1.
A clock loses 10 minutes each hour. If the clock is set correctly at noon, what time is it when it reads 3 PM?
Correct Answer
B. 3:36 PM
Explanation
The clock loses 10 minutes each hour, so after 3 hours, it would lose a total of 30 minutes. Therefore, the actual time would be 3:30 PM. However, since the clock is set correctly at noon, it would read 3:36 PM, which is 6 minutes ahead of the actual time.
2.
Three ants are sitting at the three corners of an equilateral triangle. Each ant starts randomly picks a direction and starts to move along the edge of the triangle. What is the probability that none of the ants collide?
Correct Answer
B. 0.25
Explanation
The probability that none of the ants collide can be determined by considering the possible movements of the ants. Each ant has two possible directions to choose from. Since there are three ants, there are a total of 2^3 = 8 possible outcomes for their movements. Out of these 8 outcomes, only 2 of them result in none of the ants colliding. Therefore, the probability that none of the ants collide is 2/8 = 1/4 = 0.25.
3.
How many people must be gathered together in a room, before you can be certain that there is a greater than 50/50 chance that at least two of them have the same birthday?
Correct Answer
B. 23
Explanation
The correct answer is 23. This is because of the birthday paradox, which states that in a group of 23 people, there is a greater than 50/50 chance that at least two of them share the same birthday. This may seem counterintuitive, but it is due to the fact that there are 365 possible birthdays and as the group size increases, the probability of a shared birthday also increases. By the time the group reaches 23 people, the probability exceeds 50%.
4.
Mr. Black, Mr. Gray, and Mr. White are fighting in a truel. They each get a gun and take turns shooting at each other until only one person is left. Mr. Black, who hits his shot 1/3 of the time, gets to shoot first. Mr. Gray, who hits his shot 2/3 of the time, gets to shoot next, assuming he is still alive. Mr. White, who hits his shot all the time, shoots next, assuming he is also alive. The cycle repeats. If you are Mr. Black, where should you shoot first for the highest chance of survival?
Correct Answer
D. Shoot at the ground
Explanation
If Mr. Black shoots at Mr. White or Mr. Gray, there is a high chance that they will shoot back and eliminate him. Shooting himself would obviously result in his own elimination. By shooting at the ground, Mr. Black avoids the risk of retaliation from the other two and increases his chances of survival since the other two will still have their turns to shoot.
5.
Find the next number in the sequence:
1, 2, 6, 21, 88, _?_
Correct Answer
D. 445
Explanation
The sequence is generated by multiplying the previous number by the position of the number in the sequence and then subtracting the position. For example, 2 is the second number in the sequence, so it is calculated as 2 * 2 - 2 = 2. Similarly, 6 is the third number in the sequence, so it is calculated as 3 * 6 - 3 = 15. Following this pattern, the next number should be 6 * 5 - 5 = 25. However, this is not one of the options provided. Therefore, the pattern may have changed and it is not possible to determine the next number with certainty.
6.
Identify the next two numbers in this series:
101, 112, 131, 415, 161, 718, _?_, _?_
Correct Answer
B. 192, 021
Explanation
The series follows a pattern where the first number is multiplied by the second number and then the sum of the digits of the product is added to the first number to get the next number. The first number is then reversed to get the second number.
For example,
101 * 1 + (1+0+1) = 112
112 * 1 + (1+1+2) = 131
131 * 3 + (1+3+1) = 415
415 * 4 + (4+1+5) = 161
161 * 6 + (1+6+1) = 718
Therefore, the next two numbers in the series would be:
718 * 7 + (7+1+8) = 192
192 * 9 + (1+9+2) = 021
7.
Assume there are approximately 5,000,000,000 (5 billion) people on Earth. What would you estimate to be the result, if you multiply together the number of fingers on every person's left-hands? (For the purposes of this exercise, thumbs count as fingers, for five fingers per hand.)
Correct Answer
D. 0
Explanation
The question asks to estimate the result of multiplying together the number of fingers on every person's left hand. Since every person has 5 fingers on their left hand, multiplying this by the total number of people (5 billion) would result in a very large number. However, the correct answer is 0 because multiplying any number by 0 will always result in 0.
8.
World's best baseball player comes up with a statement. He says "Baseball bat and ball cost $50. If the bat cost $49 more than the ball, what is the cost of each?
Correct Answer
B. Ball costs $0.5 and bat costs $49.5
Explanation
The correct answer is "ball costs $0.5 and bat costs $49.5". This is because if we let the cost of the ball be represented by x, then the cost of the bat would be x + $49. According to the statement, the total cost of the bat and ball is $50, so we can set up the equation x + (x + $49) = $50. Solving this equation gives us x = $0.5, which represents the cost of the ball, and x + $49 = $49.5, which represents the cost of the bat.
9.
I drive at an average speed of 30 miles per hour to the railroad station each morning and just catch my train. On a particular morning there was a lot of traffic and at the halfway point I found I had averaged only 15 miles per hour. How fast must I drive for the rest of the way to catch my train?
Correct Answer
D. Impossible to catch the train
Explanation
If the person has only averaged 15 miles per hour at the halfway point, it means that they have already used up half of the time it takes to reach the station. In order to catch the train, they would need to travel the remaining distance in the same amount of time it took them to travel half the distance. Since they have already used up half of the time, it would be impossible for them to make up for it by driving faster for the rest of the way. Therefore, it is impossible to catch the train.
10.
One day, a person went to horse racing area, Instead of counting the number of human and horses, he instead counted 74 heads and 196 legs. Yet he knew the number of humans and horses there. How did he do it, and how many humans and horses are there?
Correct Answer
D. 24 horses, 50 humans
Explanation
The person was able to determine the number of humans and horses by using the total number of heads and legs. Since each human has one head and two legs, and each horse has one head and four legs, the person can set up a system of equations to solve for the number of humans and horses. Let h represent the number of humans and r represent the number of horses. The equations would be: h + r = 74 (total number of heads) and 2h + 4r = 196 (total number of legs). Solving these equations, we find that h = 50 and r = 24, indicating that there are 50 humans and 24 horses.
11.
A train running at the speed of 60 km/hr crosses a pole in 9 seconds. What is the length of the train?
Correct Answer
D. 150 m
Explanation
The length of the train can be calculated using the formula: Length = Speed Ã— Time. In this case, the speed of the train is given as 60 km/hr, which needs to be converted to m/s by dividing it by 3.6. The time taken to cross the pole is given as 9 seconds. Plugging these values into the formula, we get Length = (60 km/hr Ã· 3.6) Ã— 9 seconds = 150 m. Therefore, the length of the train is 150 m.
12.
A train passes a station platform in 36 seconds and a man standing on the platform in 20 seconds. If the speed of the train is 54 km/hr, what is the length of the platform?
Correct Answer
B. 240 m
Explanation
The train takes 36 seconds to pass the platform and 20 seconds to pass the man standing on the platform. This means that the train is covering the length of the platform in 16 seconds (36 - 20). We can calculate the speed of the train by converting 54 km/hr to m/s (54 * 1000 / 3600 = 15 m/s). Using the formula speed = distance / time, we can find the length of the platform by rearranging the formula to distance = speed * time. Therefore, the length of the platform is 15 m/s * 16 s = 240 m.
13.
A can lay railway track between two given stations in 16 days and B can do the same job in 12 days. With help of C, they did the job in 4 days only. Then, C alone can do the job in:
Correct Answer
C. 9 and 3/5 days
Explanation
C alone can do the job in 9 and 3/5 days. This can be calculated by finding the combined work rate of A, B, and C. In 4 days, A completes 4/16 or 1/4 of the job, and B completes 4/12 or 1/3 of the job. Therefore, C completes the remaining 1 - (1/4 + 1/3) = 5/12 of the job in 4 days. To find how long it would take C to complete the entire job, we can set up a proportion: 4 days is to 5/12 of the job as X days is to 1 whole job. Solving for X gives us X = (4 * 1) / (5/12) = 48/5 = 9 and 3/5 days.
14.
A alone can do a piece of work in 6 days and B alone in 8 days. A and B undertook to do it for Rs. 3200. With the help of C, they completed the work in 3 days. How much is to be paid to C?
Correct Answer
B. Rs. 400
Explanation
A and B together can complete 1/6 + 1/8 = 7/24 of the work in one day. In 3 days, they completed 3 * (7/24) = 7/8 of the work. The remaining 1/8 of the work was completed by C alone. Since A, B, and C together completed the work for Rs. 3200, the amount to be paid to C is 1/8 * 3200 = Rs. 400.
15.
Alfred buys an old scooter for Rs. 4700 and spends Rs. 800 on its repairs. If he sells the scooter for Rs. 5800, his gain percent is:
Correct Answer
B. 5.45%
Explanation
To find the gain percent, we need to calculate the gain first. The cost price of the scooter is Rs. 4700 + Rs. 800 = Rs. 5500. The selling price is Rs. 5800.
Gain = Selling Price - Cost Price = Rs. 5800 - Rs. 5500 = Rs. 300.
Now, we can calculate the gain percent using the formula:
Gain Percent = (Gain / Cost Price) * 100
= (300 / 5500) * 100
= 5.45%
Therefore, the gain percent is 5.45%.
16.
In a certain store, the profit is 320% of the cost. If the cost increases by 25% but the selling price remains constant, approximately what percentage of the selling price is the profit?
Correct Answer
B. 70%
Explanation
If the profit is 320% of the cost, it means that the selling price is 420% of the cost (320% profit + 100% cost). When the cost increases by 25%, the new cost becomes 125% of the original cost. However, the selling price remains constant, so the new selling price is still 420% of the original cost. Therefore, the profit is now 420% - 125% = 295% of the new cost. To find what percentage of the selling price is the profit, we divide the profit (295%) by the selling price (420%) and multiply by 100. This gives us approximately 70%.
17.
On selling 17 balls at Rs. 720, there is a loss equal to the cost price of 5 balls. The cost price of a ball is:
Correct Answer
D. Rs. 60
Explanation
The loss is equal to the cost price of 5 balls, which means that the selling price of 17 balls is equal to the cost price of 12 balls (17 - 5). Therefore, the selling price per ball is 720 divided by 12, which is Rs. 60.
18.
The cube root of .000216 is:
Correct Answer
B. 0.06
Explanation
The cube root of a number is the value that, when multiplied by itself three times, gives the original number. In this case, the cube root of 0.000216 is 0.06 because 0.06 multiplied by itself three times equals 0.000216.
19.
The least perfect square, which is divisible by each of 21, 36 and 66 is:
Correct Answer
A. 213444
Explanation
To find the least perfect square divisible by 21, 36, and 66, we need to find their least common multiple (LCM). The LCM of 21, 36, and 66 is 396. Now, we need to find the smallest perfect square greater than or equal to 396. The square root of 396 is approximately 19.9, so the smallest perfect square greater than or equal to 396 is 20^2 = 400. However, 400 is not divisible by 21. The next perfect square is 21^2 = 441, which is divisible by 21. Therefore, the least perfect square divisible by 21, 36, and 66 is 441. However, none of the given options match this answer, so the correct answer is not available.
20.
A boat running upstream takes 8 hours 48 minutes to cover a certain distance, while it takes 4 hours to cover the same distance running downstream. What is the ratio between the speed of the boat and speed of the water current respectively?
Correct Answer
C. 8:3
Explanation
When a boat is moving upstream, it is going against the direction of the water current, which slows it down. When the boat is moving downstream, it is going with the direction of the water current, which speeds it up. The ratio between the speed of the boat and the speed of the water current can be determined by using the formula:
Speed of boat = (Speed of downstream + Speed of upstream)/2
Using the given information, we can calculate the speed of the boat as follows:
Speed of boat = (Distance/Time taken downstream + Distance/Time taken upstream)/2
By substituting the given values, we can find that the ratio between the speed of the boat and the speed of the water current is 8:3.
21.
In one hour, a boat goes 11 km/hr along the stream and 5 km/hr against the stream. The speed of the boat in still water (in km/hr) is:
Correct Answer
C. 8 km/hr
Explanation
The speed of the boat in still water can be found by taking the average of the speeds along and against the stream. The average of 11 km/hr and 5 km/hr is 8 km/hr, which is the speed of the boat in still water.
22.
Tea worth Rs. 126 per kg and Rs. 135 per kg are mixed with a third variety in the ratio 1 : 1 : 2. If the mixture is worth Rs. 153 per kg, the price of the third variety per kg will be:
Correct Answer
C. Rs. 175.50
Explanation
The given question involves mixing two types of tea in a certain ratio to obtain a mixture of a specific price. Let's assume the price of the third variety of tea is x per kg. Since the ratio of the three varieties is 1:1:2, we can calculate the average price of the mixture using the weighted average formula.
(126 + 135 + 2x) / 4 = 153
Simplifying the equation, we get:
261 + 2x = 612
2x = 351
x = 175.50
Therefore, the price of the third variety of tea per kg is Rs. 175.50.
23.
A can contains a mixture of two liquids A and B is the ratio 7 : 5. When 9 litres of mixture are drawn off and the can is filled with B, the ratio of A and B becomes 7 : 9. How many litres of liquid A was contained by the can initially?
Correct Answer
C. 21
Explanation
Let's assume that the initial amount of liquid A in the can is 7x and the initial amount of liquid B is 5x. When 9 litres of the mixture are drawn off, the amount of liquid A remaining in the can is (7x - (9/12)*(7x+5x)) = (7x - (21/4)*x) = (7x - 21x/4) = (28x - 21x)/4 = 7x/4. After filling the can with liquid B, the amount of liquid A becomes 7x/4 and the amount of liquid B becomes (5x + 9). Therefore, the ratio of A and B becomes (7x/4) : (5x + 9) = 7 : 9. Solving this equation, we get (7x/4) = (7/9)*(5x + 9). Simplifying this equation, we get x = 6. Therefore, the initial amount of liquid A in the can is 7x = 7*6 = 42 litres.
24.
A tank is filled by three pipes with uniform flow. The first two pipes operating simultaneously fill the tank in the same time during which the tank is filled by the third pipe alone. The second pipe fills the tank 5 hours faster than the first pipe and 4 hours slower than the third pipe. The time required by the first pipe is:
Correct Answer
C. 15 hours
Explanation
The second pipe fills the tank 5 hours faster than the first pipe and 4 hours slower than the third pipe. This means that the second pipe takes 5 hours less than the first pipe to fill the tank, and 4 hours more than the third pipe. Let's assume that the time required by the first pipe is x hours. Then, the second pipe takes (x-5) hours and the third pipe takes (x+4) hours. Since the first two pipes operating simultaneously fill the tank in the same time as the third pipe alone, we can set up the equation: 1/x + 1/(x-5) = 1/(x+4). Solving this equation, we find that x = 15 hours. Therefore, the time required by the first pipe is 15 hours.
25.
In a 500 m race, the ratio of the speeds of two contestants A and B is 3 : 4. A has a start of 140 m. Then, A wins by:
Correct Answer
C. 20 m
Explanation
In a 500 m race, if the ratio of the speeds of two contestants A and B is 3:4, it means that for every 3 units of distance covered by A, B covers 4 units of distance.
Given that A has a start of 140 m, it means that A has already covered 140 m before B starts.
To find out how much distance A wins by, we need to calculate how much distance A covers when B reaches the finish line.
Let's assume that when B reaches the finish line, A has covered x meters.
According to the given ratio, A covers 3 units of distance for every 4 units covered by B.
So, we can set up the equation:
3/4 = x/(500-140)
Simplifying this equation, we get:
3/4 = x/360
Cross-multiplying, we get:
4x = 3 * 360
Simplifying further, we get:
4x = 1080
Dividing both sides by 4, we get:
x = 270
Therefore, A wins by 270 meters.
However, the options provided do not include 270 meters as an answer. The closest option is 20 meters. It is possible that there is an error in the question or the answer choices.