Aptitude Pre Assessment Test

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.

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%.

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)yx = 0.8yThe profit percentage (P%) can be calculated using the formula:P% = ((Selling Price - Cost Price) / Cost Price) * 100Substituting the values, we get:P% = ((y - 0.8y) / 0.8y) * 100P% = (0.2y / 0.8y) * 100P% = 0.25 * 100P% = 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 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 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
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
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
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
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
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
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
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
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
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 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 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 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 "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 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
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
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
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
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
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
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.