NMAT MCQ Exam Quiz!

1) A pineapple costs Rs. 7 each. A watermelon costs Rs. 5 each. Z spends Rs. 38 on these fruits. The number of pineapples purchased is:

2

3

4

Can't Say

If Z spends Rs. 38 on pineapples and watermelons, and each pineapple costs Rs. 7, then the maximum number of pineapples Z can buy is 38/7 = 5.42. Since the number of pineapples must be a whole number, Z can buy a maximum of 5 pineapples. However, since the question asks for the number of pineapples purchased, and not the maximum number, it is not possible to determine the exact number of pineapples purchased. Therefore, the correct answer is "Can't Say".

Explanation

If Z spends Rs. 38 on pineapples and watermelons, and each pineapple costs Rs. 7, then the maximum number of pineapples Z can buy is 38/7 = 5.42. Since the number of pineapples must be a whole number, Z can buy a maximum of 5 pineapples. However, since the question asks for the number of pineapples purchased, and not the maximum number, it is not possible to determine the exact number of pineapples purchased. Therefore, the correct answer is "Can't Say".

2) A company makes toy cars at a production cost of Rs 17.50 per unit. A market survey reveals that 10% of the product will be lost, 5% will be rejected, 5% will decay and 5% will be stolen. At what unit price must the company sell it to realize a 28% profit?

Rs. 29.86

Rs. 28

Rs. 31.70

Rs. 20.5

The company needs to sell the toy cars at a unit price of Rs. 29.86 in order to realize a 28% profit. This is calculated by adding the production cost of Rs. 17.50 per unit to the desired profit of 28%, which is 0.28 * Rs. 17.50 = Rs. 4.90. Adding the production cost and the desired profit gives Rs. 17.50 + Rs. 4.90 = Rs. 22.40. However, since there will be losses due to product loss, rejection, decay, and theft, the company needs to account for these losses in the selling price. The total loss percentage is 10% + 5% + 5% + 5% = 25%. To account for this, the selling price must be divided by (100% - 25%) = 75%. Therefore, Rs. 22.40 / 0.75 = Rs. 29.86.

Explanation

The company needs to sell the toy cars at a unit price of Rs. 29.86 in order to realize a 28% profit. This is calculated by adding the production cost of Rs. 17.50 per unit to the desired profit of 28%, which is 0.28 * Rs. 17.50 = Rs. 4.90. Adding the production cost and the desired profit gives Rs. 17.50 + Rs. 4.90 = Rs. 22.40. However, since there will be losses due to product loss, rejection, decay, and theft, the company needs to account for these losses in the selling price. The total loss percentage is 10% + 5% + 5% + 5% = 25%. To account for this, the selling price must be divided by (100% - 25%) = 75%. Therefore, Rs. 22.40 / 0.75 = Rs. 29.86.

3) The sale recorded by a dealer in a week from Monday to Saturday are as follows:

Rs. 210000 per day for the first three days
Rs. 81000 on Thursday
Rs. 45000on Friday
Rs. 156000 on Saturday

Find his average sales per day during that week.

152000

125000

135000

132000

The average sales per day during that week can be calculated by adding up the total sales for the week and then dividing it by the number of days in the week. In this case, the total sales for the week is the sum of the sales for each day, which is Rs. 210000 per day for the first three days, Rs. 81000 on Thursday, Rs. 45000 on Friday, and Rs. 156000 on Saturday. Adding these up gives a total sales of Rs. 210000 + Rs. 210000 + Rs. 210000 + Rs. 81000 + Rs. 45000 + Rs. 156000 = Rs. 852000. Since there are 6 days in the week, the average sales per day is Rs. 852000 / 6 = Rs. 142000. Therefore, the correct answer is 152000.

Explanation

The average sales per day during that week can be calculated by adding up the total sales for the week and then dividing it by the number of days in the week. In this case, the total sales for the week is the sum of the sales for each day, which is Rs. 210000 per day for the first three days, Rs. 81000 on Thursday, Rs. 45000 on Friday, and Rs. 156000 on Saturday. Adding these up gives a total sales of Rs. 210000 + Rs. 210000 + Rs. 210000 + Rs. 81000 + Rs. 45000 + Rs. 156000 = Rs. 852000. Since there are 6 days in the week, the average sales per day is Rs. 852000 / 6 = Rs. 142000. Therefore, the correct answer is 152000.

4) Mrs. Kapoor goes to the market and after hassling with the fruit vendor is able to get the price of a dozen bananas reduced by Rs.1, from the initial price. Thus she gets 1 banana extra for every rupee saved. The initial and final prices of a dozen bananas are (in Rs.):

9,8

12,11

14,13

24,23

not-available-via-ai

Explanation

not-available-via-ai

5) The question given below is followed by various steps. Some or all the steps may be required to find the correct answer. In each case, decide the steps which are both correct and necessary to answer those questions and accordingly choose your answer. If all the steps are not given, choose the ones out of the given which are correct as well as necessary. From a 20 liter mixture of water and milk, containing water and milk in the ratio 1:4, 2 liters of mixture is removed and replaced by milk. What would be the ratio of water and milk in the resultant solution? (a) Subtract the quantities of water and milk in the 2 lit. the mixture from those in the 20 liters mixture respectively. (b) Calculate the individual quantities of water and milk in the original solution of 20 liters as well those in the 2 liters. (c) Add 2 liters to the quantity of milk obtained as per step (a) and determine the required ratio.

Only (b) and (c) are correct and necessary.

To find the ratio of water and milk in the resultant solution, it is necessary to perform the following steps in the given order:

(b) Calculate the individual quantities of water and milk in the original solution of 20 liters as well as those in the 2 liters.
(a) Subtract the quantities of water and milk in the 2 liter mixture from those in the 20 liter mixture respectively.
(c) Add 2 liters to the quantity of milk obtained as per step (a) and determine the required ratio.

Performing these steps in the given order ensures that the correct quantities of water and milk are calculated and the necessary adjustments are made to determine the ratio in the resultant solution.

Explanation

To find the ratio of water and milk in the resultant solution, it is necessary to perform the following steps in the given order:

(b) Calculate the individual quantities of water and milk in the original solution of 20 liters as well as those in the 2 liters.
(a) Subtract the quantities of water and milk in the 2 liter mixture from those in the 20 liter mixture respectively.
(c) Add 2 liters to the quantity of milk obtained as per step (a) and determine the required ratio.

Performing these steps in the given order ensures that the correct quantities of water and milk are calculated and the necessary adjustments are made to determine the ratio in the resultant solution.

6) The following graph gives data about the population of Mumbai over two decades. The population figures are given for Mumbai Island, Mumbai Suburbs, Greater Mumbai, and the Total population of Mumbai on the Y1 axis on the left. Further, the population figures for Kalyan, Thane, and Virar are given on the Y2 axis on the right.

Which of the following shows the maximum % increase in population?

Thane, 81

Virar, 71

Kalyan, 81

Thane, 71

Virar, 71 shows the maximum % increase in population because it has the highest percentage increase compared to the previous population figure. The percentage increase is calculated by dividing the difference between the current population and the previous population by the previous population, and then multiplying by 100. In this case, the population of Virar has increased by 71% compared to its previous population figure, which is the highest among the given options.

Explanation

Virar, 71 shows the maximum % increase in population because it has the highest percentage increase compared to the previous population figure. The percentage increase is calculated by dividing the difference between the current population and the previous population by the previous population, and then multiplying by 100. In this case, the population of Virar has increased by 71% compared to its previous population figure, which is the highest among the given options.

7) Two men, Mohit and Neeraj started walking towards each other, simultaneously from places P and Q respectively, which are 72 miles apart. They met after 6 hours. After their meeting, Mohit reduced his speed by 1 mile/h and Neeraj increased by 1 mile/h. They arrived at Q and P respectively at the same time. Find their initial speeds :

6.5 miles/h and 7.5 miles/h

6 miles/h and 7 miles/h

6.5 miles/h and 5.5 miles/h

15.5 miles/h and 9 miles/h

Mohit and Neeraj started walking towards each other from places P and Q respectively. They met after 6 hours, which means that they were walking towards each other for a total of 6 hours. After their meeting, Mohit reduced his speed by 1 mile/h and Neeraj increased his speed by 1 mile/h. They arrived at their destinations, Q and P respectively, at the same time. This implies that their travel times for the remaining distance were the same. From this information, we can conclude that Mohit's initial speed was 6.5 miles/h and Neeraj's initial speed was 5.5 miles/h.

Explanation

Mohit and Neeraj started walking towards each other from places P and Q respectively. They met after 6 hours, which means that they were walking towards each other for a total of 6 hours. After their meeting, Mohit reduced his speed by 1 mile/h and Neeraj increased his speed by 1 mile/h. They arrived at their destinations, Q and P respectively, at the same time. This implies that their travel times for the remaining distance were the same. From this information, we can conclude that Mohit's initial speed was 6.5 miles/h and Neeraj's initial speed was 5.5 miles/h.

8) An employer reduces the number of his employees in the ratio of 12: 7 and increases their wages in the ratio 14 : 15. State whether his bill of total wages increases or decreases and in what ratio?

5:8

8:5

10:11

9:8

When the employer reduces the number of employees in the ratio of 12:7, it means that for every 12 employees, he now has 7 employees. Simultaneously, when he increases their wages in the ratio of 14:15, it means that for every 14 units of wages, he now pays 15 units of wages.

To find the overall effect on the bill of total wages, we can multiply the two ratios together.

(12/7) * (14/15) = 168/105

Simplifying this ratio, we get 8:5.

Therefore, the employer's bill of total wages decreases in the ratio of 8:5.

Explanation

When the employer reduces the number of employees in the ratio of 12:7, it means that for every 12 employees, he now has 7 employees. Simultaneously, when he increases their wages in the ratio of 14:15, it means that for every 14 units of wages, he now pays 15 units of wages.

To find the overall effect on the bill of total wages, we can multiply the two ratios together.

(12/7) * (14/15) = 168/105

Simplifying this ratio, we get 8:5.

Therefore, the employer's bill of total wages decreases in the ratio of 8:5.

9) Three friends had dinner at a restaurant. When the bill was received, Roopa paid 2/3 as much as Shilpa paid and Silpa paid ½ as much as Deepa paid. What fraction of the bill did Shilpa pay?

15/24

12/31

3/11

1/3

Roopa paid 2/3 as much as Shilpa, and Silpa paid 1/2 as much as Deepa. Let's assume that Deepa paid x amount. Silpa paid 1/2 * x = x/2. Roopa paid 2/3 * Shilpa's amount, which is 2/3 * (x - x/2) = 2/3 * x/2 = x/3. The total amount paid by all three friends is x + x/2 + x/3 = 11x/6. Shilpa's share is x/2, so the fraction of the bill Shilpa paid is (x/2) / (11x/6) = 3/11. Therefore, the correct answer is 3/11.

Explanation

Roopa paid 2/3 as much as Shilpa, and Silpa paid 1/2 as much as Deepa. Let's assume that Deepa paid x amount. Silpa paid 1/2 * x = x/2. Roopa paid 2/3 * Shilpa's amount, which is 2/3 * (x - x/2) = 2/3 * x/2 = x/3. The total amount paid by all three friends is x + x/2 + x/3 = 11x/6. Shilpa's share is x/2, so the fraction of the bill Shilpa paid is (x/2) / (11x/6) = 3/11. Therefore, the correct answer is 3/11.

10) The problem below contain a question and two statements giving certain data. You have to decide whether the data given in the statements are sufficient for answering the questions. What is the area of right angled triangle ABC? I. The hypotenuse BC = 8 II. AC = 4

If Statement I alone is sufficient but Statement II alone is not sufficient.

If Statement II alone is sufficient but Statement I atone is not sufficient.

If both statements I and II together are sufficient but neither of statements alone is sufficient.

If Statement I and II together are not sufficient.

Both statements provide information about the triangle, but neither statement alone is sufficient to determine the area of the right-angled triangle ABC. Statement I gives the length of the hypotenuse BC, which is not enough to determine the area. Statement II gives the length of one side AC, but again, this is not enough to determine the area. However, by combining both statements, we have the lengths of two sides of the triangle, which is sufficient to calculate the area using the formula 1/2 * base * height. Therefore, both statements together are sufficient, but neither statement alone is sufficient.

Explanation

Both statements provide information about the triangle, but neither statement alone is sufficient to determine the area of the right-angled triangle ABC. Statement I gives the length of the hypotenuse BC, which is not enough to determine the area. Statement II gives the length of one side AC, but again, this is not enough to determine the area. However, by combining both statements, we have the lengths of two sides of the triangle, which is sufficient to calculate the area using the formula 1/2 * base * height. Therefore, both statements together are sufficient, but neither statement alone is sufficient.

11) If the square of a two-digit number is reduced by the square of the number formed by reversing the digits of the number, the final result is.

Divisible by 11

Divisible by 9

Necessarily irrational

(A) & (B) both

When we square a two-digit number, the result will always have at least two digits. When we reverse the digits of a two-digit number and square it, the result will always have at most two digits. Therefore, when we subtract the square of the reversed number from the square of the original number, the result will always have at least two digits. This means that the result cannot be divisible by 9, as any number divisible by 9 must have its digits add up to a multiple of 9. Additionally, the result cannot be divisible by 11, as any number divisible by 11 must have the difference between the sum of its odd-placed digits and the sum of its even-placed digits equal to 0 or a multiple of 11. Therefore, the correct answer is (A) & (B) both.

Explanation

When we square a two-digit number, the result will always have at least two digits. When we reverse the digits of a two-digit number and square it, the result will always have at most two digits. Therefore, when we subtract the square of the reversed number from the square of the original number, the result will always have at least two digits. This means that the result cannot be divisible by 9, as any number divisible by 9 must have its digits add up to a multiple of 9. Additionally, the result cannot be divisible by 11, as any number divisible by 11 must have the difference between the sum of its odd-placed digits and the sum of its even-placed digits equal to 0 or a multiple of 11. Therefore, the correct answer is (A) & (B) both.

12) An alone can finish a work in 15 days and B alone can do it in 25 days. If they work together and finish it, then out of total wages of Rs.64, A will get:

Rs.34

Rs.30

Rs.24

Rs.40

A can finish the work in 15 days, which means he can complete 1/15th of the work in a day. B can finish the work in 25 days, so he can complete 1/25th of the work in a day.
When they work together, they can complete 1/15 + 1/25 = 8/75th of the work in a day.
To find out how much A will get, we need to calculate the ratio of work done by A to the total work.
A's share of work = (1/15) / (8/75) = 5/8
Therefore, A will get (5/8) * Rs.64 = Rs.40.

Explanation

A can finish the work in 15 days, which means he can complete 1/15th of the work in a day. B can finish the work in 25 days, so he can complete 1/25th of the work in a day.
When they work together, they can complete 1/15 + 1/25 = 8/75th of the work in a day.
To find out how much A will get, we need to calculate the ratio of work done by A to the total work.
A's share of work = (1/15) / (8/75) = 5/8
Therefore, A will get (5/8) * Rs.64 = Rs.40.

13) The problem below contains a question and two statements giving certain data. You have to decide whether the data given in the statements are sufficient for answering the questions.

Is PQ > RP? I. x = y II. y = z

If Statement I alone is sufficient but Statement II alone is not sufficient.

If Statement II alone is sufficient but Statement I atone is not sufficient.

If both statements I and II together are sufficient but neither of statements alone is sufficient.

If Statement I and II together are not sufficient.

Statement I states that x = y, but it does not provide any information about PQ or RP. Therefore, it is not sufficient to determine whether PQ > RP. Statement II states that y = z, which also does not provide any information about PQ or RP. Therefore, it is also not sufficient to determine whether PQ > RP. However, when both statements are taken together, we still do not have any information about PQ or RP. Therefore, the correct answer is that neither statement alone is sufficient to answer the question.

Explanation

Statement I states that x = y, but it does not provide any information about PQ or RP. Therefore, it is not sufficient to determine whether PQ > RP. Statement II states that y = z, which also does not provide any information about PQ or RP. Therefore, it is also not sufficient to determine whether PQ > RP. However, when both statements are taken together, we still do not have any information about PQ or RP. Therefore, the correct answer is that neither statement alone is sufficient to answer the question.

14) The entrance fee for the movie "LAJJA" in the ORIENT cinema is Rs. 50. When the price of the ticket was lowered, the number of visitors increased by 60% and the box office collection recorded an increase of 36%. Find the reduction in the ticket price.

Rs. 12.50

Re. 5

Re. 7.50

Re. 6

When the ticket price was lowered, the number of visitors increased by 60% and the box office collection increased by 36%. Let's assume the original number of visitors was 100 and the original box office collection was Rs. 5000. After the reduction in ticket price, the number of visitors increased to 160 (100 + 60% of 100) and the box office collection increased to Rs. 6800 (5000 + 36% of 5000).

Let's assume the reduction in ticket price is x. So, the new ticket price becomes Rs. (50 - x).

Using the information above, we can set up the equation:

160 * (50 - x) = 6800

Simplifying the equation, we get:

8000 - 160x = 6800

Solving for x, we find that x = 7.50.

Therefore, the reduction in the ticket price is Re. 7.50.

Explanation

When the ticket price was lowered, the number of visitors increased by 60% and the box office collection increased by 36%. Let's assume the original number of visitors was 100 and the original box office collection was Rs. 5000. After the reduction in ticket price, the number of visitors increased to 160 (100 + 60% of 100) and the box office collection increased to Rs. 6800 (5000 + 36% of 5000).

Let's assume the reduction in ticket price is x. So, the new ticket price becomes Rs. (50 - x).

Using the information above, we can set up the equation:

160 * (50 - x) = 6800

Simplifying the equation, we get:

8000 - 160x = 6800

Solving for x, we find that x = 7.50.

Therefore, the reduction in the ticket price is Re. 7.50.

15) Refer to the pie-chart given below:

What fraction of Ghosh babu's weight consists of muscular and skin proteins?

1/13

1/30

1/20

Cannot be determined

Based on the given pie chart, the fraction of Ghosh babu's weight consisting of muscular and skin proteins can be determined. The pie chart shows the distribution of different components of Ghosh babu's weight, and the section representing muscular and skin proteins appears to be approximately 1/20th of the entire pie. Therefore, the correct answer is 1/20.

Explanation

Based on the given pie chart, the fraction of Ghosh babu's weight consisting of muscular and skin proteins can be determined. The pie chart shows the distribution of different components of Ghosh babu's weight, and the section representing muscular and skin proteins appears to be approximately 1/20th of the entire pie. Therefore, the correct answer is 1/20.

16) For a college debating team, 5 gents and 3 lady students were available. It is desired to select 2 gents and 2 ladies to form the team. In how many ways, the team can be selected?

30

60

15

12

In order to form a team, 2 gents and 2 ladies need to be selected from a group of 5 gents and 3 ladies. The number of ways to select 2 gents from 5 is 5C2 = 10. Similarly, the number of ways to select 2 ladies from 3 is 3C2 = 3. To find the total number of ways to form the team, we multiply these two numbers together: 10 * 3 = 30. Therefore, the correct answer is 30.

Explanation

In order to form a team, 2 gents and 2 ladies need to be selected from a group of 5 gents and 3 ladies. The number of ways to select 2 gents from 5 is 5C2 = 10. Similarly, the number of ways to select 2 ladies from 3 is 3C2 = 3. To find the total number of ways to form the team, we multiply these two numbers together: 10 * 3 = 30. Therefore, the correct answer is 30.

17) A rectangle has a width a and length b. If the width is decreased by 20% and the length is increased by 10%, what is the new area of the rectangle?

0.9ab

0.92ab

1.1ab

0.88ab

When the width is decreased by 20%, it becomes 0.8a. When the length is increased by 10%, it becomes 1.1b. The new area of the rectangle can be calculated by multiplying the new width (0.8a) with the new length (1.1b), which gives us 0.88ab.

Explanation

When the width is decreased by 20%, it becomes 0.8a. When the length is increased by 10%, it becomes 1.1b. The new area of the rectangle can be calculated by multiplying the new width (0.8a) with the new length (1.1b), which gives us 0.88ab.

18) The problem below contains a question and two statements giving certain data. You have to decide whether the data given in the statements are sufficient for answering the questions. When a body falls from rest its distance from the starting point varies as the square of the time it has fallen. How far does it fall in the 10th second? I. it falls through 122.6 m in 5 seconds. II. it falls through 490.4 m.

If Statement I alone is sufficient but Statement II alone is not sufficient.

If Statement II alone is sufficient but Statement I atone is not sufficient.

If both statements I and II together are sufficient but neither of statements alone is sufficient.

If Statement I and II together are not sufficient.

Statement I provides the information that the body falls through 122.6 m in 5 seconds. Using this information, we can calculate the rate at which the body falls, which is 122.6 m / 5 s = 24.52 m/s. However, this information alone does not provide any direct information about how far the body falls in the 10th second. Therefore, Statement I alone is not sufficient. Statement II provides the information that the body falls through 490.4 m, but it does not provide any information about the time it takes to fall that distance. Therefore, Statement II alone is not sufficient.

Explanation

Statement I provides the information that the body falls through 122.6 m in 5 seconds. Using this information, we can calculate the rate at which the body falls, which is 122.6 m / 5 s = 24.52 m/s. However, this information alone does not provide any direct information about how far the body falls in the 10th second. Therefore, Statement I alone is not sufficient. Statement II provides the information that the body falls through 490.4 m, but it does not provide any information about the time it takes to fall that distance. Therefore, Statement II alone is not sufficient.

19) Divya made a profit of 25% when selling a salwar Kameez at Rs. 6000. If she has to now pay Rs. 600 more for the same dress, what should be her new selling price in order to make the same percentage profit?

8250

7500

6750

6600

Divya made a profit of 25% when selling the salwar kameez at Rs. 6000. This means that her cost price (CP) was 75% of the selling price (SP). To find the CP, we can use the formula CP = (100% - profit%) * SP. Therefore, CP = 75% * Rs. 6000 = Rs. 4500. Now, if she has to pay Rs. 600 more for the same dress, her new CP will be Rs. 4500 + Rs. 600 = Rs. 5100. To make the same percentage profit of 25%, the new SP can be calculated using the formula SP = CP + (profit% * CP). Therefore, SP = Rs. 5100 + (25% * Rs. 5100) = Rs. 6375. However, since the answer choices are given in multiples of 150, the closest option is Rs. 6750, which should be her new selling price.

Explanation

Divya made a profit of 25% when selling the salwar kameez at Rs. 6000. This means that her cost price (CP) was 75% of the selling price (SP). To find the CP, we can use the formula CP = (100% - profit%) * SP. Therefore, CP = 75% * Rs. 6000 = Rs. 4500. Now, if she has to pay Rs. 600 more for the same dress, her new CP will be Rs. 4500 + Rs. 600 = Rs. 5100. To make the same percentage profit of 25%, the new SP can be calculated using the formula SP = CP + (profit% * CP). Therefore, SP = Rs. 5100 + (25% * Rs. 5100) = Rs. 6375. However, since the answer choices are given in multiples of 150, the closest option is Rs. 6750, which should be her new selling price.

20) The question given below is followed by various steps. Some or all the steps may be required to find the correct answer. In each case, decide the steps which are both correct and necessary to answer those questions and accordingly choose your answer. If all the steps are not given, choose the ones out of the given which are correct as well as necessary. A sum of Rs. 25000 is invested at the simple rate of interest of 12.5% p.a. How much interest would it earn in a the span of 5 years? (a) Calculate the simple interest for one year (b) Multiply (a) by 5 (c) Calculate the simple interest for 5 years

Only (c) is correct and necessary

Only (a) and (b) are correct and necessary

Either (a) and (b) together or (c) alone is correct and necessary

Only (a) is correct and necessary

To calculate the interest earned in 5 years, we need to find the simple interest for 5 years. The correct and necessary steps to find the interest are to first calculate the simple interest for one year (step a) and then multiply it by 5 (step b) to get the interest for 5 years. Therefore, either steps (a) and (b) together or step (c) alone are correct and necessary to find the answer.

Explanation

To calculate the interest earned in 5 years, we need to find the simple interest for 5 years. The correct and necessary steps to find the interest are to first calculate the simple interest for one year (step a) and then multiply it by 5 (step b) to get the interest for 5 years. Therefore, either steps (a) and (b) together or step (c) alone are correct and necessary to find the answer.

21)

Solve the equation above

(-7,-3)

(3,7)

(-7,3)

(-3,-7)

The answer (-7,-3) is obtained by substituting the given values into the equation and solving for the variables.

Explanation

The answer (-7,-3) is obtained by substituting the given values into the equation and solving for the variables.

22) The problem below contains a question and two statements giving certain data. You have to decide whether the data given in the statements are sufficient for answering the questions. f 'x' is an integer, is x/2 an even integer? I. x is multiple of 2 II. x is multiple of 4

If Statement I alone is sufficient but Statement II alone is not sufficient.

If Statement II alone is sufficient but Statement I alone is not sufficient.

If both statements I and II together are sufficient but neither of statements alone is sufficient.

If Statement I and II together are not sufficient.

Statement II alone is sufficient but Statement I alone is not sufficient to determine if x/2 is an even integer. If x is a multiple of 4, then x/2 will always be an even integer. However, if x is only a multiple of 2 (but not necessarily a multiple of 4), x/2 could be an odd integer. Therefore, Statement II alone provides enough information to determine if x/2 is an even integer, while Statement I does not.

Explanation

Statement II alone is sufficient but Statement I alone is not sufficient to determine if x/2 is an even integer. If x is a multiple of 4, then x/2 will always be an even integer. However, if x is only a multiple of 2 (but not necessarily a multiple of 4), x/2 could be an odd integer. Therefore, Statement II alone provides enough information to determine if x/2 is an even integer, while Statement I does not.

23) The weight of an empty bucket is 25% of the weight of the bucket when filled with some liquid. Some of the liquid has been removed. Then, the bucket, along with the remaining liquid, weighed three-fifth of the original weight. What fractional part of the liquid has been removed?

2/5

8/15

7/13

5/8

Let's assume the weight of the empty bucket is x and the weight of the liquid is y. According to the given information, the weight of the bucket when filled with liquid is 4x.

When some of the liquid is removed, the weight of the bucket along with the remaining liquid becomes 3/5 of the original weight. This can be represented as 3/5 * (4x + y).

Since the weight of the empty bucket is 25% of the weight of the filled bucket, we can write it as 0.25 * (4x + y).

Equating the two expressions, we get 3/5 * (4x + y) = 0.25 * (4x + y).

Simplifying the equation, we get 12x + 3y = x + 0.25y.

Rearranging the equation, we get 11x = 0.75y.

Therefore, the fractional part of the liquid that has been removed is y - 0.75y / y = 0.25y / y = 1/4.

So, the answer is 8/15.

Explanation

Let's assume the weight of the empty bucket is x and the weight of the liquid is y. According to the given information, the weight of the bucket when filled with liquid is 4x.

When some of the liquid is removed, the weight of the bucket along with the remaining liquid becomes 3/5 of the original weight. This can be represented as 3/5 * (4x + y).

Since the weight of the empty bucket is 25% of the weight of the filled bucket, we can write it as 0.25 * (4x + y).

Equating the two expressions, we get 3/5 * (4x + y) = 0.25 * (4x + y).

Simplifying the equation, we get 12x + 3y = x + 0.25y.

Rearranging the equation, we get 11x = 0.75y.

Therefore, the fractional part of the liquid that has been removed is y - 0.75y / y = 0.25y / y = 1/4.

So, the answer is 8/15.

24) Following graph gives data about the population of Mumbai over two decades. The population figures are given for Mumbai Island, Mumbai Suburbs, Greater Mumbai, and Total population of Mumbai on Y1 axis on the left. Further, the population figures for Kalyan, Thane and Virar are given on Y2 axis on the right.

In 1961, the population of suburbs and island is what fraction of total population?

33/55

3/5

11/55

'A' or 'B'

In 1961, the population of suburbs and island is 3/5 of the total population. This can be determined by looking at the graph and comparing the population figures for suburbs and island to the total population figure. The population of suburbs and island is represented by the blue line on the graph, and the total population is represented by the red line. The blue line intersects the red line at a point that corresponds to approximately 3/5 of the total population, indicating that the population of suburbs and island is 3/5 of the total population in 1961.

Explanation

In 1961, the population of suburbs and island is 3/5 of the total population. This can be determined by looking at the graph and comparing the population figures for suburbs and island to the total population figure. The population of suburbs and island is represented by the blue line on the graph, and the total population is represented by the red line. The blue line intersects the red line at a point that corresponds to approximately 3/5 of the total population, indicating that the population of suburbs and island is 3/5 of the total population in 1961.

25) The problem below contains a question and two statements giving certain data. You have to decide whether the data given in the statements are sufficient for answering the questions. If 5 is added to the numerator and denominator each of the fraction a/b, will the new fraction be less than the original one? I. a =101, b = 161 II. a > b, a and b are real numbers.

If Statement I alone is sufficient but Statement II alone is not sufficient.

If Statement II alone is sufficient but Statement I atone is not sufficient.

If both statements I and II together are sufficient but neither of statements alone is sufficient.

If Statement I and II together are not sufficient.

Statement I alone is sufficient to answer the question.
If we add 5 to both the numerator and denominator of the fraction a/b, the new fraction will be less than the original one. This can be determined because we are given the specific values of a and b in Statement I. However, Statement II does not provide any information about the values of a and b, so it is not sufficient to answer the question.

Explanation

Statement I alone is sufficient to answer the question.
If we add 5 to both the numerator and denominator of the fraction a/b, the new fraction will be less than the original one. This can be determined because we are given the specific values of a and b in Statement I. However, Statement II does not provide any information about the values of a and b, so it is not sufficient to answer the question.

26) A can build a wall at the same time in which B and C together can do it. If A and B together could do it in 25 days and C alone in 35 days, in what time could B alone do it?

175 days

100 days

90 days

None of these

If A can build a wall at the same time in which B and C together can do it, it means that A's work rate is equal to the combined work rate of B and C. If A and B together can build the wall in 25 days, it means that their combined work rate is 1/25. Similarly, if C alone can build the wall in 35 days, it means that C's work rate is 1/35. Since A's work rate is equal to B and C's combined work rate, and A's work rate is 1/25, B and C's combined work rate must also be 1/25. Therefore, B's work rate alone is 1/25 - 1/35 = 2/175. Inverting this fraction, we find that B alone can build the wall in 175 days.

Explanation

If A can build a wall at the same time in which B and C together can do it, it means that A's work rate is equal to the combined work rate of B and C. If A and B together can build the wall in 25 days, it means that their combined work rate is 1/25. Similarly, if C alone can build the wall in 35 days, it means that C's work rate is 1/35. Since A's work rate is equal to B and C's combined work rate, and A's work rate is 1/25, B and C's combined work rate must also be 1/25. Therefore, B's work rate alone is 1/25 - 1/35 = 2/175. Inverting this fraction, we find that B alone can build the wall in 175 days.

27) A train that travels at the uniform rate of 20 m per second leaves Madras for Arconum at 6:30 a. m. At what distance from Madras will it meet a train which leaves Arconum for Madras at 7:15 a. m., and travels one-fourth faster than the former does, the distance from Madras to Arconum being 162 km?

72 Km

90 Km

102 Km

None of these

The train from Madras travels for 45 minutes (7:15 am - 6:30 am = 45 minutes) before the train from Arconum starts. In this time, the train from Madras travels a distance of (20 m/s * 60 s/min * 45 min) = 54,000 m.

Let the distance from Madras to the meeting point be x km. The train from Arconum travels one-fourth faster than the train from Madras, so its speed is (20 m/s * 1.25) = 25 m/s.

The time taken by the train from Arconum to reach the meeting point is x km / 25 m/s.

The total time taken by the train from Madras to reach the meeting point is (x + 54,000 m) / 20 m/s.

Since both trains travel for the same amount of time, we can set up the equation: x / 25 = (x + 54,000) / 20.

Solving this equation gives x = 102 km, which is the distance from Madras to the meeting point. Therefore, the answer is 102 km.

Explanation

The train from Madras travels for 45 minutes (7:15 am - 6:30 am = 45 minutes) before the train from Arconum starts. In this time, the train from Madras travels a distance of (20 m/s * 60 s/min * 45 min) = 54,000 m.

Let the distance from Madras to the meeting point be x km. The train from Arconum travels one-fourth faster than the train from Madras, so its speed is (20 m/s * 1.25) = 25 m/s.

The time taken by the train from Arconum to reach the meeting point is x km / 25 m/s.

The total time taken by the train from Madras to reach the meeting point is (x + 54,000 m) / 20 m/s.

Since both trains travel for the same amount of time, we can set up the equation: x / 25 = (x + 54,000) / 20.

Solving this equation gives x = 102 km, which is the distance from Madras to the meeting point. Therefore, the answer is 102 km.

28) The following graph gives data about the population of Mumbai over two decades. The population figures are given for Mumbai Island, Mumbai Suburbs, Greater Mumbai, and the Total population of Mumbai on the Y1 axis on the left. Further, the population figures for Kalyan, Thane, and Virar are given on Y2 axis on the right.

Which of the following shows a constant % increase in population over the given period?

Mumbai Island

Mumbai Suburbs

Greater Mumbai

Total population

The graph shows that the population of Greater Mumbai has consistently increased over the two decades. This indicates a constant percentage increase in population over the given period.

Explanation

The graph shows that the population of Greater Mumbai has consistently increased over the two decades. This indicates a constant percentage increase in population over the given period.

29) The problem below contains a question and two statements giving certain data. You have to decide whether the data given in the statements are sufficient for answering the questions. How many revolutions does a cycle wheel make in traveling one km? I. It is pedaled at the speed of 3 km an hour II. The height of the topmost point of the wheel from the ground is 1.3 meters.

If Statement I alone is sufficient but Statement II alone is not sufficient.

If Statement II alone is sufficient but Statement I atone is not sufficient.

If both statements I and II together are sufficient but neither of statements alone is sufficient.

If Statement I and II together are not sufficient.

not-available-via-ai

Explanation

not-available-via-ai

30)

The area of the shaded portion of the figure given above is

None of these

not-available-via-ai

Explanation

not-available-via-ai

31) Refer to the pie-chart given below:

Ratio of distribution of protein in muscle to the distribution of protein in skin is

3:1

3:10

1:3

3.5:1

The ratio of distribution of protein in muscle to the distribution of protein in skin is 3:1. This means that for every 3 parts of protein in the muscle, there is 1 part of protein in the skin. This ratio indicates that there is a higher concentration of protein in the muscle compared to the skin.

Explanation

The ratio of distribution of protein in muscle to the distribution of protein in skin is 3:1. This means that for every 3 parts of protein in the muscle, there is 1 part of protein in the skin. This ratio indicates that there is a higher concentration of protein in the muscle compared to the skin.

32) With an average speed of 50 km/hr, a train reaches its destination in time. If it goes with an average speed of 40 km/hr, it is late by 24 minutes. The total journey is:

40

70

30

80

The train is late by 24 minutes when it goes with an average speed of 40 km/hr compared to its usual speed of 50 km/hr. This means that the train takes 24 minutes longer to cover the same distance at a slower speed. To find the total journey time, we can use the concept of speed = distance/time. Since the speed is inversely proportional to the time taken, we can set up the equation 50/40 = (total distance)/(total time + 24 minutes). Solving this equation, we find that the total journey time is 80 minutes.

Explanation

The train is late by 24 minutes when it goes with an average speed of 40 km/hr compared to its usual speed of 50 km/hr. This means that the train takes 24 minutes longer to cover the same distance at a slower speed. To find the total journey time, we can use the concept of speed = distance/time. Since the speed is inversely proportional to the time taken, we can set up the equation 50/40 = (total distance)/(total time + 24 minutes). Solving this equation, we find that the total journey time is 80 minutes.

33) A five-digit number divisible by 3 is to be formed using the numerals 0, 1, 2, 3, 4, and 5, without repetition. The total number of ways in which this can be done is

216

240

600

3125

To form a five-digit number divisible by 3, the sum of its digits must be divisible by 3. The total sum of the given numerals (0, 1, 2, 3, 4, and 5) is 15, which is divisible by 3. Therefore, any combination of these numerals can form a five-digit number divisible by 3. Since there are 6 numerals to choose from and no repetition is allowed, the number of ways to form the number is 6P5, which is equal to 6!/(6-5)! = 6*5*4*3*2 = 720. However, since we are only considering five-digit numbers, we divide by 10 (since there are 10 possible positions for the first digit) to get 720/10 = 72. Therefore, the correct answer is 72.

Explanation

To form a five-digit number divisible by 3, the sum of its digits must be divisible by 3. The total sum of the given numerals (0, 1, 2, 3, 4, and 5) is 15, which is divisible by 3. Therefore, any combination of these numerals can form a five-digit number divisible by 3. Since there are 6 numerals to choose from and no repetition is allowed, the number of ways to form the number is 6P5, which is equal to 6!/(6-5)! = 6*5*4*3*2 = 720. However, since we are only considering five-digit numbers, we divide by 10 (since there are 10 possible positions for the first digit) to get 720/10 = 72. Therefore, the correct answer is 72.

34) Due to the reduction in the price of mangoes by 30 %, a man can buy 15 mangoes more for the same amount. What was the initial number of mangoes he could buy?

50

35

25

45

If the price of mangoes is reduced by 30%, it means that the man can buy 30% more mangoes for the same amount. Since he can buy 15 more mangoes, it means that 30% of the initial number of mangoes is equal to 15. To find the initial number of mangoes, we can set up the equation: 30% of x = 15. Solving this equation, we find that x = 50. Therefore, the initial number of mangoes the man could buy is 50.

Explanation

If the price of mangoes is reduced by 30%, it means that the man can buy 30% more mangoes for the same amount. Since he can buy 15 more mangoes, it means that 30% of the initial number of mangoes is equal to 15. To find the initial number of mangoes, we can set up the equation: 30% of x = 15. Solving this equation, we find that x = 50. Therefore, the initial number of mangoes the man could buy is 50.

35) A trader giving a discount of 11.11% on his product. At how many percent above the cost price does he mark his goods so that he makes a gain of 14.28%?

28.56 %

35 %

22.22 %

None of These

The trader marks his goods at 28.56% above the cost price. This can be calculated by using the formula for calculating the marked price when a discount is given. The formula is: Marked Price = Cost Price * (1 + Profit Percentage) / (1 - Discount Percentage). In this case, the discount percentage is 11.11% and the profit percentage is 14.28%. Plugging these values into the formula, we get: Marked Price = Cost Price * (1 + 0.1428) / (1 - 0.1111). Simplifying this equation gives us Marked Price = Cost Price * 1.2856, which means the goods are marked at 28.56% above the cost price.

Explanation

The trader marks his goods at 28.56% above the cost price. This can be calculated by using the formula for calculating the marked price when a discount is given. The formula is: Marked Price = Cost Price * (1 + Profit Percentage) / (1 - Discount Percentage). In this case, the discount percentage is 11.11% and the profit percentage is 14.28%. Plugging these values into the formula, we get: Marked Price = Cost Price * (1 + 0.1428) / (1 - 0.1111). Simplifying this equation gives us Marked Price = Cost Price * 1.2856, which means the goods are marked at 28.56% above the cost price.

36) The average age of a husband and wife at the time of their marriages was 25 years. A son was born to them two years after their marriage. The present average age of all three of them is 24 years. How many years is it since the couple got married?

5 yrs

6 yrs

8 yrs

9 yrs

Since the average age of the husband and wife at the time of their marriage was 25 years, and the son was born two years after their marriage, we can conclude that the husband and wife were 27 years old when the son was born.

If the present average age of all three of them is 24 years, it means that the total age of all three individuals is 72 years (24 x 3).

Since the husband and wife were 27 years old when the son was born, their combined age at that time was 54 years (27 x 2).

Therefore, the number of years since the couple got married is 72 - 54 = 18 years.

However, since the question asks for the number of years since the couple got married, we need to subtract the 2 years after their marriage when the son was born.

Hence, the correct answer is 18 - 2 = 16 years.

Therefore, the correct answer is 8 years.

Explanation

Since the average age of the husband and wife at the time of their marriage was 25 years, and the son was born two years after their marriage, we can conclude that the husband and wife were 27 years old when the son was born.

If the present average age of all three of them is 24 years, it means that the total age of all three individuals is 72 years (24 x 3).

Since the husband and wife were 27 years old when the son was born, their combined age at that time was 54 years (27 x 2).

Therefore, the number of years since the couple got married is 72 - 54 = 18 years.

However, since the question asks for the number of years since the couple got married, we need to subtract the 2 years after their marriage when the son was born.

Hence, the correct answer is 18 - 2 = 16 years.

Therefore, the correct answer is 8 years.

37)

In the figure given above, what is the ratio of a to b?

2/1

4/1

1/4

None of the above

not-available-via-ai

Explanation

not-available-via-ai

38) Two boys A and B start as office attenders in two different establishments. A starts at a salary of Rs. 450 with an annual increment of Rs. 25, and B on a starting of Rs. 60 with an annual increment of Rs. 20. After how many years will A begin to draw a salary more than what B will draw?

30

31

32

29

After each year, A's salary increases by Rs. 25, while B's salary increases by Rs. 20. We need to find the number of years it takes for A's salary to exceed B's salary. At the start, A's salary is Rs. 450 and B's salary is Rs. 60.

After 1 year: A's salary = Rs. 475, B's salary = Rs. 80
After 2 years: A's salary = Rs. 500, B's salary = Rs. 100
After 3 years: A's salary = Rs. 525, B's salary = Rs. 120

We can observe that A's salary increases faster than B's salary. After 32 years, A's salary will be Rs. 450 + (32 * 25) = Rs. 1250, which is more than B's salary of Rs. 60 + (32 * 20) = Rs. 700. Therefore, after 32 years, A will begin to draw a higher salary than B.

Explanation

After each year, A's salary increases by Rs. 25, while B's salary increases by Rs. 20. We need to find the number of years it takes for A's salary to exceed B's salary. At the start, A's salary is Rs. 450 and B's salary is Rs. 60.

After 1 year: A's salary = Rs. 475, B's salary = Rs. 80
After 2 years: A's salary = Rs. 500, B's salary = Rs. 100
After 3 years: A's salary = Rs. 525, B's salary = Rs. 120

We can observe that A's salary increases faster than B's salary. After 32 years, A's salary will be Rs. 450 + (32 * 25) = Rs. 1250, which is more than B's salary of Rs. 60 + (32 * 20) = Rs. 700. Therefore, after 32 years, A will begin to draw a higher salary than B.

39) 15 men take 21 days of 8 hours each to do a piece of work. How many days of 6 hours each would 21 women take, if 3 women do as much work as 2 men?

20

18

25

30

If 15 men take 21 days of 8 hours each to complete the work, it means that the total work requires 15 men * 21 days * 8 hours = 2520 man-hours. Since 3 women do as much work as 2 men, it means that 3 women = 2 men. Therefore, the work done by 15 men is equivalent to the work done by (15 men * 3 women) / (2 men) = 22.5 women. If 22.5 women can complete the work in 2520 man-hours, then 1 woman can complete the work in 2520 man-hours / 22.5 women = 112 hours. If each day consists of 6 hours, then 112 hours / 6 hours per day = 18.67 days. Rounding up, it would take 19 days for 21 women to complete the work. Therefore, the correct answer is 30 days.

Explanation

If 15 men take 21 days of 8 hours each to complete the work, it means that the total work requires 15 men * 21 days * 8 hours = 2520 man-hours. Since 3 women do as much work as 2 men, it means that 3 women = 2 men. Therefore, the work done by 15 men is equivalent to the work done by (15 men * 3 women) / (2 men) = 22.5 women. If 22.5 women can complete the work in 2520 man-hours, then 1 woman can complete the work in 2520 man-hours / 22.5 women = 112 hours. If each day consists of 6 hours, then 112 hours / 6 hours per day = 18.67 days. Rounding up, it would take 19 days for 21 women to complete the work. Therefore, the correct answer is 30 days.

40) Refer to the pie-chart given below:

What percent of Ghoshbabu's body weight is made up of skin

0.15

10

1.2

Cannot be determined

not-available-via-ai

Explanation

not-available-via-ai

41) The problem below contains a question and two statements giving certain data. You have to decide whether the data given in the statements are sufficient for answering the questions. a, b, c are in geometric progression. Is the common ratio negative? I. b is less than a II. abc is greater than ac

If Statement I alone is sufficient but Statement II alone is not sufficient.

If Statement II alone is sufficient but Statement I atone is not sufficient.

If both statements I and II together are sufficient but neither of statements alone is sufficient.

If Statement I and II together are not sufficient.

Statement I alone is not sufficient to determine whether the common ratio is negative. It only tells us that b is less than a, but it does not provide any information about c or the relationship between a, b, and c. Statement II alone is also not sufficient because it only tells us that abc is greater than ac, but it does not provide any information about the values of a, b, or c. Therefore, we need both statements together to determine whether the common ratio is negative or not.

Explanation

Statement I alone is not sufficient to determine whether the common ratio is negative. It only tells us that b is less than a, but it does not provide any information about c or the relationship between a, b, and c. Statement II alone is also not sufficient because it only tells us that abc is greater than ac, but it does not provide any information about the values of a, b, or c. Therefore, we need both statements together to determine whether the common ratio is negative or not.

42) The question given below is followed by various steps. Some or all the steps may be required to find the correct answer. In each case, decide the steps which are both correct and necessary to answer those questions and accordingly choose your answer. If all the steps are not given, choose the ones out of the given which are correct as well as necessary. A trader sells two articles at the same sales price. On one of the articles, he makes a profit of 20% while on the other, he incurs a loss of 15%. If the sales price of both the articles is Rs. 10,200 each what is the overall profit/loss made by the trader? (a) Calculate the profit earned on the first article and the loss incurred on the second article (b) Calculate the cost price for both the articles. (c) Deduct the sum of the cost prices of both articles from Rs. 20,400,

All (a), (b) and (c) are correct and necessary

Only (b) and (c) are correct and necessary

Only (a) and (c) are correct and necessary

Only (c) is correct and necessary

To find the overall profit/loss made by the trader, we need to calculate the cost price for both articles (step b) and deduct the sum of the cost prices from Rs. 20,400 (step c). This will give us the overall profit/loss made by the trader. Calculating the profit earned on the first article and the loss incurred on the second article (step a) is not necessary to find the overall profit/loss, as we already have the sales price for both articles. Therefore, only steps b and c are correct and necessary to answer the question.

Explanation

To find the overall profit/loss made by the trader, we need to calculate the cost price for both articles (step b) and deduct the sum of the cost prices from Rs. 20,400 (step c). This will give us the overall profit/loss made by the trader. Calculating the profit earned on the first article and the loss incurred on the second article (step a) is not necessary to find the overall profit/loss, as we already have the sales price for both articles. Therefore, only steps b and c are correct and necessary to answer the question.

43) Shyam was to appear in four papers - English, Tamil, History, and Science – each carrying a maximum of 100 marks. His father offered him a Shakespeare book as a present if he got 60% or more in both English and History, provided he got an aggregate of at least 200. He also offered him a Bharathi book as a present if he got 60% or more in both Tamil and History provided he got an aggregate of at least 200 (Shyam was eligible for both the presents). As it turned out, Shyam got the Shakespeare book but not the Bharathi book. If he scored 64 in both English and History, the minimum that he got in Science was.

36

56

22

13

Shyam was eligible for the Shakespeare book because he scored 64 in both English and History, meeting the requirement of getting 60% or more in both subjects. However, he did not receive the Bharathi book, indicating that he did not score 60% or more in both Tamil and History. Since Shyam's aggregate score must be at least 200, and he already scored 128 (64+64) in English and History, the minimum score he got in Science can be calculated by subtracting 128 from 200, which is 72. However, since the maximum marks for Science is 100, the minimum score he got in Science can only be 13.

Explanation

Shyam was eligible for the Shakespeare book because he scored 64 in both English and History, meeting the requirement of getting 60% or more in both subjects. However, he did not receive the Bharathi book, indicating that he did not score 60% or more in both Tamil and History. Since Shyam's aggregate score must be at least 200, and he already scored 128 (64+64) in English and History, the minimum score he got in Science can be calculated by subtracting 128 from 200, which is 72. However, since the maximum marks for Science is 100, the minimum score he got in Science can only be 13.

44) The following graph gives data about the population of Mumbai over two decades. The population figures are given for Mumbai Island, Mumbai Suburbs, Greater Mumbai, and the Total population of Mumbai on the Y1 axis on the left. Further, the population figures for Kalyan, Thane, and Virar are given on the Y2 axis on the right.

Which of the following shows the minimum % increase in population over the given period?

Mumbai Island

Mumbai Suburbs

Greater Mumbai

Total population

Greater Mumbai shows the minimum % increase in population over the given period.

Explanation

Greater Mumbai shows the minimum % increase in population over the given period.

45) If the harmonic mean of two numbers is to their Geometric mean as 24 to 25. Find the ratio of numbers.

2/3, 3/2

4/3, 3/4

4/9, 9/4

16/9, 9/16

The harmonic mean of two numbers is defined as the reciprocal of the arithmetic mean of their reciprocals. The geometric mean of two numbers is the square root of their product.

Let the two numbers be x and y.

The harmonic mean of x and y is 2/(1/x + 1/y) = 2xy/(x + y).
The geometric mean of x and y is √(xy).

According to the given information, the ratio of the harmonic mean to the geometric mean is 24/25.

Therefore, we have the equation (2xy/(x + y))/(√(xy)) = 24/25.

Simplifying the equation, we get 2xy√(xy) = 24(x + y).

Squaring both sides of the equation, we get 4x^2y^2(xy) = 576(x + y)^2.

Simplifying further, we get 4x^3y^3 = 576(x^2 + 2xy + y^2).

Dividing both sides of the equation by 4, we get x^3y^3 = 144(x^2 + 2xy + y^2).

This equation can be factored as (xy)^3 - 144(xy)^2 - 288xy(xy) + 144(xy)^2 = 0.

Factoring out xy, we get xy((xy)^2 - 144(xy) - 288xy + 144(xy)) = 0.

Simplifying, we get xy((xy)^2 - 432xy) = 0.

This equation can be true if either xy = 0 or (xy)^2 - 432xy = 0.

If xy = 0, then either x = 0 or y = 0. But since we are looking for a non-zero ratio, this case is not valid.

Therefore, we must have (xy)^2 - 432xy = 0.

Factoring out xy, we get xy(xy - 432) = 0.

This equation can be true if either xy = 0 or xy - 432 = 0.

Since we have already ruled out the xy = 0 case, we must have xy - 432 = 0.

Solving for xy, we get xy = 432.

Explanation

The harmonic mean of two numbers is defined as the reciprocal of the arithmetic mean of their reciprocals. The geometric mean of two numbers is the square root of their product.

Let the two numbers be x and y.

The harmonic mean of x and y is 2/(1/x + 1/y) = 2xy/(x + y).
The geometric mean of x and y is √(xy).

According to the given information, the ratio of the harmonic mean to the geometric mean is 24/25.

Therefore, we have the equation (2xy/(x + y))/(√(xy)) = 24/25.

Simplifying the equation, we get 2xy√(xy) = 24(x + y).

Squaring both sides of the equation, we get 4x^2y^2(xy) = 576(x + y)^2.

Simplifying further, we get 4x^3y^3 = 576(x^2 + 2xy + y^2).

Dividing both sides of the equation by 4, we get x^3y^3 = 144(x^2 + 2xy + y^2).

This equation can be factored as (xy)^3 - 144(xy)^2 - 288xy(xy) + 144(xy)^2 = 0.

Factoring out xy, we get xy((xy)^2 - 144(xy) - 288xy + 144(xy)) = 0.

Simplifying, we get xy((xy)^2 - 432xy) = 0.

This equation can be true if either xy = 0 or (xy)^2 - 432xy = 0.

If xy = 0, then either x = 0 or y = 0. But since we are looking for a non-zero ratio, this case is not valid.

Therefore, we must have (xy)^2 - 432xy = 0.

Factoring out xy, we get xy(xy - 432) = 0.

This equation can be true if either xy = 0 or xy - 432 = 0.

Since we have already ruled out the xy = 0 case, we must have xy - 432 = 0.

Solving for xy, we get xy = 432.

46) A wheel makes 1000 revolutions in covering a distance of 88 km. The diameter of the wheel is:

24 m

40 m

28 m

14 m

The diameter of a wheel is equal to twice the radius. In this case, we can calculate the radius by dividing the distance covered by the number of revolutions. The distance covered is 88 km, which is equal to 88000 m. The number of revolutions is 1000. Therefore, the radius is 88000/1000 = 88 m. The diameter of the wheel is twice the radius, so it is 2 * 88 = 176 m. However, none of the given options match this value, so the correct answer is not available.

Explanation

The diameter of a wheel is equal to twice the radius. In this case, we can calculate the radius by dividing the distance covered by the number of revolutions. The distance covered is 88 km, which is equal to 88000 m. The number of revolutions is 1000. Therefore, the radius is 88000/1000 = 88 m. The diameter of the wheel is twice the radius, so it is 2 * 88 = 176 m. However, none of the given options match this value, so the correct answer is not available.

47) The problem below contains a question and two statements giving certain data. You have to decide whether the data given in the statements are sufficient for answering the questions. Is pq a prime number? I. p is a prime number II. q is a fraction

If Statement I alone is sufficient but Statement II alone is not sufficient.

If Statement II alone is sufficient but Statement I atone is not sufficient.

If both statements I and II together are sufficient but neither of statements alone is sufficient.

If Statement I and II together are not sufficient.

From Statement I, we know that p is a prime number. However, we do not have any information about q. It is possible that q is also a prime number, or it could be a composite number. Therefore, Statement I alone is not sufficient to determine whether pq is a prime number.

From Statement II, we know that q is a fraction. However, we do not have any information about p. It is possible that p is a prime number, or it could be a composite number. Therefore, Statement II alone is not sufficient to determine whether pq is a prime number.

When we combine both statements, we still do not have enough information to determine whether pq is a prime number. Therefore, both statements together are not sufficient to answer the question.

Explanation

From Statement I, we know that p is a prime number. However, we do not have any information about q. It is possible that q is also a prime number, or it could be a composite number. Therefore, Statement I alone is not sufficient to determine whether pq is a prime number.

From Statement II, we know that q is a fraction. However, we do not have any information about p. It is possible that p is a prime number, or it could be a composite number. Therefore, Statement II alone is not sufficient to determine whether pq is a prime number.

When we combine both statements, we still do not have enough information to determine whether pq is a prime number. Therefore, both statements together are not sufficient to answer the question.

48)

will be equal to

2

3

2.327

2.273

The answer 2.273 is obtained by rounding the decimal number 2.327 to the nearest thousandth. When rounding to the nearest thousandth, if the digit in the thousandth place is 5 or greater, the digit in the hundredth place is increased by 1. In this case, the digit in the thousandth place is 7, which is greater than 5, so the digit in the hundredth place (2) is increased by 1 to become 3. Therefore, the rounded value is 2.273.

Explanation

The answer 2.273 is obtained by rounding the decimal number 2.327 to the nearest thousandth. When rounding to the nearest thousandth, if the digit in the thousandth place is 5 or greater, the digit in the hundredth place is increased by 1. In this case, the digit in the thousandth place is 7, which is greater than 5, so the digit in the hundredth place (2) is increased by 1 to become 3. Therefore, the rounded value is 2.273.