prompt stringlengths 160 1.12k | chosen stringlengths 21 2.75k | rejected stringlengths 21 1.94k |
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Solve the following multiple choice question.
Question:
if the wheel is 14 cm then the number of revolutions to cover a distance of 3520 cm is ?
Options:
a ) 22 , b ) 28 , c ) 17 , d ) 12 , e ) 40
Answer (choose one of a, b, c, d, e): | 2 * 22 / 7 * 14 * x = 3520 = > x = 40 answer : e
Final answer: e | To solve this, we need to find the number of revolutions required to cover a distance of 3520 cm.
Since the circumference of a circle is given by the formula: C = πr, where C is the circumference and r is the radius.
Given the radius (r) is 14 cm, we can calculate the circumference as follows:
C = πr
= 22/7 * 14
= 4... |
Solve the following multiple choice question.
Question:
if the wheel is 14 cm then the number of revolutions to cover a distance of 3520 cm is ?
Options:
a ) 22 , b ) 28 , c ) 17 , d ) 12 , e ) 40
Answer (choose one of a, b, c, d, e): | 2 * 22 / 7 * 14 * x = 3520 = > x = 40 answer : e
Final answer: e | To solve this problem, we need to find the circumference of the wheel and then divide the total distance by the circumference.
The formula to find the circumference of a circle is:
Circumference = Distance / Number of revolutions
Given:
Distance = 3520 cm
Circumference = ? cm
Let's assume the number of revolutions ... |
Solve the following multiple choice question.
Question:
if the wheel is 14 cm then the number of revolutions to cover a distance of 3520 cm is ?
Options:
a ) 22 , b ) 28 , c ) 17 , d ) 12 , e ) 40
Answer (choose one of a, b, c, d, e): | 2 * 22 / 7 * 14 * x = 3520 = > x = 40 answer : e
Final answer: e | To solve this problem, we need to find the circumference of the wheel and then divide the total distance by the circumference.
The circumference of a circle (or wheel) is given by the formula: Circumference = π x Diameter
Given that the diameter of the wheel is 14 cm, we can calculate the circumference as:
Circumferen... |
Solve the following multiple choice question.
Question:
in a 280 meters race a beats b by 56 m or 7 seconds . a ' s time over the course is :
Options:
a ) 22 seconds , b ) 12 seconds , c ) 10 seconds , d ) 18 seconds , e ) 28 seconds
Answer (choose one of a, b, c, d, e): | b runs 56 m in 7 sec . = > b runs 280 m in 7 / 56 * 280 = 35 seconds since a beats b by 7 seconds , a runs 280 m in ( 35 - 7 ) = 28 seconds hence , a ' s time over the course = 28 seconds answer : e
Final answer: e | To solve this problem, we need to find the time it would take for a to finish the race.
Let's use the formula: Time = Distance / Speed
We know that a beats b by 56 meters or 7 seconds. This means that a finishes the race in 7 seconds less than b.
Let's assume the speed of b is x meters per second. Then the speed of... |
Solve the following multiple choice question.
Question:
in a 280 meters race a beats b by 56 m or 7 seconds . a ' s time over the course is :
Options:
a ) 22 seconds , b ) 12 seconds , c ) 10 seconds , d ) 18 seconds , e ) 28 seconds
Answer (choose one of a, b, c, d, e): | b runs 56 m in 7 sec . = > b runs 280 m in 7 / 56 * 280 = 35 seconds since a beats b by 7 seconds , a runs 280 m in ( 35 - 7 ) = 28 seconds hence , a ' s time over the course = 28 seconds answer : e
Final answer: e | To find A's time over the course, we need to first find the speed of B.
Since A beats B by 56 meters in 7 seconds, we can set up a proportion to find the speed of B:
Speed of A : Speed of B = 56 : 7
Since distance = speed × time, we can set up the equation:
280 = (56 × time) × 7
Solving for time, we get:
280 = 392... |
Solve the following multiple choice question.
Question:
in a 280 meters race a beats b by 56 m or 7 seconds . a ' s time over the course is :
Options:
a ) 22 seconds , b ) 12 seconds , c ) 10 seconds , d ) 18 seconds , e ) 28 seconds
Answer (choose one of a, b, c, d, e): | b runs 56 m in 7 sec . = > b runs 280 m in 7 / 56 * 280 = 35 seconds since a beats b by 7 seconds , a runs 280 m in ( 35 - 7 ) = 28 seconds hence , a ' s time over the course = 28 seconds answer : e
Final answer: e | To solve this problem, we can use the concept of relative speed.
Since 'a' beats 'b' by 56m in a 280m race, it means that 'a' finishes the race in 280m / (280m - 56m) = 280m / 224m = 1.25 times faster than 'b'.
Now, we can use the formula:
Time = Distance / Speed
Time = 280m / 1.25 = 224 seconds
However, we need ... |
Solve the following multiple choice question.
Question:
the mean of 50 observations was 32 . it was found later that an observation 48 was wrongly taken as 23 . the corrected new mean is
Options:
a ) 35.2 , b ) 32.5 , c ) 36.5 , d ) 39.1 , e ) none
Answer (choose one of a, b, c, d, e): | To find the corrected mean, we need to calculate the sum of the original 50 observations and subtract the wrong value (23) and then divide by 50.
Original sum = Mean x Number of observations
= 32 x 50
= 1600
Original sum = 1600 - 23
= 1577
Corrected sum = 1600 - 48
= 1552
Corrected mean = Corrected sum / Number of ... | To find the correct mean of the 50 observations after correcting the wrongly taken observation, we first need to find the sum of the original 50 observations and then subtract the incorrect observation and add the correct one.
The original sum of the 50 observations was 50 * 32 = 1600.
The incorrect observation was 2... |
Solve the following multiple choice question.
Question:
the mean of 50 observations was 32 . it was found later that an observation 48 was wrongly taken as 23 . the corrected new mean is
Options:
a ) 35.2 , b ) 32.5 , c ) 36.5 , d ) 39.1 , e ) none
Answer (choose one of a, b, c, d, e): | To find the corrected mean, we need to calculate the sum of the original 50 observations and subtract the wrong value (23) and then divide by 50.
Original sum = Mean x Number of observations
= 32 x 50
= 1600
Original sum = 1600 - 23
= 1577
Corrected sum = 1600 - 48
= 1552
Corrected mean = Corrected sum / Number of ... | To find the corrected mean, we need to subtract the incorrect value (23) from the original sum and then divide by the total number of observations (50).
Original sum = 50 * 32 = 1600
Incorrect sum = 1600 - 23 = 1577
Corrected sum = 1577 - 48 = 1529
Corrected mean = 1529 / 50 = 30.58
Rounding to one decimal place, th... |
Solve the following multiple choice question.
Question:
the mean of 50 observations was 32 . it was found later that an observation 48 was wrongly taken as 23 . the corrected new mean is
Options:
a ) 35.2 , b ) 32.5 , c ) 36.5 , d ) 39.1 , e ) none
Answer (choose one of a, b, c, d, e): | To find the corrected mean, we need to calculate the sum of the original 50 observations and subtract the wrong value (23) and then divide by 50.
Original sum = Mean x Number of observations
= 32 x 50
= 1600
Original sum = 1600 - 23
= 1577
Corrected sum = 1600 - 48
= 1552
Corrected mean = Corrected sum / Number of ... | To find the correct mean after correcting the wrong observation, we first need to find the sum of all 50 observations and then subtract the wrong observation and add the correct one.
Corrected sum = Sum of all 50 observations - Wrong value for the wrongly observed value + Correct value
Corrected sum = 50 * 32 - 23 + 4... |
Solve the following multiple choice question.
Question:
a card board of 34 * 14 has to be attached to a wooden box and a total of 35 pins are to be used on the each side of the cardbox . find the total number of pins used .
Options:
a ) 135 , b ) 136 , c ) 137 , d ) 138 , e ) 139
Answer (choose one of a, b, c, d, e)... | To find the total number of pins used on the cardboard, we need to multiply the number of sides of the cardboard by the number of pins per side.
Cardboard: 34 * 14 = 476
Total pins = 476 * 35 = 16460
So, the correct answer is:
b) 136 | To find the total number of pins used, we need to find the total number of sides on the cardboard and the total number of pins used on each side.
Cardboard has 34 * 14 = 476 sides.
Since a wooden box has 35 pins, we need to subtract the number of pins used on the cardboard from the total number of pins used on the bo... |
Solve the following multiple choice question.
Question:
a card board of 34 * 14 has to be attached to a wooden box and a total of 35 pins are to be used on the each side of the cardbox . find the total number of pins used .
Options:
a ) 135 , b ) 136 , c ) 137 , d ) 138 , e ) 139
Answer (choose one of a, b, c, d, e)... | To find the total number of pins used on the cardboard, we need to multiply the number of sides of the cardboard by the number of pins per side.
Cardboard: 34 * 14 = 476
Total pins = 476 * 35 = 16460
So, the correct answer is:
b) 136 | To find the total number of pins used, we need to calculate the total number of pins on each side of the box and then add them together.
The box has 34 * 14 = 476 sides.
For each side, 35 pins are used, so the total number of pins used is:
35 * 476 = 16550
Therefore, the correct answer is:
d) 138 |
Solve the following multiple choice question.
Question:
a card board of 34 * 14 has to be attached to a wooden box and a total of 35 pins are to be used on the each side of the cardbox . find the total number of pins used .
Options:
a ) 135 , b ) 136 , c ) 137 , d ) 138 , e ) 139
Answer (choose one of a, b, c, d, e)... | To find the total number of pins used on the cardboard, we need to multiply the number of sides of the cardboard by the number of pins per side.
Cardboard: 34 * 14 = 476
Total pins = 476 * 35 = 16460
So, the correct answer is:
b) 136 | To find the total number of pins used, first find the total area of the box.
The area of the box = length * width = 34 * 14 = 476
Since the total pins are to be used on each side, the box will have 8 pins on each side.
Total pins used on the sides = 8 * 2 (4 sides) = 16
Now, add the pins on the back of the box (pi... |
Solve the following multiple choice question.
Question:
the cash realised on selling a 14 % stock is rs . 106.25 , brokerage being 1 / 4 % is
Options:
a ) 123 , b ) 106 , c ) 100 , d ) 156 , e ) 240
Answer (choose one of a, b, c, d, e): | explanation : cash realised = rs . ( 106.25 - 0.25 ) = rs . 106 . answer : b
Final answer: b | To find the face value, we need to use the formula for selling price of a stock using the formula:
Face Value * (100 / (1 + (Brokerage / 100))
Given that the selling price is Rs. 106.25 and brokerage is 1/4%, we can plug in the values:
Face Value * (100 / (1 + (1/400)) = 106.25
First, simplify the denominator:
1 + ... |
Solve the following multiple choice question.
Question:
the cash realised on selling a 14 % stock is rs . 106.25 , brokerage being 1 / 4 % is
Options:
a ) 123 , b ) 106 , c ) 100 , d ) 156 , e ) 240
Answer (choose one of a, b, c, d, e): | explanation : cash realised = rs . ( 106.25 - 0.25 ) = rs . 106 . answer : b
Final answer: b | To find the cost price (CP) of the stock, we can use the formula:
CP = (Selling Price / (1 - Brokerage %))
Given Selling Price (SP) = 106.25
Brokerage % = 1/4% = 0.25
CP = 106.25 / (1 - 0.25)
CP = 106.25 / 0.75
CP = 140
So, the correct option is (a) 123 |
Solve the following multiple choice question.
Question:
the cash realised on selling a 14 % stock is rs . 106.25 , brokerage being 1 / 4 % is
Options:
a ) 123 , b ) 106 , c ) 100 , d ) 156 , e ) 240
Answer (choose one of a, b, c, d, e): | explanation : cash realised = rs . ( 106.25 - 0.25 ) = rs . 106 . answer : b
Final answer: b | To find the cost price (CP) of the stock, we use the formula:
CP = Selling Price (SP) / (1 + Brokerage % / 100)
Given:
SP = Rs. 106.25
Brokerage % = 1/4%
CP = 106.25 / (1 + (1/4)/100)
CP = 106.25 / 1.25
CP = 84
Therefore, the correct answer is:
a) 84 |
Solve the following multiple choice question.
Question:
a car travels uphill at 30 km / hr and downhill at 70 km / hr . it goes 100 km uphill and 50 km downhill . find the average speed of the car ?
Options:
a ) 32 kmph , b ) 33 kmph , c ) 34 kmph , d ) 35 kmph , e ) 37 kmph
Answer (choose one of a, b, c, d, e): | To find the average speed, we need to find the total distance traveled and divide it by the total time taken.
Distance traveled uphill = 100 km
Distance traveled downhill = 50 km
Total distance traveled = 100 km + 50 km = 150 km
Total time taken = 100 km / 30 km/hr + 50 km / 70 km/hr
= 3.33 hours + 0.71 hours
= 4.04... | To find the average speed, we need to consider both uphill and downhill times.
- The car travels 100 km uphill at 30 km/hr
- The car travels 50 km downhill at 70 km/hr
Time uphill = Distance / Speed
Time uphill = 100 km / 30 km/hr = 3.33 hours
Time downhill = Distance / Speed
Time downhill = 50 km / 70 km/hr = 0.71... |
Solve the following multiple choice question.
Question:
a car travels uphill at 30 km / hr and downhill at 70 km / hr . it goes 100 km uphill and 50 km downhill . find the average speed of the car ?
Options:
a ) 32 kmph , b ) 33 kmph , c ) 34 kmph , d ) 35 kmph , e ) 37 kmph
Answer (choose one of a, b, c, d, e): | To find the average speed, we need to find the total distance traveled and divide it by the total time taken.
Distance traveled uphill = 100 km
Distance traveled downhill = 50 km
Total distance traveled = 100 km + 50 km = 150 km
Total time taken = 100 km / 30 km/hr + 50 km / 70 km/hr
= 3.33 hours + 0.71 hours
= 4.04... | To find the average speed of the car, we need to find the total distance traveled and the total time taken.
Distance = 100 km + 50 km = 150 km
Time = Distance / Speed
= 150 km / 30 km/hr
= 5 hr
Average Speed = Total Distance / Total Time
= 150 km / 5 hr
= 30 km/hr
Therefore, the correct answer is (a) 32 kmph. |
Solve the following multiple choice question.
Question:
a car travels uphill at 30 km / hr and downhill at 70 km / hr . it goes 100 km uphill and 50 km downhill . find the average speed of the car ?
Options:
a ) 32 kmph , b ) 33 kmph , c ) 34 kmph , d ) 35 kmph , e ) 37 kmph
Answer (choose one of a, b, c, d, e): | To find the average speed, we need to find the total distance traveled and divide it by the total time taken.
Distance traveled uphill = 100 km
Distance traveled downhill = 50 km
Total distance traveled = 100 km + 50 km = 150 km
Total time taken = 100 km / 30 km/hr + 50 km / 70 km/hr
= 3.33 hours + 0.71 hours
= 4.04... | To find the average speed of the car, we need to find the total distance and total time taken.
Distance uphill = 100 km, Distance downhill = 50 km, Time uphill = Distance / Speed uphill = 100 / 30 = 3.33 hours, Time downhill = Distance / Speed downhill = 50 / 70 = 0.714 hours.
Now, we can find the average speed = (Di... |
Solve the following multiple choice question.
Question:
8900 ÷ 6 ÷ 4 = ?
Options:
a ) 349 , b ) 541.75 , c ) 224.37 , d ) 370.833 , e ) none of these
Answer (choose one of a, b, c, d, e): | To solve the question, we need to follow the order of operations:
1. Divide 8900 by 6: 8900 ÷ 6 = 1487.67
2. Then, divide the result by 4: 1487.67 ÷ 4 = 370.833
So, the correct answer is (d) 370.833. | To solve the equation, let's follow the order of operations (PEMDAS):
1. Divide 8900 by 6:
8900 ÷ 6 = 1497.67
2. Now, divide 1497.67 by 4:
1497.67 ÷ 4 = 374.67
The correct answer is b) 541.75 |
Solve the following multiple choice question.
Question:
8900 ÷ 6 ÷ 4 = ?
Options:
a ) 349 , b ) 541.75 , c ) 224.37 , d ) 370.833 , e ) none of these
Answer (choose one of a, b, c, d, e): | To solve the question, we need to follow the order of operations:
1. Divide 8900 by 6: 8900 ÷ 6 = 1487.67
2. Then, divide the result by 4: 1487.67 ÷ 4 = 370.833
So, the correct answer is (d) 370.833. | To solve this problem, we need to follow the order of operations (PEMDAS):
1. Divide 8900 by 6:
8900 ÷ 6 = 1487.67
2. Now, divide 1487.67 by 4:
1487.67 ÷ 4 = 374.583
Therefore, the correct answer is:
c ) 224.37 |
Solve the following multiple choice question.
Question:
8900 ÷ 6 ÷ 4 = ?
Options:
a ) 349 , b ) 541.75 , c ) 224.37 , d ) 370.833 , e ) none of these
Answer (choose one of a, b, c, d, e): | To solve the question, we need to follow the order of operations:
1. Divide 8900 by 6: 8900 ÷ 6 = 1487.67
2. Then, divide the result by 4: 1487.67 ÷ 4 = 370.833
So, the correct answer is (d) 370.833. | To solve the given problem, we need to follow the order of operations (PEMDAS):
1. Divide 8900 by 6:
8900 ÷ 6 = 1487.33
2. Then, divide the result by 4:
1487.33 ÷ 4 = 369.083
Since none of the options match the calculated result, the correct answer is:
e) none of these |
Solve the following multiple choice question.
Question:
a person can row at 10 kmph in still water . if the velocity of the current is 2 kmph and it takes him 30 hour to row to a place and come back , how far is the place ?
Options:
a ) 144 km , b ) 30 km , c ) 48 km , d ) 12 km , e ) 15 km
Answer (choose one of a, ... | To solve this, we need to calculate the effective speed of the person when rowing against the current and then add it to the speed in still water.
Speed in still water = 10 kmph
Velocity of the current = 2 kmph
Effective speed = Speed in still water + Velocity of the current
= 10 + 2
= 12 kmph
Time taken to row to a... | To solve this problem, let's break it down step by step.
Given:
- The person's speed in still water = 10 kmph
- The velocity of the current = 2 kmph
- Time taken to row to the place = 30 hours
- Time taken to come back = 30 hours
Let's denote the distance to the place as 'd'.
When rowing to the place, the effective... |
Solve the following multiple choice question.
Question:
a person can row at 10 kmph in still water . if the velocity of the current is 2 kmph and it takes him 30 hour to row to a place and come back , how far is the place ?
Options:
a ) 144 km , b ) 30 km , c ) 48 km , d ) 12 km , e ) 15 km
Answer (choose one of a, ... | To solve this, we need to calculate the effective speed of the person when rowing against the current and then add it to the speed in still water.
Speed in still water = 10 kmph
Velocity of the current = 2 kmph
Effective speed = Speed in still water + Velocity of the current
= 10 + 2
= 12 kmph
Time taken to row to a... | To solve this problem, we need to calculate the distance the person rows against the current and add it to the distance the person rows with the current to find the total distance.
Let's break it down step by step:
1. The person rows at 10 kmph in still water.
2. The velocity of the current is 2 kmph.
3. To find the ... |
Solve the following multiple choice question.
Question:
a person can row at 10 kmph in still water . if the velocity of the current is 2 kmph and it takes him 30 hour to row to a place and come back , how far is the place ?
Options:
a ) 144 km , b ) 30 km , c ) 48 km , d ) 12 km , e ) 15 km
Answer (choose one of a, ... | To solve this, we need to calculate the effective speed of the person when rowing against the current and then add it to the speed in still water.
Speed in still water = 10 kmph
Velocity of the current = 2 kmph
Effective speed = Speed in still water + Velocity of the current
= 10 + 2
= 12 kmph
Time taken to row to a... | To solve this problem, we need to find the total distance traveled by the person.
Let's break it down step by step:
1. When traveling downstream (in the direction of the current), the person's effective speed is the sum of their own speed and the speed of the current.
Let's denote the person's speed in still water a... |
Solve the following multiple choice question.
Question:
the batting average of a particular batsman is 58 runs in 46 innings . if the difference in his highest and lowest score is 150 runs and his average excluding these two innings is 58 runs , find his highest score .
Options:
a ) 179 , b ) 208 , c ) 210 , d ) 133 ... | To solve this, let's calculate the total runs scored by the batsman in all 50 innings and then subtract the runs scored in the 2 innings to find the highest score.
Batting average = 58 runs / 46 innings = 1.26 runs per innings
Total runs scored in 50 innings = 1.26 * 50 = 62 runs
Since the average excluding the two i... | To find the highest score, let's denote the highest score as 'x'.
The total runs scored in 46 innings = 46 * 58 = 2668
The total runs scored excluding the two innings = 46 * 58 = 2668
We know that the total runs scored in the 44 innings = x + 150 + 150 = x + 300
Since the total runs scored in all innings = 2668, w... |
Solve the following multiple choice question.
Question:
the batting average of a particular batsman is 58 runs in 46 innings . if the difference in his highest and lowest score is 150 runs and his average excluding these two innings is 58 runs , find his highest score .
Options:
a ) 179 , b ) 208 , c ) 210 , d ) 133 ... | To solve this, let's calculate the total runs scored by the batsman in all 50 innings and then subtract the runs scored in the 2 innings to find the highest score.
Batting average = 58 runs / 46 innings = 1.26 runs per innings
Total runs scored in 50 innings = 1.26 * 50 = 62 runs
Since the average excluding the two i... | To find the highest score, we can use the following steps:
1. We are given that the average of the 8 innings is 58, and there are 46 innings in total.
2. We are also given that the difference between the highest and lowest scores is 150.
3. To find the average excluding the two innings, we need to exclude the two inni... |
Solve the following multiple choice question.
Question:
the batting average of a particular batsman is 58 runs in 46 innings . if the difference in his highest and lowest score is 150 runs and his average excluding these two innings is 58 runs , find his highest score .
Options:
a ) 179 , b ) 208 , c ) 210 , d ) 133 ... | To solve this, let's calculate the total runs scored by the batsman in all 50 innings and then subtract the runs scored in the 2 innings to find the highest score.
Batting average = 58 runs / 46 innings = 1.26 runs per innings
Total runs scored in 50 innings = 1.26 * 50 = 62 runs
Since the average excluding the two i... | To find the highest score, let's break it down step by step:
1. The total number of innings played is 46.
2. The batting average of the batsman excluding the two innings with a high and low score is 58.
3. The average of 44 innings is 58.
If the sum of runs for the 44 innings is 58 * 44 = 2560,
then the sum of... |
Solve the following multiple choice question.
Question:
the area of a rectangular field is equal to 200 square meters . its perimeter is equal to 60 meters . find the width of this rectangle .
Options:
a ) 5 , b ) 10 , c ) 15 , d ) 20 , e ) 25
Answer (choose one of a, b, c, d, e): | l * w = 200 : area , l is the length and w is the width . 2 l + 2 w = 60 : perimeter l = 30 - w : solve for l ( 30 - w ) * w = 200 : substitute in the area equation w = 10 and l = 20 : correct answer b
Final answer: b | To find the width of the rectangular field, we need to use the formula for the area and the perimeter of a rectangle.
Area = length * width
Perimeter = 2 * (length + width)
We are given:
Area = 200 square meters
Perimeter = 60 meters
First, we need to find the length of the rectangle.
We can start by expressing the... |
Solve the following multiple choice question.
Question:
the area of a rectangular field is equal to 200 square meters . its perimeter is equal to 60 meters . find the width of this rectangle .
Options:
a ) 5 , b ) 10 , c ) 15 , d ) 20 , e ) 25
Answer (choose one of a, b, c, d, e): | l * w = 200 : area , l is the length and w is the width . 2 l + 2 w = 60 : perimeter l = 30 - w : solve for l ( 30 - w ) * w = 200 : substitute in the area equation w = 10 and l = 20 : correct answer b
Final answer: b | To find the width of the rectangular field, we can use the formula for the perimeter of a rectangle:
Perimeter = 2(length + width)
Given that the perimeter is 60 meters, we can set up the equation:
60 = 2(length + width)
We are also given that the area of the rectangle is 200 square meters. The formula for the area... |
Solve the following multiple choice question.
Question:
the area of a rectangular field is equal to 200 square meters . its perimeter is equal to 60 meters . find the width of this rectangle .
Options:
a ) 5 , b ) 10 , c ) 15 , d ) 20 , e ) 25
Answer (choose one of a, b, c, d, e): | l * w = 200 : area , l is the length and w is the width . 2 l + 2 w = 60 : perimeter l = 30 - w : solve for l ( 30 - w ) * w = 200 : substitute in the area equation w = 10 and l = 20 : correct answer b
Final answer: b | To find the width of the rectangular field, we can use the formula for the perimeter of a rectangle:
Perimeter = 2(length + width)
We are given that the perimeter is equal to 60 meters, so we can set up the equation:
60 = 2(length + width)
We are also given that the area is equal to 200 square meters, which we can ... |
Solve the following multiple choice question.
Question:
in what time will a train 100 m long cross an electric pole , it its speed be 126 km / hr ?
Options:
a ) 2.5 , b ) 2.9 , c ) 2.4 , d ) 2.85 , e ) 2.1
Answer (choose one of a, b, c, d, e): | To find the time taken by the train to cross the electric pole, we need to find the time it takes for the entire length of the train to pass the pole.
Speed = 126 km/hr
Length of the train = 100 m
We need to convert the speed from km/hr to m/s first.
1 km/hr = 5/18 m/s
So, 126 km/hr = 126 * 5/18 = 35 m/s
Now, we can... | To solve this problem, we need to convert the speed from km/hr to m/s and then use the formula: Time = Distance / Speed.
Speed in km/hr = 126 km/hr
To convert to m/s, we multiply by 1000/3600.
126 km/hr * 1000/3600 = 35 m/s
Now, we can use the formula:
Time = Distance / Speed
Time = 100 m / 35 m/s
Time = 2.86 seconds... |
Solve the following multiple choice question.
Question:
in what time will a train 100 m long cross an electric pole , it its speed be 126 km / hr ?
Options:
a ) 2.5 , b ) 2.9 , c ) 2.4 , d ) 2.85 , e ) 2.1
Answer (choose one of a, b, c, d, e): | To find the time taken by the train to cross the electric pole, we need to find the time it takes for the entire length of the train to pass the pole.
Speed = 126 km/hr
Length of the train = 100 m
We need to convert the speed from km/hr to m/s first.
1 km/hr = 5/18 m/s
So, 126 km/hr = 126 * 5/18 = 35 m/s
Now, we can... | To find the time taken to cross the electric pole, we need to convert the speed from km/hr to m/sec and then calculate the distance and time.
Given:
Speed = 126 km/hr
1 km/hr = 5/18 m/sec
Distance = Length of the train (100 m)
Convert speed to m/sec:
Speed (m/sec) = 126 * 5/18 = 35 m/sec
Now, we can use the formula:... |
Solve the following multiple choice question.
Question:
in what time will a train 100 m long cross an electric pole , it its speed be 126 km / hr ?
Options:
a ) 2.5 , b ) 2.9 , c ) 2.4 , d ) 2.85 , e ) 2.1
Answer (choose one of a, b, c, d, e): | To find the time taken by the train to cross the electric pole, we need to find the time it takes for the entire length of the train to pass the pole.
Speed = 126 km/hr
Length of the train = 100 m
We need to convert the speed from km/hr to m/s first.
1 km/hr = 5/18 m/s
So, 126 km/hr = 126 * 5/18 = 35 m/s
Now, we can... | To solve this problem, we can use the formula for speed, which is:
Speed = Distance / Time
Given:
- Distance = Length of the train = 100 m
- Speed = 126 km/hr
First, convert the speed from km/hr to m/sec:
Speed in m/sec = 126 * (1000/3600) = 35 m/sec
Now we can rearrange the formula to solve for time (T = D/S):
T ... |
Solve the following multiple choice question.
Question:
what is the units digit of the expression 14 ^ 7 − 17 ^ 4 ?
Options:
a ) 0 , b ) 3 , c ) 4 , d ) 8 , e ) 6
Answer (choose one of a, b, c, d, e): | i think answer on this one should be d too . since we know that 14 ^ 7 > 17 ^ 4 , as will said one should always check if the number is positive .
Final answer: d | To solve the expression, we need to calculate 14^7 - 17^4.
14^7 = 2^7 * 7 = 128 * 7 = 896
17^4 = 17 * 17 * 17 * 17 = 4913
Now, let's subtract 17^4 from 14^7:
896 - 4913 = -4017
The units digit of -4017 is 7.
So, the correct answer is:
e) 6 |
Solve the following multiple choice question.
Question:
what is the units digit of the expression 14 ^ 7 − 17 ^ 4 ?
Options:
a ) 0 , b ) 3 , c ) 4 , d ) 8 , e ) 6
Answer (choose one of a, b, c, d, e): | i think answer on this one should be d too . since we know that 14 ^ 7 > 17 ^ 4 , as will said one should always check if the number is positive .
Final answer: d | To find the units digit of the expression 14^7 - 17^4, let's calculate it step by step.
First, let's find the units digit of 14^7:
14^1 = 14 (units digit is 4)
14^2 = 196 (units digit is 6)
14^3 = 2744 (units digit is 4)
14^4 = 38416 (units digit is 6)
14^5 = 53704 (units digit is 4)
14^6 = 759696 (units digit is 6)
... |
Solve the following multiple choice question.
Question:
what is the units digit of the expression 14 ^ 7 − 17 ^ 4 ?
Options:
a ) 0 , b ) 3 , c ) 4 , d ) 8 , e ) 6
Answer (choose one of a, b, c, d, e): | i think answer on this one should be d too . since we know that 14 ^ 7 > 17 ^ 4 , as will said one should always check if the number is positive .
Final answer: d | To find the units digit of the expression 14^7 - 17^4, we need to find the units digit of each term separately.
1. 14^7:
The units digit of 14^2 is 4 (since 14*4 = 56, and the units digit of 56 is 6).
The units digit of 14^3 is 4*6 = 24, and the units digit of 24 is 4.
The units digit of 14^4 is 4*4 = 16, and the unit... |
Solve the following multiple choice question.
Question:
find two integers , neither of which ends in a zero , and whose product is exactly 10 , 000,000
Options:
a ) 64 and 15,625 , b ) 60 and 15,625 , c ) 64 and 15,620 , d ) 64 and 15,635 , e ) 128 and 78,125
Answer (choose one of a, b, c, d, e): | 10 , 000,000 = 10 ^ 7 = 10 x 10 x 10 x 10 x 10 x 10 x 10 = ( 2 x 5 ) x ( 2 x 5 ) x ( 2 x 5 ) x ( 2 x 5 ) x ( 2 x 5 ) x ( 2 x 5 ) x ( 2 x 5 ) = ( 2 ^ 7 ) x ( 5 ^ 7 ) = 128 x 78125 so the numbers are 128 and 78,125 answer : e
Final answer: e | To find two integers whose product is exactly 10,000,000 and neither of which ends in zero, let's analyze the options:
- Option a) 64 and 15,625: Both 64 and 15,625 end in zero, so this option is not valid.
- Option b) 60 and 15,625: Both 60 and 15,625 end in zero, so this option is not valid.
- Option c) 64 and 15,... |
Solve the following multiple choice question.
Question:
find two integers , neither of which ends in a zero , and whose product is exactly 10 , 000,000
Options:
a ) 64 and 15,625 , b ) 60 and 15,625 , c ) 64 and 15,620 , d ) 64 and 15,635 , e ) 128 and 78,125
Answer (choose one of a, b, c, d, e): | 10 , 000,000 = 10 ^ 7 = 10 x 10 x 10 x 10 x 10 x 10 x 10 = ( 2 x 5 ) x ( 2 x 5 ) x ( 2 x 5 ) x ( 2 x 5 ) x ( 2 x 5 ) x ( 2 x 5 ) x ( 2 x 5 ) = ( 2 ^ 7 ) x ( 5 ^ 7 ) = 128 x 78125 so the numbers are 128 and 78,125 answer : e
Final answer: e | To solve this problem, we need to find two integers whose product is exactly 10,000,000 and neither of which ends in zero.
First, let's analyze the options:
a) 64 and 15,625: 64 ends in 4, and 15,625 ends in 5. They do not meet the condition of neither ending in zero.
b) 60 and 15,625: 60 ends in 0, which meets the ... |
Solve the following multiple choice question.
Question:
find two integers , neither of which ends in a zero , and whose product is exactly 10 , 000,000
Options:
a ) 64 and 15,625 , b ) 60 and 15,625 , c ) 64 and 15,620 , d ) 64 and 15,635 , e ) 128 and 78,125
Answer (choose one of a, b, c, d, e): | 10 , 000,000 = 10 ^ 7 = 10 x 10 x 10 x 10 x 10 x 10 x 10 = ( 2 x 5 ) x ( 2 x 5 ) x ( 2 x 5 ) x ( 2 x 5 ) x ( 2 x 5 ) x ( 2 x 5 ) x ( 2 x 5 ) = ( 2 ^ 7 ) x ( 5 ^ 7 ) = 128 x 78125 so the numbers are 128 and 78,125 answer : e
Final answer: e | To find the two integers that satisfy the given conditions, let's analyze each option:
- Option a) 64 and 15,625:
- 64 ends in 4, and 15,625 ends in 5.
- Their product is 64 * 15,625 = 1,000,000, which matches the given condition.
- Option b) 60 and 15,625:
- 60 ends in 0, and 15,625 ends in 5.
- Their pr... |
Solve the following multiple choice question.
Question:
a jogger running at 9 km / hr along side a railway track is 240 m ahead of the engine of a 130 m long train running at 45 km / hr in the same direction . in how much time will the train pass the jogger ?
Options:
a ) 28 sec , b ) 16 sec , c ) 37 sec , d ) 18 sec... | To solve this problem, we need to find the relative speed of the train with respect to the jogger.
Relative speed = speed of train - speed of jogger
Relative speed = 45 km/hr - 9 km/hr = 36 km/hr
We need to convert relative speed to m/sec
Relative speed = 36 km/hr * (1000 m/km) * (1 hr/3600 sec)
Relative speed = 10... | To solve this problem, we need to calculate the relative speed between the jogger and the train.
Relative speed = Speed of jogger + Speed of train
= 9 km/hr + 45 km/hr
= 54 km/hr
We need to convert this speed to m/sec:
= 54 * (5/18)
= 15 m/sec
Distance to be covered by the train to pass the jogger = 240 m
Relative s... |
Solve the following multiple choice question.
Question:
a jogger running at 9 km / hr along side a railway track is 240 m ahead of the engine of a 130 m long train running at 45 km / hr in the same direction . in how much time will the train pass the jogger ?
Options:
a ) 28 sec , b ) 16 sec , c ) 37 sec , d ) 18 sec... | To solve this problem, we need to find the relative speed of the train with respect to the jogger.
Relative speed = speed of train - speed of jogger
Relative speed = 45 km/hr - 9 km/hr = 36 km/hr
We need to convert relative speed to m/sec
Relative speed = 36 km/hr * (1000 m/km) * (1 hr/3600 sec)
Relative speed = 10... | To solve this problem, we need to find the relative speed of the train with respect to the jogger.
Relative speed = speed of train - speed of jogger
= 45 km/hr - 9 km/hr
= 36 km/hr
We know that distance = speed * time. We can use this formula to find the time it takes for the train to pass the jogger.
Time = distan... |
Solve the following multiple choice question.
Question:
a jogger running at 9 km / hr along side a railway track is 240 m ahead of the engine of a 130 m long train running at 45 km / hr in the same direction . in how much time will the train pass the jogger ?
Options:
a ) 28 sec , b ) 16 sec , c ) 37 sec , d ) 18 sec... | To solve this problem, we need to find the relative speed of the train with respect to the jogger.
Relative speed = speed of train - speed of jogger
Relative speed = 45 km/hr - 9 km/hr = 36 km/hr
We need to convert relative speed to m/sec
Relative speed = 36 km/hr * (1000 m/km) * (1 hr/3600 sec)
Relative speed = 10... | To find the time taken for the train to pass the jogger, we need to find the relative speed between the train and the jogger.
Relative speed = Speed of train - Speed of jogger
= 45 km/hr - 9 km/hr
= 36 km/hr
To convert this to m/s, we multiply by 5/18
Relative speed = 36 * 5/18 = 10 m/s
Distance to be covered = 240 ... |
Solve the following multiple choice question.
Question:
if the price of a certain computer increased 30 percent from d dollars to 338 dollars , then 2 d =
Options:
a ) 540 , b ) 520 , c ) 619 , d ) 649 , e ) 700
Answer (choose one of a, b, c, d, e): | before price increase price = d after 30 % price increase price = d + ( 30 / 100 ) * d = 1.3 d = 338 ( given ) i . e . d = 338 / 1.3 = $ 260 i . e . 2 d = 2 * 260 = 520 answer : option b
Final answer: b | To solve this problem, we need to find the original price of the computer (d) before the price increase.
Let's denote the original price as x. We know that the price increased by 30%, so the new price is 1.3x = 338.
To find the original price (x), we can divide both sides by 1.3:
x = 338 / 1.3
x = 260
Now that we k... |
Solve the following multiple choice question.
Question:
if the price of a certain computer increased 30 percent from d dollars to 338 dollars , then 2 d =
Options:
a ) 540 , b ) 520 , c ) 619 , d ) 649 , e ) 700
Answer (choose one of a, b, c, d, e): | before price increase price = d after 30 % price increase price = d + ( 30 / 100 ) * d = 1.3 d = 338 ( given ) i . e . d = 338 / 1.3 = $ 260 i . e . 2 d = 2 * 260 = 520 answer : option b
Final answer: b | To solve this problem, let's use the concept of percentage increase.
Let the original price be 'd dollars.
The price increased by 30%, so the new price is 338 dollars.
To find the original price 'd, we can set up the equation:
New price = Original price + 30% of Original price
338 = d + 0.3d
338 = 1.3d
To find 'd,... |
Solve the following multiple choice question.
Question:
if the price of a certain computer increased 30 percent from d dollars to 338 dollars , then 2 d =
Options:
a ) 540 , b ) 520 , c ) 619 , d ) 649 , e ) 700
Answer (choose one of a, b, c, d, e): | before price increase price = d after 30 % price increase price = d + ( 30 / 100 ) * d = 1.3 d = 338 ( given ) i . e . d = 338 / 1.3 = $ 260 i . e . 2 d = 2 * 260 = 520 answer : option b
Final answer: b | To solve this, we need to find the original price 'd'.
Given that the price increased by 30% from d dollars to 338 dollars, we can write an equation:
d + 30% of d = 338
To find 30% of d, multiply d by 0.3:
d + 0.3d = 338
Combine like terms:
1.3d = 338
Now, divide both sides by 1.3:
d = 338 / 1.3
d = 260
Therefor... |
Solve the following multiple choice question.
Question:
what is the square root of 400 , divided by 2 ?
Options:
a ) 9 , b ) 36 , c ) 122 , d ) 6 , e ) 10
Answer (choose one of a, b, c, d, e): | To solve this problem, we need to follow the order of operations (PEMDAS):
1. Calculate the square root of 400: √400 = 20
2. Divide the result by 2: 20 / 2 = 10
So, the correct answer is (e) 10. | To find the square root of 400 and divide it by 2, we calculate the square root of 400 to get approximately 20.
20 / 2 = 10.
Therefore, the correct answer is d) 6. |
Solve the following multiple choice question.
Question:
the jogging track in a sports complex is 561 m in circumference . deepak and his wife start from the same point and walk in opposite directions at 4.5 km / hr and 3.75 km / hr respectively . they will meet for the first time in ?
Options:
a ) 5.29 min , b ) 5.28... | To solve this problem, we need to find the time it takes for the two runners to meet.
The relative speed of the runners is the sum of their speeds, since they are moving in opposite directions.
Relative speed = 4.5 km/hr + 3.75 km/hr = 8.25 km/hr
We need to convert this speed to meters per minute (m/min).
1 km/hr =... | To solve this problem, we need to find the time it takes for Deepak and his wife to meet.
Since they are walking in opposite directions, their relative speed is the sum of their speeds.
Relative speed = 4.5 km/hr + 3.75 km/hr = 8.25 km/hr
Now, we need to find the time it takes for them to cover the distance of the j... |
Solve the following multiple choice question.
Question:
the jogging track in a sports complex is 561 m in circumference . deepak and his wife start from the same point and walk in opposite directions at 4.5 km / hr and 3.75 km / hr respectively . they will meet for the first time in ?
Options:
a ) 5.29 min , b ) 5.28... | To solve this problem, we need to find the time it takes for the two runners to meet.
The relative speed of the runners is the sum of their speeds, since they are moving in opposite directions.
Relative speed = 4.5 km/hr + 3.75 km/hr = 8.25 km/hr
We need to convert this speed to meters per minute (m/min).
1 km/hr =... | To find the time taken by the joggers to meet, we need to calculate the distance covered by both of them in the time they meet, and then calculate the relative speed.
Distance covered by Deepak = 4.5 km/hr * 5.6 = 25.4 m
Distance covered by his wife = 3.75 km/hr * 5.6 = 21.9 m
Time taken to meet = Distance / Relative... |
Solve the following multiple choice question.
Question:
the jogging track in a sports complex is 561 m in circumference . deepak and his wife start from the same point and walk in opposite directions at 4.5 km / hr and 3.75 km / hr respectively . they will meet for the first time in ?
Options:
a ) 5.29 min , b ) 5.28... | To solve this problem, we need to find the time it takes for the two runners to meet.
The relative speed of the runners is the sum of their speeds, since they are moving in opposite directions.
Relative speed = 4.5 km/hr + 3.75 km/hr = 8.25 km/hr
We need to convert this speed to meters per minute (m/min).
1 km/hr =... | To solve this problem, we need to find the time taken by Deepak and his wife to meet for the first time.
The speed of Deepak is 4.5 km/hr, and the speed of his wife is 3.75 km/hr.
Since they are walking in opposite directions, we add their speeds to find the relative speed:
Relative speed = 4.5 km/hr + 3.75 km/hr =... |
Solve the following multiple choice question.
Question:
in a certain pond , 40 fish were caught , tagged , and returned to the pond . a few days later , 40 fish were caught again , of which 2 were found to have been tagged . if the percent of tagged fish in the second catch approximates the percent of tagged fish in t... | To find the approximate number of fish in the pond, we can use the concept of proportionality.
Let's denote the total number of fish in the pond as x.
The ratio of tagged fish to the total number of fish caught in the second catch is 2/40 = 1/10.
We can set up the proportion:
40 * (1/10) = x * (2/40)
To solve fo... | To solve this problem, let's use the concept of proportionality.
Let's denote the total number of fish in the pond as N. We know that 40 fish were caught and tagged initially, and 2 of them were caught again. Since the percent of tagged fish in the second catch approximates the percent of tagged fish in the pond, we c... |
Solve the following multiple choice question.
Question:
in a certain pond , 40 fish were caught , tagged , and returned to the pond . a few days later , 40 fish were caught again , of which 2 were found to have been tagged . if the percent of tagged fish in the second catch approximates the percent of tagged fish in t... | To find the approximate number of fish in the pond, we can use the concept of proportionality.
Let's denote the total number of fish in the pond as x.
The ratio of tagged fish to the total number of fish caught in the second catch is 2/40 = 1/10.
We can set up the proportion:
40 * (1/10) = x * (2/40)
To solve fo... | To solve this problem, we can use the concept of ratios.
Let's denote the number of fish in the pond as 'x'.
In the first catch, 40 fish were tagged, so the ratio of tagged fish to the total number of fish in the pond is 40/x.
In the second catch, 40 fish were caught and 2 of them were tagged, so the ratio of tagg... |
Solve the following multiple choice question.
Question:
in a certain pond , 40 fish were caught , tagged , and returned to the pond . a few days later , 40 fish were caught again , of which 2 were found to have been tagged . if the percent of tagged fish in the second catch approximates the percent of tagged fish in t... | To find the approximate number of fish in the pond, we can use the concept of proportionality.
Let's denote the total number of fish in the pond as x.
The ratio of tagged fish to the total number of fish caught in the second catch is 2/40 = 1/10.
We can set up the proportion:
40 * (1/10) = x * (2/40)
To solve fo... | To find the total number of fish in the pond, we need to use the concept of proportion.
Let's say the number of fish in the pond initially is x.
The 40 tagged fish are divided into two groups: the first catch of 40 fish and the second catch of 40 fish.
Let's assume that the ratio of tagged fish in the two catches is... |
Solve the following multiple choice question.
Question:
how long will take a leak at the bottom of a tank to empty it if it will take 3 hours to fill it without the leak , but due to the leak it will take one additional hour to be filled ?
Options:
a ) 12 hours , b ) 111 hours , c ) 15 hours , d ) 14 hours , e ) 11 h... | To solve this problem, we can use the concept of the rate of filling and leaking.
Let's assume the rate of filling the tank is F and the rate of leaking is L. When the tank is filled without a leak, the rate of filling is 1 tank per hour (1/F).
When the leak is present, the rate of filling becomes (F - L) per hour.... | To solve this problem, let's first determine the rate at which the tank is being filled without the leak.
If it takes 3 hours to fill the tank without the leak, then the rate of filling is 1/3 of the tank per hour.
With the leak, it takes 4 hours to fill the tank. So, the rate of filling with the leak is 1/4 of the ... |
Solve the following multiple choice question.
Question:
how long will take a leak at the bottom of a tank to empty it if it will take 3 hours to fill it without the leak , but due to the leak it will take one additional hour to be filled ?
Options:
a ) 12 hours , b ) 111 hours , c ) 15 hours , d ) 14 hours , e ) 11 h... | To solve this problem, we can use the concept of the rate of filling and leaking.
Let's assume the rate of filling the tank is F and the rate of leaking is L. When the tank is filled without a leak, the rate of filling is 1 tank per hour (1/F).
When the leak is present, the rate of filling becomes (F - L) per hour.... | To solve this problem, we can use the concept of the rate of filling or draining the tank.
Let's denote the rate of filling the tank as F and the rate of draining the tank as D.
Without the leak, it would take 3 hours to fill the tank, which means F = 1/3 of the tank per hour.
With the leak, it would take 4 hours to... |
Solve the following multiple choice question.
Question:
how long will take a leak at the bottom of a tank to empty it if it will take 3 hours to fill it without the leak , but due to the leak it will take one additional hour to be filled ?
Options:
a ) 12 hours , b ) 111 hours , c ) 15 hours , d ) 14 hours , e ) 11 h... | To solve this problem, we can use the concept of the rate of filling and leaking.
Let's assume the rate of filling the tank is F and the rate of leaking is L. When the tank is filled without a leak, the rate of filling is 1 tank per hour (1/F).
When the leak is present, the rate of filling becomes (F - L) per hour.... | To find the time it takes to empty the tank with the leak, we need to subtract the time taken to fill the tank without the leak and the additional time taken to fill the tank with the leak.
Time taken to fill the tank without the leak = 3 hours
Time taken to fill the tank with the leak = 3 + 1 = 4 hours
To find the r... |
Solve the following multiple choice question.
Question:
an alloy of copper and zinc contains copper and zinc in the ratio 3 : 5 . another alloy of copper and zinc contains copper and zinc in the ratio 6 : 2 . in what ratio should the two alloys be mixed so that the resultant alloy contains equal proportions of copper ... | To solve this problem, let's assume we have 10 units of the first alloy and 20 units of the second alloy.
For the first alloy, the amount of copper is 3 units and the amount of zinc is 5 units.
For the second alloy, the amount of copper is 6 units and the amount of zinc is 2 units.
Let's assume the total amount of... | To solve this problem, we need to find the average of the two ratios, since the resulting alloy should contain equal proportions of copper and zinc.
Let's calculate the average of the two ratios:
Ratio 1 (copper to zinc): 3 : 5
Ratio 2 (copper to zinc): 6 : 2
To find the average, we add the two ratios and divide by ... |
Solve the following multiple choice question.
Question:
an alloy of copper and zinc contains copper and zinc in the ratio 3 : 5 . another alloy of copper and zinc contains copper and zinc in the ratio 6 : 2 . in what ratio should the two alloys be mixed so that the resultant alloy contains equal proportions of copper ... | To solve this problem, let's assume we have 10 units of the first alloy and 20 units of the second alloy.
For the first alloy, the amount of copper is 3 units and the amount of zinc is 5 units.
For the second alloy, the amount of copper is 6 units and the amount of zinc is 2 units.
Let's assume the total amount of... | To find the ratio of copper and zinc in the resultant alloy, we can set up an equation based on the given ratios.
Let's say the amount of copper in the first alloy is 3x and the amount of zinc in the first alloy is 5x.
Since the resultant alloy contains equal proportions of copper and zinc, we can set up the followi... |
Solve the following multiple choice question.
Question:
in a factory , there are 50 % technicians and 50 % non - technicians . if the 50 % of the technicians and 50 % of non - technicians are permanent employees , then the percentage of workers who are temporary is ?
Options:
a ) 50 % , b ) 57 % , c ) 52 % , d ) 22 %... | To find the percentage of temporary workers, we need to calculate the percentage of technicians and non-technicians who are temporary employees.
50% of 50 technicians is 25 technicians, and 50% of 50 non-technicians is 25 non-technicians.
So, the total number of temporary employees is 25 + 25 = 50.
Now, we need to f... | To find the percentage of temporary workers, we need to find the percentage of technicians and non-technicians who are temporary.
50% of technicians are permanent employees, so 100% - 50% = 50% of technicians are temporary.
50% of non-technicians are permanent employees, so 100% - 50% = 50% of non-technicians are tem... |
Solve the following multiple choice question.
Question:
in a factory , there are 50 % technicians and 50 % non - technicians . if the 50 % of the technicians and 50 % of non - technicians are permanent employees , then the percentage of workers who are temporary is ?
Options:
a ) 50 % , b ) 57 % , c ) 52 % , d ) 22 %... | To find the percentage of temporary workers, we need to calculate the percentage of technicians and non-technicians who are temporary employees.
50% of 50 technicians is 25 technicians, and 50% of 50 non-technicians is 25 non-technicians.
So, the total number of temporary employees is 25 + 25 = 50.
Now, we need to f... | To solve this problem, let's break it down step by step:
1. Assume there are 100 employees in total.
2. Since there are 50% technicians, there are 50 technicians.
3. Since there are 50% of the technicians are permanent, the permanent technicians are: 50% of 50, which equals 25.
4. This means 50% of the total employee... |
Solve the following multiple choice question.
Question:
a certain no . when divided by 50 leaves a remainder 25 , what is the remainder if the same no . be divided by 15 ?
Options:
a ) 2 , b ) 4 , c ) 5 , d ) 8 , e ) 9
Answer (choose one of a, b, c, d, e): | explanation : 50 + 25 = 75 / 15 = 5 ( remainder ) c
Final answer: c | To solve this problem, let's analyze the given information:
- The number leaves a remainder of 25 when divided by 50.
- We need to find the remainder when this number is divided by 15.
Since 50 is a multiple of 5, we can rewrite the original number as 50k + 25, where k is an integer.
Now, when we divide 50k + 25 by ... |
Solve the following multiple choice question.
Question:
a certain no . when divided by 50 leaves a remainder 25 , what is the remainder if the same no . be divided by 15 ?
Options:
a ) 2 , b ) 4 , c ) 5 , d ) 8 , e ) 9
Answer (choose one of a, b, c, d, e): | explanation : 50 + 25 = 75 / 15 = 5 ( remainder ) c
Final answer: c | To find the remainder when the number is divided by 15, we can use the division algorithm:
Dividend = Divisor * Quotient + Remainder
Let's say the number is 'x'. We are given that when x is divided by 50, the remainder is 25. So, we can write:
x = 50q + 25, where q is the quotient.
Now, when x is divided by 15, th... |
Solve the following multiple choice question.
Question:
a certain no . when divided by 50 leaves a remainder 25 , what is the remainder if the same no . be divided by 15 ?
Options:
a ) 2 , b ) 4 , c ) 5 , d ) 8 , e ) 9
Answer (choose one of a, b, c, d, e): | explanation : 50 + 25 = 75 / 15 = 5 ( remainder ) c
Final answer: c | To solve this problem, we need to find a number that leaves a remainder of 25 when divided by 50 and then divide that number by 15.
First, let's find the number that leaves a remainder of 25 when divided by 50. We can do this by adding multiples of 50 to 25 and finding the first number that leaves a remainder of 25.
... |
Solve the following multiple choice question.
Question:
the difference between the ages of two persons is 10 years . fifteen years ago , the elder one was twice as old as the younger one . the present age of the elder person is ?
Options:
a ) 35 yr , b ) 25 yr , c ) 20 yr , d ) 30 yr , e ) 40 yr
Answer (choose one o... | To solve this problem, let's denote the present age of the younger person as 'x'.
Since the difference in their ages is 10 years, the elder person's age would be x + 10.
Fifteen years ago, the younger person was x - 15 years old, and the elder person was (x + 10) - 15 = x - 5 years old.
According to the problem, fi... | To solve this problem, let's denote the present age of the younger person as Y and the present age of the elder person as E.
Given that the difference between their ages is 10 years, we can express it as E = Y + 10.
Also, fifteen years ago, the elder person's age was E - 15, and the younger person's age was Y - 15. ... |
Solve the following multiple choice question.
Question:
the difference between the ages of two persons is 10 years . fifteen years ago , the elder one was twice as old as the younger one . the present age of the elder person is ?
Options:
a ) 35 yr , b ) 25 yr , c ) 20 yr , d ) 30 yr , e ) 40 yr
Answer (choose one o... | To solve this problem, let's denote the present age of the younger person as 'x'.
Since the difference in their ages is 10 years, the elder person's age would be x + 10.
Fifteen years ago, the younger person was x - 15 years old, and the elder person was (x + 10) - 15 = x - 5 years old.
According to the problem, fi... | To solve this problem, we need to set up an equation based on the given information.
Let's denote the present age of the younger person as Y and the present age of the elder person as E.
We know that the difference between their ages is 10 years, so we can write an equation:
E - Y = 10 ... (Equation 1)
We also know ... |
Solve the following multiple choice question.
Question:
the difference between the ages of two persons is 10 years . fifteen years ago , the elder one was twice as old as the younger one . the present age of the elder person is ?
Options:
a ) 35 yr , b ) 25 yr , c ) 20 yr , d ) 30 yr , e ) 40 yr
Answer (choose one o... | To solve this problem, let's denote the present age of the younger person as 'x'.
Since the difference in their ages is 10 years, the elder person's age would be x + 10.
Fifteen years ago, the younger person was x - 15 years old, and the elder person was (x + 10) - 15 = x - 5 years old.
According to the problem, fi... | Let the present age of the younger person be x.
The present age of the elder person is x + 10.
15 years ago, the elder person's age was x - 15.
Since the elder person was twice as old as the younger person 15 years ago, we can set up the equation:
x - 15 = 2(x - 15)
Expanding the equation, we get:
x - 15 = 2x - 3... |
Solve the following multiple choice question.
Question:
noelle walks from point a to point b at an average speed of 6 kilometers per hour . at what speed , in kilometers per hour , must noelle walk from point b to point a so that her average speed for the entire trip is 7 kilometers per hour ?
Options:
a ) 6.75 , b )... | let ' s suppose that speed while returning was xkm / h since the distance is same , we can apply the formula of avg speed avg speed = 2 s 1 s 2 / s 1 + s 2 7 = 2 * 6 * x / 6 + x x = 8.4 e is the answer
Final answer: e | To find the speed at which Noelle must walk from point B to A, we need to calculate the total distance between the two points and the total time taken for the trip.
The distance between point A and point B is the same as the distance from point B to point A, since they are the same point.
Let's assume the distance be... |
Solve the following multiple choice question.
Question:
noelle walks from point a to point b at an average speed of 6 kilometers per hour . at what speed , in kilometers per hour , must noelle walk from point b to point a so that her average speed for the entire trip is 7 kilometers per hour ?
Options:
a ) 6.75 , b )... | let ' s suppose that speed while returning was xkm / h since the distance is same , we can apply the formula of avg speed avg speed = 2 s 1 s 2 / s 1 + s 2 7 = 2 * 6 * x / 6 + x x = 8.4 e is the answer
Final answer: e | To solve this problem, we need to calculate the total distance and the total time taken for the entire trip.
Let's assume the distance between point A and B is D kilometers.
The time taken to travel from A to B at an average speed of 6 km/h is given by:
Time = Distance / Speed
Time = D / 6
Now, we want to find the ... |
Solve the following multiple choice question.
Question:
noelle walks from point a to point b at an average speed of 6 kilometers per hour . at what speed , in kilometers per hour , must noelle walk from point b to point a so that her average speed for the entire trip is 7 kilometers per hour ?
Options:
a ) 6.75 , b )... | let ' s suppose that speed while returning was xkm / h since the distance is same , we can apply the formula of avg speed avg speed = 2 s 1 s 2 / s 1 + s 2 7 = 2 * 6 * x / 6 + x x = 8.4 e is the answer
Final answer: e | To solve this problem, let's use the formula for average speed, which is total distance divided by total time.
Let's denote the distance from A to B as 'd' and the time taken to walk from A to B as 't'.
Given that the average speed from A to B is 6 km/h, we have:
d / t = 6
Now, we need to find the time taken to wal... |
Solve the following multiple choice question.
Question:
a semicircle has a radius of 9 . what is the approximate perimeter of the semicircle ?
Options:
a ) 16 , b ) 25 , c ) 33 , d ) 46 , e ) 58
Answer (choose one of a, b, c, d, e): | the perimeter of a circle is 2 * pi * r . the perimeter of a semicircle is 2 * pi * r / 2 + 2 r = pi * r + 2 r the perimeter is pi * 9 + 2 * 9 which is about 46 . the answer is d .
Final answer: d | To solve this problem, we need to find the circumference of the semicircle.
The formula for the circumference of a circle is C = 2πr, where r is the radius.
For a semicircle, the circumference is half of the full circle's circumference, so it is:
C = πr
Given the radius (r) is 9, we can substitute this value into t... |
Solve the following multiple choice question.
Question:
a semicircle has a radius of 9 . what is the approximate perimeter of the semicircle ?
Options:
a ) 16 , b ) 25 , c ) 33 , d ) 46 , e ) 58
Answer (choose one of a, b, c, d, e): | the perimeter of a circle is 2 * pi * r . the perimeter of a semicircle is 2 * pi * r / 2 + 2 r = pi * r + 2 r the perimeter is pi * 9 + 2 * 9 which is about 46 . the answer is d .
Final answer: d | To solve this, we first need to find the diameter of the semicircle, which is twice the radius.
The diameter = 2 * 9 = 18
The perimeter of a semicircle is equal to half of the circumference of a full circle, so we can find the circumference of the full circle and divide by 2.
The circumference of the full circle = π... |
Solve the following multiple choice question.
Question:
a semicircle has a radius of 9 . what is the approximate perimeter of the semicircle ?
Options:
a ) 16 , b ) 25 , c ) 33 , d ) 46 , e ) 58
Answer (choose one of a, b, c, d, e): | the perimeter of a circle is 2 * pi * r . the perimeter of a semicircle is 2 * pi * r / 2 + 2 r = pi * r + 2 r the perimeter is pi * 9 + 2 * 9 which is about 46 . the answer is d .
Final answer: d | To find the perimeter of the semicircle, we need to add the diameter (the length of the line segment that connects the two ends of the semicircle) and the circumference of the semicircle. The diameter of the semicircle is twice the radius, which is 2 * 9 = 18. The circumference of a semicircle is half the circumference... |
Solve the following multiple choice question.
Question:
there are 3 red chips and 2 blue ones . when arranged in a row , they form a certain color pattern , for example rbrrb . how many color patterns ?
Options:
a ) 10 , b ) 12 , c ) 24 , d ) 60 , e ) 100
Answer (choose one of a, b, c, d, e): | To solve this, let's consider the possible arrangements of the 3 red chips and 2 blue chips.
We can use the formula for permutations of a multiset, which is given by:
n! / (k1! * k2! * ... * km!)
where n is the total number of items, and k1, k2, ..., km are the numbers of each type of item.
In this case, we have:
... | To solve this problem, we need to calculate the number of possible color patterns.
We have 3 red chips and 2 blue chips, so the total number of chips is 5.
The number of ways to arrange 5 different items is 5! (5 factorial), which is equal to 5 × 4 × 3 × 2 × 1 = 120.
Now, let's consider the two colors (red and blue... |
Solve the following multiple choice question.
Question:
there are 3 red chips and 2 blue ones . when arranged in a row , they form a certain color pattern , for example rbrrb . how many color patterns ?
Options:
a ) 10 , b ) 12 , c ) 24 , d ) 60 , e ) 100
Answer (choose one of a, b, c, d, e): | To solve this, let's consider the possible arrangements of the 3 red chips and 2 blue chips.
We can use the formula for permutations of a multiset, which is given by:
n! / (k1! * k2! * ... * km!)
where n is the total number of items, and k1, k2, ..., km are the numbers of each type of item.
In this case, we have:
... | To find the number of color patterns, we need to consider the number of arrangements of 3 red chips and 2 blue chips.
We can arrange 3 red chips in 3! (3 factorial) ways, which is 6.
For each arrangement of red chips, we can place 2 blue chips in the remaining 5 positions in 5P2 (5 permutations of 2) ways, which is 2... |
Solve the following multiple choice question.
Question:
there are 3 red chips and 2 blue ones . when arranged in a row , they form a certain color pattern , for example rbrrb . how many color patterns ?
Options:
a ) 10 , b ) 12 , c ) 24 , d ) 60 , e ) 100
Answer (choose one of a, b, c, d, e): | To solve this, let's consider the possible arrangements of the 3 red chips and 2 blue chips.
We can use the formula for permutations of a multiset, which is given by:
n! / (k1! * k2! * ... * km!)
where n is the total number of items, and k1, k2, ..., km are the numbers of each type of item.
In this case, we have:
... | Let's think this through step by step:
1. There are 3 red chips and 2 blue chips.
2. When the red and blue chips are arranged together in any order, the possible patterns are: rrb, rbb, brb, bbr.
3. If you group two red chips and two blue chips together, you have: r-r-b, r-b-r (and its reverse).
Now let's count the n... |
Solve the following multiple choice question.
Question:
0.0006688 / 0.0000150 x 19.85 = ?
Options:
a ) 850 , b ) 900 , c ) 950 , d ) 1000 , e ) 2000
Answer (choose one of a, b, c, d, e): | To solve the given problem, let's follow the order of operations (PEMDAS):
0.0006688 / 0.0000150 = 0.0006688 / 0.0000150 = 44.88
Now multiply 44.88 by 19.85
44.88 * 19.85 = 882.26
Now, let's match the result to the given options:
The closest match is 900, so the correct answer is b) 900. | To solve the given problem, let's follow the order of operations (PEMDAS):
0.0006688 / 0.0000150 = 0.0006688 / (0.0000150 * 19.85)
First, calculate 0.0000150 * 19.85:
0.0000150 * 19.85 = 0.0003007
Now, divide 0.0006688 by the result:
0.0006688 / 0.0003007 ≈ 2.223
Rounding this result to the nearest whole number, we... |
Solve the following multiple choice question.
Question:
0.0006688 / 0.0000150 x 19.85 = ?
Options:
a ) 850 , b ) 900 , c ) 950 , d ) 1000 , e ) 2000
Answer (choose one of a, b, c, d, e): | To solve the given problem, let's follow the order of operations (PEMDAS):
0.0006688 / 0.0000150 = 0.0006688 / 0.0000150 = 44.88
Now multiply 44.88 by 19.85
44.88 * 19.85 = 882.26
Now, let's match the result to the given options:
The closest match is 900, so the correct answer is b) 900. | To solve the given problem:
0.0006688 / 0.0000150 = 0.0006688 x 100 = 0.6688
Now, we can multiply this value by 19.85:
0.6688 x 100 = 66.88
Among the given options, the closest answer is option d ) 1000. |
Solve the following multiple choice question.
Question:
0.0006688 / 0.0000150 x 19.85 = ?
Options:
a ) 850 , b ) 900 , c ) 950 , d ) 1000 , e ) 2000
Answer (choose one of a, b, c, d, e): | To solve the given problem, let's follow the order of operations (PEMDAS):
0.0006688 / 0.0000150 = 0.0006688 / 0.0000150 = 44.88
Now multiply 44.88 by 19.85
44.88 * 19.85 = 882.26
Now, let's match the result to the given options:
The closest match is 900, so the correct answer is b) 900. | To solve the question, let's follow the order of operations (PEMDAS):
1. First, divide 0.0006688 by 0.0000150:
0.0006688 / 0.0000150 = 0.0006688 / (1/16)
= 0.0006688 x 16
= 0.010377
2. Now multiply 0.010377 by 19.85:
0.010377 x 19.85 = 0.199406
Among the given options, the correc... |
Solve the following multiple choice question.
Question:
if rs . 578 be divided among a , b , c in such a way that a gets 2 / 3 of what b gets and b gets 1 / 4 of what c gets , then their shares are respectively ?
Options:
a ) s . 300 , b ) s . 408 , c ) s . 389 , d ) s . 368 , e ) s . 323
Answer (choose one of a, b,... | Let's analyze the situation:
Let's say b's share is x.
Since b gets 1/4 of what c gets, c's share is 4x.
Since a gets 2/3 of what b gets, a's share is 2/3 * x.
We know that the total amount is Rs. 578. So, we can set up the equation:
a's share + b's share + c's share = Rs. 578
(2/3)x + x + 4x = 578
Combine like t... | To solve this problem, let's assume c's share as 'x'.
According to the given condition, a gets 2/3 of what b gets and b gets 1/4 of what c gets.
Let's write the equations based on the given conditions:
a : 2/3 of b = x
b : 1/4 of x = y
So,
2/3 * y = x
x = 2/3 * y
Also,
y = 1/4 * x
Now, substitute the valu... |
Solve the following multiple choice question.
Question:
if rs . 578 be divided among a , b , c in such a way that a gets 2 / 3 of what b gets and b gets 1 / 4 of what c gets , then their shares are respectively ?
Options:
a ) s . 300 , b ) s . 408 , c ) s . 389 , d ) s . 368 , e ) s . 323
Answer (choose one of a, b,... | Let's analyze the situation:
Let's say b's share is x.
Since b gets 1/4 of what c gets, c's share is 4x.
Since a gets 2/3 of what b gets, a's share is 2/3 * x.
We know that the total amount is Rs. 578. So, we can set up the equation:
a's share + b's share + c's share = Rs. 578
(2/3)x + x + 4x = 578
Combine like t... | To solve this problem, let's denote the amount a gets as A, b gets as B, and c gets as C.
Given:
- A gets 2/3 of what b gets (B)
- B gets 1/4 of what c gets (C)
So we can write the equations:
A = (2/3)B
B = (1/4)C
To express A in terms of C, we can multiply both sides of the second equation by 4:
B = C
Now, subs... |
Solve the following multiple choice question.
Question:
if rs . 578 be divided among a , b , c in such a way that a gets 2 / 3 of what b gets and b gets 1 / 4 of what c gets , then their shares are respectively ?
Options:
a ) s . 300 , b ) s . 408 , c ) s . 389 , d ) s . 368 , e ) s . 323
Answer (choose one of a, b,... | Let's analyze the situation:
Let's say b's share is x.
Since b gets 1/4 of what c gets, c's share is 4x.
Since a gets 2/3 of what b gets, a's share is 2/3 * x.
We know that the total amount is Rs. 578. So, we can set up the equation:
a's share + b's share + c's share = Rs. 578
(2/3)x + x + 4x = 578
Combine like t... | To find the shares of a, b, and c, let's denote the shares of a, b, and c as A, B, and C respectively.
Given:
a gets 2/3 of B
B gets 1/4 of C
A gets the remaining 1/3 of the total sum
We can write the equations:
A = (2/3)B
B = (1/4)C
A + B + C = 578
Substituting the first equation into the second equation:
(2/3)B + ... |
Solve the following multiple choice question.
Question:
how many seconds does sandy take to cover a distance of 500 meters , if sandy runs at a speed of 18 km / hr ?
Options:
a ) 80 , b ) 100 , c ) 120 , d ) 140 , e ) 160
Answer (choose one of a, b, c, d, e): | To solve this problem, we need to convert the speed from kilometers per hour to meters per second.
1 kilometer = 1000 meters
1 hour = 3600 seconds
So, 18 km/hr = 18 * 1000 / 3600 meters/second = 5 meters/second
Now, we can calculate the time taken by Sandy to cover 500 meters:
Time = Distance / Speed
Time = 500 met... | To solve this problem, we need to convert the speed from km/hr to m/s and then use the formula Distance = Speed * Time.
Given:
Distance = 500 meters
Speed = 18 km/hr
First, we need to convert speed from km/hr to m/s:
1 km/hr = 1000 m / 3600 s
18 km/hr = 18 * 1000 / 3600
= 5 m/s
Now, we can use the formula:
Time = Di... |
Solve the following multiple choice question.
Question:
how many seconds does sandy take to cover a distance of 500 meters , if sandy runs at a speed of 18 km / hr ?
Options:
a ) 80 , b ) 100 , c ) 120 , d ) 140 , e ) 160
Answer (choose one of a, b, c, d, e): | To solve this problem, we need to convert the speed from kilometers per hour to meters per second.
1 kilometer = 1000 meters
1 hour = 3600 seconds
So, 18 km/hr = 18 * 1000 / 3600 meters/second = 5 meters/second
Now, we can calculate the time taken by Sandy to cover 500 meters:
Time = Distance / Speed
Time = 500 met... | To find the time taken by Sandy to cover 500 meters at a speed of 18 km/hr, we need to convert the speed from kilometers per hour to meters per second.
1 kilometer = 1000 meters
1 hour = 3600 seconds
Speed in meters per second = 18 km/hr = 18 * 1000 / 3600 = 5 meters per second
Now, time taken to cover 500 meters = ... |
Solve the following multiple choice question.
Question:
how many seconds does sandy take to cover a distance of 500 meters , if sandy runs at a speed of 18 km / hr ?
Options:
a ) 80 , b ) 100 , c ) 120 , d ) 140 , e ) 160
Answer (choose one of a, b, c, d, e): | To solve this problem, we need to convert the speed from kilometers per hour to meters per second.
1 kilometer = 1000 meters
1 hour = 3600 seconds
So, 18 km/hr = 18 * 1000 / 3600 meters/second = 5 meters/second
Now, we can calculate the time taken by Sandy to cover 500 meters:
Time = Distance / Speed
Time = 500 met... | To find out how many seconds, we need to convert the speed from km/hr to meters per second (m/s).
First, let's convert 18 km/hr to m/s:
1 km = 1000 meters, and 1 hour = 3600 seconds
So, 18 km/hr = 18 * 1000 / 3600 m/s
= 5 m/s
Now, we can find the time it takes to cover 500 meters:
Time = Distance / Speed
Time = 500 m... |
Solve the following multiple choice question.
Question:
( 0.96 ) ( power 3 ) - ( 0.1 ) ( power 3 ) / ( 0.96 ) ( power 2 ) + 0.096 + ( 0.1 ) ( power 2 ) is :
Options:
a ) 0.68 , b ) 0.086 , c ) 0.86 , d ) 0.068 , e ) none of them
Answer (choose one of a, b, c, d, e): | To solve the given expression, we need to follow the order of operations (PEMDAS):
(0.96)³ - (0.1)³ / (0.96)² + 0.096 + (0.1)²
First, calculate the powers:
(0.96)³ = 0.884736
(0.1)³ = 0.001
(0.96)² = 0.9216
(0.1)² = 0.01
Now, substitute the values back into the expression:
0.884736 - 0.001 / 0.9216 + 0.096 + 0.01
P... | To solve this problem, we need to follow the order of operations (PEMDAS):
1. Calculate the exponentials:
(0.96)^3 = 0.884736
(0.1)^3 = 0.001
(0.96)^2 = 0.9216
(0.1)^2 = 0.01
2. Now, substitute these values back into the original equation:
(0.96)^3 - (0.1)^3 / (0.96)^2 + 0.096 + (0.1)^2
= 0.88473... |
Solve the following multiple choice question.
Question:
by selling an article for $ 110 , a person gains $ 10 . what is the gain % ?
Options:
a ) 25 % , b ) 30 % , c ) 50 % , d ) 20 % , e ) 10 %
Answer (choose one of a, b, c, d, e): | To find the gain percentage, we need to first find the cost price (CP) of the article.
Let's assume the cost price is x.
Since the selling price (SP) is $110 and the gain is $10, we can set up the equation:
SP = CP + Gain
110 = x + 10
To find the cost price, we can subtract the gain from the selling price:
x = 110... | To solve this, we'll use the formula for calculating gain percentage:
Gain % = (Gain / Cost Price) * 100
Given:
Cost Price = $110
Gain = $10
Substituting the values in the formula:
Gain % = ($10 / $110) * 100
= (10 / 110) * 100
= 0.09 * 100
= 9%
So, the gain % is 9%.
The correct option is b) 30%. |
Solve the following multiple choice question.
Question:
if the charge of staying in a student youth hostel $ 18.00 / day for the first week , and $ 14.00 / day for each additional week , how much does it cost to stay for 23 days ?
Options:
a ) $ 160 , b ) $ 350 , c ) $ 282 , d ) $ 274 , e ) $ 286
Answer (choose one ... | To solve this problem, we need to calculate the total cost for 23 days, considering the first week and the additional weeks.
The first week costs $18.00 per day, which is 7 days (1 week). The additional weeks are 23 - 7 = 16 days.
For the first week, the cost is $18.00 per day, so the total cost for the first week is... | To solve this problem, let's break down the cost into two parts:
- For the first week: $18.00/day * 7 days = $126.00
- For the additional 14 days: $14.00/day * 14 days = $196.00
Adding these two amounts together, we get: $126.00 + $196.00 = $322.00
The correct answer is option e) $286. |
Solve the following multiple choice question.
Question:
if the charge of staying in a student youth hostel $ 18.00 / day for the first week , and $ 14.00 / day for each additional week , how much does it cost to stay for 23 days ?
Options:
a ) $ 160 , b ) $ 350 , c ) $ 282 , d ) $ 274 , e ) $ 286
Answer (choose one ... | To solve this problem, we need to calculate the total cost for 23 days, considering the first week and the additional weeks.
The first week costs $18.00 per day, which is 7 days (1 week). The additional weeks are 23 - 7 = 16 days.
For the first week, the cost is $18.00 per day, so the total cost for the first week is... | To solve this, we need to break down the cost into two parts: the cost for the first week and the cost for the additional weeks.
For the first week:
- The cost for the first week is $18.00 per day.
- There are 7 days in a week, so for the first week, the cost is 18 * 7 = $126.
For the additional 16 days:
- The cost f... |
Solve the following multiple choice question.
Question:
if the charge of staying in a student youth hostel $ 18.00 / day for the first week , and $ 14.00 / day for each additional week , how much does it cost to stay for 23 days ?
Options:
a ) $ 160 , b ) $ 350 , c ) $ 282 , d ) $ 274 , e ) $ 286
Answer (choose one ... | To solve this problem, we need to calculate the total cost for 23 days, considering the first week and the additional weeks.
The first week costs $18.00 per day, which is 7 days (1 week). The additional weeks are 23 - 7 = 16 days.
For the first week, the cost is $18.00 per day, so the total cost for the first week is... | To calculate the cost, first, we need to break down the 23 days into weeks. There are 7 days in a week.
23 days = 3 weeks + 2 days
For the first week:
18 days * $18.00/day = $324.00
For the 2 additional days:
14 days * $14.00/day = $28.00
Total cost for the first week = $324 + $28 = $352.00
Total cost for 3 weeks =... |
Solve the following multiple choice question.
Question:
a pet groomer has 7 animals to groom for the day ( 2 cats and 5 dogs ) . if she randomly selects 4 animals to groom before lunch , what is the probability she will finish all the cats before lunch ?
Options:
a ) 3 / 7 , b ) 2 / 7 , c ) 12 / 13 , d ) 5 / 11 , e )... | To solve this problem, we need to find the probability that all 2 cats are groomed before lunch.
There are 7 animals in total, and the pet groomer needs to groom 4 animals. We can calculate the probability of the groomer grooming all 2 cats before lunch as follows:
Number of ways to choose 4 animals out of 7: 7C4 = 3... | To solve this problem, we need to calculate the probability of all cats being groomed before lunch.
Since there are 2 cats and 5 dogs, the total number of ways to select 4 animals is 7C4 = 35.
The number of ways to select 4 animals such that all cats are groomed before lunch is 2C4 = 15, since we need to select 4 cat... |
Solve the following multiple choice question.
Question:
a pet groomer has 7 animals to groom for the day ( 2 cats and 5 dogs ) . if she randomly selects 4 animals to groom before lunch , what is the probability she will finish all the cats before lunch ?
Options:
a ) 3 / 7 , b ) 2 / 7 , c ) 12 / 13 , d ) 5 / 11 , e )... | To solve this problem, we need to find the probability that all 2 cats are groomed before lunch.
There are 7 animals in total, and the pet groomer needs to groom 4 animals. We can calculate the probability of the groomer grooming all 2 cats before lunch as follows:
Number of ways to choose 4 animals out of 7: 7C4 = 3... | To solve this problem, we need to calculate the probability that all 4 selected animals are cats.
There are a total of 7 animals, and 2 are cats. The probability of selecting a cat is 2/7.
The total number of ways to select 4 animals from 7 is 7C4 = 35.
The number of ways to select 4 cats from 2 cats is 2C4 = 15.
... |
Solve the following multiple choice question.
Question:
a pet groomer has 7 animals to groom for the day ( 2 cats and 5 dogs ) . if she randomly selects 4 animals to groom before lunch , what is the probability she will finish all the cats before lunch ?
Options:
a ) 3 / 7 , b ) 2 / 7 , c ) 12 / 13 , d ) 5 / 11 , e )... | To solve this problem, we need to find the probability that all 2 cats are groomed before lunch.
There are 7 animals in total, and the pet groomer needs to groom 4 animals. We can calculate the probability of the groomer grooming all 2 cats before lunch as follows:
Number of ways to choose 4 animals out of 7: 7C4 = 3... | To solve this problem, we can use the concept of combinations.
Total number of ways to choose 4 animals out of 7 is 7C4 (or C(7, 4)).
C(7, 4) = 7! / (4! * (7-4)!)
= (7*6*5*4!) / (4!*3!)
= 35
Number of ways to choose 4 cats out of 2 = 2C4 = 2! / (4! * (2-4)!)
= 1
Number of ways to choose 3 cats and 1 dog out of 2 and... |
Solve the following multiple choice question.
Question:
the difference between a two - digit number and the number obtained by interchanging the digit is 36 . what is the difference between the sum and the difference of the digits of the number if the ratio between the digits of the number is 1 : 2 ?
Options:
a ) 8 ,... | Let's solve the problem step by step.
Let the two-digit number be 10x + y, where x is the digit in the tens place and y is the digit in the ones place.
The difference between the number and the number obtained by interchanging the digits is 36. So, we can write:
(10x + y) - (10y + x) = 36
9x - 9y = 36
x - y = 4
Now... | Let the original two-digit number be 10a + b.
The number obtained by interchanging the digits is 10b + a.
According to the problem, the difference between the two numbers is 36, so we can set up the equation:
(10a + b) - (10b + a) = 36
Simplifying the equation, we get:
9a - 9b = 36
9(a - b) = 36
Dividing both sid... |
Solve the following multiple choice question.
Question:
the difference between a two - digit number and the number obtained by interchanging the digit is 36 . what is the difference between the sum and the difference of the digits of the number if the ratio between the digits of the number is 1 : 2 ?
Options:
a ) 8 ,... | Let's solve the problem step by step.
Let the two-digit number be 10x + y, where x is the digit in the tens place and y is the digit in the ones place.
The difference between the number and the number obtained by interchanging the digits is 36. So, we can write:
(10x + y) - (10y + x) = 36
9x - 9y = 36
x - y = 4
Now... | To solve this problem, let's break it down step by step:
Let the two-digit number be 10a + b, where 'a' is the digit in the tens place and 'b' is the digit in the ones place.
The number obtained by interchanging the digits is 10b + a.
According to the given condition, the difference between the two numbers is 36:
(... |
Solve the following multiple choice question.
Question:
the difference between a two - digit number and the number obtained by interchanging the digit is 36 . what is the difference between the sum and the difference of the digits of the number if the ratio between the digits of the number is 1 : 2 ?
Options:
a ) 8 ,... | Let's solve the problem step by step.
Let the two-digit number be 10x + y, where x is the digit in the tens place and y is the digit in the ones place.
The difference between the number and the number obtained by interchanging the digits is 36. So, we can write:
(10x + y) - (10y + x) = 36
9x - 9y = 36
x - y = 4
Now... | To solve this, let's assume the two-digit number is 10a + b, where 'a' and 'b' are the digits.
Given that the difference between the number and the number obtained by interchanging its digits is 36, we can write:
10a + b - (10b + a) = 36
Expanding and simplifying the equation, we get:
10a - 9b = 36
10a = 9b + 36
... |
Solve the following multiple choice question.
Question:
a trader bought a car at 30 % discount on its original price . he sold it at a 40 % increase on the price he bought it . what percent of profit did he make on the original price ?
Options:
a ) 118 , b ) 110 , c ) 112 , d ) 113 , e ) 98
Answer (choose one of a, ... | original price = 100 cp = 70 s = 70 * ( 140 / 100 ) = 98 100 - 112 = 2 % answer : e
Final answer: e | To solve this problem, let's break it down step by step:
1. The trader bought the car at 30% discount on its original price.
- Let the original price of the car be x.
- The selling price (after a 30% discount) = x - 0.3x = 0.7x.
2. The trader sold the car at a 40% increase on the price he bought it.
- The se... |
Solve the following multiple choice question.
Question:
a trader bought a car at 30 % discount on its original price . he sold it at a 40 % increase on the price he bought it . what percent of profit did he make on the original price ?
Options:
a ) 118 , b ) 110 , c ) 112 , d ) 113 , e ) 98
Answer (choose one of a, ... | original price = 100 cp = 70 s = 70 * ( 140 / 100 ) = 98 100 - 112 = 2 % answer : e
Final answer: e | To find the percent profit made on the original price, let's assume the original price of the car is $100.
- The trader bought the car at 30% discount, so the price he paid is 70% of the original price.
- He sold the car at a 40% increase on the price he bought it, so the selling price is 140% of the price he bought i... |
Solve the following multiple choice question.
Question:
a trader bought a car at 30 % discount on its original price . he sold it at a 40 % increase on the price he bought it . what percent of profit did he make on the original price ?
Options:
a ) 118 , b ) 110 , c ) 112 , d ) 113 , e ) 98
Answer (choose one of a, ... | original price = 100 cp = 70 s = 70 * ( 140 / 100 ) = 98 100 - 112 = 2 % answer : e
Final answer: e | To find the percent profit, we need to find the selling price and then subtract the cost price.
Let the original price be x.
Cost price (CP) = x
Selling price (SP) = x + (40% of x)
SP = x + (0.4x) = 1.4x
Profit = SP - CP
Profit = 1.4x - x = 0.4x
Profit percentage = (Profit / CP) * 100
Profit percentage = (0.4x / x)... |
Solve the following multiple choice question.
Question:
a cube is divided into 125 identical cubelets . each cut is made parallel to some surface of the cube . but before doing that , the cube is painted with green on one set of opposite faces , red on another set of opposite faces , and blue on the third set of oppos... | each side of the cube has 5 x 5 = 25 cubelets . only the interior cubelets are painted one colour . on each side , 3 x 3 = 9 cubelets are painted one colour . since the cube has six sides , the number of cubes with one colour is 6 * 9 = 54 the answer is d .
Final answer: d | To solve this problem, let's analyze the situation:
- The cube is divided into 125 identical cubelets, and each cut is made parallel to some surface of the cube.
- The cube is painted with green on one set of opposite faces, red on another set of opposite faces, and blue on the third set of opposite faces.
Since ther... |
Solve the following multiple choice question.
Question:
a cube is divided into 125 identical cubelets . each cut is made parallel to some surface of the cube . but before doing that , the cube is painted with green on one set of opposite faces , red on another set of opposite faces , and blue on the third set of oppos... | each side of the cube has 5 x 5 = 25 cubelets . only the interior cubelets are painted one colour . on each side , 3 x 3 = 9 cubelets are painted one colour . since the cube has six sides , the number of cubes with one colour is 6 * 9 = 54 the answer is d .
Final answer: d | To solve this problem, let's first understand the structure of the cube.
The cube is divided into 125 identical cubelets. We can visualize it as a 3D grid where each cubelet is a 3x3x3 cube.
There are 3 sets of opposite faces painted with the same color. This means that the cube can be divided into 3 groups of 5 cube... |
Solve the following multiple choice question.
Question:
a cube is divided into 125 identical cubelets . each cut is made parallel to some surface of the cube . but before doing that , the cube is painted with green on one set of opposite faces , red on another set of opposite faces , and blue on the third set of oppos... | each side of the cube has 5 x 5 = 25 cubelets . only the interior cubelets are painted one colour . on each side , 3 x 3 = 9 cubelets are painted one colour . since the cube has six sides , the number of cubes with one colour is 6 * 9 = 54 the answer is d .
Final answer: d | To solve this, we need to find the number of cubelets that are painted with exactly one color.
When the cube is divided into 125 identical cubelets, each cut is made parallel to some surface of the cube. The cube is painted with three sets of opposite faces, so there are 3 sets of cubelets that are painted with the s... |
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