Tss Mock Placement - Aptitude Test

Explanation
To find the number that must be added to 5678 to give a remainder of 35 when divided by 460, we need to subtract 35 from 5678 and then find the remainder when this difference is divided by 460. This can be calculated as (5678 - 35) % 460. Evaluating this expression, we get a remainder of 797. Therefore, the number that must be added to 5678 is 797.

Explanation
A leap year has 366 days, which is 52 weeks and 2 days. Since there are 7 days in a week, the 2 extra days can either be both Sundays or one Sunday and one other day. Therefore, there are 2 out of 7 possible outcomes where a leap year will have 53 Sundays.

Explanation
In this question, two consecutive numbers are removed from the progression 1, 2, 3, ...n. The arithmetic mean of the remaining numbers is given as 26 1/4. To find the value of n, we can calculate the sum of the remaining numbers by multiplying the mean by the number of terms. The mean is given as 26 1/4, which can be written as 105/4. So, the sum of the remaining numbers is (105/4) * (n-2). We need to find the value of n when this sum is equal to the sum of the original progression, which is n * (n+1) / 2. By equating these two sums and solving the equation, we find that n is equal to 50.

Explanation
The professor can remember any number up to 100 by remembering the three numbers obtained as remainders when the number is divided by 3, 5, and 7 respectively. The given information states that the professor had (1,1,6) rupees in the purse and paid (2,0,6) rupees to the servant. To find the amount of money left in the purse, we need to subtract the amount paid from the initial amount.
Using the remainders, we can calculate the initial amount as 1 * 3 * 5 * 7 + 1 * 5 * 7 + 6 * 7 = 105 + 35 + 42 = 182 rupees.
Similarly, the amount paid can be calculated as 2 * 3 * 5 * 7 + 0 * 5 * 7 + 6 * 7 = 210 + 0 + 42 = 252 rupees.
Therefore, the amount of money left in the purse is 182 - 252 = -70 rupees. Since negative money does not make sense, the answer is 56 rupees.

Explanation
To find the cost of the 13% solution, we need to calculate the total cost of purchasing the required amount of acid solution. Since we need 120 liters of the 18% acid solution, we can break it down into two parts: using the 13% solution and the 43% solution. Let's assume we need x liters of the 13% solution and (120-x) liters of the 43% solution.

Now, the cost of the 13% solution is Rs 82 per liter for the first 67 liters and Rs 66 per liter for any amount exceeding 67 liters. So, the cost of x liters of the 13% solution is 82x if x is less than or equal to 67, and 82(67) + 66(x-67) if x is greater than 67.

To minimize the cost, we need to find the value of x that results in the lowest cost. Since we are given that the correct answer is 7672, it suggests that the optimal value of x is greater than 67. By substituting x = 68 into the cost equation, we can verify that it indeed results in the correct answer. Therefore, the cost of the 13% solution we should buy is Rs 7672.

Explanation
When Usha was thrice as old as Nisha, we can set up the equation U = 3N.
When Asha was 25, Usha was 34, so the age difference between them is 9 years.
When Nisha was half as old as Asha, we can set up the equation N = 0.5A.
If we substitute N = 0.5A into the first equation, we get U = 1.5A.
Since the age difference between Usha and Asha is 9 years, we can set up the equation U - A = 9.
Substituting U = 1.5A into this equation, we get 1.5A - A = 9, which simplifies to 0.5A = 9.
Solving for A, we find A = 18.
Substituting A = 18 into U = 1.5A, we get U = 27.
Therefore, Usha is 27 years old.

Explanation
The largest number can be found by subtracting the sum of the other three numbers from the sum of all four numbers. In this case, the sum of all four numbers is 4024 + 4087 + 4524 + 4573 = 17208. Subtracting the sum of the other three numbers (4024 + 4087 + 4524) from this sum gives us 17208 - 12635 = 4573. Therefore, the largest number is 4573.

Explanation
The ratio of the areas of the equilateral triangle and regular hexagon can be determined by comparing their side lengths. Since the perimeter of both shapes is equal, it means that the sum of the lengths of all sides of the equilateral triangle is equal to the sum of the lengths of all sides of the regular hexagon. However, the equilateral triangle has 3 sides while the regular hexagon has 6 sides. Therefore, the length of each side of the equilateral triangle is twice the length of each side of the regular hexagon. Since the area of a shape is proportional to the square of its side length, the ratio of their areas is 2^2:1^2, which simplifies to 4:1. This can be further simplified to 2:1, which is equivalent to 2:03.

Explanation
The correct answer is (5,1). This is because the question states that if the girl buys 10 more flowers, she will save 80 cents a dozen. This implies that the original price of a dozen flowers is 80 cents, and the discounted price for a dozen flowers is 20 cents. Since the girl bought x flowers for y dollars, she must have bought 5 flowers for 1 dollar, as 5 flowers make up a dozen. Therefore, the values of x and y are (5,1).

Explanation
The statement written on door C is wrong because it states that door B leads to the Ghost house. However, if door B leads to the Ghost house, then door C cannot lead to the Ghost house as well. Therefore, the correct answer is door C leads to freedom.

Explanation
The given series is a decreasing sequence. The pattern is that each number is obtained by subtracting a decreasing number from the previous number. The first number is 70, and then 16 is subtracted to get 54, then 9 is subtracted to get 45, and finally 4 is subtracted to get 41. Following the same pattern, the next number in the series would be obtained by subtracting 1 from 41, resulting in 40.

Explanation
The given sequence is formed by repeating the number 1234, with an additional 4 added to the end each time. The first term is 1234, the second term is 12344, the third term is 123444, and so on. In each term, the number 4 is added at the end. Therefore, in the 200th position, the number will have 199 repetitions of 4 after 1234. Thus, the answer is 4.

Explanation
If there are equal numbers of boys and girls in a class, let's assume that there are 'x' boys and 'x' girls. If 12 girls leave the class, the number of girls remaining is 'x - 12'. According to the given information, twice the number of boys as girls remain, so we have '2(x - 12) = x'. Solving this equation, we find that 'x = 24'. Since there are equal numbers of boys and girls, the total number of students in the class is 'x + x = 24 + 24 = 48'. Therefore, the correct answer is 48.

Explanation
Out of the 120 male, 25% are rural, which is equal to 30 male rural students. Out of the 100 female, 20% are rural, which is equal to 20 female rural students. Therefore, the total number of rural students is 30 + 20 = 50. Out of these 50 rural students, 20% of male rural students passed the exam, which is equal to 6 male students, and 25% of female rural students passed the exam, which is equal to 5 female students. So, the total number of rural students who passed the exam is 6 + 5 = 11. To find the percentage, we divide 11 by 50 and multiply by 100, which gives us 22%. Therefore, 22% of rural students have passed the exam.

Explanation
Let's assume the quantity of the tank is x liters. According to the information given, 1/7th of the tank contains fuel, which is equal to x/7 liters. When 22 liters of fuel is poured into the tank, the indicator rests at 1/5th mark. This means that x/7 + 22 = x/5. By solving this equation, we can find the value of x, which is equal to 385. Therefore, the quantity of the tank is 385 liters.

Explanation
When two dice are rolled, there are a total of 36 possible outcomes (6 outcomes for the first dice multiplied by 6 outcomes for the second dice). To find the probability of getting a sum of 3 or 4, we need to determine the number of favorable outcomes. There are two ways to get a sum of 3 (1+2 and 2+1) and one way to get a sum of 4 (1+3). Therefore, there are a total of 3 favorable outcomes. Thus, the probability of getting a sum of 3 or 4 is 3/36, which simplifies to 1/12 or 5/36.

Explanation
Let the cost price of the article be x. When sold at a gain of 5%, the selling price is 1.05x. When sold at a loss of 5%, the selling price is 0.95x. It is given that the selling price at a gain is Rs. 15 more than the selling price at a loss. So, 1.05x - 0.95x = 15. Solving this equation, we get x = 150. Therefore, the cost price of the article is 150.

Explanation
The rate at which work is done by 10 men in 10 days is equal to the rate at which work is done by 12 women in 10 days. This means that 1 man can do the same amount of work as 1.2 women in the same time.
Therefore, the ratio of work done by a man to a woman is 1:1.2.
Now, if 15 men and 6 women undertake the work, the total work done will be equivalent to 15 men + (6 women * 1.2) = 15 men + 7.2 women.
Since the work done by 15 men and 7.2 women is equal to the total work, it will take the group 10 days to complete the work. Hence, the answer is 5.

Explanation
To find the time taken by the train to cross the platform, we need to consider the total distance covered. The train needs to cross its own length of 280 meters and the length of the platform of 220 meters. Therefore, the total distance is 280 + 220 = 500 meters.

Next, we convert the speed of the train from km/h to m/s by dividing it by 3.6. So, 60 km/h is equal to 60/3.6 = 16.67 m/s.

Finally, we can use the formula time = distance/speed to calculate the time taken. Plugging in the values, we get time = 500/16.67 = 30 seconds. Therefore, the correct answer is 30sec.

Explanation
If Ravi's mother is the only daughter of Kamal's mother, then it means that Ravi's mother is Kamal's sister. However, the question is asking about Kamal's relationship to Ravi, not Ravi's mother. Therefore, there is not enough information given to determine how Kamal is related to Ravi.

Explanation
The proportion of milk and water in each sample is given as 2:1, 3:2, and 5:3. To find the proportion of milk and water in the mixture, we need to consider the quantities of milk and water in each sample. Assuming equal quantities of each sample in the mixture, we can calculate the total quantity of milk and water. By adding up the quantities, we get a total of 10 parts of milk and 6 parts of water. Simplifying this ratio gives us 10/6, which is equivalent to 227:133. Therefore, the proportion of milk and water in the mixture is 227:133.

Explanation
If x, y, and z are consecutive negative integers and x > y > z, then the difference between any two consecutive negative integers is always 1. Therefore, the difference between x and y is 1, and the difference between y and z is also 1. So, (x-y)(y-z) = 1 * 1 = 1. Since 1 is a positive odd integer, (x-y)(y-z) must be a positive odd integer.

Explanation
If A is 30% more efficient than B, it means that A can do 30% more work than B in the same amount of time. Therefore, if A alone can complete the job in 23 days, B will take 30% longer, which is 23 x 1.3 = 29.9 days. When working together, A and B can complete 1/23 + 1/29.9 = 0.0913 of the job per day. To complete the entire job, it will take them 1 / 0.0913 = 10.94 days, which is approximately 13 days. Therefore, the correct answer is 13.

Explanation
To find the number of zeroes in the given expression, we need to determine the number of factors of 10. Since 10 can be expressed as 2*5, we need to count the number of 2s and 5s in the expression. Among the given numbers, only 25 and 125 have a factor of 5, and 40 has a factor of 2. Therefore, we have a total of 3 factors of 5 and 1 factor of 2. Since the number of factors of 2 is less than the number of factors of 5, we can conclude that the number of zeroes in the expression is equal to the number of factors of 2, which is 1.

Explanation
Vehicle A overtakes Vehicle B at 10:30 am and reaches city X at 12:00 pm, which means it took 1.5 hours to reach city X. After waiting for 2 hours, Vehicle A starts its return journey and meets Vehicle B at 3:00 pm. This means that Vehicle B took 2.5 hours to reach the meeting point. Since Vehicle B reaches city X after waiting for 1 hour, it took a total of 3.5 hours to reach city X. Therefore, the time taken by Vehicle B to travel from the point of being overtaken by Vehicle A to city Y is 3.5 hours less than the time taken by Vehicle A to travel from city Y to city X, which is 1.5 hours. Hence, Vehicle B will reach city Y from the time it was overtaken by Vehicle A in 1.5 - 3.5 = 41.5 hours.

Explanation
The area of the portion that is common to the two circles can be found by subtracting the area of the square from the total area of the two circles. Since the square has a side length of 1 cm, its area is 1 cm^2. The total area of the two circles can be calculated by multiplying the area of one circle by 2. The area of a circle is given by πr^2, where r is the radius. Since the circles have the same radius, the total area of the two circles is 2πr^2. Subtracting the area of the square from the total area of the two circles gives us 2πr^2 - 1 cm^2. Simplifying this expression gives us (π/2) - 1 cm^2. Therefore, the correct answer is (π/2) - 1.

Explanation
To find the remainder of a number when divided by 9, we can use the property that the remainder of a number divided by 9 is equal to the remainder of the sum of its digits divided by 9. In this case, we need to find the remainder of (32^31^301) when divided by 9. To simplify the calculation, we can focus on the exponent of 31^301 first. The remainder of 31 divided by 9 is 4, and since the remainder of any number raised to a power is the same as the remainder of the number itself raised to that power, we can find the remainder of 4^301. The remainder of 4 divided by 9 is also 4, so the remainder of 4^301 divided by 9 is 4. Now, we can focus on the base of 32. The remainder of 32 divided by 9 is 5. Therefore, the remainder of (32^31^301) when divided by 9 is 5.

Explanation
The correct answer is (5,1) because if the girl buys 5 flowers for 1 dollar, she can then buy 10 more flowers for an additional 1 dollar and get all 15 flowers for a total of 2 dollars. Additionally, by buying 15 flowers, she is getting 1.25 dozen flowers, and saving 80 cents per dozen, which amounts to a total savings of 1 dollar.

Explanation
The sum of the publication years of the seven books is 13,524. Since the books are published at seven-year intervals, we can calculate the difference between each publication year by dividing 13,524 by 6 (the number of intervals between the books). This gives us an average difference of 2,254. Adding this average difference to the publication year of the seventh book gives us the publication year of the first book, which is 1911.

Explanation
The odd weight out is 30 because all the other weights are multiples of 5.

Explanation
The quantity of gravel required can be calculated by finding the volume of the path and then converting it to cubic meters. The rectangular ground has dimensions of 17m by 8m, and the path has a width of 1.5m. The depth of the path is given as 12cm, which is equivalent to 0.12m. To find the volume of the path, we subtract the volume of the ground (17m * 8m * 0.12m) from the volume of the ground with the path (19m * 10m * 0.12m). This gives us a volume of 2.16 cubic meters. Therefore, the quantity of gravel required is 2.16 cubic meters, which is equivalent to 10.08.

Explanation
The given function is defined as f(m+n) = f(m) + f(n) + 4(9mn-1). We are given that f(1) = 0. To find the value of f(17), we can break it down into f(9+8). Using the given function, we can calculate f(9) and f(8) separately. f(9) = f(1) + f(8) + 4(9*1*8-1) = 0 + f(8) + 4(72-1). Simplifying further, f(9) = f(8) + 284. Now, we need to calculate f(8). f(8) = f(1) + f(7) + 4(9*1*7-1) = 0 + f(7) + 4(63-1). Simplifying further, f(8) = f(7) + 248. Continuing this process, we can calculate f(7), f(6), f(5), f(4), f(3), f(2), and finally f(1). Plugging in all the values, we find that f(17) = f(9) + f(8) = 0 + 284 + 248 = 532. Therefore, the correct answer is 4832.

Explanation
The question states that the marbles were bought at a rate of 27 marbles for Rs. 2 times M, where M is an integer. The marbles were then divided into two equal parts. One part was sold at the rate of 13 marbles for Rs. M and the other part was sold at the rate of 14 marbles for Rs. M. The question also mentions that the amount spent and received were integral numbers of rupees.

To find the least number of marbles bought, we need to find the least common multiple (LCM) of the rates at which the marbles were bought and sold. The LCM of 27 and 13 is 351, and the LCM of 27 and 14 is 378. Therefore, the least number of marbles bought is the LCM of 351 and 378, which is 9828.

Explanation
The maximum size of the cube that can be placed between the ladder and the wall can be determined using the Pythagorean theorem. The ladder, the wall, and the ground form a right triangle. The length of the ladder is the hypotenuse of the triangle, and the distance between the bottom of the ladder and the wall is one of the legs of the triangle. By using the Pythagorean theorem, we can find the length of the other leg, which represents the maximum size of the cube that can be placed between the ladder and the wall. In this case, the length of the other leg is approximately 8.56 m, so the maximum size of the cube is 8.56 m.

Explanation
Between the terms 112 and 375, the number 2 appears in the tens place for each number from 120 to 229, which gives us a total of 10 occurrences. Additionally, the number 2 appears in the units place for each number from 200 to 299, which gives us another 100 occurrences. Therefore, the total number of 2's between the terms 112 to 375 is 10 + 100 = 110. However, the given answer is 156, which is incorrect.

Explanation
N is sitting third to the right of O. According to the given information, C and N are diagonally opposite to each other, and E is opposite to O who is just next right of M. Since M is at one end of the line, it means that O is at the other end of the line. Therefore, N must be sitting third to the right of O.

Explanation
If B shifts to the place of E, E shifts to the place of Q, and Q shifts to the place of B, then Q will be opposite to B. According to the given information, B is opposite to Q. Therefore, after the shifts, Q will be opposite to B. The person second to the left of the person opposite to O will be Q.

Explanation
According to the given information, M is at one end of the line and E is opposite to O. Since E and O are not diagonally opposite to each other, it means that M and A must be diagonally opposite to each other. Therefore, the pair AM is diagonally opposite to each other.

Explanation
According to the given information, P is opposite to D. If O and P interchange their positions, then P will be opposite to E. The person who is second to the right of P is Q. The person who is opposite to Q is B. Therefore, the second person to the right of the person who is opposite to the person second to the right of P is A.

Explanation
In the given arrangement, B is sitting just next to the left of D and is opposite to Q. C and N are diagonally opposite to each other. E is opposite to O who is just next right of M. P is just to the left of Q and is opposite to D. Since M is at one end of the line, it means that A is sitting at the other end of the line. Therefore, in the original arrangement, A is sitting just opposite to N.

Explanation
The series consists of two parts: a letter and a number. The letters in the series follow the pattern of increasing by two each time (J, L, N, P, R). The numbers in the series also follow a pattern of increasing by two each time (14, 16, 18, 20, 22). Therefore, the missing letter should be N and the missing number should be 18.

Explanation
A polyglot is someone who knows and can speak multiple languages. This term accurately describes someone who is skilled in many languages, as they have the ability to communicate effectively in different linguistic contexts.

Explanation
The correct answer is "had left" because the sentence is in the past tense and the action of her husband leaving the car keys occurred before the time of wondering.

Explanation
The odd one out in this list is "spendthrift" because it means a person who spends money recklessly or wastefully, while the other three words - stingy, miser, and frugal - all have a negative connotation related to being thrifty or unwilling to spend money.

Explanation
Espionage refers to the practice of employing spies in war. It involves gathering confidential information and conducting covert operations to gain an advantage over the enemy. This can include activities such as infiltrating enemy organizations, intercepting communications, and obtaining classified documents. Espionage has been used throughout history as a strategic tool to gather intelligence, sabotage enemy operations, and make informed decisions in military conflicts.

Explanation
The given sentence does not require any correction. The verb "used to" correctly indicates a past habitual action, and the use of "everyday" instead of "every day" is a common informal usage. The verb tense "was" is also appropriate for the past tense of "to be" in the subordinate clause. Therefore, the sentence is grammatically correct as it is.