Problem stringlengths 5 967 | category class label 6
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how many different pairs of positive integers ( a , b ) satisfy the equation 1 / a + 1 / b = 34 / 51 ? | 0general |
a telephone company needs to create a set of 3 - digit area codes . the company is entitled to use only digits 2 , 4 and 8 , which can be repeated . if the product of the digits in the area code must be even , how many different codes can be created ? | 0general |
the average age of one class strength 32 students is 16 yrs . if the staff ' s age is also included , the average increases by one year . find the age of the staff | 0general |
the area of a rectangular plot is 460 square metres . if the length is 15 % more than the breadth , what is the breadth of the plot ? | 3geometry |
a man purchased 5 blankets @ rs . 100 each , 5 blankets @ rs . 150 each and two blankets at a certain rate which is now slipped off from his memory . but he remembers that the average price of the blankets was rs . 150 . find the unknown rate of two blankets ? | 0general |
working simultaneously and independently at an identical constant rate , 5 machines of a certain type can produce a total of x units of product p in 8 days . how many of these machines , working simultaneously and independently at this constant rate , can produce a total of 3 x units of product p in 4 days ? | 0general |
in a rectangular axis system , what is the area of a parallelogram with the coordinates : ( 2,2 ) , ( 8,2 ) , ( 3,5 ) , ( 9,5 ) ? | 3geometry |
on a saturday night , each of the rooms at a certain motel was rented for either $ 40 or $ 60 . if 10 of the rooms that were rented for $ 60 had instead been rented for $ 40 , then the total rent the motel charged for that night would have been reduced by 10 percent . what was the total rent the motel actually charged for that night ? | 2gain |
there is 60 lit of milk and water in which milk forms 84 % . howmuch water must be added to this solution to make it solution in which milk forms 50 % | 2gain |
jill invests $ 10000 in an account that pays an annual rate of 3.96 % , compounding semi - annually . approximately how much q does she have in her account after two years ? | 2gain |
machine p and machine q are each used to manufacture 440 sprockets . it takes machine p 10 hours longer to produce 440 sprockets than machine q . machine q produces 10 % more sprockets per hour than machine a . how many sprockets per hour does machine a produce ? | 2gain |
a retailer buys 100 pens at the market price of 36 pens from a wholesaler , if he sells these pens giving a discount of 1 % , what is the profit % ? | 2gain |
3 litre of water is added to 11 litre of a solution containing 42 % of alcohol in the water . the percentage of alcohol in the new mixture is ? | 0general |
from a pack of 52 cards , 1 card is drawn at random . what is the probability that a red card is drawn ? | 4probability |
a trader sells 85 meters of cloth for rs . 8925 at the profit of rs . 10 per metre of cloth . what is the cost price of one metre of cloth ? | 1physics |
a trailer carries 3 , 4 and 5 crates on a trip . each crate weighs no less than 120 kg . what is the maximum weight of the crates on a single trip ? | 0general |
a student completes a 3 part exam as follows . the student completes sections a in 24 minutes and takes an equal time to complete the two remaining sections . what is the ratio of time spent on section c to section a if the total duration is 1 hour ? | 1physics |
the average of first 3 prime numbers greater than 20 is ? | 0general |
a reduction of 44 % in the price of bananas would enable a man to obtain 64 more for rs . 40 , what is reduced price per dozen ? | 2gain |
if x and y are integers , what is the least positive number of 24 x + 16 y ? | 0general |
a certain company retirement plan has arule of 70 provision that allows an employee to retire when the employee ' s age plus years of employment with the company total at least 70 . in what year could a female employee hired in 1987 on her 32 nd birthday first be eligible to retire under this provision ? | 0general |
a cistern is filled by a tap in 3 1 / 2 hours . due to leak in the bottom of the cistern , it takes half an hour longer to fill the cistern . if the cistern is full how long will it take the leak to empty it ? | 1physics |
in the coordinate plane , points ( x , 1 ) and ( 10 , y ) are on line k . if line k passes through the origin and has slope 1 / 3 , then x + y = | 0general |
a 40 gallon solution of salt and water is 10 % salt . how many gallons of water must be added to the solution in order to decrease the salt to 8 % of the volume ? | 0general |
if 10 boys meet at a reunion and each boy shakes hands exactly once with each of the others , then what is the total number of handshakes | 0general |
6 x – 5 y + 3 z = 22 4 x + 8 y – 11 z = 7 5 x – 6 y + 2 z = 12 given the equations above , x + y + z = ? | 0general |
the output of a factory is increased by 10 % to keep up with rising demand . to handle the holiday rush , this new output is increased by 60 % . by approximately what percent would the output of the factory now have to be decreased in order to restore the original output ? | 0general |
car x began traveling at an average speed of 35 miles per hour . after 72 minutes , car y began traveling at an average speed of 38 miles per hour . when both cars had traveled the same distance , both cars stopped . how many miles did car x travel from the time car y began traveling until both cars stopped ? | 1physics |
a certain car ' s price decreased by 2.5 % ( from the original price ) each year from 1996 to 2002 , during that time the owner of the car invested in a new carburetor and a new audio system for the car , which increased car ' s price by $ 2,500 . if the price of the car in 1996 was $ 22,000 , what is the car ' s price in 2002 ? | 2gain |
jerry travels 8 miles at an average speed of 40 miles per hour , stops for 15 minutes , and then travels another 20 miles at an average speed of 60 miles per hour . what is jerry ’ s average speed , in miles per hour , for this trip ? | 1physics |
john makes $ 40 a week from his job . he earns a raise and now makes $ 60 a week . what is the % increase ? | 2gain |
- 69 * 39 + 450 = ? | 0general |
when n is divided by 24 , the remainder is 4 . what is the remainder when 3 n is divided by 8 ? | 0general |
two pipes a and b can separately fill a cistern in 45 minutes and 60 minutes respectively . there is a third pipe in the bottom of the cistern to empty it . if all the three pipes are simultaneously opened , then the cistern is full in 40 minutes . in how much time , the third pipe alone can empty the cistern ? | 1physics |
a car takes 6 hours to cover a distance of 450 km . how much should the speed in kmph be maintained to cover the same direction in 3 / 2 th of the previous time ? | 1physics |
a letter lock consists of 3 rings each marked with 6 different letters . the number of distinct unsuccessful attempts to open the lock is at the most - . | 4probability |
the ratio between the length and the breadth of a rectangular park is 3 : 2 . if a man cycling along the boundary of the park at the speed of 12 km / hr completes one round in 10 minutes , then the area of the park ( in sq . m ) is | 1physics |
average of money that group of 4 friends pay for rent each month is $ 800 . after one persons rent is increased by 16 % the new mean is $ 850 . what was original rent of friend whose rent is increased ? | 0general |
a person started from point a to point b and returned back to a with a speed of 60 kmh . if the distance between a and b is 120 km , calculate the time he travelled | 1physics |
a meeting has to be conducted with 5 managers . find the number of ways in which the managers may be selected from among 7 managers , if there are 2 managers who refuse to attend the meeting together . | 4probability |
ravi and sunil are partners in a business . ravi invests rs . 15,000 for 8 months and sunil invested rs . 8000 for 10 months then after one year ratio of their profits will be | 2gain |
on a saturday night , each of the rooms at a certain motel was rented for either $ 50 or $ 60 . if 10 of the rooms that were rented for $ 60 had instead been rented for $ 50 , then the total rent the motel charged for that night would have been reduced by 25 percent . what was the total rent the motel actually charged for that night ? | 2gain |
if price of t . v set is reduced by 10 % , then its sale increases by 85 % , find net effect on sale value | 2gain |
a retailer buys a radio for rs 225 . his overhead expenses are rs 20 . he sellis the radio for rs 300 . the profit percent of the retailer is | 2gain |
which number should replace both the asterisks in ( * / 18 ) x ( * / 162 ) = 1 ? | 0general |
anne bought doughnuts for a class breakfast party . she bought 5 chocolate doughnuts , 6 coconut doughnuts , and 11 jam - filled doughnuts . how many doughnuts did anne buy in all ? | 0general |
a certain music store stocks 800 cellos and 600 violas . of these instruments , there are 120 cello - viola pairs , such that a cello and a viola were both made with wood from the same tree ( each tree can make at most one viola and one cello , so there are no pairs other than these 90 ) . if one viola and one cello are chosen at random , what is the probability that the two instruments are made with wood from the same tree ? | 5other |
a man is walking at the rate of 10 km / hr crosses a bridge in 15 minutes . the length of the bridge is | 2gain |
826924 × 9999 = ? | 0general |
the megatek corporation is displaying its distribution of employees by department in a circle graph . the size of each sector of the graph representing a department is proportional to the percentage of total employees in that department . if the section of the circle graph representing the manufacturing department takes up 144 ° of the circle , what percentage of megatek employees are in manufacturing ? | 1physics |
a train speeds past a pole in 15 seconds and a platfrom 100 m long in 25 seconds . its length is : | 1physics |
gopi gives rs . 90 plus one turban as salary to his servant for one year . the servant leaves after 9 months and receives rs . 55 and the turban . find the price of the turban . | 0general |
in a ratio which is equal to 2 : 4 , if the antecedent is 50 , then the consequent is ? | 5other |
before leaving home for the town of madison , pete checks a map which shows that madison is 5 inches from his current location , gardensquare . pete arrives in madison 1.5 hours later and drove at an average speed of 60 miles per hour . at what scale , in inches per mile , is the map drawn ? | 1physics |
the average of 50 numbers is 38 . if two numbers 45 and 55 are discarded , the average of the remaining set of numbers is | 0general |
i bought two books ; for rs . 420 . i sold one at a loss of 15 % and other at a gain of 19 % and then i found each book was sold at the same price . find the cost of the book sold at a loss ? | 2gain |
the ratio of the ages of mini and minakshi is 4 : 3 . the sum of their ages is 28 years . the ratio of their ages after 6 years will be | 0general |
50 men took a dip in a water tank 40 m long and 20 m broad on a religious day . if the average displacement of water by a man is 5 m 3 , then the rise in the water level in the tank will be : | 1physics |
if the price of petrol increases by 20 , by how much must a user cut down his consumption so that his expenditure on petrol remains constant ? | 0general |
thirty percent of the women in a college class are science majors , and the non - science majors make up 60 % of the class . what percentage of the men are science majors if 40 % of the class are men ? | 2gain |
a cargo ship carrying 4 kinds of items , doohickies , geegaws , widgets , and yamyams , arrives at the port . each item weighs 2 , 11 , 5 , and 7 pounds , respectively , and each item is weighed as it is unloaded . if , in the middle of the unloading process , the product of the individual weights of the unloaded items equals 104 , 350400 pounds , how many widgets have been unloaded ? | 0general |
what is the sum of all the composite numbers up to 18 ? | 0general |
if 10,000 microns = 1 decimeter , and 1 , 000,000 angstroms = 1 decimeter , how many angstroms equal 1 micron ? | 0general |
this year , mbb consulting fired 5 % of its employees and left remaining employee salaries unchanged . sally , a first - year post - mba consultant , noticed that that the average ( arithmetic mean ) of employee salaries at mbb was 10 % more after the employee headcount reduction than before . the total salary pool allocated to employees after headcount reduction is what percent of that before the headcount reduction ? | 0general |
during a certain two - week period , 75 percent of the movies rented from a video store were comedies , and of the remaining movies rented , there were 2 / 3 times as many dramas as action movies . if no other movies were rented during that two - week period and there were a action movies rented , then how many comedies , in terms of a , were rented during that two - week period ? | 0general |
rs 60000 is divided into two parts one part is given to a person with 10 % interest and another part is given to a person with 20 % interest . at the end of first year he gets profit 7000 find money given by 10 % ? | 2gain |
in measuring the sides of a rectangle , one side is taken 5 % in excess , and the other 4 % in deficit . find the error percent in the area calculated from these measurements . | 3geometry |
a box contains 100 balls , numbered from 1 to 100 . if 3 balls are selected at random and with replacement from the box . if the 3 numbers on the balls selected contain two odd and one even . what is the probability g that the first ball picked up is odd numbered ? | 4probability |
a gardener wants to plant trees in his garden in such a way that the number of trees in each row should be the same . if there are 2 rows or 4 rows or 4 rows , then no tree will be left . find the least number of trees required | 0general |
bert left the house with n dollars . he spent 1 / 4 of this at the hardware store , then $ 9 at the dry cleaners , and then half of what was left at the grocery store . when he got home , he had $ 15 left in his pocket . what was the value of n ? | 0general |
a company has $ 329864 in its account . what is the least amount of money ( in whole number of dollars ) that it must add to the account if the money is paid evenly among 9 of its vendors ? | 0general |
an escalator moves towards the top level at the rate of 10 ft . sec and its length is 112 feet . if a person walks on the moving escalator at the rate of 4 feet per second towards the top level , how much time does he take to cover the entire length . | 2gain |
if - 2 / ( a - 6 ) = 4 / ( a + 4 ) , then a = ? | 0general |
what is the total surface area in square meters of a rectangular solid whose length is 5 meters , width is 4 meters , and depth is 1 meters ? | 3geometry |
in a group of ducks and cows , the total number of legs are 34 more than twice the no . of heads . find the total no . of buffaloes . | 0general |
what is the units digit of ( 7 ! * 6 ! + 6 ! * 4 ! ) / 2 ? | 0general |
in a division sum , the remainder is 0 . as student mistook the divisor by 12 instead of 21 and obtained 63 as quotient . what is the correct quotient ? | 0general |
a cube is painted red on all faces . it is then cut into 27 equal smaller cubes . how many v cubes are painted on only 2 faces ? | 3geometry |
a tank can supply water to a village for 30 days . if a leak at the bottom of the tank drains out 15 liters per day , the supply lasts for 20 days only . for how many days will the supply last if the leak drains out 20 liters per day ? | 1physics |
the volume of a sphere with radius r is ( 4 / 3 ) * pi * r ^ 3 and the surface area is 4 * pi * r ^ 3 . if a sperical balloon has a volume of 12348 pi cubic centimeters , what is hte surface area of the balloon in square centimeters ? | 3geometry |
a room of 2 m 40 cm long and 4 m 20 cm broad is to be paved with square tiles . find the least number of square tiles required to cover the floor . | 1physics |
how many times in a day , the hands of a clock are shows opposite directions ? | 1physics |
the difference between a positive proper fraction and its reciprocal is 9 / 20 . then the fraction is : | 0general |
a sum of money is to be distributed among a , b , c , d in the proportion of 6 : 3 : 5 : 4 . if c gets rs . 1000 more than d , what is b ' s share ? | 0general |
a sports equipment store sold ping pong rackets for a total of $ 686 . if the average ( arithmetic mean ) price of a pair of rackets is $ 9.8 , how many pairs were sold ? | 0general |
one woman and one man can build a wall together in four hours , but the woman would need the help of two girls in order to complete the same job in the same amount of time . if one man and one girl worked together , it would take them eight hours to build the wall . assuming that rates for men , women and girls remain constant , how many hours would it take one woman , one man , and one girl , working together , to build the wall ? | 1physics |
what is the least number to be subtracted from 1300 to make it a perfect square ? | 0general |
the average weight of 8 person ' s increases by 3.5 kg when a new person comes in place of one of them weighing 65 kg . what might be the weight of the new person ? | 0general |
the area of a square is 6400 sq cm . find the ratio of the breadth and the length of a rectangle whose length is thrice the side of the square and breadth is 30 cm less than the side of the square ? | 3geometry |
if xy > 0 , 1 / x + 1 / y = 15 , and 1 / xy = 5 , then ( x + y ) / 5 = ? | 0general |
a man complete a journey in 10 hours . he travels first half of the journey at the rate of 21 km / hr and second half at the rate of 26 km / hr . find the total journey in km . | 1physics |
a bookseller sells his books at a 10 % markup in price . if he sells a book for $ 11.00 , how much did he pay for it ? | 2gain |
there are 60 doors marked with numbers 1 to 60 . there are 60 individuals marked 1 to 60 . an operation on a door is defined as changing the status of the door from open to closed or vice versa . all the doors are closed to start with . one at a time , one randomly chosen individual goes and operates the doors . the individual however operates only those doors which are a multiple of the number he / she is carrying . for example , the individual marked with number 5 operates the doors marked with 5 , 10 , 15 , 20 , 25 , 30 , 35 , 40 , 45 , 50 , 55 , and 60 . if every individual in the group gets one turn , then how many doors are open at the end ? | 0general |
a train 220 m long is running with a speed of 59 kmph . in what time will it pass a man who is running at 7 kmph in the direction opposite to that in which the train is going ? | 1physics |
the perimeter of a triangle is 28 cm and the inradius of the triangle is 2.0 cm . what is the area of the triangle ? | 3geometry |
due to construction , the speed limit along an 9 - mile section of highway is reduced from 55 miles per hour to 20 miles per hour . approximately how many minutes more will it take to travel along this section of highway at the new speed limit than it would have taken at the old speed limit ? | 1physics |
the area of a triangle will be when a = 1 m , b = 2 m , c = 7 m , a , b , c being lengths of respective sides ? | 3geometry |
a train 125 m long takes 6 sec to cross a man walking at 5 kmph in a direction opposite to that of the train . find the speed of the train ? | 1physics |
what is the units digit of the expression 14 ^ 7 − 15 ^ 4 ? | 0general |
at what rate percent on simple interest will rs . 750 amount to rs . 1050 in 5 years ? | 2gain |
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