Problem stringlengths 5 967 | Rationale stringlengths 1 2.74k | options stringlengths 37 300 | correct stringclasses 5
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in a certain math department , students are required to enroll in either calculus or trigonometry , each of which is offered in beginner and advanced courses . the number of students enrolled in trigonometry is 50 % greater than the number of students enrolled in calculus , and 90 % of calculus students are enrolled in... | "let x be the number of students in calculus . then the number of students in trigonometry is 1.5 x the number of students on beginner calculus is 0.9 x the number of students in beginner trigonometry is 4 / 5 * ( 2.5 x ) - 0.9 x = 1.1 x the number of students in advanced trigonometry is 0.4 x the percentage in advance... | a ) 12 % , b ) 16 % , c ) 20 % , d ) 24 % , e ) 40 % | b | multiply(divide(subtract(multiply(add(add(multiply(50, const_2), 50), multiply(50, const_2)), divide(4, 5)), 90), add(add(multiply(50, const_2), 50), multiply(50, const_2))), multiply(50, const_2)) | divide(n2,n3)|multiply(n0,const_2)|add(n0,#1)|add(#2,#1)|multiply(#3,#0)|subtract(#4,n1)|divide(#5,#3)|multiply(#6,#1)| | gain |
a certain club has 10 members , including jarry . one of the 10 members is chosen at random to be the president , one of the remaining 9 members is to be chosen at random to be the secretary , and one of the remaining 8 members is to be chosen at random to be the treasurer . what is the probability that jarry will be e... | in order to become a secretary the person can not be chosen as a president . this can be done in 9 / 10 ways . then to become a secretary this person ' s probability is 1 / 9 probability to become a secretary = ( 9 / 10 * 1 / 9 ) = 1 / 10 similar concept for treasurer . probability of not president = 9 / 10 , probabili... | a ) 1 / 720 , b ) 1 / 80 , c ) 1 / 10 , d ) 1 / 9 , e ) 1 / 5 | e | subtract(const_1, add(divide(const_1, 10), multiply(multiply(divide(9, 10), divide(8, 9)), divide(subtract(8, const_1), 8)))) | divide(const_1,n0)|divide(n2,n0)|divide(n3,n2)|subtract(n3,const_1)|divide(#3,n3)|multiply(#1,#2)|multiply(#4,#5)|add(#0,#6)|subtract(const_1,#7) | probability |
two dice are thrown simultaneously . what is the probability of getting two numbers whose product is not an even ? | total number of cases = 6 * 6 = 36 favourable cases = [ ( 1,3 ) , ( 1,5 ) , ( 1,1 ) , ( 3,1 ) , ( 3,3 ) , ( 3,5 ) , ( 5,1 ) , ( 5,3 ) , ( 5,5 ) ] = 9 so probability = 9 / 36 = 1 / 4 answer is b | a ) 1 / 2 , b ) 1 / 4 , c ) 2 / 3 , d ) 2 / 5 , e ) 3 / 7 | b | multiply(divide(const_3, add(const_3, const_3)), divide(const_3, add(const_3, const_3))) | add(const_3,const_3)|divide(const_3,#0)|multiply(#1,#1) | probability |
the difference between a number and its two - fifth is 510 . what is 40 % of that number ? | "let the number be x . then , x - 2 / 5 x = 510 x = ( 510 * 5 ) / 3 = 850 40 % of 850 = 340 . answer : b" | a ) 342 , b ) 340 , c ) 344 , d ) 346 , e ) 348 | b | divide(multiply(510, add(const_4, const_1)), add(const_1, const_2)) | add(const_1,const_4)|add(const_1,const_2)|multiply(n0,#0)|divide(#2,#1)| | general |
a and b can do a piece of work in 9 days . with the help of c they finish the work in 5 days . c alone can do that piece of work in ? | "c = 1 / 5 – 1 / 9 = 4 / 45 = > 11.25 days answer : a" | a ) 11.25 days , b ) 19.5 days , c ) 17.5 days , d ) 16.5 days , e ) 18.5 days | a | inverse(subtract(5, divide(5, 9))) | divide(n1,n0)|subtract(n1,#0)|inverse(#1)| | physics |
if n is a positive integer and the product of all the integers from 1 to n , inclusive , is a multiple of 123 , what is the least possible value of n ? | 123 is 3 * 41 , so n needs to be at least 41 , so the answer is c . | a ) 37 , b ) 123 , c ) 41 , d ) 52 , e ) 87 | c | divide(123, const_2) | divide(n1,const_2)| | general |
the elevator in an 11 - story office building travels at the rate of one floor per 1 / 4 minute , which allows time for picking up and discharging passengers . at the main floor and at the top floor , the operator stops for 1 minute . how many complete trips will an operator make during a 4 - hour period ? | complete trip = 10 floors up and 10 floors down = 20 floors = 20 * 1 / 4 = 5 minutes plus 2 minutes = 7 minutes . 4 hour = 240 minutes . in 240 minutes operator can make 240 / 7 = 34 trips . answer : d . | a ) 88 , b ) 56 , c ) 42 , d ) 34 , e ) 64 | d | divide(multiply(4, const_60), add(add(multiply(add(subtract(11, 1), subtract(11, 1)), inverse(const_4)), 1), 1)) | inverse(const_4)|multiply(n2,const_60)|subtract(n0,n1)|add(#2,#2)|multiply(#3,#0)|add(n1,#4)|add(n1,#5)|divide(#1,#6) | physics |
johnny travels a total of one hour to and from school . on the way there he jogs at 5 miles per hour and on the return trip he gets picked up by the bus and returns home at 30 miles per hour . how far is it to the school ? | "answer : e ) 6.9 miles . average speed for round trip = 2 * a * b / ( a + b ) , where a , b are speeds so , average speed was = 2 * 5 * 30 / ( 5 + 30 ) = 6.9 m / hr the distance between schoolhome should be half of that . ie . 6.9 miles answer e" | a ) 2 miles , b ) 4 miles , c ) 4.8 miles , d ) 8 miles , e ) 6.9 miles | e | multiply(divide(const_1, add(divide(const_1, 5), divide(const_1, 30))), const_1_6) | divide(const_1,n0)|divide(const_1,n1)|add(#0,#1)|divide(const_1,#2)|multiply(#3,const_1_6)| | physics |
find the product of the localvalue and absolutevalue of 7 in 20768 ? | "local value of 7 = 7 x 100 = 700 place value of 7 = 7 there fore = 7 x 700 = 4900 c" | a ) 9200 , b ) 1100 , c ) 4900 , d ) 3200 , e ) 1600 | c | multiply(multiply(7, const_1000), 7) | multiply(n0,const_1000)|multiply(n0,#0)| | general |
a certain no . when divided by 35 leaves a remainder 25 , what is the remainder if the same no . be divided by 15 ? | "explanation : 35 + 25 = 60 / 15 = 4 ( remainder ) b" | a ) 2 , b ) 4 , c ) 7 , d ) 8 , e ) 9 | b | subtract(subtract(subtract(35, 25), const_4), const_2) | subtract(n0,n1)|subtract(#0,const_4)|subtract(#1,const_2)| | general |
you have a flashlight that takes 2 working batteries . you have 8 batteries but only 4 of them work . what is the fewest number of pairs you need to test to guarantee you can get the flashlight on ? | if you break the batteries into 3 groups : two groups of 3 and one group of 2 . by doing this you guarantee that one of the groups has 2 working batteries . both of the groups of 3 have 3 possible combinations of 2 batteries and the group of 2 only has 1 combination . so , 3 + 3 + 1 = 7 tries at most to find two workin... | a ) 5 , b ) 8 , c ) 7 , d ) 6 , e ) 4 | c | add(multiply(add(2, const_1), 2), const_1) | add(n0,const_1)|multiply(n0,#0)|add(#1,const_1) | physics |
a certain rectangular window is two times as long as it is wide . if its perimeter is 30 feet , what are its dimensions in terms of length by width ? | "2 x + 2 y = 30 x + y = 15 x + 2 x = 15 3 x = 15 x = 5 answer d" | a ) 12 by 2 , b ) 11 by 3 , c ) 10.5 by 3.5 , d ) 10 by 5 , e ) 9 by 3 | d | rectangle_area(30, const_4) | rectangle_area(n0,const_4)| | geometry |
the average mark of the students of a class in a particular exam is 80 . if 5 students whose average mark in that exam is 40 are excluded , the average mark of the remaining will be 90 . find the number of students who wrote the exam ? | "let the number of students who wrote the exam be x . total marks of students = 80 x . total marks of ( x - 5 ) students = 90 ( x - 5 ) 80 x - ( 5 * 40 ) = 90 ( x - 5 ) 250 = 10 x = > x = 25 answer : c" | a ) 22 , b ) 26 , c ) 25 , d ) 28 , e ) 12 | c | divide(subtract(multiply(90, 5), multiply(5, 40)), subtract(90, 80)) | multiply(n1,n3)|multiply(n1,n2)|subtract(n3,n0)|subtract(#0,#1)|divide(#3,#2)| | general |
in a certain alphabet , 16 letters contain a dot and a straight line . 30 letters contain a straight line but do not contain a dot . if that alphabet has 50 letters , all of which contain either a dot or a straight line or both , how many letters contain a dot but do not contain a straight line ? | "we are told that all of the letters contain either a dot or a straight line or both , which implies that there are no letters without a dot and a line ( no line / no dot box = 0 ) . first we find the total # of letters with lines : 16 + 30 = 46 ; next , we find the total # of letters without line : 50 - 46 = 4 ; final... | a ) 4 , b ) 8 , c ) 12 , d ) 16 , e ) 20 | a | subtract(50, add(16, 30)) | add(n0,n1)|subtract(n2,#0)| | other |
evaluate : 13 + sqrt ( - 4 + 5 ã — 3 ã · 3 ) = ? | "according to order of operations , inner brackets first where 5 x 3 ã · 3 is first calculated since it has a multiplication and a division . 5 ã — 3 ã · 3 = 15 ã · 3 = 5 hence 13 + sqrt ( - 4 + 5 ã — 3 ã · 3 ) = 13 + sqrt ( - 4 + 5 ) = 13 + sqrt ( 1 ) = 13 + 1 = 14 correct answer c ) 14" | a ) 12 , b ) 13 , c ) 14 , d ) 15 , e ) 16 | c | add(13, sqrt(subtract(divide(multiply(5, const_4.0), 3), 4))) | multiply(n3,n2)|divide(#0,n4)|subtract(#1,n1)|sqrt(#2)|add(n0,#3)| | general |
at what rate percent on simple interest will rs . 750 amount to rs . 1125 in 5 years ? | "375 = ( 750 * 5 * r ) / 100 r = 10 % . answer : b" | a ) 2 , b ) 10 , c ) 4 , d ) 5 , e ) 6 | b | multiply(divide(divide(subtract(1125, 750), 750), 5), const_100) | subtract(n1,n0)|divide(#0,n0)|divide(#1,n2)|multiply(#2,const_100)| | gain |
if two positive numbers are in the ratio 1 / 6 : 1 / 5 , then by what percent is the second number more than the first ? | "given ratio = 1 / 6 : 1 / 5 = 5 : 6 let first number be 5 x and the second number be 9 x . the second number is more than first number by 1 x . required percentage = x / 5 x * 100 = 20 % . answer : e" | a ) 70 % , b ) 90 % , c ) 60 % , d ) 50 % , e ) 20 % | e | multiply(divide(1, 5), const_100) | divide(n0,n3)|multiply(#0,const_100)| | general |
given two cylindrical containers - - a and b . cylinder a has a diameter of 12 meters and a height of 10 meters . cylinder b has a radius of 2 meters and a height of 4 meters . if cylinder a is filled to capacity with water , how many cylinder b will be filled to capacity with the content of cylinder a ? | calculate the volume of the larger cylinder and divide it by the volume of the smaller cylinder . volume of cylinder = π r 2 h cylinder a volume = 1130.97 cylinder b volume = 50.27 therefore the number of cylinders b that can be filled to capacity = 1130.97 / 50.27 = 22.5 answer is b only 22 cylinders b can be filled t... | ['a ) 23', 'b ) 22', 'c ) 21', 'd ) 25', 'e ) 24'] | b | divide(volume_cylinder(divide(12, 2), 10), volume_cylinder(2, 4)) | divide(n0,n2)|volume_cylinder(n2,n3)|volume_cylinder(#0,n1)|divide(#2,#1) | geometry |
a 3 by 4 rectangle is inscribed in circle . what is the circumference of the circle ? | "if a rectangle is inscribed in a circle , then the diagonal of the rectangle = diameter of the circle . in this case , diagonal = ( 9 + 16 ) ^ ( 1 / 2 ) = 5 hence the radius = 2.5 circumference = 2 π r = 2 π * 2.5 = 5 π correct option : c" | a ) 2.5 π , b ) 3 π , c ) 5 π , d ) 4 π , e ) 10 π | c | circumface(divide(sqrt(add(power(3, 4), power(4, 4))), 4)) | power(n0,n1)|power(n1,n1)|add(#0,#1)|sqrt(#2)|divide(#3,n1)|circumface(#4)| | geometry |
jerome anticipated that the webweb . com stock price would fall and sold all his webweb . com stocks for $ 5 per stock . he paid $ 10,000 tax on the revenue . a week later , jerome became convinced that the webweb . com stock price would rise , and he used the money that he had gotten from selling the webweb . com stoc... | "let the number of shares be x . 5 * x - 10000 ( money paid in taxes ) = 6 ( x - 6000 ) solving for x , we get the shares as 16000 . ans : ( option e )" | a ) 10,000 , b ) 11,600 , c ) 12,000 , d ) 14,000 , e ) 16,000 | e | add(5, 6) | add(n0,n2)| | gain |
a man bought 40 shares of rs . 60 at 5 discount , the rate of dividend being 12 % the rate of interest obtained is | "explanation : face value of a share = rs . 60 he bought each share at rs . 60 - rs . 5 = rs . 55 number of shares = 40 dividend = 12 % dividend per share = 60 × 12 × 100 = rs . 7 1 / 5 total dividend = ( 40 × 7 1 / 5 ) ie , he got a dividend of ( 40 × 7 1 / 5 ) for an investment of rs . ( 40 × 55 ) interest obtained =... | a ) 13.09 % , b ) 15.5 % , c ) 14 % , d ) 14.25 % , e ) 14.95 % | a | divide(multiply(multiply(40, 60), divide(12, const_100)), multiply(40, subtract(60, 5))) | divide(n3,const_100)|multiply(n0,n1)|subtract(n1,n2)|multiply(#0,#1)|multiply(n0,#2)|divide(#3,#4)| | gain |
what is the sum of 60 consecutive integers from - 30 inclusive , in a increasing order ? | from - 39 to - 1 - - > 30 nos . zero - - > 1 number from + 1 to + 29 - - > 29 nos . when we add up nos . from - 30 to + 29 sum will be - 30 for total 60 numbers . c is the answer . | a ) - 29 , b ) 29 , c ) - 30 , d ) 30 , e ) 60 | c | add(30, const_1) | add(n1,const_1) | general |
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 take... | answer : a 18 ° divided by 360 ° equals 0.05 , therefore the sector is equal to 5 % of the total | a ) 5 % , b ) 25 % , c ) 30 % , d ) 35 % , e ) 72 % | a | multiply(divide(18, divide(const_3600, const_10)), const_100) | divide(const_3600,const_10)|divide(n0,#0)|multiply(#1,const_100) | physics |
what is the remainder when 1201 × 1202 × 1203 × 1204 is divided by 6 ? | "the remainders when dividing each number by six are : 1 , 2 , 3 , and 4 . the product is 1 * 2 * 3 * 4 = 24 the remainder when dividing 24 by 6 is 0 . the answer is a ." | a ) 0 , b ) 1 , c ) 2 , d ) 3 , e ) 4 | a | reminder(multiply(1202, 1201), 1203) | multiply(n0,n1)|reminder(#0,n2)| | general |
find two numbers whose sum is 26 and whose product is 165 . | let the two numbers be a and b and use the sum and product to write two equations with two unknowns a + b = 26 and a b = 165 solve the first equation for b b = 26 - a substitute b in the equation a b = 165 by 26 - a a ( 26 - a ) = 165 write the above equation in standard form - a 2 + 26 a - 165 = 0 solve the above equa... | a ) 11 and 12 , b ) 11 and 13 , c ) 11 and 15 , d ) 11 and 16 , e ) 11 and 19 | c | subtract(multiply(subtract(multiply(add(add(const_10, const_1), const_4), 165), multiply(add(const_10, const_1), 165)), const_2), 165) | add(const_1,const_10)|add(#0,const_4)|multiply(n1,#0)|multiply(n1,#1)|subtract(#3,#2)|multiply(#4,const_2)|subtract(#5,n1) | general |
a river 7 m deep and 75 m wide is flowing at the rate of 4 kmph the amount of water that runs into the sea per minute is ? | "rate of water flow - 4 kmph - - 4000 / 60 - - 66.66 m / min depth of river - - 7 m width of river - - 75 m vol of water per min - - 66.66 * 7 * 75 - - - 34996.5 answer c" | a ) 54996.5 , b ) 32296.5 , c ) 34996.5 , d ) 34996.5 , e ) 31255.5 | c | divide(multiply(multiply(7, 75), multiply(4, const_1000)), multiply(const_1, const_60)) | multiply(n0,n1)|multiply(n2,const_1000)|multiply(const_1,const_60)|multiply(#0,#1)|divide(#3,#2)| | physics |
what is the largest 4 digit number exactly divisible by 24 ? | "largest 4 digit number = 9999 9999 ÷ 24 = 416 , remainder = 15 hence largest 4 digit number exactly divisible by 24 = 9999 - 15 = 9984 answer : e" | a ) 4676 , b ) 4678 , c ) 8888 , d ) 9504 , e ) 9984 | e | multiply(floor(divide(power(const_10, 4), 24)), 24) | power(const_10,n0)|divide(#0,n1)|floor(#1)|multiply(n1,#2)| | general |
a survey of n people in the town of eros found that 50 % of them preferred brand a . another survey of 110 people in the town of angie found that 60 % preferred brand a . in total , 55 % of all the people surveyed together preferred brand a . what is the total number of people surveyed ? | "it is simply a weighted average question . since the given average of 50 % and 60 % is 55 % ( right in the middle ) , it means the number of people surveyed in eros ( n ) is same as the number of people surveyed in angie . so n = 110 total = 110 + 110 = 220 answer ( e )" | a ) 50 , b ) 100 , c ) 150 , d ) 200 , e ) 220 | e | divide(subtract(multiply(110, divide(60, const_100)), multiply(110, divide(55, const_100))), subtract(divide(55, const_100), divide(50, const_100))) | divide(n2,const_100)|divide(n3,const_100)|divide(n0,const_100)|multiply(n1,#0)|multiply(n1,#1)|subtract(#1,#2)|subtract(#3,#4)|divide(#6,#5)| | general |
if k ^ 3 is divisible by 540 , what is the least possible value of integer k ? | "540 = 2 ^ 2 * 3 ^ 3 * 5 therefore k must include at least 2 * 3 * 5 = 30 . the answer is b ." | a ) 12 , b ) 30 , c ) 60 , d ) 90 , e ) 120 | b | divide(divide(540, const_2), const_2) | divide(n1,const_2)|divide(#0,const_2)| | general |
the average weight of 8 persons increases by 1.5 kg when a person weighting 65 kg is replaced by a new person . what could be the weight of the new person ? | "explanation : let the average weight of 8 persons be ‘ x ’ years and the age of the new person be ‘ y ’ years so , ( 8 x – 65 + y ) / 8 = x + 1.5 so , y = 77 kgs 65 + 8 x 1.5 = 77 kgs answer b" | a ) 67 kg , b ) 77 kg , c ) 87 kg , d ) 97 kg , e ) none of these | b | add(65, multiply(8, 1.5)) | multiply(n0,n1)|add(n2,#0)| | general |
what is the remainder when ( 71 ) ( 73 ) is divided by 8 ? | "( 71 ) ( 73 ) = ( 72 - 1 ) ( 72 + 1 ) = 72 ^ 2 - 1 which is 1 less than a multiple of 8 . then the remainder will be 7 . the answer is e ." | a ) 1 , b ) 2 , c ) 4 , d ) 5 , e ) 7 | e | reminder(multiply(73, 71), 8) | multiply(n0,n1)|reminder(#0,n2)| | general |
if the product of 8 integers is negative , at most how many of the integers can be negative ? | "the product of 8 integers is negative thus an odd number of integers need to be negative to have a negative product we are asked at most how many are required . so , the highest odd integer before 6 , i . e . 7 correct option : e" | a ) 2 , b ) 3 , c ) 4 , d ) 5 , e ) 7 | e | subtract(8, const_1) | subtract(n0,const_1)| | general |
shopkeeper rise price by 35 % and gives successive discount of 10 % and 15 % . what is overall % gain or loss ? | "let d initial price be 100 35 % rise now price = 135 / 100 * 100 = 135 10 % discount then price = 135 * 90 / 100 = 121.5 15 % discount then price = 121.5 * 85 / 100 = 103.275 so gain = 103.275 - 100 = 3.275 gain % = gain * 100 / cp = = > 3.275 * 100 / 100 = 3.275 % answer : c" | a ) 5.275 % , b ) 4.275 % , c ) 3.275 % , d ) 6.275 % , e ) 7.275 % | c | subtract(multiply(multiply(add(const_100, 35), divide(subtract(const_100, 10), const_100)), divide(subtract(const_100, 15), const_100)), const_100) | add(n0,const_100)|subtract(const_100,n2)|subtract(const_100,n1)|divide(#1,const_100)|divide(#2,const_100)|multiply(#0,#4)|multiply(#3,#5)|subtract(#6,const_100)| | gain |
in what ratio must tea at rs . 65 per kg be mixed with tea at rs . 70 per kg so that the mixture must be worth rs . 6 per kg ? | "required ratio = 500 : 500 = 1 : 1 answer a" | a ) 1 : 1 , b ) 3 : 2 , c ) 4 : 3 , d ) 5 : 3 , e ) none | a | divide(subtract(70, 6), subtract(6, 65)) | subtract(n1,n2)|subtract(n2,n0)|divide(#0,#1)| | other |
a briefcase has a number - lock system containing a combination of 3 digits ( each digit can be of numbers 0 to 8 ) . if the correct combination is unknown , how much maximum time would be required to open the bag if each “ trial ” of combination takes 3 seconds ? | explanation : maximum number of trials required = 9 * 9 * 9 = 729 . since for each combination trial , 3 seconds are required to open the briefcase is given as 3 * 729 = 2187 seconds = 36.45 minutes . answer : a | a ) 36.45 minutes , b ) 36.47 minutes , c ) 36.41 minutes , d ) 36.42 minutes , e ) 36.65 minutes | a | divide(multiply(multiply(multiply(add(8, const_1), add(8, const_1)), add(8, const_1)), 3), const_60) | add(n2,const_1)|multiply(#0,#0)|multiply(#0,#1)|multiply(n0,#2)|divide(#3,const_60) | general |
a driver just filled the car ' s gas tank with 27 liters of gasohol , a mixture consisting of 5 % ethanol and 95 % gasoline . if the car runs best on a mixture consisting of 10 % ethanol and 90 % gasoline , how many liters of ethanol must be added into the gas tank for the car to achieve optimum performance ? | let x be the number of liters of ethanol added to the gas tank . 0.05 ( 27 ) + x = 0.1 ( 27 + x ) 0.9 x = 2.7 - 1.35 = 1.35 x = 1.5 liters the answer is b . | a ) 1.2 , b ) 1.5 , c ) 1.8 , d ) 2.1 , e ) 2.4 | b | divide(multiply(27, 5), subtract(const_100, 10)) | multiply(n0,n1)|subtract(const_100,n3)|divide(#0,#1) | general |
if money is invested at r percent interest , compounded annually , the amount of investment will double in approximately 70 / r years . if pat ' s parents invested $ 8000 in a long term bond that pays 4 percent interest , compounded annually , what will be the approximate total amount of investment 36 years later , whe... | "since investment doubles in 70 / r years then for r = 4 it ' ll double in 70 / 4 = ~ 18 years ( we are not asked about the exact amount so such an approximation will do ) . thus in 36 years investment will double twice and become ( $ 8,000 * 2 ) * 2 = $ 32,000 ( after 18 years investment will become $ 8,000 * 2 = $ 16... | a ) $ 20000 , b ) $ 15000 , c ) $ 32000 , d ) $ 10000 , e ) $ 9000 | c | multiply(multiply(8000, const_2), const_2) | multiply(n1,const_2)|multiply(#0,const_2)| | general |
eddy and freddy start simultaneously from city a and they travel to city b and city c respectively . eddy takes 3 hours and freddy takes 4 hours to complete the journey . if the distance between city a and city b is 600 kms and city a and city c is 460 kms . what is the ratio of their average speed of travel ? ( eddy :... | "distance traveled by eddy = 600 km time taken by eddy = 3 hours average speed of eddy = 600 / 3 = 200 km / hour distance traveled by freddy = 460 km time taken by freddy = 4 hours average speed of freddy = 460 / 4 = 115 km / hour ratio of average speed of eddy to freddy = 200 / 115 = 40 / 23 answer e" | a ) 8 / 3 , b ) 3 / 8 , c ) 8 / 5 , d ) 5 / 8 , e ) 40 / 23 | e | divide(divide(600, 3), divide(460, 4)) | divide(n2,n0)|divide(n3,n1)|divide(#0,#1)| | physics |
in a division sum , the remainder is 0 . as student mistook the divisor by 12 instead of 21 and obtained 42 as quotient . what is the correct quotient ? | "12 * 42 = 504 504 % 21 = 24 answer : e" | a ) 0 , b ) 12 , c ) 13 , d ) 20 , e ) 24 | e | divide(multiply(12, 42), 21) | multiply(n1,n3)|divide(#0,n2)| | general |
in the x - y plane , there are 4 points ( 0,0 ) , ( 0,4 ) , ( 7,4 ) , and ( 7,0 ) . if these 4 points makes a rectangle , what is the probability that x + y < 4 ? | "the line y = - x + 4 intersects the rectangle and these three points of intersection ( 0,0 ) , ( 0,4 ) and ( 4,0 ) form a triangle . the points below the line y = - x + 4 satisfy x + y < 4 . the area of this triangle is ( 1 / 2 ) ( 4 ) ( 4 ) = 8 the area of the rectangle is 28 . p ( x + y < 4 ) = 8 / 28 = 2 / 7 the an... | a ) 2 / 3 , b ) 3 / 5 , c ) 2 / 7 , d ) 4 / 9 , e ) 7 / 10 | c | divide(divide(multiply(4, 4), const_2), multiply(4, add(const_1, 4))) | add(const_1,n0)|multiply(n0,n0)|divide(#1,const_2)|multiply(n0,#0)|divide(#2,#3)| | general |
the owner of a furniture shop charges his customer 60 % more than the cost price . if a customer paid rs . 1000 for a computer table , then what was the cost price of the computer table ? | "cp = sp * ( 100 / ( 100 + profit % ) ) = 1000 ( 100 / 160 ) = rs . 625 . answer : b" | a ) 750 , b ) 650 , c ) 625 , d ) 115 , e ) 400 | b | divide(1000, add(const_1, divide(60, const_100))) | divide(n0,const_100)|add(#0,const_1)|divide(n1,#1)| | gain |
one - third of 1206 is what percent of 200 ? | "answer let one - third of 1206 is n % of 200 . ∵ 1206 / 3 = ( n x 200 ) / 100 ∴ n = ( 402 x 100 ) / 200 = 201 correct option : b" | a ) 3 , b ) 201 , c ) 300 , d ) none of these , e ) can not be determined | b | multiply(const_100, divide(divide(1206, const_3), 200)) | divide(n0,const_3)|divide(#0,n1)|multiply(#1,const_100)| | gain |
machine p and machine q are each used to manufacture 660 sprockets . it takes machine p 10 hours longer to produce 660 sprockets than machine q . machine q produces 10 % more sprockets per hour than machine a . how many sprockets per hour does machine a produce ? | "p makes x sprockets per hour . then q makes 1.1 x sprockets per hour . 660 / x = 660 / 1.1 x + 10 1.1 ( 660 ) = 660 + 11 x 11 x = 66 x = 6 the answer is e ." | a ) 5 , b ) 15 , c ) 55 , d ) 95 , e ) 6 | e | divide(subtract(660, divide(660, add(divide(10, const_100), const_1))), 10) | divide(n1,const_100)|add(#0,const_1)|divide(n0,#1)|subtract(n0,#2)|divide(#3,n1)| | gain |
a train 280 m long is running at a speed of 54 km / hr . in what time will it pass a bridge 200 m long ? | "total length = 280 + 200 = 480 speed = 54 km / h = ( 54 * 5 ) / 18 = 15 / 1 m / s time = ( 480 * 1 ) / 15 = 32 sec . answer : a" | a ) 32 sec , b ) 42 sec , c ) 45 sec , d ) 18 sec , e ) 49 sec | a | divide(280, multiply(subtract(54, 200), const_0_2778)) | subtract(n1,n2)|multiply(#0,const_0_2778)|divide(n0,#1)| | physics |
a marketing survey of anytown found that the ratio of trucks to sedans to motorcycles was 3 : 7 : 2 , respectively . given that there are 10,500 sedans in anytown , how many motorcycles are there ? | "let the total number of trucks = 3 x total number of sedans = 7 x total number of motorcycles = 2 x total number of sedans = 10500 = > 7 x = 10500 = > x = 1500 total number of motorcycles = 2 x = 2 * 1500 = 3000 answer b" | a ) 1260 , b ) 3000 , c ) 3600 , d ) 4200 , e ) 5200 | b | multiply(divide(add(multiply(multiply(3, 3), const_1000), const_100), 7), 2) | multiply(n0,n0)|multiply(#0,const_1000)|add(#1,const_100)|divide(#2,n1)|multiply(n2,#3)| | other |
what is the sum of the 1 st 6 prime numbers greater than 10 ? | required numbers are = ( 11 + 13 + 17 + 19 + 23 + 29 ) = 112 note : 1 is not a prime number answer a | a ) 112 , b ) 111 , c ) 212 , d ) 115 , e ) 113 | a | add(add(add(add(add(add(1, 10), add(add(1, 10), const_2)), add(add(add(1, 10), const_2), const_4)), add(add(add(add(1, 10), const_2), const_4), const_2)), add(add(add(add(add(1, 10), const_2), const_4), const_2), const_4)), add(add(add(add(add(add(1, 10), const_2), const_4), const_2), const_4), 6)) | add(n0,n2)|add(#0,const_2)|add(#0,#1)|add(#1,const_4)|add(#2,#3)|add(#3,const_2)|add(#4,#5)|add(#5,const_4)|add(#6,#7)|add(n1,#7)|add(#8,#9) | general |
$ 8,000 is deposited in a savings account that pays 12 % annual interest compounded semiannually . to the nearest dollar , how much is in the account at the end of the year ? | "this is the case of semi - annual compoundingso , multiply time period by 2 and divide rate by 2 so , new time = 2 periods and new rate = 12 / 2 = 6 % now , ca = 8000 ( 1 + 6 / 100 ) ^ 2 = $ 8988.80 hence answer is c" | a ) $ 8288.55 , b ) $ 8985.10 , c ) $ 8988.80 , d ) $ 8977.14 , e ) $ 8964.95 | c | multiply(const_100, const_100) | multiply(const_100,const_100)| | gain |
a , b and c can do a piece of work in 9 days , 14 days and 28 days respectively . how long will they taken , if all the three work together ? | 1 / 9 + 1 / 14 + 1 / 28 = 55 / 252 = > 252 / 55 days = > 4.52 days answer : b | a ) 4.12 days , b ) 4.52 days , c ) 3.52 days , d ) 2.52 days , e ) 4.92 days | b | inverse(add(inverse(28), add(inverse(9), inverse(14)))) | inverse(n0)|inverse(n1)|inverse(n2)|add(#0,#1)|add(#3,#2)|inverse(#4) | physics |
in a division sum , the divisor is 12 times the quotient and 6 times the remainder . if the remainder is 24 , what is the divident ? | "solution : dividend = [ divisor * quotient ] + remainder - - - - > ( 1 ) . given divisor = 6 * 24 = 144 . 12 * quotient = 144 = > quotient = 144 / 12 = 12 . substitute these values in the ( 1 ) then we get 1752 as dividend . answer b" | a ) 1738 , b ) 1752 , c ) 1846 , d ) 1648 , e ) none | b | multiply(multiply(6, 24), divide(multiply(6, 24), 12)) | multiply(n1,n2)|divide(#0,n0)|multiply(#1,#0)| | general |
to be considered for “ movie of the year , ” a film must appear in at least 1 / 4 of the top - 10 - movies lists submitted by the cinematic academy ’ s 775 members . what is the smallest number of top - 10 lists a film can appear on and still be considered for “ movie of the year ” ? | "total movies submitted are 775 . as per question we need to take 1 / 4 of 775 to be considered for top 10 movies = 193.75 approximate the value we 194 . imo option b is the correct answer . . ." | a ) 191 , b ) 194 , c ) 193 , d ) 212 , e ) 213 | b | divide(775, 4) | divide(n3,n1)| | general |
a certain characteristic in a large population has a distribution that is symmetric about the mean a . if 68 % of the distribution lies one standard deviation d of the mean , what percent of the distribution is less than a + d ? | "16 % ________________________________________________ a + d 34 % ________________________________________________ a 34 % ________________________________________________ a - d 16 % since 68 % lies one standard deviation from mean a , = > 50 % of 68 % lies on either side as it is symmetric about a . thus 16 % lie below... | a ) 16 % , b ) 32 % , c ) 48 % , d ) 84 % , e ) 92 % | d | subtract(const_100, divide(subtract(const_100, 68), const_2)) | subtract(const_100,n0)|divide(#0,const_2)|subtract(const_100,#1)| | general |
if a / b = 1 / 3 , b / c = 2 , c / d = 1 / 2 , d / e = 3 and e / f = 1 / 8 , then what is the value of abc / def ? | "say a = 2 . then : a / b = 1 / 3 - - > b = 6 ; b / c = 2 - - > c = 3 ; c / d = 1 / 2 - - > d = 6 ; d / e = 3 - - > e = 2 ; e / f = 1 / 8 - - > f = 16 . abc / def = ( 2 * 6 * 3 ) / ( 6 * 2 * 16 ) = 3 / 16 . answer : d ." | a ) 27 / 4 , b ) 27 / 8 , c ) 3 / 4 , d ) 3 / 16 , e ) 1 / 4 | d | divide(multiply(3, 3), multiply(2, multiply(3, 8))) | multiply(n1,n1)|multiply(n1,n7)|multiply(n2,#1)|divide(#0,#2)| | general |
share rs . 4320 among john , jose & binoy in the ration 2 : 4 : 6 . find the amount received by john ? | "amount received by sanjay . 4 / 12 x 4320 = 1440 = ( related ratio / sum of ratio ) x total amount so , the amount received by sanjay is 1440 . e" | a ) 900 , b ) 980 , c ) 1200 , d ) 1240 , e ) 1440 | e | subtract(divide(4320, 2), divide(4320, 6)) | divide(n0,n1)|divide(n0,n3)|subtract(#0,#1)| | other |
a man rows his boat 78 km downstream and 56 km upstream , taking 4 hours each time . find the speed of the stream ? | "speed downstream = d / t = 78 / ( 4 ) = 20 kmph speed upstream = d / t = 56 / ( 4 ) = 14 kmph the speed of the stream = ( 20 - 14 ) / 2 = 3 kmph answer : e" | a ) 6 , b ) 5 , c ) 7 , d ) 8 , e ) 3 | e | divide(subtract(divide(78, 4), divide(56, 4)), const_2) | divide(n0,n2)|divide(n1,n2)|subtract(#0,#1)|divide(#2,const_2)| | physics |
tom purchased 8 kg of apples at the rate of 70 per kg and 9 kg of mangoes at the rate of 55 per kg . how much amount did he pay to the shopkeeper ? | "cost of 8 kg apples = 70 × 8 = 560 . cost of 9 kg of mangoes = 55 × 9 = 490 . total cost he has to pay = 560 + 490 = 1055 . c )" | a ) 1040 , b ) 1045 , c ) 1055 , d ) 1060 , e ) 1075 | c | add(multiply(8, 70), multiply(9, 55)) | multiply(n0,n1)|multiply(n2,n3)|add(#0,#1)| | gain |
a car traveling at a certain constant speed takes 10 seconds longer to travel 1 kilometer than it would take to travel 1 kilometer at 40 kilometers per hour . at what speed , in kilometers per hour , is the car traveling ? | "40 * t = 1 km = > t = 1 / 40 km / h v * ( t + 10 / 3600 ) = 1 v ( 1 / 40 + 10 / 3600 ) = 1 v ( 100 / 3600 ) = 1 v = 36 km / h the answer is c ." | a ) 35 , b ) 35.5 , c ) 36 , d ) 36.5 , e ) 37 | c | divide(1, divide(add(multiply(const_3600, divide(1, 40)), 10), const_3600)) | divide(n1,n3)|multiply(#0,const_3600)|add(n0,#1)|divide(#2,const_3600)|divide(n1,#3)| | physics |
a camera lens filter kit containing 5 filters sells for $ 87.50 . if the filters are purchased individually , 2 of them are priced at $ 16.45 each , 2 at $ 14.05 each , 1 at $ 19.50 . the amount saved by purchasing the kit is what percent of the total price of the 5 filters purchased individually ? | "cost of kit = $ 87.50 if filters are purchased individually - $ 16.45 * 2 + $ 14.05 * 2 + $ 19.50 = $ 80.50 amount saved = $ 87.50 - $ 80.50 = $ 7 required % age = ( $ 7 / $ 87.50 ) * 100 = 8 % so , the correct answer is b ." | a ) 7 % , b ) 8 % , c ) 9 % , d ) 10 % , e ) 11 % | b | divide(multiply(subtract(87.50, add(19.50, add(multiply(2, 16.45), multiply(2, 14.05)))), const_100), 87.50) | multiply(n2,n3)|multiply(n2,n5)|add(#0,#1)|add(n7,#2)|subtract(n1,#3)|multiply(#4,const_100)|divide(#5,n1)| | general |
a man swims downstream 30 km and upstream 18 km taking 3 hours each time , what is the speed of the man in still water ? | 30 - - - 3 ds = 10 ? - - - - 1 18 - - - - 3 us = 6 ? - - - - 1 m = ? m = ( 10 + 6 ) / 2 = 8 answer : b | a ) 3 , b ) 8 , c ) 9 , d ) 4 , e ) 2 | b | divide(add(divide(18, 3), divide(30, 3)), const_2) | divide(n1,n2)|divide(n0,n2)|add(#0,#1)|divide(#2,const_2) | physics |
if a speaks the truth 75 % of the times , b speaks the truth 60 % of the times . what is the probability that they tell the truth at the same time | "explanation : probability that a speaks truth is 75 / 100 = 0.75 probability that b speaks truth is 60 / 100 = 0.6 since both a and b are independent of each other so probability of a intersection b is p ( a ) × p ( b ) = 0.75 × 0.6 = 0.45 answer : c" | a ) 0.49 , b ) 0.48 , c ) 0.45 , d ) 0.482 , e ) 0.411 | c | multiply(divide(75, multiply(multiply(const_4, const_5), const_5)), divide(60, multiply(multiply(const_4, const_5), const_5))) | multiply(const_4,const_5)|multiply(#0,const_5)|divide(n0,#1)|divide(n1,#1)|multiply(#2,#3)| | gain |
what is the dividend . divisor 16 , the quotient is 9 and the remainder is 5 ? | "d = d * q + r d = 16 * 9 + 5 d = 144 + 5 d = 149 answer c" | a ) a ) 130 , b ) b ) 134 , c ) c ) 149 , d ) d ) 158 , e ) e ) 160 | c | add(multiply(16, 9), 5) | multiply(n0,n1)|add(n2,#0)| | general |
what is the positive difference between the sum of the squares of the first 3 positive integers and the sum of the prime numbers between the first square and fourth square ? | "forget conventional ways of solving math questions . in ps , ivy approach is the easiest and quickest way to find the answer . the sum of the squares of the first 4 positive integers = 1 ^ 2 + 2 ^ 2 + 3 ^ 2 = 14 the sum of the prime numbers between the first square ( = 1 ) and fourth square ( = 16 ) = 2 + 3 + 5 + 7 + ... | a ) 11 , b ) 12 , c ) 13 , d ) 24 , e ) 27 | e | subtract(add(add(add(add(add(const_1, power(const_2, const_2)), power(const_3, const_2)), power(const_4, const_2)), power(add(const_4, const_1), const_2)), power(3, const_2)), add(add(add(const_4, const_3), 3), add(add(add(add(const_2, const_3), add(const_4, const_1)), add(const_4, const_3)), add(add(const_2, const_3),... | add(const_1,const_4)|add(const_3,const_4)|add(const_2,const_3)|power(const_2,const_2)|power(const_3,const_2)|power(const_4,const_2)|power(n0,const_2)|add(#3,const_1)|add(n0,#1)|add(#2,#0)|add(n0,#2)|power(#0,const_2)|add(#7,#4)|add(#9,#1)|add(#12,#5)|add(#13,#10)|add(#14,#11)|add(#8,#15)|add(#16,#6)|subtract(#18,#17)| | general |
the charge for a single room at hotel p is 40 percent less than the charge for a single room at hotel r and 10 percent less than the charge for a single room at hotel g . the charge for a single room at hotel r is what percent greater than the charge for a single room at hotel g ? | "p = 0.6 r = 0.9 g r = 0.9 g / 0.6 = 1.5 * g thus r is 50 % greater than g . the answer is d ." | a ) 15 % , b ) 20 % , c ) 40 % , d ) 50 % , e ) e . 150 % | d | multiply(divide(subtract(const_100, multiply(divide(subtract(const_100, 40), subtract(const_100, 10)), const_100)), multiply(divide(subtract(const_100, 40), subtract(const_100, 10)), const_100)), const_100) | subtract(const_100,n0)|subtract(const_100,n1)|divide(#0,#1)|multiply(#2,const_100)|subtract(const_100,#3)|divide(#4,#3)|multiply(#5,const_100)| | gain |
sale of rs 6835 , rs . 9927 , rs . 6855 , rs . 7230 and rs . 6562 for 5 consecutive months . how much sale must he have in the sixth month so that he gets an average sale of rs , 6800 ? | "total sale for 5 months = rs . ( 6435 + 6927 + 6855 + 7230 + 6562 ) = rs . 34009 . required sale = rs . [ ( 6800 x 6 ) - 34009 ] = rs . ( 40800 - 34009 ) = rs . 6791 answer : b" | a ) 4966 , b ) 6791 , c ) 2877 , d ) 2676 , e ) 1881 | b | multiply(subtract(divide(add(add(add(add(6835, 9927), 6855), 7230), 6562), 5), 6800), 5) | add(n0,n1)|add(n2,#0)|add(n3,#1)|add(n4,#2)|divide(#3,n5)|subtract(#4,n6)|multiply(n5,#5)| | general |
in a group of cheerleaders , the group made of 10 males and 16 females . every cheerleader gets to choose between a coke or malt . the number of those that choose malt is double the number that chose coke , if all the 6 males choose malt , how many females chose malt ? | number of cheerleaders = 27 number of male = 10 number of female = 17 coke = 9 maly = 17 female who chose malt = 17 - 9 = 8 answer = c | a ) 30 , b ) 5 , c ) 8 , d ) 20 , e ) 10 | c | subtract(16, floor(divide(add(10, 16), add(const_2, const_1)))) | add(n0,n1)|add(const_1,const_2)|divide(#0,#1)|floor(#2)|subtract(n1,#3) | other |
if a certain number is divided by 5 , the quotient , dividend , and divisor , added together , will amount to 65 . what is the number ? | "let x = the number sought . then x / 5 + x + 5 = 65 . x = 50 . e" | a ) 18 , b ) 28 , c ) 48 , d ) 38 , e ) 50 | e | divide(multiply(subtract(65, 5), 5), add(5, const_1)) | add(n0,const_1)|subtract(n1,n0)|multiply(n0,#1)|divide(#2,#0)| | general |
if t = 5 / 9 * ( k - 32 ) , and if t = 105 , then what is the value of k ? | "k - 32 = 9 t / 5 k = 9 t / 5 + 32 k = 9 ( 105 ) / 5 + 32 = 221 the answer is e ." | a ) 209 , b ) 212 , c ) 215 , d ) 218 , e ) 221 | e | add(divide(multiply(105, 9), 5), 32) | multiply(n1,n3)|divide(#0,n0)|add(n2,#1)| | general |
a camera lens filter kit containing 5 filters sells for $ 57.50 . if the filters are purchased individually , 2 of them are priced at $ 10.45 each , 2 at $ 12.05 each , 1 at $ 17.50 . the amount saved by purchasing the kit is what percent of the total price of the 5 filters purchased individually ? | "cost of kit = $ 57.50 if filters are purchased individually - $ 10.45 * 2 + $ 12.05 * 2 + $ 17.50 = $ 62.50 amount saved = $ 62.50 - $ 57.50 = $ 5 required % age = ( $ 5 / $ 62.50 ) * 100 = 8 % so , the correct answer is b ." | a ) 7 % , b ) 8 % , c ) 8.5 % , d ) 10 % , e ) 11 % | b | divide(multiply(subtract(57.50, add(17.50, add(multiply(2, 10.45), multiply(2, 12.05)))), const_100), 57.50) | multiply(n2,n3)|multiply(n2,n5)|add(#0,#1)|add(n7,#2)|subtract(n1,#3)|multiply(#4,const_100)|divide(#5,n1)| | general |
there were two candidates in an election . winner candidate received 75 % of votes and won the election by 500 votes . find the number of votes casted to the winning candidate ? | "w = 75 % l = 25 % 75 % - 25 % = 50 % 50 % - - - - - - - - 500 75 % - - - - - - - - ? = > 750 answer : c" | a ) 228 , b ) 744 , c ) 750 , d ) 199 , e ) 231 | c | divide(multiply(divide(500, divide(subtract(75, subtract(const_100, 75)), const_100)), 75), const_100) | subtract(const_100,n0)|subtract(n0,#0)|divide(#1,const_100)|divide(n1,#2)|multiply(n0,#3)|divide(#4,const_100)| | gain |
if 170 ! / 10 ^ n is an integer , what is the largest possible value of n ? | "the question actually asks the highest power of 10 which divides 300 ! ( for a number to be an integer - without any remainder all the trailing zeroe ' s must be divided by the denominator ) 10 = 2 x 5 170 factorial will have 41 as - 170 / 5 = 34 34 / 5 = 6 6 / 5 = 1 so answer will be ( c ) 41" | a ) 47 , b ) 46 , c ) 41 , d ) 48 , e ) 45 | c | add(divide(divide(170, add(const_4, const_1)), add(const_4, const_1)), divide(170, add(const_4, const_1))) | add(const_1,const_4)|divide(n0,#0)|divide(#1,#0)|add(#2,#1)| | general |
the ratio of spinsters to cats is 2 to 7 . if there are 35 more cats than spinsters , how many spinsters are there ? | let 2 x be the number of spinsters . then 7 x is the number of cats . 7 x - 2 x = 35 x = 7 and the number of spinsters is 2 ( 7 ) = 14 . the answer is a . | a ) 14 , b ) 21 , c ) 28 , d ) 35 , e ) 42 | a | multiply(divide(35, subtract(7, 2)), 2) | subtract(n1,n0)|divide(n2,#0)|multiply(n0,#1) | other |
chris mixed 3 pounds of raisins with 3 pounds of nuts . if a pound of nuts costs 3 times as much as a pound of raisins , then the total cost of the raisins was what fraction of the total cost of the mixture ? | "1 lbs of raisin = $ 1 3 lbs of raisin = $ 3 1 lbs of nuts = $ 3 3 lbs of nuts = $ 9 total value of mixture = 9 + 3 = 12 fraction of the value of raisin = 3 / 12 = 1 / 4 ans : c" | a ) 1 / 7 , b ) 1 / 5 , c ) 1 / 4 , d ) 1 / 3 , e ) 3 / 7 | c | divide(3, add(multiply(3, 3), 3)) | multiply(n1,n2)|add(n0,#0)|divide(n0,#1)| | general |
in 2008 , the profits of company n were 10 percent of revenues . in 2009 , the revenues of company n fell by 20 percent , but profits were 9 percent of revenues . the profits in 2009 were what percent of the profits in 2008 ? | "x = profits r = revenue x / r = 0,1 x = 10 r = 100 2009 : r = 80 x / 80 = 0,09 = 9 / 100 x = 80 * 9 / 100 x = 7.2 7.2 / 10 = 0.72 = 72 % , answer b" | a ) 80 % , b ) 72 % , c ) 120 % , d ) 124.2 % , e ) 138 % | b | multiply(divide(multiply(9, subtract(const_1, divide(20, const_100))), 10), const_100) | divide(n3,const_100)|subtract(const_1,#0)|multiply(n4,#1)|divide(#2,n1)|multiply(#3,const_100)| | gain |
how many bricks , each measuring 25 cm x 11.25 cm x 6 cm , will be needed to build a wall of 4 m x 2 m x 25 cm ? | "number of bricks = volume of the wall / volume of 1 brick = ( 400 x 200 x 25 ) / ( 25 x 11.25 x 6 ) = 1185 . answer : option c" | a ) 5600 , b ) 6000 , c ) 1185 , d ) 7200 , e ) 8600 | c | divide(multiply(multiply(multiply(4, const_100), multiply(2, const_100)), 25), multiply(multiply(25, 11.25), 6)) | multiply(n3,const_100)|multiply(n4,const_100)|multiply(n0,n1)|multiply(#0,#1)|multiply(n2,#2)|multiply(n5,#3)|divide(#5,#4)| | physics |
a theater charges $ 12 for seats in the orchestra and $ 8 for seats in the balcony . on a certain night , a total of 370 tickets were sold for a total cost of $ 3320 . how many more tickets were sold that night for seats in the balcony than for seats in the orchestra ? | orchestra seats - a balcony seats - b a + b = 370 and 12 a + 8 b = 3320 solving equations simultaneously ( multiply equation 1 with 8 and subtract from second equation ) 4 a = 3320 - 8 * 370 = 3320 - 2960 = 360 i . e . a = 90 and b = 370 - 90 = 280 more seats in balcony than orchestra = b - a = 280 - 90 = 190 answer : ... | a ) 90 , b ) 190 , c ) 120 , d ) 130 , e ) 220 | b | subtract(subtract(370, divide(subtract(3320, multiply(8, 370)), subtract(12, 8))), divide(subtract(3320, multiply(8, 370)), subtract(12, 8))) | multiply(n1,n2)|subtract(n0,n1)|subtract(n3,#0)|divide(#2,#1)|subtract(n2,#3)|subtract(#4,#3) | general |
what is the sum of natural numbers between 40 and 100 | "a = first number l = last number sn = n / 2 [ a + l ] between 40 and 100 numbers = 61 = > 100 - 40 = 60 + 1 = 61 sn = 61 / 2 ã — 140 = 61 ã — 70 = 4270 answer : b" | a ) 4800 , b ) 4270 , c ) 5000 , d ) 5500 , e ) 5550 | b | add(100, const_1) | add(n1,const_1)| | general |
if 4 consecutive letters are selected at random from the english alphabet , then the probability that one of the letters is a vowel is ? | total no . of ways of selecting 4 consecutive letters = > 23 [ like abcd , bcde , efgh , . . etc ] no . of ways of having one is a vowel = > abcd , bcde , cdef , defg , efgh , fghi , ghij , hijk , ijkl , lmno , mnop , nopq , opqr , rstu , stuv , tuvw , uvwx . . . = 17 p ( one of letter is vowel ) = 17 / 23 answer : d | a ) 13 / 23 , b ) 16 / 23 , c ) 11 / 23 , d ) 17 / 23 , e ) 18 / 23 | d | subtract(const_1, divide(const_6, subtract(const_26, const_3))) | subtract(const_26,const_3)|divide(const_6,#0)|subtract(const_1,#1) | probability |
a man is 36 years older than his son . in three years , his age will be thrice the age of his son . the present age of this son is | "let ' s son age is x , then father age is x + 36 . = > 3 ( x + 3 ) = ( x + 36 + 3 ) = > 3 x + 9 = x + 39 = > 2 x = 30 years = 15 years answer : e" | a ) 28 years , b ) 22 years , c ) 18 years , d ) 16 years , e ) 15 years | e | divide(subtract(36, subtract(multiply(const_2, const_2), const_2)), subtract(const_2, const_1)) | multiply(const_2,const_2)|subtract(const_2,const_1)|subtract(#0,const_2)|subtract(n0,#2)|divide(#3,#1)| | general |
how much 60 % of 50 is greater than 50 % of 30 ? | "( 60 / 100 ) * 50 – ( 50 / 100 ) * 30 30 - 15 = 15 answer : e" | a ) 18 , b ) 91 , c ) 11 , d ) 17 , e ) 15 | e | subtract(divide(multiply(60, 50), const_100), divide(multiply(50, 30), const_100)) | multiply(n0,n1)|multiply(n2,n3)|divide(#0,const_100)|divide(#1,const_100)|subtract(#2,#3)| | gain |
a pair of articles was bought for $ 50 at a discount of 10 % . what must be the marked price of each of the article ? | "s . p . of each of the article = 50 / 2 = $ 25 let m . p = $ x 90 % of x = 25 x = 25 * . 9 = $ 22.50 answer is b" | a ) $ 25 , b ) $ 22.50 , c ) $ 29.65 , d ) $ 35.95 , e ) $ 45.62 | b | divide(multiply(subtract(const_100, 10), divide(50, const_2)), const_100) | divide(n0,const_2)|subtract(const_100,n1)|multiply(#0,#1)|divide(#2,const_100)| | gain |
a meal cost $ 37.25 adn there was no tax . if the tip was more than 10 pc but less than 15 pc of the price , then the total amount paid should be : | "10 % ( 37.25 ) = 3.725 15 % ( 37.25 ) = 5.5875 total amount could have been 37.25 + 3.725 and 37.25 + 5.5875 = > could have been between 40.975 and 42.8375 = > approximately between 41 and 43 answer is b ." | a ) 42 - 45 , b ) 41 - 43 , c ) 39 - 41 , d ) 37 - 39 , e ) 36 - 37 | b | add(divide(multiply(37.25, 10), const_100), 37.25) | multiply(n0,n1)|divide(#0,const_100)|add(n0,#1)| | general |
a train moves at average speed of 40 kmph reaches its destination on time . what its average speed becomes 35 kmph , then it reaches its destination 15 late . find the length of the journey ? | difference between timings = 15 mis = 1 / 4 hr let the length of the journey be x km . then x / 35 - x / 40 = 1 / 4 8 x - 7 x = 70 x = 70 km answer ( a ) | a ) 70 km , b ) 85 km , c ) 38 km , d ) 14 km , e ) 1 km | a | multiply(divide(divide(multiply(35, 15), subtract(40, 35)), const_60), 40) | multiply(n1,n2)|subtract(n0,n1)|divide(#0,#1)|divide(#2,const_60)|multiply(n0,#3) | physics |
evaluate 25 % of 450 + 45 % of 250 | "explanation : = ( 25 / 100 ) * 450 + ( 45 / 100 ) * 250 = 225 option a" | a ) 225 , b ) 242 , c ) 252 , d ) 262 , e ) 272 | a | divide(25, divide(450, 25)) | divide(n1,n0)|divide(n0,#0)| | gain |
if a lends rs . 3500 to b at 10 % p . a . and b lends the same sum to c at 11.5 % p . a . , then the gain of b ( in rs . ) in a period of 3 years is | explanation : we need to calculate the profit of b . it will be , si on the rate b lends - si on the rate b gets gain of b = 3500 × 11.5 × 3 / 100 − 3500 × 10 × 3 / 100 = 157.50 option d | a ) rs . 154.50 , b ) rs . 155.50 , c ) rs . 156.50 , d ) rs . 157.50 , e ) none of these | d | subtract(divide(multiply(multiply(3500, 11.5), 3), const_100), divide(multiply(multiply(3500, 10), 3), const_100)) | multiply(n0,n2)|multiply(n0,n1)|multiply(n3,#0)|multiply(n3,#1)|divide(#2,const_100)|divide(#3,const_100)|subtract(#4,#5) | gain |
at a certain high school , the senior class is twice the size of the junior class . if 1 / 8 of the seniors and 3 / 4 of the juniors study japanese , what fraction of the students in both classes study japanese ? | start by deciding on a number of students to represent the number of students in the senior class . for this example i will choose 200 students . that would make the number of students in the junior class 100 . then we can find out how many students are taking japanese in each grade and add them together . ( 1 / 8 ) * ... | a ) 3 / 8 , b ) 3 / 4 , c ) 1 / 3 , d ) 4 / 5 , e ) 1 / 2 | c | divide(4, add(8, 4)) | add(n1,n3)|divide(n3,#0) | general |
the length of each side of square a is increased by 100 percent to make square b . if the length of the side of square b is increased by 25 percent to make square c , by what percent is the area of square c greater than the sum of the areas of squares a and b ? | "let length of each side of square a be 10 area of a = 10 ^ 2 = 100 since , length of each side of square a is increased by 100 percent to make square b length of each side of square b = 2 * 10 = 20 area of b = 20 ^ 2 = 400 since , length of the side of square b is increased by 25 percent to make square c length of eac... | a ) 75 % , b ) 25 % , c ) 10 % , d ) 45 % , e ) 180 % | d | multiply(divide(subtract(subtract(square_area(add(add(const_1, divide(100, 100)), divide(multiply(add(const_1, divide(100, 100)), 25), 100))), const_1), const_4), add(const_1, square_area(add(const_1, divide(100, 100))))), 100) | divide(n0,n0)|add(#0,const_1)|multiply(n1,#1)|square_area(#1)|add(#3,const_1)|divide(#2,n0)|add(#1,#5)|square_area(#6)|subtract(#7,const_1)|subtract(#8,const_4)|divide(#9,#4)|multiply(n0,#10)| | geometry |
the sum of ages of 5 children born 3 years different each is 55 yrs . what is the age of the elder child ? | "let the ages of children be x , ( x + 3 ) , ( x + 6 ) , ( x + 9 ) and ( x + 12 ) years . then , x + ( x + 3 ) + ( x + 6 ) + ( x + 9 ) + ( x + 12 ) = 55 5 x = 25 x = 5 . x + 12 = 5 + 12 = 17 a" | a ) 17 , b ) 19 , c ) 16 , d ) 18 , e ) 21 | a | divide(add(add(add(add(3, const_4), add(3, const_4)), add(const_4, const_4)), 55), 5) | add(n1,const_4)|add(const_4,const_4)|add(#0,#0)|add(#2,#1)|add(n2,#3)|divide(#4,n0)| | general |
there are 7 girls and 3 chairs . in how many ways girls can occupy the chairs ? | "total girls = 7 total chairs = 3 1 st chair can be occupy in 7 ways 2 nd chair can be occupy in 6 ways 3 rd chair can be occupy in 5 ways total number of ways = 7 * 6 * 5 = 210 ways correct option is b" | a ) 760 , b ) 210 , c ) 560 , d ) 740 , e ) 800 | b | divide(7, 3) | divide(n0,n1)| | probability |
in a mixed college 160 students are there in one class . out of this 160 students 3 / 5 students are girls . how many boys are there ? | "total number of students : 160 total girls : 160 * 3 / 5 = 96 total boys : 160 - 96 = 64 answer is b" | a ) a ) 40 , b ) b ) 64 , c ) c ) 80 , d ) d ) 120 , e ) e ) 140 | b | multiply(divide(160, 5), const_3) | divide(n0,n3)|multiply(#0,const_3)| | general |
a train running at 7 / 11 of its own speed reached a place in 22 hours . how much time could be saved if the train would have run at its own speed ? | "new speed = 7 / 11 of usual speed new time = 11 / 7 of usual time 11 / 7 of usual time = 22 hrs usual time = 22 * 7 / 11 = 14 hrs time saved = 22 - 44 = 8 hrs answer is c" | a ) 4 hrs , b ) 6 hrs , c ) 8 hrs , d ) 9 hrs , e ) 11 hrs | c | multiply(divide(7, 11), 22) | divide(n0,n1)|multiply(n2,#0)| | physics |
a alone can finish a work in 10 days which b alone can finish in 15 days . if they work together and finish it , then out of a total wages of rs . 3300 , a will get : | "explanation : ratio of working days of a : b = 10 : 15 therefore , their wages ratio = reverse ratio = 15 : 10 therefore , a will get 15 units of ratio total ratio = 25 1 unit of ratio = 3000 / 25 = 132 so , a ’ s amount = 120 × 15 = rs . 1980 . answer : option c" | a ) rs . 1200 , b ) rs . 1500 , c ) rs . 1980 , d ) rs . 2000 , e ) none of these | c | multiply(divide(divide(multiply(15, const_2), 10), add(divide(multiply(15, const_2), 10), divide(multiply(15, const_2), 15))), 3300) | multiply(n1,const_2)|divide(#0,n0)|divide(#0,n1)|add(#1,#2)|divide(#1,#3)|multiply(n2,#4)| | physics |
a line that passes through ( – 2 , – 4 ) and ( 3 , k ) has a slope = k . what is the value of k ? | "slope = ( y 2 - y 1 ) / ( x 2 - x 1 ) = > k = ( k + 4 ) / ( 3 + 2 ) = > 5 k = k + 4 = > k = 1 ans b it is !" | a ) 3 / 4 , b ) 1 , c ) 4 / 3 , d ) 2 , e ) 7 / 2 | b | divide(4, 3) | divide(n1,n2)| | general |
a dishonest milkman wants to make a profit on the selling of milk . he would like to mix water ( costing nothing ) with milk costing rs . 33 per litre so as to make a profit of 30 % on cost when he sells the resulting milk and water mixture for rs . 36 in what ratio should he mix the water and milk ? | "water = w ( liter ) milk = m ( liter ) = = > cost = price x quantity = 0.33 m = = > revenue = price x quantity = 0.36 ( m + w ) = = > profit = 0.36 ( m + w ) - 0.33 m = 0.3 * ( 0.33 m ) [ 30 % of cost ] = = > 0.36 m + 0.36 w - 0.33 m = 0.099 m = = > 0.069 m = 0.36 w = = > m / w = 0.36 / 0.069 = 120 / 23 - - or - - w /... | a ) 1 : 20 , b ) 23 : 120 , c ) 1 : 8 , d ) 1 : 4 , e ) 6 : 11 | b | divide(const_1, divide(30, const_2)) | divide(n1,const_2)|divide(const_1,#0)| | gain |
carol is 5 times alice ’ s age but only twice as old as betty . alice is 12 years younger than carol . how old is betty ? | given that c = 5 a = 2 b . . and a = c - 12 = 5 a - 12 - - > 4 a = 12 - - > a = 3 substituting the values a = 3 , c = 15 and b = 6 . . ans a = 6 . . | a ) 6 , b ) 9 , c ) 12 , d ) 18 , e ) 24 | a | add(5, const_1) | add(n0,const_1) | general |
a cheese factory sells its cheese in rectangular blocks . a normal block has a volume of 5 cubic feet . if a large block has twice the width , twice the depth , and the same length of a normal block , what is the volume of cheese in a large block in cubic feet ? | "volume of cube = lbh = 5 new cube l , b , h are increases of l , 2 b , 2 h new volume of cube = l * 2 b * 2 h = 4 * lbh = 4 * 5 = 20 answer : c" | a ) 15 , b ) 30 , c ) 20 , d ) 18 , e ) 25 | c | multiply(multiply(multiply(const_2, const_2), const_2), 5) | multiply(const_2,const_2)|multiply(#0,const_2)|multiply(n0,#1)| | geometry |
in a box of 10 pens , a total of 2 are defective . if a customer buys 2 pens selected at random from the box , what is the probability that neither pen will be defective ? | "# defective pens = 2 # good pens = 8 probability of the 1 st pen being good = 8 / 10 probability of the 2 nd pen being good = 7 / 9 total probability = 8 / 10 * 7 / 9 = 28 / 45 the answer is d ." | a ) 7 / 12 , b ) 11 / 20 , c ) 17 / 30 , d ) 28 / 45 , e ) 51 / 90 | d | multiply(divide(subtract(10, 2), 10), divide(subtract(subtract(10, 2), const_1), subtract(10, const_1))) | subtract(n0,n1)|subtract(n0,const_1)|divide(#0,n0)|subtract(#0,const_1)|divide(#3,#1)|multiply(#2,#4)| | general |
if the sum of the 4 th term and the 12 th term of an arithmetic progression is 30 , what is the sum of the first 15 terms of the progression ? | 4 th term + 12 th term = 30 i . e . , ( a + 3 d ) + ( a + 11 d ) = 30 now , sum of first 15 terms = ( 15 / 2 ) * [ 2 a + ( 15 - 1 ) d ] = ( 15 / 2 ) * [ 2 a + 14 d ] = ( 15 / 2 ) * 30 - - - - - - - - - - - - - - - from ( 1 ) = 225 answer : d | a ) 250 , b ) 275 , c ) 260 , d ) 225 , e ) 230 | d | multiply(divide(15, const_2), 30) | divide(n3,const_2)|multiply(n2,#0) | general |
if x and y are numbers such that ( x + 5 ) ( y - 5 ) = 0 , what is the smallest possible value of x ^ 2 + y ^ 2 | "from ( x + 5 ) ( y - 5 ) = 0 it follows that either x = - 5 or y = 5 . thus either x ^ 2 = 25 or y ^ 2 = 25 . now , if x ^ 2 = 8125 , then the least value of y ^ 2 is 0 , so the least value of x ^ 2 + y ^ 2 = 25 + 0 = 25 . similarly if y ^ 2 = 25 , then the least value of x ^ 2 is 0 , so the least value of x ^ 2 + y ^... | a ) 0 , b ) 4 , c ) 9 , d ) 25 , e ) 16 | d | power(5, 2) | power(n0,n3)| | general |
find the value of ( 19 + 43 / 151 ) × 151 | "= ( 19 + 43 / 151 ) × 151 = ( 2869 + 43 ) / 151 × 151 = 2912 / 151 × 151 = 2912 answer is d ." | a ) 2924 , b ) 2916 , c ) 2614 , d ) 2912 , e ) 2215 | d | multiply(add(divide(43, 151), 19), 151) | divide(n1,n2)|add(n0,#0)|multiply(#1,n2)| | general |
the lcm of two numbers is 2310 and hcf is 61 . if one of the numbers is 210 . then what is the other number ? | "first number * second number = lcm * hcf other number = 2310 * 61 / 210 = 11 * 61 = 671 answer : b" | a ) 715 , b ) 671 , c ) 330 , d ) 582 , e ) 465 | b | divide(multiply(2310, 61), 210) | multiply(n0,n1)|divide(#0,n2)| | physics |
the c . p of 30 books is equal to the s . p of 40 books . find his gain % or loss % ? | "explanation : 30 cp = 40 sp 40 - - - 10 cp loss 100 - - - ? = > 25 % loss answer : c" | a ) 23 % , b ) 24 % , c ) 25 % , d ) 50 % , e ) 40 % | c | multiply(subtract(const_1, divide(30, 40)), const_100) | divide(n0,n1)|subtract(const_1,#0)|multiply(#1,const_100)| | gain |
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