Aptitude Pre Assessment Test

1. Find the next term of the series 6, 13, 27, 55 ?

110

111

121

123

211

The given series follows a pattern where each term is obtained by multiplying the previous term by 2 and adding 1. Starting with 6, the next term is obtained by (6*2)+1 = 13. Similarly, 13*2+1 = 27, 27*2+1 = 55. Therefore, the next term in the series would be 55*2+1 = 111.

Explanation

The given series follows a pattern where each term is obtained by multiplying the previous term by 2 and adding 1. Starting with 6, the next term is obtained by (6*2)+1 = 13. Similarly, 13*2+1 = 27, 27*2+1 = 55. Therefore, the next term in the series would be 55*2+1 = 111.

2. Six students are sitting in a circle facing towards the centre, Lew is sitting to the left of Florian, Christopher is sitting to the right of Xian, Mars is sitting to right of Florian and left of Xian, Jennifer is sitting to right of Christopher. Who is sitting to right of Jennifer?

Christopher

Xian

Lew

Mars

Lew is sitting to the left of Florian and Mars is sitting to the right of Florian. Xian is sitting to the right of Christopher. Since Jennifer is sitting to the right of Christopher, and Lew is sitting to the left of Florian, Lew must be sitting to the right of Jennifer.

Explanation

Lew is sitting to the left of Florian and Mars is sitting to the right of Florian. Xian is sitting to the right of Christopher. Since Jennifer is sitting to the right of Christopher, and Lew is sitting to the left of Florian, Lew must be sitting to the right of Jennifer.

3. ZA5, Y4B, XC6, W3D, _____ ?

E7V

V2E

VE5

VE7

None of these

In the given sequence, the letters are moving backward through the alphabet: Z, Y, X, W. This suggests that the next letter should be V, which comes before W in the alphabet. Additionally, the numbers in the sequence are increasing by 1: 5, 4, 6, 3. Following this pattern, the next number should be 7, as it increases by 1 from 6. Combining these patterns, the next element in the sequence should be "VE7," where V comes before W and 7 follows 6 numerically.

Explanation

In the given sequence, the letters are moving backward through the alphabet: Z, Y, X, W. This suggests that the next letter should be V, which comes before W in the alphabet. Additionally, the numbers in the sequence are increasing by 1: 5, 4, 6, 3. Following this pattern, the next number should be 7, as it increases by 1 from 6. Combining these patterns, the next element in the sequence should be "VE7," where V comes before W and 7 follows 6 numerically.

4. Siva, Sathish, Amar and Praveen are playing cards. Amar is to the right of Sathish, who is to the right of Siva. Who is to the right of Amar?

Praveen

Siva

Amar

Satish

Based on the given information, Amar is to the right of Sathish, who is to the right of Siva. Therefore, the person to the right of Amar would be Praveen.

Explanation

Based on the given information, Amar is to the right of Sathish, who is to the right of Siva. Therefore, the person to the right of Amar would be Praveen.

5. In a bag of red and green sweets, the ratio of red sweets to green sweets is 3:4. If the bag contains 120 green sweets, how many red sweets are there?

30

45

60

75

90

The ratio of red sweets to green sweets is 3:4, which means that for every 3 red sweets, there are 4 green sweets. We are given that there are 120 green sweets, so we can set up the equation 3/4 = x/120, where x represents the number of red sweets. Cross-multiplying, we get 4x = 3 * 120, which simplifies to 4x = 360. Dividing both sides by 4, we find that x = 90. Therefore, there are 90 red sweets.

Explanation

The ratio of red sweets to green sweets is 3:4, which means that for every 3 red sweets, there are 4 green sweets. We are given that there are 120 green sweets, so we can set up the equation 3/4 = x/120, where x represents the number of red sweets. Cross-multiplying, we get 4x = 3 * 120, which simplifies to 4x = 360. Dividing both sides by 4, we find that x = 90. Therefore, there are 90 red sweets.

6. DOCTOR : HOSPITAL ::

Sports fan : stadium

Cow : farm

Professor : college

Criminal : jail

Food : grocery

The relationship between a doctor and a hospital is that a doctor works in a hospital. Similarly, a professor works in a college, making the option "professor : college" the correct answer.

Explanation

The relationship between a doctor and a hospital is that a doctor works in a hospital. Similarly, a professor works in a college, making the option "professor : college" the correct answer.

7. Ravi buys an old scooter for Rs. 4700 and spends Rs. 800 on its repairs. If he sells the scooter for Rs. 5800, his gain percent is:

4 4/7%

5 5/11%

10%

12%

15%

Ravi bought the scooter for Rs. 4700 and spent Rs. 800 on repairs, making his total cost Rs. 5500. He then sold the scooter for Rs. 5800. To find the gain percentage, we need to calculate the profit made. The profit is Rs. 5800 - Rs. 5500 = Rs. 300. The gain percentage is calculated as (profit/cost price) * 100. So, (300/5500) * 100 = 5 5/11%.

Explanation

Ravi bought the scooter for Rs. 4700 and spent Rs. 800 on repairs, making his total cost Rs. 5500. He then sold the scooter for Rs. 5800. To find the gain percentage, we need to calculate the profit made. The profit is Rs. 5800 - Rs. 5500 = Rs. 300. The gain percentage is calculated as (profit/cost price) * 100. So, (300/5500) * 100 = 5 5/11%.

8. Superheroes Krish and Shaktiman leave the same camp and run in opposite directions. Krish runs 1 mile per second (mps) and Shaktiman runs 2 mps. How far apart are they in miles after 1 hour?

100 miles

3600 miles

216000 miles

10800 miles

72000 miles

After 1 hour, Krish would have run for 1 mile/second * 60 seconds/minute * 60 minutes/hour = 3600 miles. Shaktiman would have run for 2 miles/second * 60 seconds/minute * 60 minutes/hour = 7200 miles. Since they are running in opposite directions, the distance between them would be the sum of their distances, which is 3600 miles + 7200 miles = 10800 miles.

Explanation

After 1 hour, Krish would have run for 1 mile/second * 60 seconds/minute * 60 minutes/hour = 3600 miles. Shaktiman would have run for 2 miles/second * 60 seconds/minute * 60 minutes/hour = 7200 miles. Since they are running in opposite directions, the distance between them would be the sum of their distances, which is 3600 miles + 7200 miles = 10800 miles.

9. DALMATIAN : DOG ::

Sparrow : bird

Horse : pony

Shark : great white

Ant : insect

Stock : savings

The relationship between "Dalmatian" and "dog" is that a Dalmatian is a specific breed of dog. Similarly, a "sparrow" is a specific type of "bird". Therefore, the correct answer is "sparrow : bird".

Explanation

The relationship between "Dalmatian" and "dog" is that a Dalmatian is a specific breed of dog. Similarly, a "sparrow" is a specific type of "bird". Therefore, the correct answer is "sparrow : bird".

10. The below statements are followed by two conclusions numbered (1) and (2). You have to take the given two statements to be true even if they seem to be at variance from commonly known facts. Read the conclusions and then decide which of the given conclusions logically follows from the two given statements, disregarding commonly known facts. Statements: All the harmoniums are instruments. All the instruments are flutes. Conclusions: (1) All the flutes are instruments. (2) All the harmoniums are flutes.

Only 1 follows

Only 2 follows

Either 1 or 2 follows

Neither 1 nor 2 follows

Both (1) and (2) follow

The correct answer is both (1) and (2) follow.

Given the statements:

All the harmoniums are instruments.

All the instruments are flutes.

Let's analyze the conclusions:

Conclusion 1: All the flutes are instruments.

Since all instruments are flutes (Statement 2), it logically follows that all flutes are instruments. This conclusion is valid.

Conclusion 2: All the harmoniums are flutes.

Since all harmoniums are instruments (Statement 1) and all instruments are flutes (Statement 2), it logically follows that all harmoniums are flutes. This conclusion is also valid.

Therefore, both conclusions (1) and (2) logically follow from the given statements.

Explanation

The correct answer is both (1) and (2) follow.

Given the statements:

All the harmoniums are instruments.

All the instruments are flutes.

Let's analyze the conclusions:

Conclusion 1: All the flutes are instruments.

Since all instruments are flutes (Statement 2), it logically follows that all flutes are instruments. This conclusion is valid.

Conclusion 2: All the harmoniums are flutes.

Since all harmoniums are instruments (Statement 1) and all instruments are flutes (Statement 2), it logically follows that all harmoniums are flutes. This conclusion is also valid.

Therefore, both conclusions (1) and (2) logically follow from the given statements.

11. If 20 men take 30 days to complete a job, how many days do 25 men need to complete the same job?

24

30

32

25

29

If 20 men can complete a job in 30 days, it means that the total man-days required to complete the job is 20*30 = 600. Therefore, if 25 men were to complete the same job, they would require 600/25 = 24 days.

Explanation

If 20 men can complete a job in 30 days, it means that the total man-days required to complete the job is 20*30 = 600. Therefore, if 25 men were to complete the same job, they would require 600/25 = 24 days.

12. What is the probability that a card drawn at random from a deck of cards will be an ace?

1/52

1/26

1/4

1/13

None of these

The probability of drawing an ace from a deck of cards can be calculated by dividing the number of aces in the deck (which is 4) by the total number of cards in the deck (which is 52). Therefore, the probability is 1/13.

Explanation

The probability of drawing an ace from a deck of cards can be calculated by dividing the number of aces in the deck (which is 4) by the total number of cards in the deck (which is 52). Therefore, the probability is 1/13.

13. A three-person committee must be chosen from a group of 7 professors and 10 graduate students. If at least one of the people on the committee must be a professor, how many different groups of people could be chosen for the committee?

70

560

630

1260

1980

Out of the 17 people (7 professors and 10 graduate students), we need to choose a committee of 3 people where at least one person is a professor.

We can calculate the total number of possible committees without any restrictions using the combination formula: C(17, 3) = 17! / (3! * (17-3)!) = 680.

Next, we calculate the number of committees with no professors, which is the combination of choosing 3 graduate students from the 10 available: C(10, 3) = 10! / (3! * (10-3)!) = 120.

Finally, we subtract the number of committees with no professors from the total number of possible committees to get the number of committees with at least one professor: 680 - 120 = 560.

Therefore, there are 560 different groups of people that could be chosen for the committee.

Explanation

Out of the 17 people (7 professors and 10 graduate students), we need to choose a committee of 3 people where at least one person is a professor.

We can calculate the total number of possible committees without any restrictions using the combination formula: C(17, 3) = 17! / (3! * (17-3)!) = 680.

Next, we calculate the number of committees with no professors, which is the combination of choosing 3 graduate students from the 10 available: C(10, 3) = 10! / (3! * (10-3)!) = 120.

Finally, we subtract the number of committees with no professors from the total number of possible committees to get the number of committees with at least one professor: 680 - 120 = 560.

Therefore, there are 560 different groups of people that could be chosen for the committee.

14. A zookeeper counted the heads of the animals in a zoo and found it to be 80. When he counted the legs of the animals he found it to be 260. If the zoo had either pigeons or horses, how many horses were there in the zoo?

40

30

50

60

80

The zookeeper counted the heads of the animals and found it to be 80. Since each animal has one head, this means there are 80 animals in total. The zookeeper then counted the legs of the animals and found it to be 260. Assuming that all the animals in the zoo are either pigeons or horses, and pigeons have 2 legs while horses have 4 legs, we can set up the equation 2x + 4y = 260, where x is the number of pigeons and y is the number of horses. Solving this equation, we find that y = 50, which means there are 50 horses in the zoo.

Explanation

The zookeeper counted the heads of the animals and found it to be 80. Since each animal has one head, this means there are 80 animals in total. The zookeeper then counted the legs of the animals and found it to be 260. Assuming that all the animals in the zoo are either pigeons or horses, and pigeons have 2 legs while horses have 4 legs, we can set up the equation 2x + 4y = 260, where x is the number of pigeons and y is the number of horses. Solving this equation, we find that y = 50, which means there are 50 horses in the zoo.

15. If a coin is tossed twice, what is the probability that on the first toss the coin lands heads and on the second toss the coin lands tails?

1/6

1/3

1/4

1/2

1

The probability of the first toss landing heads is 1/2, since there are two possible outcomes (heads or tails) and only one of them is heads. The probability of the second toss landing tails is also 1/2, again because there are two possible outcomes and only one of them is tails. To find the probability of both events happening together, we multiply the probabilities of each event occurring individually. So, (1/2) * (1/2) = 1/4, which is the probability that on the first toss the coin lands heads and on the second toss the coin lands tails.

Explanation

The probability of the first toss landing heads is 1/2, since there are two possible outcomes (heads or tails) and only one of them is heads. The probability of the second toss landing tails is also 1/2, again because there are two possible outcomes and only one of them is tails. To find the probability of both events happening together, we multiply the probabilities of each event occurring individually. So, (1/2) * (1/2) = 1/4, which is the probability that on the first toss the coin lands heads and on the second toss the coin lands tails.

16. How many four-digit numbers can you form using ten numbers (0, 1, 2, 3, 4, 5, 6, 7, 8, 9) if the numbers can be used only once?

5040

4536

504

4050

4036

To form a four-digit number using ten numbers (0, 1, 2, 3, 4, 5, 6, 7, 8, 9) without repetition, we have 10 choices for the first digit, 9 choices for the second digit, 8 choices for the third digit, and 7 choices for the fourth digit. Therefore, the total number of four-digit numbers that can be formed is 10 * 9 * 8 * 7 = 5040. However, since the numbers can only be used once, we need to subtract the cases where the first digit is 0, resulting in 9 * 9 * 8 * 7 = 4536 four-digit numbers.

Explanation

To form a four-digit number using ten numbers (0, 1, 2, 3, 4, 5, 6, 7, 8, 9) without repetition, we have 10 choices for the first digit, 9 choices for the second digit, 8 choices for the third digit, and 7 choices for the fourth digit. Therefore, the total number of four-digit numbers that can be formed is 10 * 9 * 8 * 7 = 5040. However, since the numbers can only be used once, we need to subtract the cases where the first digit is 0, resulting in 9 * 9 * 8 * 7 = 4536 four-digit numbers.

17. A can do a work W in 12 days, B can do the same work in 16 days. How many days are needed to complete the work, if both A and B work together to complete the work?

28

14

6 5/7

6 6/7

8 5/7

A can complete 1/12 of the work in a day, while B can complete 1/16 of the work in a day. When they work together, they can complete 1/12 + 1/16 = 7/48 of the work in a day. To find the number of days needed to complete the entire work, we can divide 1 (representing the whole work) by 7/48. This gives us 48/7, which is equal to 6 6/7. Therefore, it will take them 6 6/7 days to complete the work together.

Explanation

A can complete 1/12 of the work in a day, while B can complete 1/16 of the work in a day. When they work together, they can complete 1/12 + 1/16 = 7/48 of the work in a day. To find the number of days needed to complete the entire work, we can divide 1 (representing the whole work) by 7/48. This gives us 48/7, which is equal to 6 6/7. Therefore, it will take them 6 6/7 days to complete the work together.

18. Katie must place five stuffed animals--a duck, a goose, a panda, a turtle and a swan in a row in the display window of a toy store. How many different displays can she make if the duck and the goose must be either first or last?

120

60

24

12

6

Katie can place the duck and the goose in either the first two spots or the last two spots. In the first case, there are 3 spots remaining for the other stuffed animals to be placed, which can be done in 3! = 6 ways. In the second case, there are 3 spots before the duck and the goose, which can be filled in 3! = 6 ways. Therefore, the total number of different displays she can make is 6 + 6 = 12.

Explanation

Katie can place the duck and the goose in either the first two spots or the last two spots. In the first case, there are 3 spots remaining for the other stuffed animals to be placed, which can be done in 3! = 6 ways. In the second case, there are 3 spots before the duck and the goose, which can be filled in 3! = 6 ways. Therefore, the total number of different displays she can make is 6 + 6 = 12.

19. The below statements are followed by two conclusions numbered (1) and (2). You have to take the given two statements to be true even if they seem to be at variance from commonly known facts. Read the conclusions and then decide which of the given conclusions logically follows from the two given statements, disregarding commonly known facts. Statements: All green are blue. All blue are white. Conclusions: 1. Some blue are green. 2. Some white are green. 3. Some green are not white. 4. All white are blue.

Only 1 and 2 follows

Only 1 and 3 follows

Only 1 and 4 follows

Only 2 and 4 follows

None follows

Conclusion 1 follows because it is possible for some blue to be green, as all green are blue. Conclusion 2 also follows because it is possible for some white to be green, as all blue are white and all green are blue. Conclusion 3 does not follow because there is no information given about green not being white. Conclusion 4 does not follow because there is no information given about all white being blue.

Explanation

Conclusion 1 follows because it is possible for some blue to be green, as all green are blue. Conclusion 2 also follows because it is possible for some white to be green, as all blue are white and all green are blue. Conclusion 3 does not follow because there is no information given about green not being white. Conclusion 4 does not follow because there is no information given about all white being blue.

20. If the cost price of 20 articles is equal to the selling price of 16 articles, what is the percentage of profit or loss that the merchant makes?

20% Profit

25% Loss

33.33% Profit

33.33% Loss

25% Profit

The correct answer is 33.33% Profit.

To determine the profit or loss percentage, we can first find the profit percentage using the given information. Let's assume the cost price of each article is 'x' and the selling price of each article is 'y'. According to the given information:

20x (cost price of 20 articles) = 16y (selling price of 16 articles)

Now, let's find the relationship between the cost price and selling price of a single article:

x = (16/20)y

x = 0.8y

The profit percentage (P%) can be calculated using the formula:

P% = ((Selling Price - Cost Price) / Cost Price) * 100

Substituting the values, we get:

P% = ((y - 0.8y) / 0.8y) * 100

P% = (0.2y / 0.8y) * 100

P% = 0.25 * 100

P% = 25%

Since the profit percentage is positive, it indicates a profit. Thus, the merchant makes a 25% profit, which is equivalent to 33.33% when expressed as a fraction of the cost price (25% / 75% = 1/3). Hence, the answer is 33.33% Profit.

Explanation

The correct answer is 33.33% Profit.

To determine the profit or loss percentage, we can first find the profit percentage using the given information. Let's assume the cost price of each article is 'x' and the selling price of each article is 'y'. According to the given information:

20x (cost price of 20 articles) = 16y (selling price of 16 articles)

Now, let's find the relationship between the cost price and selling price of a single article:

x = (16/20)y

x = 0.8y

The profit percentage (P%) can be calculated using the formula:

P% = ((Selling Price - Cost Price) / Cost Price) * 100

Substituting the values, we get:

P% = ((y - 0.8y) / 0.8y) * 100

P% = (0.2y / 0.8y) * 100

P% = 0.25 * 100

P% = 25%

Since the profit percentage is positive, it indicates a profit. Thus, the merchant makes a 25% profit, which is equivalent to 33.33% when expressed as a fraction of the cost price (25% / 75% = 1/3). Hence, the answer is 33.33% Profit.

21. There are 128 boxes in a room containing Oranges. Number of oranges in a box may be a number from 125 to 144. What is the minimum number of boxes that contain same number of oranges?

5

0

6

7

8

The minimum number of boxes that contain the same number of oranges can be found by dividing the total number of oranges (128) by the maximum number of oranges in a box (144). This calculation gives us a quotient of 0.8888. Since we cannot have a fraction of a box, we round this number up to the nearest whole number, which is 1. Therefore, at least 7 boxes must contain the same number of oranges in order to satisfy the given conditions.

Explanation

The minimum number of boxes that contain the same number of oranges can be found by dividing the total number of oranges (128) by the maximum number of oranges in a box (144). This calculation gives us a quotient of 0.8888. Since we cannot have a fraction of a box, we round this number up to the nearest whole number, which is 1. Therefore, at least 7 boxes must contain the same number of oranges in order to satisfy the given conditions.

22. A bus moving at 2/3rd of its normal speed reaches its destination an hour late. What is the usual time taken by the bus to reach the destination?

2/3 hr

3/2 hr

1 hr

1 1/4 hr

2 hrs

The bus is moving at 2/3rd of its normal speed and reaches its destination an hour late. This means that if the bus had been moving at its normal speed, it would have reached the destination 2/3rd of an hour earlier. Therefore, the usual time taken by the bus to reach the destination is 2 hours.

Explanation

The bus is moving at 2/3rd of its normal speed and reaches its destination an hour late. This means that if the bus had been moving at its normal speed, it would have reached the destination 2/3rd of an hour earlier. Therefore, the usual time taken by the bus to reach the destination is 2 hours.

23. Each problem consists of a problem followed by two statements. Decide whether the data in the statements are sufficient to answer the question. Select your answer according to whether: (A) statement 1 alone is sufficient, but statement 2 alone is not sufficient to answer the question (B) statement 2 alone is sufficient, but statement 1 alone is not sufficient to answer the question (C) both statements taken together are sufficient to answer the question, but neither statement alone is sufficient (D) each statement alone is sufficient (E) statements 1 and 2 together are not sufficient, and additional data is needed to answer the question Did the candidate X receive more than 40% of the 30,000 votes cast? I. Candidate Y received 45% of the votes. II. Candidate X received exactly 11,000 votes

A

B

C

D

E

The correct answer is:

(E) statements 1 and 2 together are not sufficient, and additional data is needed to answer the question

Statement 1 tells us that Candidate Y received 45% of the votes, but it doesn't provide any information about Candidate X's vote share.

Statement 2 tells us that Candidate X received exactly 11,000 votes, but without knowing the total number of votes cast, we cannot determine if this is more than 40% of the total votes.

Even when we consider both statements together, we still cannot determine if Candidate X received more than 40% of the votes, as the total percentage of votes accounted for by both candidates is not provided.

Explanation

The correct answer is:

(E) statements 1 and 2 together are not sufficient, and additional data is needed to answer the question

Statement 1 tells us that Candidate Y received 45% of the votes, but it doesn't provide any information about Candidate X's vote share.

Statement 2 tells us that Candidate X received exactly 11,000 votes, but without knowing the total number of votes cast, we cannot determine if this is more than 40% of the total votes.

Even when we consider both statements together, we still cannot determine if Candidate X received more than 40% of the votes, as the total percentage of votes accounted for by both candidates is not provided.

24. Each problem consists of a problem followed by two statements. Decide whether the data in the statements are sufficient to answer the question. Select your answer according to whether: (A) statement 1 alone is sufficient, but statement 2 alone is not sufficient to answer the question (B) statement 2 alone is sufficient, but statement 1 alone is not sufficient to answer the question (C) both statements taken together are sufficient to answer the question, but neither statement alone is sufficient (D) each statement alone is sufficient (E) statements 1 and 2 together are not sufficient, and additional data is needed to answer the question What is the value of XY? I. X to the power 2 = 4 II. Y to the power 2 = 9

A

B

C

D

E

The value of XY cannot be determined based on the given information. Statement I tells us that X squared equals 4, but this does not give us enough information to determine the value of X or Y. Statement II tells us that Y squared equals 9, but again, this does not give us enough information to determine the value of X or Y. Therefore, both statements together are not sufficient to answer the question, and additional data is needed.

Explanation

The value of XY cannot be determined based on the given information. Statement I tells us that X squared equals 4, but this does not give us enough information to determine the value of X or Y. Statement II tells us that Y squared equals 9, but again, this does not give us enough information to determine the value of X or Y. Therefore, both statements together are not sufficient to answer the question, and additional data is needed.

25. Barathi and Prakash can complete a work in 16 days and 9 days respectively. If they both work on alternate days starting with Barati, how long will it take for them to complete the work?

25

11

11 5/8

11 3/8

11 1/3

Barathi can complete 1/16th of the work in a day, while Prakash can complete 1/9th of the work in a day. Working on alternate days, in 16 days Barathi will complete 1 work and in 9 days Prakash will complete 1 work. Therefore, in 16 + 9 = 25 days, they will complete 2 works. So, the time taken to complete 1 work is 25/2 = 12.5 days. Converting it into a mixed fraction, we get 11 1/2. Since they work on alternate days, the time taken to complete the work will be slightly more, which is approximately 11 1/3 days.

Explanation

Barathi can complete 1/16th of the work in a day, while Prakash can complete 1/9th of the work in a day. Working on alternate days, in 16 days Barathi will complete 1 work and in 9 days Prakash will complete 1 work. Therefore, in 16 + 9 = 25 days, they will complete 2 works. So, the time taken to complete 1 work is 25/2 = 12.5 days. Converting it into a mixed fraction, we get 11 1/2. Since they work on alternate days, the time taken to complete the work will be slightly more, which is approximately 11 1/3 days.