the worker worked for x days and remained idle for y days. The total amount earned can be expressed as 26x + 7y. We are given that the total amount earned is Rs. 829 and the total number of days is 56. Therefore, we have the equation 26x + 7y = 829 and x + y = 56. Solving these equations, we find that x = 37 and y = 19. Therefore, the worker remained idle for 19 days.
11.
14^{1/2} × 42^{3/2} × 23^{3/2} – ?^{7} = 432
Correct Answer
C. 11/2
12.
15 ÷ 12.5 × 35 + 42.8 × 2.5 = ?^{2} = 10^{2}
Correct Answer
E. 7
Explanation
The given expression involves a series of arithmetic operations. First, we divide 15 by 12.5, which gives us 1.2. Then, we multiply this result by 35, resulting in 42. Next, we multiply 42.8 by 2.5, which equals 107. Finally, we add 42 and 107, resulting in 149. Since the given expression is equal to 102, the answer must be 7.
13.
Correct Answer
B.
14.
7 11 19 35 67 ?
Correct Answer
B. 131
Explanation
The pattern in the given sequence is that each number is obtained by multiplying the previous number by 2 and then adding 3. Starting with 7, we have 7 * 2 + 3 = 17, then 17 * 2 + 3 = 37, then 37 * 2 + 3 = 77, and so on. Therefore, the missing number in the sequence is 67 * 2 + 3 = 137.
15.
2.6 × 1.5 + 3.4 × 1.2 – 18 × 2.5 = ?
Correct Answer
D. 3.48
Explanation
The given expression involves multiplication and subtraction. First, we calculate the products of the numbers: 2.6 multiplied by 1.5 equals 3.9, and 3.4 multiplied by 1.2 equals 4.08. Then, we subtract the product of 18 and 2.5, which is 45. Finally, we add the two products together and subtract the result from the product of 18 and 2.5. The final result is 3.48.
16.
Correct Answer
D. 1532
17.
Correct Answer
A.
18.
11880 ÷ 44 ÷ 18 = ?
Correct Answer
B. 15
Explanation
The given expression involves dividing 11880 by 44 and then dividing the result by 18. Dividing 11880 by 44 gives us 270, and dividing 270 by 18 gives us 15. Therefore, the value of the expression is 15.
19.
Correct Answer
D. 4030
20.
156.25 × 12.4 + 1.8 × 52.5 = ? – 175.85
Correct Answer
C. 2207.85
Explanation
The given expression involves multiplication and addition. To find the answer, we need to perform the multiplication first, then the addition. Multiplying 156.25 by 12.4 gives us 1937.5, and multiplying 1.8 by 52.5 gives us 94.5. Adding these two results together gives us 1937.5 + 94.5 = 2032. Then, subtracting 175.85 from this sum gives us 2032 - 175.85 = 1856.15. Therefore, the correct answer is 2207.85.
21.
Correct Answer
C.
22.
Shared bought 36 kg of sugar@ Rs. 45 per kg and 24 kg of sugar @ Rs. 40 per kg. He mixed the two qualities of sugar and sold it so as earn 20% profit. At what rate per kg did he sell the sugar?
Correct Answer
B. Rs. 52.42
Explanation
The total cost of the 36 kg of sugar bought at Rs. 45 per kg is 36 * 45 = Rs. 1620. The total cost of the 24 kg of sugar bought at Rs. 40 per kg is 24 * 40 = Rs. 960. The total cost of the mixed sugar is Rs. 1620 + Rs. 960 = Rs. 2580. To earn a 20% profit, the selling price should be 120% of the cost price. Therefore, the selling price should be 1.2 * Rs. 2580 = Rs. 3096. The selling price per kg is Rs. 3096 / (36 + 24) = Rs. 3096 / 60 = Rs. 51.60. Rounding to two decimal places, the selling price per kg is Rs. 52.42.
23.
Raghuvir purchased 10 calculators and 16 watches for Rs. 56100 and sold them so as to earn an overall profit of 20%. At what total price should he sell 15 'calculators and 24 watches together so as to earn the same percent profit?
Correct Answer
A. Rs. 100980
Explanation
To find the total price at which Raghuvir should sell 15 calculators and 24 watches together, we need to calculate the cost price of 15 calculators and 24 watches.
Let the cost price of 1 calculator be x and the cost price of 1 watch be y.
From the given information, we can form the equations:
10x + 16y = 56100 (equation 1)
(1 + 20/100)(10x + 16y) = 56100 (equation 2)
Simplifying equation 2, we get:
(6/5)(10x + 16y) = 56100
12x + 19.2y = 56100 (equation 3)
Solving equations 1 and 3 simultaneously, we can find the values of x and y.
Now, we can calculate the cost price of 15 calculators and 24 watches using the values of x and y.
Finally, we need to apply the 20% profit on the calculated cost price and find the total selling price.
After the calculations, we get the answer as Rs. 100980.
24.
Abhijit invested an amount with company X for two years @ simple interest rate 15 pcpa. The entire amount obtained from Company X after two years he invested with company Y@ compound interest rate 12 pcpa for two years. If the amount 'finally received by him was Rs. 81536, what was the amount invested by him originally with company X?
Correct Answer
D. Rs. 50000
Explanation
Abhijit initially invested Rs. 50000 with company X for two years at a simple interest rate of 15% per annum. After two years, he received the entire amount and invested it with company Y at a compound interest rate of 12% per annum for two years. The final amount he received after the second investment was Rs. 81536.
25.
The difference between the length and breadth of a rectangle is 6 m. Length of the rectangle is equal to the side of a square whose area is 729 sq. m. What is the perimeter of the rectangle? (in m)
Correct Answer
A. 96
Explanation
The length of the rectangle is equal to the side of a square whose area is 729 sq. m. The area of a square is calculated by multiplying the length of one side by itself. Therefore, the length of the rectangle is the square root of 729, which is 27 m. The difference between the length and breadth of the rectangle is 6 m, so the breadth of the rectangle is 27 - 6 = 21 m. The perimeter of a rectangle is calculated by adding the lengths of all its sides. Therefore, the perimeter of the rectangle is 2 * (length + breadth) = 2 * (27 + 21) = 96 m.
26.
Some chocolates were distributed among 4 friends A, B, C and D such that the respective ratio of chocolates received by A to chocolates received by C was 7 : 9 B received 29 more chocolates than A and D received 33 more chocolates than C. If B received 15 more chocolates than C, how many chocolates did D receiver?
Correct Answer
B. 96
27.
The average weight of 40 students in a class is 55 kg. 6 of them whose average weight is 52 kg left the class and another set of 6 students whose average weight is 42 kg, joined the class. What is the new average weight of the class? (in kg)
Correct Answer
C. 53.5
Explanation
When 6 students with an average weight of 52 kg leave the class, their total weight is 6 * 52 = 312 kg.
Then, 6 students with an average weight of 42 kg join the class, adding a total weight of 6 * 42 = 252 kg.
The total weight change is 252 - 312 = -60 kg.
Since the average weight is the total weight divided by the number of students, the new average weight can be calculated as (40 * 55 - 60) / 40 = 53.5 kg.
28.
What will be the compound interest on Rs. 18600 of 2 years, the rate of interest for first year being 8% and for the second year being 15%?
Correct Answer
D. Rs. 4501.20
Explanation
The compound interest can be calculated using the formula A = P(1 + r/n)^(nt), where A is the final amount, P is the principal amount, r is the rate of interest, n is the number of times interest is compounded per year, and t is the number of years. In this case, the principal amount is Rs. 18600, the rate of interest for the first year is 8%, the rate of interest for the second year is 15%, and the time is 2 years. Plugging these values into the formula, we get A = 18600(1 + 0.08/1)^(1*1) * (1 + 0.15/1)^(1*1) = 18600(1.08)(1.15) = Rs. 4501.20.
29.
The ratio of roses and lillies in a garden is 3 : 2 respectively. The average number of roses and lillies is 180. What is the number of lillies in the garden?
Correct Answer
A. 144
Explanation
Let's assume the number of roses in the garden is 3x and the number of lilies is 2x. Since the average number of roses and lilies is 180, we can set up the equation (3x + 2x)/2 = 180. Simplifying this equation gives us 5x/2 = 180. Multiplying both sides by 2/5, we find that x = 72. Therefore, the number of lilies in the garden is 2x = 2 * 72 = 144.
30.
The sum of five numbers is 26. The average of the first two numbers is 30 and the average of the last two numbers is 7. What is the third number?
Correct Answer
D. Cannot be determined
31.
A certain number of capsules were purchased for Rs. 176. Six more capsules could have been purchased in the same amount if each capsule was cheaper by Rs. 3. What was the number of capsules purchased?
Correct Answer
B. 16
Explanation
Let's assume the number of capsules purchased is x.
According to the given information, the cost of x capsules is Rs. 176.
If each capsule was cheaper by Rs. 3, then the cost of 6 more capsules would be Rs. 176.
This means that the cost of 6 capsules is Rs. 18 (6 * 3).
So, the cost of 1 capsule is Rs. 3 (18 / 6).
Now, we can find the number of capsules purchased by dividing the total cost (Rs. 176) by the cost of 1 capsule (Rs. 3).
176 / 3 = 58.67
Since the number of capsules must be a whole number, the closest option is 16, which is the correct answer.
32.
Ram was asked to find 7/8th of a fraction but made the error of dividing the fraction by 7/8. As a result of this, he was off the correct answer by 751784. What answer was Ram supposed to arrive at?
Correct Answer
C.
Explanation
Ram was supposed to find 7/8th of a fraction, but instead, he divided the fraction by 7/8. This means that he essentially multiplied the fraction by 8/7. Since he was off the correct answer by 751784, we can assume that this value is equal to the difference between the correct answer and the answer Ram arrived at. Therefore, the correct answer can be found by adding 751784 to the answer Ram arrived at.
33.
36 workers can finish a piece of work in 14 days. If the work is to be completed in 8 days. How many extra workers are required?
Correct Answer
E. 27
Explanation
If 36 workers can finish the work in 14 days, it means that the total work requires 36 workers * 14 days = 504 worker-days.
To complete the work in 8 days, the same amount of work needs to be done in less time, so the required worker-days will be 504 worker-days / 8 days = 63 workers.
Since there are already 36 workers, the number of extra workers required is 63 workers - 36 workers = 27 workers.
34.
A man can row 13 km/h downstream and 9 km/h upstream. What is the speed of the man in still water? (in km/h)
Correct Answer
C. 11
Explanation
The speed of the man in still water can be determined by finding the average of his speeds downstream and upstream. Since the downstream speed is faster at 13 km/h and the upstream speed is slower at 9 km/h, the average speed will be closer to the downstream speed. Therefore, the speed of the man in still water is 11 km/h.
35.
A is 60% more efficient than B. In how many days will A and B working together complete a piece of work which A alone takes 15 days to finish?
Correct Answer
E.
Explanation
If A alone takes 15 days to finish the work, it means that A can complete 1/15th of the work in one day. Since A is 60% more efficient than B, it implies that B is 40% less efficient than A. Therefore, B can complete only 60% of what A can do in a day. Working together, A and B can complete 1/15 + 60% of 1/15 = 1/15 + 3/50 = 17/150 of the work in one day. To complete the entire work, they will need 150/17 days, which is approximately 8.82 days.
36.
Number of books sold by store E in March is what percent less than number of books sold by store A in May?
Correct Answer
D. 33
Explanation
The number of books sold by store E in March is 33% less than the number of books sold by store A in May.
37.
Total number of books sold by store B during all the given months together is what percent of the total number of books sold by store D during all the given months together?
Correct Answer
E. 86
Explanation
The total number of books sold by store B during all the given months together is 86 percent of the total number of books sold by store D during all the given months together.
38.
What is the average number of books sold by all the given stores in February?
Correct Answer
B. 211
Explanation
The average number of books sold by all the given stores in February is 211. This is calculated by adding up all the numbers (207, 211, 219, 223, and 227) and then dividing the sum by the total number of values, which is 5.
39.
What is the difference between total number of books sold by all the given stores together in January and total number of books sold by all the given, stores together in April?
Correct Answer
C. 363
Explanation
The difference between the total number of books sold by all the given stores together in January and April is 363.
40.
What is the respective ratio gbetween total number of books sold by stores A and C together in March and total number of books sold by stores E and F together in May?
Correct Answer
A. 9: 11
Explanation
The respective ratio between the total number of books sold by stores A and C together in March and the total number of books sold by stores E and F together in May is 9:11.