options stringlengths 37 300 | correct stringclasses 5
values | annotated_formula stringlengths 7 727 | problem stringlengths 5 967 | rationale stringlengths 1 2.74k | program stringlengths 10 646 |
|---|---|---|---|---|---|
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)) | 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 the beginner course . if 4 / 5 of students are in the beginner courses , and one student is selected at random , what is the probability that an advanced trigonometry student is selected ? | "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 advanced trigonometry is 0.4 x / 2.5 x = 16 % the answer is b ." | a = 50 * 2
b = a + 50
c = 50 * 2
d = b + c
e = 4 / 5
f = d * e
g = f - 90
h = 50 * 2
i = h + 50
j = 50 * 2
k = i + j
l = g / k
m = 50 * 2
n = l * m
|
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)))) | 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 either the member chose to be secretary or the member chose to be treasurer ? | 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 , probability of not secretary = 8 / 9 , probability of treasurer 1 / 8 probability to become a treasurer = ( 9 / 10 * 8 / 9 * 1 / 8 ) = 1 / 10 since , the problem is saying jarry secretary or treasurer it is addition : 1 / 10 + 1 / 10 = 1 / 5 = e | a = 1 / 10
b = 9 / 10
c = 8 / 9
d = b * c
e = 8 - 1
f = e / 8
g = d * f
h = a + g
i = 1 - h
|
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))) | 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 = 3 + 3
b = 3 / a
c = 3 + 3
d = 3 / c
e = b * d
|
a ) 342 , b ) 340 , c ) 344 , d ) 346 , e ) 348 | b | divide(multiply(510, add(const_4, const_1)), add(const_1, const_2)) | 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 = 4 + 1
b = 510 * a
c = 1 + 2
d = b / c
|
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))) | 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 = 5 / 9
b = 5 - a
c = 1/(b)
|
a ) 37 , b ) 123 , c ) 41 , d ) 52 , e ) 87 | c | divide(123, const_2) | 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 = 123 / 2
|
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)) | 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 = 4 * const_60
b = 11 - 1
c = 11 - 1
d = b + c
e = 1/(4)
f = d * e
g = f + 1
h = g + 1
i = a / h
|
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) | 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 = 1 / 5
b = 1 / 30
c = a + b
d = 1 / c
e = d * const_1_6
|
a ) 9200 , b ) 1100 , c ) 4900 , d ) 3200 , e ) 1600 | c | multiply(multiply(7, const_1000), 7) | 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 = 7 * 1000
b = a * 7
|
a ) 2 , b ) 4 , c ) 7 , d ) 8 , e ) 9 | b | subtract(subtract(subtract(35, 25), const_4), const_2) | 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 = 35 - 25
b = a - 4
c = b - 2
|
a ) 5 , b ) 8 , c ) 7 , d ) 6 , e ) 4 | c | add(multiply(add(2, const_1), 2), const_1) | 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 working batteries . | a = 2 + 1
b = a * 2
c = b + 1
|
a ) 22 , b ) 26 , c ) 25 , d ) 28 , e ) 12 | c | divide(subtract(multiply(90, 5), multiply(5, 40)), subtract(90, 80)) | 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 = 90 * 5
b = 5 * 40
c = a - b
d = 90 - 80
e = c / d
|
a ) 4 , b ) 8 , c ) 12 , d ) 16 , e ) 20 | a | subtract(50, add(16, 30)) | 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 ; finally , we find the # of letters that contain a dot but do not contain a straight line : 4 - 0 = 4 . answer : a" | a = 16 + 30
b = 50 - a
|
a ) 12 , b ) 13 , c ) 14 , d ) 15 , e ) 16 | c | add(13, sqrt(subtract(divide(multiply(5, const_4.0), 3), 4))) | 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 = 5 * 4
b = a / 3
c = b - 4
d = math.sqrt(c)
e = 13 + d
|
a ) 2 , b ) 10 , c ) 4 , d ) 5 , e ) 6 | b | multiply(divide(divide(subtract(1125, 750), 750), 5), const_100) | 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 = 1125 - 750
b = a / 750
c = b / 5
d = c * 100
|
a ) 70 % , b ) 90 % , c ) 60 % , d ) 50 % , e ) 20 % | e | multiply(divide(1, 5), const_100) | 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 = 1 / 5
b = a * 100
|
['a ) 23', 'b ) 22', 'c ) 21', 'd ) 25', 'e ) 24'] | b | divide(volume_cylinder(divide(12, 2), 10), volume_cylinder(2, 4)) | 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 to capacity . | a = 12 / 2
b = volume_cylinder / (
|
a ) 10,000 , b ) 11,600 , c ) 12,000 , d ) 14,000 , e ) 16,000 | e | add(5, 6) | 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 stocks to purchase them again , this time at $ 6 per stock . if jerome ended up having 6000 webweb . com stocks fewer than the number he had before selling them , how many webweb . com stocks did he have originally ? | "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 = 5 + 6
|
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))) | 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 = 40 × 7 1 / 5 × 100 / 40 × 55 = 13.09 % answer : option a" | a = 40 * 60
b = 12 / 100
c = a * b
d = 60 - 5
e = 40 * d
f = c / e
|
a ) - 29 , b ) 29 , c ) - 30 , d ) 30 , e ) 60 | c | add(30, const_1) | 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 = 30 + 1
|
a ) 5 % , b ) 25 % , c ) 30 % , d ) 35 % , e ) 72 % | a | multiply(divide(18, divide(const_3600, const_10)), const_100) | 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 18 ° of the circle , what percentage of megatek employees are in manufacturing ? | answer : a 18 ° divided by 360 ° equals 0.05 , therefore the sector is equal to 5 % of the total | a = 3600 / 10
b = 18 / a
c = b * 100
|
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) | 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 equation for a a = 11 and a = 15 . use b = 26 - a to find b when a = 11 , b = 15 and when a = 15 , b = 11 . the two numbers are 11 and 15 . answer c | a = 10 + 1
b = a + 4
c = b * 165
d = 10 + 1
e = d * 165
f = c - e
g = f * 2
h = g - 165
|
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)) | 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 = 7 * 75
b = 4 * 1000
c = a * b
d = 1 * const_60
e = c / d
|
a ) 4676 , b ) 4678 , c ) 8888 , d ) 9504 , e ) 9984 | e | multiply(floor(divide(power(const_10, 4), 24)), 24) | 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 = 10 ** 4
b = a / 24
c = math.floor(b)
d = c * 24
|
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))) | 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 = 60 / 100
b = 110 * a
c = 55 / 100
d = 110 * c
e = b - d
f = 55 / 100
g = 50 / 100
h = f - g
i = e / h
|
a ) 12 , b ) 30 , c ) 60 , d ) 90 , e ) 120 | b | divide(divide(540, const_2), const_2) | 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 = 540 / 2
b = a / 2
|
a ) 67 kg , b ) 77 kg , c ) 87 kg , d ) 97 kg , e ) none of these | b | add(65, multiply(8, 1.5)) | 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 = 8 * 1
b = 65 + a
|
a ) 2 , b ) 3 , c ) 4 , d ) 5 , e ) 7 | e | subtract(8, const_1) | 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 = 8 - 1
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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) | 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 = 100 + 35
b = 100 - 10
c = b / 100
d = a * c
e = 100 - 15
f = e / 100
g = d * f
h = g - 100
|
a ) 1 : 1 , b ) 3 : 2 , c ) 4 : 3 , d ) 5 : 3 , e ) none | a | divide(subtract(70, 6), subtract(6, 65)) | 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 = 70 - 6
b = 6 - 65
c = a / b
|
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) | 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 = 8 + 1
b = 8 + 1
c = a * b
d = 8 + 1
e = c * d
f = e * 3
g = f / const_60
|
a ) 1.2 , b ) 1.5 , c ) 1.8 , d ) 2.1 , e ) 2.4 | b | divide(multiply(27, 5), subtract(const_100, 10)) | 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 = 27 * 5
b = 100 - 10
c = a / b
|
a ) $ 20000 , b ) $ 15000 , c ) $ 32000 , d ) $ 10000 , e ) $ 9000 | c | multiply(multiply(8000, const_2), const_2) | 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 , when pat is ready for college ? | "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 = $ 16,000 and in another 18 years it ' ll become $ 16,000 * 2 = $ 32,000 ) . answer : c ." | a = 8000 * 2
b = a * 2
|
a ) 8 / 3 , b ) 3 / 8 , c ) 8 / 5 , d ) 5 / 8 , e ) 40 / 23 | e | divide(divide(600, 3), divide(460, 4)) | 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 : freddy ) | "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 = 600 / 3
b = 460 / 4
c = a / b
|
a ) 0 , b ) 12 , c ) 13 , d ) 20 , e ) 24 | e | divide(multiply(12, 42), 21) | 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 = 12 * 42
b = a / 21
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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))) | 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 answer is c ." | a = 4 * 4
b = a / 2
c = 1 + 4
d = 4 * c
e = b / d
|
a ) 750 , b ) 650 , c ) 625 , d ) 115 , e ) 400 | b | divide(1000, add(const_1, divide(60, const_100))) | 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 = 60 / 100
b = 1 + a
c = 1000 / 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)) | 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 = 1206 / 3
b = a / 200
c = 100 * b
|
a ) 5 , b ) 15 , c ) 55 , d ) 95 , e ) 6 | e | divide(subtract(660, divide(660, add(divide(10, const_100), const_1))), 10) | 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 = 10 / 100
b = a + 1
c = 660 / b
d = 660 - c
e = d / 10
|
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)) | 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 = 54 - 200
b = a * const_0_2778
c = 280 / 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) | 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 = 3 * 3
b = a * 1000
c = b + 100
d = c / 7
e = d * 2
|
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)) | 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 = 1 + 10
b = 1 + 10
c = b + 2
d = a + c
e = 1 + 10
f = e + 2
g = f + 4
h = d + g
i = 1 + 10
j = i + 2
k = j + 4
l = k + 2
m = h + l
n = 1 + 10
o = n + 2
p = o + 4
q = p + 2
r = q + 4
s = m + r
t = 1 + 10
u = t + 2
v = u + 4
w = v + 2
x = w + 4
y = x + 6
z = s + y
|
a ) $ 8288.55 , b ) $ 8985.10 , c ) $ 8988.80 , d ) $ 8977.14 , e ) $ 8964.95 | c | multiply(const_100, const_100) | $ 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 = 100 * 100
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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)))) | 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 = 1/(28)
b = 1/(9)
c = 1/(14)
d = b + c
e = a + d
f = 1/(e)
|
a ) 1738 , b ) 1752 , c ) 1846 , d ) 1648 , e ) none | b | multiply(multiply(6, 24), divide(multiply(6, 24), 12)) | 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 = 6 * 24
b = 6 * 24
c = b / 12
d = a * c
|
a ) 191 , b ) 194 , c ) 193 , d ) 212 , e ) 213 | b | divide(775, 4) | 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 = 775 / 4
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a ) 16 % , b ) 32 % , c ) 48 % , d ) 84 % , e ) 92 % | d | subtract(const_100, divide(subtract(const_100, 68), const_2)) | 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 - d and 16 % lie above a + d now below a + d = 16 + 34 + 34 = 84 % hence d" | a = 100 - 68
b = a / 2
c = 100 - b
|
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))) | 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 = 3 * 3
b = 3 * 8
c = 2 * b
d = a / c
|
a ) 900 , b ) 980 , c ) 1200 , d ) 1240 , e ) 1440 | e | subtract(divide(4320, 2), divide(4320, 6)) | 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 = 4320 / 2
b = 4320 / 6
c = a - b
|
a ) 6 , b ) 5 , c ) 7 , d ) 8 , e ) 3 | e | divide(subtract(divide(78, 4), divide(56, 4)), const_2) | 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 = 78 / 4
b = 56 / 4
c = a - b
d = c / 2
|
a ) 1040 , b ) 1045 , c ) 1055 , d ) 1060 , e ) 1075 | c | add(multiply(8, 70), multiply(9, 55)) | 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 = 8 * 70
b = 9 * 55
c = a + b
|
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)) | 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 = 1 / 40
b = 3600 * a
c = b + 10
d = c / 3600
e = 1 / d
|
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) | 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 = 2 * 16
b = 2 * 14
c = a + b
d = 19 + 50
e = 87 - 50
f = e * 100
g = f / 87
|
a ) 3 , b ) 8 , c ) 9 , d ) 4 , e ) 2 | b | divide(add(divide(18, 3), divide(30, 3)), const_2) | 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 = 18 / 3
b = 30 / 3
c = a + b
d = c / 2
|
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))) | 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 = 4 * 5
b = a * 5
c = 75 / b
d = 4 * 5
e = d * 5
f = 60 / e
g = c * f
|
a ) a ) 130 , b ) b ) 134 , c ) c ) 149 , d ) d ) 158 , e ) e ) 160 | c | add(multiply(16, 9), 5) | 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 = 16 * 9
b = a + 5
|
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), 3)))) | 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 + 11 + 13 = 41 . so the difference between 41 and 14 is 27 . so the answer is ( e ) ." | a = 2 ** 2
b = 1 + a
c = 3 ** 2
d = b + c
e = 4 ** 2
f = d + e
g = 4 + 1
h = g ** 2
i = f + h
j = 3 ** 2
k = i + j
l = 4 + 3
m = l + 3
n = 2 + 3
o = 4 + 1
p = n + o
q = 4 + 3
r = p + q
s = 2 + 3
t = s + 3
u = r + t
v = m + u
w = k - v
|
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) | 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 = 100 - 40
b = 100 - 10
c = a / b
d = c * 100
e = 100 - d
f = 100 - 40
g = 100 - 10
h = f / g
i = h * 100
j = e / i
k = j * 100
|
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) | 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 = 6835 + 9927
b = a + 6855
c = b + 7230
d = c + 6562
e = d / 5
f = e - 6800
g = f * 5
|
a ) 30 , b ) 5 , c ) 8 , d ) 20 , e ) 10 | c | subtract(16, floor(divide(add(10, 16), add(const_2, const_1)))) | 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 = 10 + 16
b = 2 + 1
c = a / b
d = math.floor(c)
e = 16 - d
|
a ) 18 , b ) 28 , c ) 48 , d ) 38 , e ) 50 | e | divide(multiply(subtract(65, 5), 5), add(5, const_1)) | 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 = 65 - 5
b = a * 5
c = 5 + 1
d = b / c
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a ) 209 , b ) 212 , c ) 215 , d ) 218 , e ) 221 | e | add(divide(multiply(105, 9), 5), 32) | 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 = 105 * 9
b = a / 5
c = b + 32
|
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) | 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 = 2 * 10
b = 2 * 12
c = a + b
d = 17 + 50
e = 57 - 50
f = e * 100
g = f / 57
|
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) | 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 = 100 - 75
b = 75 - a
c = b / 100
d = 500 / c
e = d * 75
f = e / 100
|
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))) | 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 = 4 + 1
b = 170 / a
c = 4 + 1
d = b / c
e = 4 + 1
f = 170 / e
g = d + f
|
a ) 14 , b ) 21 , c ) 28 , d ) 35 , e ) 42 | a | multiply(divide(35, subtract(7, 2)), 2) | 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 = 7 - 2
b = 35 / a
c = b * 2
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a ) 1 / 7 , b ) 1 / 5 , c ) 1 / 4 , d ) 1 / 3 , e ) 3 / 7 | c | divide(3, add(multiply(3, 3), 3)) | 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 = 3 * 3
b = a + 3
c = 3 / 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) | 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 = 20 / 100
b = 1 - a
c = 9 * b
d = c / 10
e = d * 100
|
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)) | 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 = 4 * 100
b = 2 * 100
c = a * b
d = c * 25
e = 25 * 11
f = e * 6
g = d / f
|
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))) | 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 : option b | a = 8 * 370
b = 3320 - a
c = 12 - 8
d = b / c
e = 370 - d
f = 8 * 370
g = 3320 - f
h = 12 - 8
i = g / h
j = e - i
|
a ) 4800 , b ) 4270 , c ) 5000 , d ) 5500 , e ) 5550 | b | add(100, const_1) | 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 = 100 + 1
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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))) | 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 = const_26 - 3
b = 6 / a
c = 1 - b
|
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)) | 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 = 2 * 2
b = a - 2
c = 36 - b
d = 2 - 1
e = c / d
|
a ) 18 , b ) 91 , c ) 11 , d ) 17 , e ) 15 | e | subtract(divide(multiply(60, 50), const_100), divide(multiply(50, 30), const_100)) | how much 60 % of 50 is greater than 50 % of 30 ? | "( 60 / 100 ) * 50 – ( 50 / 100 ) * 30 30 - 15 = 15 answer : e" | a = 60 * 50
b = a / 100
c = 50 * 30
d = c / 100
e = b - d
|
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) | 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 = 100 - 10
b = 50 / 2
c = a * b
d = c / 100
|
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) | 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 = 37 * 25
b = a / 100
c = b + 37
|
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) | 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 = 35 * 15
b = 40 - 35
c = a / b
d = c / const_60
e = d * 40
|
a ) 225 , b ) 242 , c ) 252 , d ) 262 , e ) 272 | a | divide(25, divide(450, 25)) | evaluate 25 % of 450 + 45 % of 250 | "explanation : = ( 25 / 100 ) * 450 + ( 45 / 100 ) * 250 = 225 option a" | a = 450 / 25
b = 25 / a
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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)) | 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 = 3500 * 11
b = a * 3
c = b / 100
d = 3500 * 10
e = d * 3
f = e / 100
g = c - f
|
a ) 3 / 8 , b ) 3 / 4 , c ) 1 / 3 , d ) 4 / 5 , e ) 1 / 2 | c | divide(4, add(8, 4)) | 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 ) * 200 = 25 and ( 3 / 4 ) * 100 = 75 . 25 + 75 = 100 . there are a total of 300 students in the junior class and senior class combined ( 100 + 200 = 300 ) , and there are 100 total students in japanese , so 100 students in japanese / 300 total students equals 1 / 3 of the students in both classes that study japanese . answer : c | a = 8 + 4
b = 4 / a
|
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) | 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 each side of square c = 1.25 * 20 = 25 area of c = 25 ^ 2 = 625 difference in areas of c and cummulative areas of a and b = 625 - ( 400 + 100 ) = 225 percent is the area of square c greater than the sum of the areas of squares a and b = ( 225 / 500 ) * 100 % = 45 % answer d" | a = 100 / 100
b = 1 + a
c = 100 / 100
d = 1 + c
e = d * 25
f = e / 100
g = b + f
h = square_area - (
i = h - 1
j = i / 4
k = 100 / 100
l = 1 + k
m = 1 + square_area
n = j * m
|
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) | 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 = 3 + 4
b = 3 + 4
c = a + b
d = 4 + 4
e = c + d
f = e + 55
g = f / 5
|
a ) 760 , b ) 210 , c ) 560 , d ) 740 , e ) 800 | b | divide(7, 3) | 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 = 7 / 3
|
a ) a ) 40 , b ) b ) 64 , c ) c ) 80 , d ) d ) 120 , e ) e ) 140 | b | multiply(divide(160, 5), const_3) | 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 = 160 / 5
b = a * 3
|
a ) 4 hrs , b ) 6 hrs , c ) 8 hrs , d ) 9 hrs , e ) 11 hrs | c | multiply(divide(7, 11), 22) | 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 = 7 / 11
b = a * 22
|
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) | 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 = 15 * 2
b = a / 10
c = 15 * 2
d = c / 10
e = 15 * 2
f = e / 15
g = d + f
h = b / g
i = h * 3300
|
a ) 3 / 4 , b ) 1 , c ) 4 / 3 , d ) 2 , e ) 7 / 2 | b | divide(4, 3) | 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 = 4 / 3
|
a ) 1 : 20 , b ) 23 : 120 , c ) 1 : 8 , d ) 1 : 4 , e ) 6 : 11 | b | divide(const_1, divide(30, const_2)) | 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 / m = 23 / 120 b is correct ." | a = 30 / 2
b = 1 / a
|
a ) 6 , b ) 9 , c ) 12 , d ) 18 , e ) 24 | a | add(5, const_1) | 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 = 5 + 1
|
a ) 15 , b ) 30 , c ) 20 , d ) 18 , e ) 25 | c | multiply(multiply(multiply(const_2, const_2), const_2), 5) | 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 = 2 * 2
b = a * 2
c = b * 5
|
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))) | 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 = 10 - 2
b = a / 10
c = 10 - 2
d = c - 1
e = 10 - 1
f = d / e
g = b * f
|
a ) 250 , b ) 275 , c ) 260 , d ) 225 , e ) 230 | d | multiply(divide(15, const_2), 30) | 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 = 15 / 2
b = a * 30
|
a ) 0 , b ) 4 , c ) 9 , d ) 25 , e ) 16 | d | power(5, 2) | 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 ^ 2 = 0 + 25 = 25 . answer : d ." | a = 5 ** 2
|
a ) 2924 , b ) 2916 , c ) 2614 , d ) 2912 , e ) 2215 | d | multiply(add(divide(43, 151), 19), 151) | find the value of ( 19 + 43 / 151 ) × 151 | "= ( 19 + 43 / 151 ) × 151 = ( 2869 + 43 ) / 151 × 151 = 2912 / 151 × 151 = 2912 answer is d ." | a = 43 / 151
b = a + 19
c = b * 151
|
a ) 715 , b ) 671 , c ) 330 , d ) 582 , e ) 465 | b | divide(multiply(2310, 61), 210) | 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 = 2310 * 61
b = a / 210
|
a ) 23 % , b ) 24 % , c ) 25 % , d ) 50 % , e ) 40 % | c | multiply(subtract(const_1, divide(30, 40)), const_100) | 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 = 30 / 40
b = 1 - a
c = b * 100
|
a ) 15 , b ) 6 , c ) 7 , d ) 9 , e ) 5 | a | divide(280, multiply(add(60, 6), const_0_2778)) | a train 280 m long is running with a speed of 60 km / hr . in what time will it pass a man who is running at 6 km / hr in the direction opposite to that in which the train is going ? | "speed of train relative to man = 60 + 6 = 66 km / hr . = 66 * 5 / 18 = 55 / 3 m / sec . time taken to pass the men = 280 * 3 / 55 = 15 sec . answer : a" | a = 60 + 6
b = a * const_0_2778
c = 280 / b
|
a ) rs . 223.20 , b ) rs . 323.20 , c ) rs . 423.20 , d ) rs . 523.20 , e ) none of these | a | multiply(divide(30, const_100), add(multiply(25, 12), add(multiply(const_2, multiply(25, 6)), multiply(multiply(12, 6), const_2)))) | a tank is 25 m long 12 m wide and 6 m deep . the cost of plastering its walls and bottom at 30 paise per sq m is | "explanation : area to be plastered = [ 2 ( l + b ) ã — h ] + ( l ã — b ) = [ 2 ( 25 + 12 ) ã — 6 ] + ( 25 ã — 12 ) = 744 sq m cost of plastering = 744 ã — ( 30 / 100 ) = rs . 223.20 answer : a" | a = 30 / 100
b = 25 * 12
c = 25 * 6
d = 2 * c
e = 12 * 6
f = e * 2
g = d + f
h = b + g
i = a * h
|
a ) 6 / 7 , b ) 3 / 10 , c ) 3 / 18 , d ) 3 / 16 , e ) 3 / 11 | a | divide(add(multiply(divide(subtract(8, 2), subtract(6, 3)), 5), 2), add(multiply(6, divide(subtract(8, 2), subtract(6, 3))), 2)) | 3 men and 8 women complete a task in same time as 6 men and 2 women do . how much fraction of work will be finished in same time if 5 men and 2 women will do that task . | "3 m + 8 w = 6 m + 2 w 3 m = 6 w 1 m = 2 w therefore 3 m + 8 w = 14 w 5 m + 2 w = 12 w answer is 12 / 14 = 6 / 7 answer : a" | a = 8 - 2
b = 6 - 3
c = a / b
d = c * 5
e = d + 2
f = 8 - 2
g = 6 - 3
h = f / g
i = 6 * h
j = i + 2
k = e / j
|
a ) 500 , b ) 698 , c ) 780 , d ) 910 , e ) 725 | e | subtract(824, divide(multiply(subtract(854, 824), 3), 4)) | a sum of money at simple interest amounts to rs . 824 in 3 years and to rs . 854 in 4 years . the sum is : | "sol . s . i . for 1 year = rs . ( 854 - 824 ) = rs . 30 . s . i . for 3 years = rs . ( 30 * 3 ) = rs . 90 . â ˆ ´ principal = rs . ( 815 - 90 ) = rs . 725 answer e" | a = 854 - 824
b = a * 3
c = b / 4
d = 824 - c
|
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