Problem stringlengths 5 967 | category class label 6
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x , y , and z are consecutive numbers and x > y > z . also , 2 x + 3 y + 3 z = 5 y + 8 . what is the value of z ? | 0general |
in the coordinate plane , points ( x , 6 ) and ( 10 , y ) are on line k . if line k passes through the origin and has slope 1 / 2 , then x * y = | 0general |
a vessel of capacity 3 litre has 25 % of alcohol and another vessel of capacity 5 litre had 40 % alcohol . the total liquid of 8 litre was poured out in a vessel of capacity 10 litre and thus the rest part of the vessel was filled with the water . what is the new concentration of mixture ? | 0general |
a jar contains 18 balls . 3 blue balls are removed from the jar and not replaced . now the probability of getting a blue ball is 1 / 5 then how many blue balls jar contains initially ? | 4probability |
a rectangular grassy plot 110 m by 65 cm has a gravel path . 5 cm wide all round it on the inside . find the cost of gravelling the path at 80 paise per sq . mt ? | 1physics |
a motorcyclist goes from nagpur to delhi , a distance of 600 kms at an average of 60 kmph speed . another man starts from nagpur by car 5 â ½ hours after the first , and reaches delhi â ½ hour earlier . what is the ratio of the speed of the motorcycle and the car ? | 1physics |
according to the directions on a packet of smoothie mix , 1 3 - ounce packet of smoothie mix is to be combined with 12 ounces of water to make a smoothie . how many 3 - ounce packets of smoothie mix are required to prepare 120 12 - ounce smoothies ? | 0general |
there are 20 balls in a jar . you take out 2 blue balls without putting them back inside , and now the probability of pulling out a blue ball is 1 / 5 . how many blue balls were there in the beginning ? | 4probability |
the volume of the greatest sphere that can be cut off from a cylindrical log of wood of base radius 1 cm and height 5 cm is : | 3geometry |
a = { 20 , 1 , - 3 , 6 , - 8 } b = { - 1 , 2 , - 4 , 7 , - 620 } if a is a number that is randomly selected from set a , and b is a number that is randomly selected from set b , what is the probability that ab > 0 ? | 0general |
if x is 40 percent greater than 88 , then x = | 0general |
the perimeter of an isosceles right triangle is 4 + 4 sq rt 2 . what is the length of the hypotenuse of the triangle ? | 3geometry |
an 11 - meter long wire is cut into two pieces . if the longer piece is then used to form a perimeter of a square , what is the probability that the area of the square will be more than 4 if the original wire was cut at an arbitrary point ? | 3geometry |
how many different positive integers are factors of 36 ? | 5other |
the list price of an article is rs . 65 . a customer pays rs . 57.33 for it . he was given two successive discounts , one of them being 10 % . the other discount is ? | 2gain |
the supplementary of an angle is thrice its complimentary . find the angle . | 3geometry |
9 log 9 ( 2 ) = ? | 5other |
there are 2 vessels a & b containing 25 liters each of pure milk and pure water respectively . 5 liters of milk from a is taken and poured into b , then 6 liters of mixture from b is taken and poured in a . what is ratio of water a and b respectively . | 5other |
tim and é lan are 150 miles away from one another . they are starting to move towards each other simultaneously , tim at a speed of 10 mph and é lan at a speed of 5 mph . if every hour they double their speeds , what is the distance that tim will pass until he meets é lan ? | 1physics |
16 boys or 24 girls can construct the wall in 6 days . the number of days that 8 boys and 4 girls will take to construct ? | 1physics |
30 pens and 75 pencils were purchased for 630 . if the average price of a pencil was 2.00 , find the average price of a pen . | 0general |
a tank contains 10,000 gallons of a solution that is 5 percent sodium chloride by volume . if 1,600 gallons of water evaporate from the tank , the remaining solution will be approximately what percent sodium chloride ? | 2gain |
find the cost of fencing around a circular field of diameter 34 m at the rate of rs . 2 a meter ? | 1physics |
a man covered a certain distance at some speed . if he had moved 3 kmph faster , he would have taken 40 minutes less . if he had moved 2 kmph slower , he would have taken 40 minutes more . what is the the distance in km ? | 1physics |
if x + y = 280 , x - y = 200 , for integers of x and y , y = ? | 0general |
there are 10 students named alphabetically from a to j . what is the probability that a and d do not sit together if all 10 sit around a circular table ? | 4probability |
a pipe can empty 2 / 3 rd of a cistern in 10 mins . in 8 mins , what part of the cistern will be empty ? | 1physics |
if $ 10 be allowed as true discount on a bill of $ 110 due at the end of a certain time , then the discount allowed on the same sum due at the end of double the time is : | 0general |
if you multiply two integers together and then add 4 , the result is 40 . which of the following could not be the sum of the two numbers ? | 0general |
a train 460 m long is running at a speed of 45 km / hr . in what time will it pass a bridge 140 m long ? | 1physics |
the average weight of 8 person ' s increases by 2.5 kg when a new person comes in place of one of them weighing 45 kg . what might be the weight of the new person ? | 0general |
a shopkeeper loses 15 % , if an article is sold for rs . 187 . what should be the selling price of the article to gain 20 % ? | 2gain |
if 9 a - b = 10 b + 65 = - 12 b - 2 a , what is the value of 11 a + 11 b ? | 0general |
find the average of all numbers between 1 and 76 which are divisible by 5 | 0general |
a cricketer makes a score of 134 runs in the 22 nd inning and thus increases his average by 3.5 . find his average after 22 nd inning . | 0general |
for each of her sales , a saleswoman receives a commission equal to 20 percent of the first $ 500 of the total amount of the sale , plus 30 percent of the total amount in excess of $ 500 . if the total amount of one of her sales was $ 800 , the saleswoman ’ s commission was approximately what percent of the total amount of the sale ? | 0general |
in a certain brick wall , each row of bricks above the bottom row contains one less brick than the row just below it . if there are 6 rows in all and a total of 135 bricks in the wall , how many bricks does the bottom row contain ? | 0general |
the average marks of a class of 25 students is 50 and that of another class of 40 students is 65 . find the average marks of all the students ? | 0general |
how many plants will be there in a circular bed whose outer edge measure 34 cms , allowing 4 cm 2 for each plant ? | 1physics |
a person buys an article at rs . 500 . at what price should he sell the article so as to make a profit of 10 % ? | 2gain |
stacy and helon are 30 miles apart and walk towards each other along the same route . stacy walks at constant rate that is 1 mile per hour faster than helon ' s constant rate of 5 miles / hour . if helon starts her journey 24 minutes after stacy , how far from the original destination has helon walked when the two meet ? | 1physics |
if log 2 = 0.30103 and log 3 = 0.4771 , find the number of digits in ( 648 ) 5 | 5other |
if the ratio of the areas of two squares is 225 : 256 , then the ratio of their perimeters is : | 3geometry |
what least number must be subtracted from 12702 to get number exactly 99 ? | 0general |
if x is 20 percent greater than 40 , then x = | 0general |
in a theater , the first row has 14 seats and each row has 2 more seats than previous row . if the last row has 56 seats , what is the total number of seats in the theater ? | 0general |
a certain automobile company ’ s best - selling model is the speedster . the speedster , like all of their other models , comes in coupe and convertible styles . 2 / 3 of the current inventory is speedsters , of which 4 / 5 are convertibles . if there are 60 vehicles that are not speedsters , how many speedster convertibles are there ? | 1physics |
a bag of potatoes weighs 12 lbs divided by half of its weight . how much does the bag of potatoes weight ? | 0general |
the price of 80 apples is equal to that of 120 oranges . the price of 60 apples and 75 oranges together is rs . 1320 . the total price of 25 apples and 40 oranges is | 0general |
two vessels a and b contain spirit and water in the ratio 5 : 2 and 7 : 6 respectively . find the ratio in which these mixture be mixed to obtain a new mixture in vessel c containing spirit and water in the ration 8 : 5 ? | 5other |
a scale 7 ft . 6 inches long is divided into 5 equal parts . find the length of each part . | 0general |
a cheese factory sells its cheese in rectangular blocks . a normal block has a volume of three cubic feet . if a large block has twice the width , twice the depth , and three times the length of a normal block , what is the volume of cheese in a large block in cubic feet ? | 3geometry |
having received his weekly allowance , a student spent 3 / 5 of his allowance at the arcade . the next day he spent one third of his remaining allowance at the toy store , and then spent his last $ 0.60 at the candy store . what is this student ’ s weekly allowance ? | 0general |
there are 14 players in a chess group , and each player plays each of the others once . given that each game is played by two players , how many total games will be played ? | 0general |
a team won 40 percent of its first 30 games in a particular season , and 80 percent of its remaining games . if the team won a total of 60 percent of its games that season , what was the total number of games that the team played ? | 2gain |
cereal a is 11 % sugar by weight , whereas healthier but less delicious cereal b is 2 % sugar by weight . to make a delicious and healthy mixture that is 4 % sugar , what should be the ratio of cereal a to cereal b , by weight ? | 0general |
10 years ago a was half of b in age . if the ratio of their present ages is 3 : 4 , what will be the total of their present ages | 0general |
a rectangular tiled patio is composed of 126 square tiles . the rectangular patio will be rearranged so that there will be 2 fewer columns of tiles and 4 more rows of tiles . after the change in layout , the patio will still have 126 tiles , and it will still be rectangular . how many rows are in the tile patio before the change in layout ? | 3geometry |
in a class of 39 students 26 play football and play 20 long tennis , if 17 play above , many play neither ? | 5other |
a rectangular floor is covered by a rug except for a strip 2 meters wide along each of the four edge . if the floor is 10 meters by 8 meters , what is the area of the rug in square meters ? | 3geometry |
if a * b denotes the greatest common divisor of a and b , then ( ( 12 * 16 ) * ( 18 * 12 ) ) = ? | 0general |
if 24 men take 15 days to to complete a job , in how many days can 18 men finish that work ? | 1physics |
the circumference of the front wheel of a cart is 40 ft long and that of the back wheel is 48 ft long . what is the distance travelled by the cart , when the front wheel has done five more revolutions than the rear wheel ? | 1physics |
a train requires 10 seconds to pass a pole while it requires 30 seconds to cross a stationary train which is 600 mtrs long . find the speed of the train . | 1physics |
the average of runs of a cricket player of 10 innings was 36 . how many runs must he make in his next innings so as to increase his average of runs by 4 ? | 0general |
john had a stock of 800 books in his bookshop . he sold 62 on monday , 62 on tuesday , 60 on wednesday , 48 on thursday and 40 on friday . what percentage of the books were not sold ? | 2gain |
a certain city with a population of 180,000 is to be divided into 11 voting districts , and no district is to have a population that is more than 10 percent greater than the population of any other district what is the minimum possible population that the least populated district could have ? | 0general |
a palindrome is a number that reads the same front - to - back as it does back - to - front ( e . g . 202 , 575 , 1991 , etc . ) p is the smallest integer greater than 100 that is both a prime and a palindrome . what is the sum of the digits of p ? | 0general |
circular gears l and r start to rotate at the same time at the same rate . gear l makes 20 complete revolutions per minute and gear r makes 40 revolutions per minute . how many seconds after the gears start to rotate will gear r have made exactly 6 more revolutions than gear l ? | 1physics |
two pipes a and b can fill a tank in 4 and 12 minutes respectively . if both the pipes are used together , then how long will it take to fill the tank ? | 1physics |
a girl was asked to multiply a certain number by 43 . she multiplied it by 34 and got his answer less than the correct one by 1206 . find the number to be multiplied . | 0general |
a company pays 18.5 % dividend to its investors . if an investor buys rs . 50 shares and gets 25 % on investment , at what price did the investor buy the shares ? | 2gain |
1000 men have provisions for 20 days . if 650 more men join them , for how many days will the provisions last now ? | 1physics |
david ' s bank ' s saving amount is decreased 10 % due to loan payment and current balance is rs . 90000 . find the actual balance before deduction ? | 2gain |
the ratio of incomes of two person p 1 and p 2 is 5 : 4 and the ratio of their expenditures is 3 : 2 . if at the end of the year , each saves rs . 2200 , then what is the income of p 1 ? | 5other |
3 math classes : x , y , and z , take an algebra test . the average score in class x is 83 . the average score in class y is 76 . the average score in class z is 85 . the average score of all students in classes x and y together is 79 . the average score of all students in classes y and z together is 81 . what is the average score for all the 3 classes , taken together ? | 0general |
a can finish a piece of work in 4 days . b can do it in 14 days . they work together for two days and then a goes away . in how many days will b finish the work ? | 1physics |
the population of a town increased from 1 , 34,000 to 2 , 32,500 in a decade . the average percent increase of population per year is : | 0general |
if r is the product of the integers from 1 to 30 , inclusive , what is the greatest integer k for which 3 ^ k is a factor of r ? | 0general |
rs . 460 was divided among 41 boys and girls such that each boy rs . 12 and each girl got rs . 8 . what is the number of boys ? | 0general |
a shopkeeper sells 200 metres of cloth for rs . 18000 at a loss of rs . 5 per metre . find his cost price for one metre of cloth ? | 2gain |
find the total number of prime factors in the expression ( 4 ) ^ 11 x ( 7 ) ^ 5 x ( 11 ) ^ 2 . | 0general |
1235 1253 1325 . . . . . . . . . + 5321 the addition problem above shows 4 of the 24 different integers that can be formed by using each of the digits 12 , 35 exactly once in each integer . what is the sum of these 24 integers ? | 0general |
a glucose solution contains 15 grams of glucose per 100 cubic centimeters of solution . if 45 cubic centimeters of the solution were poured into an empty container , how many grams of glucose would be in the container ? | 1physics |
two trains of equal lengths take 5 sec and 15 sec respectively to cross a telegraph post . if the length of each train be 120 m , in what time will they cross other travelling in opposite direction ? | 1physics |
machine a and machine b are each used to manufacture 880 sprockets . it takes machine a 10 hours longer to produce 880 sprockets than machine b . machine b produces 10 % more sprockets per hour than machine a . how many sprockets per hour does machineaproduce ? | 2gain |
an empty fuel tank with a capacity of 204 gallons was filled partially with fuel a and then to capacity with fuel b . fuel a contains 12 % ethanol by volume and fuel b contains 16 % ethanol by volume . if the full fuel tank contains 30 gallons of ethanol , how many gallons of fuel a were added ? | 2gain |
what is the largest 4 digit number exactly divisible by 50 ? | 0general |
if teena is driving at 55 miles per hour and is currently 7.5 miles behind poe , who is driving at 40 miles per hour in the same direction then in how many minutes will teena be 15 miles ahead of poe ? | 1physics |
the compound interest earned on a sum for the second and the third years are $ 1400 and $ 1512 respectively . what is the rate of interest ? | 2gain |
in a division sum , the remainder is 6 and the divisor is 5 times the quotient and is obtained by adding 2 to the thrice of the remainder . the dividend is | 0general |
a number when divided by 44 , gives 432 as quotient and 0 as remainder . what will be the remainder when dividing the same number by 31 | 0general |
if $ 120 invested at a certain rate of simple interest amounts to $ 160 at the end of 3 years , how much will $ 150 amount to at the same rate of interest in 6 years ? | 2gain |
the population of a town increased from 1 , 33,400 to 1 , 93,500 in a decade . the average percent increase of population per year is : | 0general |
a person distributed 20 % of his income to his 3 children each . he deposited 30 % of his income to his wife ' s account . he donated 5 % of remaining amount to an orphan house . finally he has $ 60000 . find his total income ? | 2gain |
a = 5 ^ 15 - 625 ^ 3 and a / x is an integer , where x is a positive integer greater than 1 , such that it does not have a factor p such that 1 < p < x , then how many different values for x are possible ? | 0general |
a car takes 6 hours to cover a distance of 360 km . how much should the speed in kmph be maintained to cover the same direction in 3 / 2 th of the previous time ? | 1physics |
if 4 people are selected from a group of 7 married couples , what is the probability that none of them would be married to each other ? | 4probability |
a shopkeeper has 100 kg of apples . he sells 50 % of these at 25 % profit and remaining 50 % at 30 % profit . find his % profit on total . | 2gain |
a card game called “ high - low ” divides a deck of 52 playing cards into 2 types , “ high ” cards and “ low ” cards . there are an equal number of “ high ” cards and “ low ” cards in the deck and “ high ” cards are worth 2 points , while “ low ” cards are worth 1 point . if you draw cards one at a time , how many ways can you draw “ high ” and “ low ” cards to earn 6 points if you must draw exactly 4 “ low ” cards ? | 0general |
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