Problem stringlengths 5 967 | Rationale stringlengths 1 2.74k | options stringlengths 37 300 | correct stringclasses 5
values | annotated_formula stringlengths 7 6.48k | linear_formula stringlengths 8 925 | category stringclasses 6
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there are 79 people that own pets . 15 people own only dogs , 10 people own only cats , 5 people own only cats and dogs , 3 people own cats , dogs and snakes . how many total snakes are there ? | lets assign variables to all the areas in venn diagram of three . three different units are dog , cat , snake = total = 79 only dog = d = 15 only cat = c = 10 only snake = s exactly dog and cat = 5 exactly dog and snake = x exactly cat and snake = y all three = 3 so 79 = 15 + 10 + 5 + 3 + x + y + s we need to know tota... | a ) 2 , b ) 4 , c ) 8 , d ) 49 , e ) 32 | d | add(subtract(79, add(add(add(15, 10), 5), 3)), 3) | add(n1,n2)|add(n3,#0)|add(n4,#1)|subtract(n0,#2)|add(n4,#3) | general |
a man traveled a total distance of 900 km . he traveled one - third of the whole trip by plane and the distance traveled by train is two - thirds of the distance traveled by bus . if he traveled by train , plane and bus , how many kilometers did he travel by bus ? | "total distance traveled = 900 km . distance traveled by plane = 300 km . distance traveled by bus = x distance traveled by train = 2 x / 3 x + 2 x / 3 + 300 = 900 5 x / 3 = 600 x = 360 km the answer is d ." | a ) 240 , b ) 280 , c ) 320 , d ) 360 , e ) 400 | d | divide(multiply(divide(multiply(900, const_2), const_3), const_3), add(const_2, const_3)) | add(const_2,const_3)|multiply(n0,const_2)|divide(#1,const_3)|multiply(#2,const_3)|divide(#3,#0)| | physics |
the cash difference between the selling prices of an article at a profit of 2 % and 6 % is rs . 3 . the ratio of the two selling prices is ? | "let c . p . of the article be rs . x . then , required ratio = 102 % of x / 106 % of x = 102 / 106 = 51 / 53 = 51 : 53 answer : e" | a ) 52 : 56 , b ) 52 : 53 , c ) 52 : 50 , d ) 22 : 56 , e ) 51 : 53 | e | divide(add(const_100, 2), add(const_100, 6)) | add(n0,const_100)|add(n1,const_100)|divide(#0,#1)| | gain |
in an it company , there are a total of 60 employees including 50 programmers . the number of male employees is 80 , including 35 male programmers . how many employees must be selected to guaranty that we have 3 programmers of the same sex ? | "you could pick 10 non - programmers , 2 male programmers , and 2 female programmers , and still not have 3 programmers of the same sex . but if you pick one more person , you must either pick a male or a female programmer , so the answer is 15 . a" | a ) 15 , b ) 50 , c ) 55 , d ) 35 , e ) 65 | a | add(subtract(80, 60), subtract(50, 35)) | subtract(n2,n0)|subtract(n1,n3)|add(#0,#1)| | general |
machine a takes 20 hours to complete a certain job and starts that job at 6 am . after four hour of working alone , machine a is joined by machine b and together they complete the job at 1 pm . how long would it have taken machine b to complete the job if it had worked alone for the entire job ? | "let us assume total job = 100 units a finishes 100 units in 20 hrs ( given ) hence a ( working rate ) = 5 units / hr now given that a works for 4 hr ( so 20 units done ) then a and b finish total work in 7 hours . hence a and b finish 80 units in 3 hours . of these 3 x 5 = 15 units were done by a . hence b did 65 unit... | a ) 9.99 , b ) 3,615 , c ) 3.62 , d ) 4.62 , e ) 6.14 | d | inverse(subtract(divide(subtract(const_1, multiply(inverse(20), const_2)), subtract(subtract(multiply(1, const_2), 6), const_2)), inverse(20))) | inverse(n0)|multiply(n2,const_2)|multiply(#0,const_2)|subtract(#1,n1)|subtract(const_1,#2)|subtract(#3,const_2)|divide(#4,#5)|subtract(#6,#0)|inverse(#7)| | physics |
two pipes can fill the cistern in 10 hr and 12 hr respectively , while the third empty it in 15 hr . if all pipes are opened simultaneously , then the cistern will be filled in | "solution : work done by all the tanks working together in 1 hour . 1 / 10 + 1 / 12 − 1 / 15 = 7 / 60 hence , tank will be filled in 60 / 7 = 8.57 hour option ( c )" | a ) 7.5 hr , b ) 8 hr , c ) 8.57 hr , d ) 10 hr , e ) none of these | c | inverse(subtract(add(divide(const_1, 10), divide(const_1, 12)), divide(const_1, 15))) | divide(const_1,n0)|divide(const_1,n1)|divide(const_1,n2)|add(#0,#1)|subtract(#3,#2)|inverse(#4)| | physics |
to fill a tank , 100 buckets of water is required . how many buckets of water will be required to fill the same tank if the capacity of the bucket is reduced to four - fifth of its present ? | "let the capacity of 1 bucket = x . then , the capacity of tank = 100 x . new capacity of bucket = 4 / 5 x therefore , required number of buckets = ( 100 x ) / ( 4 x / 5 ) = ( 100 x ) x 5 / 4 x = 500 / 4 = 125 answer is b ." | a ) 100 , b ) 125 , c ) 150 , d ) 175 , e ) 200 | b | divide(multiply(100, add(const_4, const_1)), const_2) | add(const_1,const_4)|multiply(n0,#0)|divide(#1,const_2)| | physics |
in what time will a railway train 65 m long moving at the rate of 32 kmph pass a telegraph post on its way ? | "t = 65 / 32 * 18 / 5 = 7 sec answer : e" | a ) 3 sec , b ) 4 sec , c ) 5 sec , d ) 6 sec , e ) 7 sec | e | divide(65, multiply(32, const_0_2778)) | multiply(n1,const_0_2778)|divide(n0,#0)| | physics |
a rectangular grass field is 75 m * 55 m , it has a path of 2.8 m wide all round it on the outside . find the area of the path and the cost of constructing it at rs . 2 per sq m ? | "area = ( l + b + 2 d ) 2 d = ( 75 + 55 + 2.8 * 2 ) 2 * 2.8 = > 759.4 759.4 * 2 = rs . 1518.8 answer : a" | a ) s . 1518.8 , b ) s . 1327 , c ) s . 1328 , d ) s . 1397 , e ) s . 1927 | a | multiply(subtract(rectangle_area(add(75, multiply(2.8, 2)), add(55, multiply(2.8, 2))), rectangle_area(75, 55)), 2) | multiply(n2,n3)|rectangle_area(n0,n1)|add(n0,#0)|add(n1,#0)|rectangle_area(#2,#3)|subtract(#4,#1)|multiply(n3,#5)| | geometry |
the rational number for recurring decimal 0.125125 . . . . is : | 0.125125 . . . = 0.125 = 125 / 999 answer is b . | a ) 125 / 990 , b ) 125 / 999 , c ) 125 / 900 , d ) 12 / 999 , e ) 12 / 990 | b | divide(floor(multiply(0.125125, const_1000)), multiply(multiply(add(multiply(add(const_1, const_10), const_10), const_1), const_3), const_3)) | add(const_1,const_10)|multiply(n0,const_1000)|floor(#1)|multiply(#0,const_10)|add(#3,const_1)|multiply(#4,const_3)|multiply(#5,const_3)|divide(#2,#6) | other |
if n is a natural number , then ( 7 ( n 2 ) + 7 n ) is always divisible by : | "solution ( 7 n 2 + 7 n ) = 7 n ( n + 1 ) , which is always divisible by 7 and 14 both , since n ( n + 1 ) is always even . answer d" | a ) 3 and 7 , b ) 14 only , c ) 7 only , d ) 7 and 14 , e ) none | d | add(multiply(7, const_100), multiply(2, 7)) | multiply(n0,const_100)|multiply(n0,n1)|add(#0,#1)| | general |
how many of the positive divisors of 360 are also multiples of 4 not including 360 ? | "360 = 2 ^ 5 * 3 * 5 = ( 4 ) * 2 * 3 ^ 2 * 5 besides ( 4 ) , the exponents of 2 , 3 , and 5 are 1 , 2 , and 1 . there are ( 1 + 1 ) ( 2 + 1 ) ( 1 + 1 ) = 12 ways to make multiples of 4 . we must subtract 1 because one of these multiples is 360 . the answer is b ." | a ) 8 , b ) 11 , c ) 12 , d ) 15 , e ) 16 | b | divide(divide(divide(360, 4), const_2), const_3) | divide(n0,n1)|divide(#0,const_2)|divide(#1,const_3)| | general |
3 candidates in an election and received 1136 , 8236 and 11628 votes respectively . what % of the total votes did the winning candidate gotin that election ? | "total number of votes polled = ( 1136 + 8236 + 11628 ) = 21000 so , required percentage = 11628 / 21000 * 100 = 55.4 % b" | a ) 40 % , b ) 55.4 % , c ) 57 % , d ) 60 % , e ) 62 % | b | multiply(divide(11628, add(add(1136, 8236), 11628)), const_100) | add(n1,n2)|add(n3,#0)|divide(n3,#1)|multiply(#2,const_100)| | gain |
if 12 men or 20 women can do a piece of work in 81 days , then in how many days can 9 men and 12 women together do the work ? | "d 60 days given that 12 m = 20 w = > 3 m = 5 w 9 men + 12 women = 15 women + 12 women = 27 women 20 women can do the work in 81 days . so , 27 women can do it in ( 20 * 81 ) / 27 = 60 days ." | a ) 10 days , b ) 30 days , c ) 20 days , d ) 60 days , e ) 40 days | d | inverse(add(divide(9, multiply(12, 81)), divide(12, multiply(20, 81)))) | multiply(n0,n2)|multiply(n1,n2)|divide(n3,#0)|divide(n4,#1)|add(#2,#3)|inverse(#4)| | physics |
increasing the original price of an article by 15 percent and then increasing the new price by 15 percent is equivalent to increasing the original price by | "you can do this by approximation , or with straight math by calculating 100 * 1.15 ^ 2 . or step by step : if you increase 100 by 15 % you ' ll get 115 , then if you increase 115 = 100 + 15 by 15 % again , 100 will gain 15 again and 15 will gain its 15 % which is 2.25 , so total gain is 15 + 2.25 = 17.25 - - > 115 + 1... | a ) 32.25 % , b ) 31.00 % , c ) 30.25 % , d ) 30.00 % , e ) 22.50 % | a | multiply(const_100, subtract(multiply(add(const_1, divide(15, const_100)), add(const_1, divide(15, const_100))), const_1)) | divide(n0,const_100)|add(#0,const_1)|multiply(#1,#1)|subtract(#2,const_1)|multiply(#3,const_100)| | gain |
a merchant purchased a jacket for $ 48 and then determined a selling price that equalled the purchase price of the jacket plus a markup that was 40 percent of the selling price . during a sale , the merchant discounted the selling price by 20 percent and sold the jacket . what was the merchant ’ s gross profit on this ... | "actual cost = $ 48 sp = actual cost + mark up = actual cost + 40 % sp = 48 * 100 / 60 on sale sp = 80 / 100 ( 48 * 100 / 60 ) = 64 gross profit = $ 16 answer is e" | a ) $ 0 , b ) $ 3 , c ) $ 4 , d ) $ 12 , e ) $ 16 | e | subtract(multiply(divide(48, subtract(const_1, divide(40, const_100))), subtract(const_1, divide(20, const_100))), 48) | divide(n1,const_100)|divide(n2,const_100)|subtract(const_1,#0)|subtract(const_1,#1)|divide(n0,#2)|multiply(#4,#3)|subtract(#5,n0)| | gain |
pascal has 96 miles remaining to complete his cycling trip . if he reduced his current speed by 4 miles per hour , the remainder of the trip would take him 16 hours longer than it would if he increased his speed by 50 % . what is his current speed o ? | let the current speed be x miles per hour . time taken if speed is 50 % faster ( i . e . 3 x / 2 = 1.5 x ) = 96 / 1.5 x time taken if speed is reduced by 4 miles / hr ( i . e . ( x - 4 ) ) = 96 / ( x - 4 ) as per question , 96 / ( x - 4 ) - 96 / 1.5 x = 16 solving this o we get x = 8 . b . | a ) 6 , b ) 8 , c ) 10 , d ) 12 , e ) 16 | b | divide(add(divide(96, 16), sqrt(add(multiply(multiply(divide(divide(96, 16), add(const_1, divide(50, const_100))), 4), const_4), power(divide(96, 16), const_2)))), const_2) | divide(n0,n2)|divide(n3,const_100)|add(#1,const_1)|power(#0,const_2)|divide(#0,#2)|multiply(n1,#4)|multiply(#5,const_4)|add(#6,#3)|sqrt(#7)|add(#0,#8)|divide(#9,const_2) | physics |
in the standard formulation of a flavored drink the ratio by volume of flavoring to corn syrup to water is 1 : 12 : 30 . in the sport formulation , the ratio of flavoring to corn syrup is three times as great as in the standard formulation , and the ratio of flavoring to water is half that of the standard formulation .... | "f : c : w 1 : 12 : 30 sport version : f : c 3 : 12 f : w 1 : 60 or 3 : 180 so c : f : w = 12 : 3 : 180 c / w = 12 / 180 = 3 ounces / x ounces x = 6 * 180 / 12 = 90 ounces of water e" | a ) 45 , b ) 50 , c ) 55 , d ) 60 , e ) 90 | e | multiply(divide(multiply(divide(1, 12), const_3), divide(divide(1, 30), const_2)), 6) | divide(n0,n1)|divide(n0,n2)|divide(#1,const_2)|multiply(#0,const_3)|divide(#3,#2)|multiply(n3,#4)| | other |
the probability that a number selected at random from the first 100 natural numbers is a composite number is ? | "explanation : the number of exhaustive events = 100 c ₁ = 100 . we have 25 primes from 1 to 100 . number of favourable cases are 75 . required probability = 75 / 50 = 3 / 2 . answer is d" | a ) 2 / 3 , b ) 3 / 5 , c ) 3 / 4 , d ) 3 / 2 , e ) 5 / 2 | d | divide(multiply(subtract(multiply(const_6, const_3), const_1), const_2), 100) | multiply(const_3,const_6)|subtract(#0,const_1)|multiply(#1,const_2)|divide(#2,n0)| | probability |
a circular logo is enlarged to fit the lid of a jar . the new diameter is 60 per cent larger than the original . by what percentage has the area of the logo increased ? | let old diameter be 4 , so radius is 2 old area = 4 π new diameter is 6.24 , so radius is 3.12 new area = 9.7344 π increase in area is 5.7344 π % increase in area = 5.7344 / 4 * 100 so , % increase is 143.36 % answer will be ( d ) | ['a ) 50', 'b ) 80', 'c ) 100', 'd ) 143.36', 'e ) 250'] | d | multiply(divide(subtract(power(add(divide(multiply(60, const_2), const_1000), const_3), const_2), const_4), const_4), const_100) | multiply(n0,const_2)|divide(#0,const_1000)|add(#1,const_3)|power(#2,const_2)|subtract(#3,const_4)|divide(#4,const_4)|multiply(#5,const_100) | geometry |
if 4 men working 10 hours a day earn rs . 1000 per week , then 9 men working 6 hours a day will earn how much per week ? | explanation : ( men 4 : 9 ) : ( hrs / day 10 : 6 ) : : 1000 : x hence 4 * 10 * x = 9 * 6 * 1000 or x = 9 * 6 * 1000 / 4 * 10 = 1350 answer : b | a ) rs 840 , b ) rs 1350 , c ) rs 1620 , d ) rs 1680 , e ) none of these | b | multiply(divide(multiply(9, 6), multiply(4, 10)), 1000) | multiply(n3,n4)|multiply(n0,n1)|divide(#0,#1)|multiply(n2,#2) | physics |
the ages of two person differ by 20 years . if 10 years ago , the elder one be 5 times as old as the younger one , their present ages ( in years ) are respectively | "let their ages be x and ( x + 20 ) years . then , 5 ( x - 10 ) = ( x + 20 - 10 ) = > 4 x = 60 = > x = 15 their present ages are 35 years and 15 year . answer : d" | a ) 30 , 10 , b ) 25 , 5 , c ) 29 , 9 , d ) 35 , 15 , e ) 20,10 | d | add(divide(add(multiply(5, 10), subtract(20, 10)), subtract(5, const_1)), 20) | multiply(n1,n2)|subtract(n0,n1)|subtract(n2,const_1)|add(#0,#1)|divide(#3,#2)|add(n0,#4)| | general |
a company has 15 managers and 75 associates . the 15 managers have an average salary of $ 90,000 . the 75 associates have an average salary of $ 30,000 . what is the average salary for the company ? | another method is to get ratios say 30000 = a and we know the # of people are in 1 : 5 ratio average = ( 3 a * 1 + a * 5 ) / 6 = 8 a / 6 = 40000 answer is b . $ 40,000 | a ) $ 35,000 , b ) $ 40,000 , c ) $ 55,000 , d ) $ 65,000 , e ) $ 75,000 | b | divide(add(multiply(multiply(multiply(const_3, const_3), const_10), multiply(const_100, const_10)), multiply(multiply(const_3, const_10), multiply(const_100, const_10))), add(75, 15)) | add(n0,n1)|multiply(const_3,const_3)|multiply(const_10,const_100)|multiply(const_10,const_3)|multiply(#1,const_10)|multiply(#3,#2)|multiply(#4,#2)|add(#6,#5)|divide(#7,#0) | general |
in an election , candidate a got 75 % of the total valid votes . if 15 % of the total votes were declared invalid and the total numbers of votes is 560000 , find the number of valid vote polled in favour of candidate ? | "total number of invalid votes = 15 % of 560000 = 15 / 100 × 560000 = 8400000 / 100 = 84000 total number of valid votes 560000 – 84000 = 476000 percentage of votes polled in favour of candidate a = 75 % therefore , the number of valid votes polled in favour of candidate a = 75 % of 476000 = 75 / 100 × 476000 = 35700000... | a ) 358000 , b ) 368000 , c ) 357000 , d ) 358000 , e ) 367000 | c | multiply(multiply(560000, subtract(const_1, divide(15, const_100))), divide(75, const_100)) | divide(n0,const_100)|divide(n1,const_100)|subtract(const_1,#1)|multiply(n2,#2)|multiply(#0,#3)| | gain |
if 7 is one solution of the equation x ^ 2 + 3 x + k = 10 , where k is a constant , what is the other solution ? | "the phrase “ 7 is one solution of the equation ” means that one value of x is 7 . thus , we first must plug 7 for x into the given equation to determine the value of k . so we have 7 ^ 2 + ( 3 ) ( 7 ) + k = 10 49 + 21 + k = 10 70 + k = 10 k = - 60 next we plug - 60 into the given equation for k and then solve for x . ... | a ) - 7 , b ) - 4 , c ) - 3 , d ) 1 , e ) - 10 | e | divide(subtract(10, add(power(7, 2), multiply(3, 7))), 7) | multiply(n0,n2)|power(n0,n1)|add(#0,#1)|subtract(n3,#2)|divide(#3,n0)| | general |
if both 112 and 33 are factors of the number a * 43 * 62 * 1311 , then what is the smallest possible value of a ? | explanatory answer step 1 : prime factorize the given expression a * 43 * 62 * 1311 can be expressed in terms of its prime factors as a * 28 * 32 * 1311 step 2 : find factors missing after excluding ' a ' to make the number divisible by both 112 and 33 112 is a factor of the given number . if we do not include ' a ' , ... | a ) 121 , b ) 3267 , c ) 363 , d ) 33 , e ) none of the above | c | lcm(power(add(const_10, const_1), const_2), divide(subtract(33, const_3), const_10)) | add(const_1,const_10)|subtract(n1,const_3)|divide(#1,const_10)|power(#0,const_2)|lcm(#2,#3) | other |
two isosceles triangles have equal vertical angles and their areas are in the ratio 9 : 25 . find the ratio of their corresponding heights . | "we are basically given that the triangles are similar . in two similar triangles , the ratio of their areas is the square of the ratio of their sides and also , the square of the ratio of their corresponding heights . therefore , area / area = height ^ 2 / height ^ 2 = 9 / 25 - - > height / height = 3 / 5 . answer : e... | a ) 4 / 5 , b ) 5 / 4 , c ) 3 / 2 , d ) 5 / 7 , e ) 3 / 5 | e | divide(sqrt(9), sqrt(25)) | sqrt(n0)|sqrt(n1)|divide(#0,#1)| | geometry |
a straight line in the xy - plane has y - intercept of 20 . on this line the x - coordinate of the point is 150 and y - coordinate is 600 then what is the slope of the line ? | "eq of line = y = mx + c c = 20 x = 150 y = 150 m + 20 , substitute y by 600 as given in question . 600 = 150 m + 20 , m = 3.9 correct option is a" | a ) 3.9 , b ) 4.6 , c ) 5.2 , d ) 6 , e ) 8.1 | a | divide(subtract(600, 20), 150) | subtract(n2,n0)|divide(#0,n1)| | general |
a case contains c cartons . each carton contains b boxes , and each box contains 400 paper clips . how many paper clips are contained in 2 cases ? | "2 cases * c cartons / case * b boxes / carton * 400 clips / box = 800 bc paper clips the answer is c ." | a ) 400 bc , b ) 400 b / c , c ) 800 bc , d ) 800 b / c , e ) 800 / bc | c | multiply(2, 400) | multiply(n0,n1)| | general |
the length of a rectangular plot is 20 metres more than its breadth . if the cost of fencing the plot @ rs . 26.50 per metre is rs . 5300 , what is the length of the plot in metres ? | "let length of plot = l meters , then breadth = l - 20 meters and perimeter = 2 [ l + l - 20 ] = [ 4 l - 40 ] meters [ 4 l - 40 ] * 26.50 = 5300 [ 4 l - 40 ] = 5300 / 26.50 = 200 4 l = 240 l = 240 / 4 = 60 meters . answer : b" | a ) 238 , b ) 200 , c ) 287 , d ) 117 , e ) 198 | b | subtract(divide(divide(5300, 26.50), const_2), multiply(const_2, 20)) | divide(n2,n1)|multiply(n0,const_2)|divide(#0,const_2)|subtract(#2,#1)| | physics |
mohit sold an article for $ 15000 . had he offered a discount of 10 % on the selling price , he would have earned a profit of 8 % . what is the cost price of the article ? | "let the cp be $ x . had he offered 10 % discount , profit = 8 % profit = 8 / 100 x and hence his sp = x + 8 / 100 x = $ 1.08 x = 15000 - 10 / 100 ( 15000 ) = 15000 - 1500 = $ 13500 = > 1.08 x = 13500 = > x = 12500 a" | a ) 12500 , b ) 25000 , c ) 15000 , d ) 18000 , e ) 17000 | a | multiply(divide(subtract(15000, divide(multiply(15000, 10), const_100)), add(const_100, 8)), const_100) | add(n2,const_100)|multiply(n0,n1)|divide(#1,const_100)|subtract(n0,#2)|divide(#3,#0)|multiply(#4,const_100)| | gain |
calculate the time it will take for a train that is 250 meter long to pass a bridge of 150 meter length , if the speed of the train is 35 km / hour ? | "speed = 35 km / hr = 35 * ( 5 / 18 ) m / sec = 9.72 m / sec total distance = 250 + 150 = 400 meter time = distance / speed = 400 * ( 1 / 9.72 ) = 41.15 seconds answer : c" | a ) 56 seconds , b ) 3515 seconds , c ) 41.15 seconds , d ) 30 seconds , e ) 36 seconds | c | divide(add(250, 150), divide(35, const_3_6)) | add(n0,n1)|divide(n2,const_3_6)|divide(#0,#1)| | physics |
a number increased by 20 % gives 480 . the number is ? | formula = total = 100 % , increase = ` ` + ' ' decrease = ` ` - ' ' a number means = 100 % that same number increased by 20 % = 120 % 120 % - - - - - - - > 480 ( 120 × 4 = 480 ) 100 % - - - - - - - > 400 ( 100 × 4 = 400 ) option ' c ' | a ) 200 , b ) 300 , c ) 400 , d ) 500 , e ) 600 | c | divide(480, add(const_1, divide(20, const_100))) | divide(n0,const_100)|add(#0,const_1)|divide(n1,#1) | gain |
if k ^ 3 is divisible by 1620 , what is the least possible value of integer k ? | "1620 = 2 ^ 2 * 3 ^ 4 * 5 therefore k must include at least 2 * 3 ^ 2 * 5 = 90 . the answer is d ." | a ) 12 , b ) 30 , c ) 60 , d ) 90 , e ) 120 | d | divide(divide(1620, const_2), const_2) | divide(n1,const_2)|divide(#0,const_2)| | general |
what least number should be added to 1052 , so that the sum is completely divisible by 23 | "explanation : ( 1052 / 23 ) gives remainder 17 17 + 6 = 23 , so we need to add 6 answer : option c" | a ) a ) 4 , b ) b ) 1 , c ) c ) 6 , d ) d ) 3 , e ) e ) 5 | c | subtract(23, reminder(1052, 23)) | reminder(n0,n1)|subtract(n1,#0)| | general |
ramesh purchased a refrigerator for rs . 12500 after getting a discount of 20 % on the labelled price . he spent rs . 125 on transport and rs . 250 on installation . at what price should it be sold so that the profit earned would be 16 % if no discount was offered ? | price at which the tv set is bought = rs . 12,500 discount offered = 20 % marked price = 12500 * 100 / 80 = rs . 15625 the total amount spent on transport and installation = 125 + 250 = rs . 375 \ total price of tv set = 15625 + 375 = rs . 16000 the price at which the tv should be sold to get a profit of 16 % if no dis... | a ) 17608 , b ) 17606 , c ) 17604 , d ) 17600 , e ) 18560 | e | divide(multiply(add(const_100, 16), add(divide(multiply(12500, const_100), subtract(const_100, 20)), add(125, 250))), const_100) | add(n4,const_100)|add(n2,n3)|multiply(n0,const_100)|subtract(const_100,n1)|divide(#2,#3)|add(#1,#4)|multiply(#0,#5)|divide(#6,const_100) | gain |
in a simultaneous throw of a pair of dice , find the probability of getting a total more than 7 | "total number of cases = 6 * 6 = 36 favourable cases = [ ( 2,6 ) , ( 3,5 ) , ( 3,6 ) , ( 4,4 ) , ( 4,5 ) , ( 4,6 ) , ( 5,4 ) , ( 5,6 ) , ( 5,3 ) , ( 5,5 ) , ( 6,2 ) , ( 6,3 ) , ( 6,4 ) , ( 6,5 ) , ( 6,6 ) ] = 15 so probability = 15 / 36 = 5 / 12 answer is d" | a ) 1 / 2 , b ) 7 / 12 , c ) 5 / 13 , d ) 5 / 12 , e ) 6 / 17 | d | divide(subtract(7, multiply(const_2, const_3)), 7) | multiply(const_2,const_3)|subtract(n0,#0)|divide(#1,n0)| | general |
a certain taxi company charges $ 3.00 for the first 1 / 5 of a mile plus $ 0.40 for each additional 1 / 5 of a mile . what would this company charge for a taxi ride that was 8 miles long ? | "a certain taxi company charges $ 3.00 for the first 1 / 5 of a mile plus $ 0.40 for each additional 1 / 5 of a mile . what would this company charge for a taxi ride that was 8 miles long ? a . 15.60 b . 16.00 c . 17.50 d . 18.70 e . 19.10 1 / 5 miles = 0.2 miles . the cost of 8 miles long ride would be $ 3.00 for the ... | a ) 15.6 , b ) 16.0 , c ) 17.5 , d ) 18.6 , e ) 19.1 | d | add(3.00, multiply(subtract(divide(8, divide(1, 5)), 1), 0.40)) | divide(n1,n2)|divide(n6,#0)|subtract(#1,n1)|multiply(n3,#2)|add(n0,#3)| | general |
the sum of 3 consecutive even numbers is 246 . what are the numbers ? | first x make the first x second x + 2 even numbers , sowe add 2 to get the next third x + 4 add 2 more ( 4 total ) to get the third f + s + t = 246 summeansaddfirst ( f ) plussecond ( s ) plusthird ( t ) ( x ) + ( x + 2 ) + ( x + 4 ) = 246 replace each f , s , and t withwhatwe labeled them x + x + 2 + x + 4 = 246 here ... | a ) 80 , 8284 , b ) 65 , 6871 , c ) 45 , 4742 , d ) 100 , 10249 , e ) 87 , 8889 | a | divide(subtract(246, add(const_2, const_4)), 3) | add(const_2,const_4)|subtract(n1,#0)|divide(#1,n0) | physics |
if 4 men can colour 48 m long cloth in 2 days , then 6 men can colour 36 m long cloth in | "the length of cloth painted by one man in one day = 48 / 4 × 2 = 6 m no . of days required to paint 36 m cloth by 6 men = 36 / 6 × 6 = 1 day . a" | a ) 1 day , b ) 2 days , c ) 3 days , d ) 4 days , e ) 5 days | a | divide(36, multiply(divide(48, multiply(4, 2)), 6)) | multiply(n0,n2)|divide(n1,#0)|multiply(n3,#1)|divide(n4,#2)| | physics |
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 40 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 40 percent to make square c length of each... | ['a ) 75.00 %', 'b ) 56.80 %', 'c ) 110 %', 'd ) 150 %', 'e ) 180 %'] | b | multiply(divide(subtract(subtract(square_area(add(add(const_1, divide(100, 100)), divide(multiply(add(const_1, divide(100, 100)), 40), 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 |
a fruit seller had some apples . he sells 40 % apples and still he has 420 . originally he had how many apples ? | suppose originally he had x apples then ( 100 - 40 ) % of x = 420 60 x / 100 = 420 x = 700 answer is c | a ) 400 , b ) 500 , c ) 700 , d ) 450 , e ) 650 | c | original_price_before_loss(40, 420) | original_price_before_loss(n0,n1) | gain |
a sells a cricket bat to b at a profit of 20 % . b sells it to c at a profit of 25 % . if c pays $ 228 for it , the cost price of the cricket bat for a is : | "a 152 125 % of 120 % of a = 228 125 / 100 * 120 / 100 * a = 228 a = 228 * 2 / 3 = 152 ." | a ) 152 , b ) 120 , c ) 130 , d ) 160 , e ) 210 | a | divide(228, multiply(add(const_1, divide(20, const_100)), add(const_1, divide(25, const_100)))) | divide(n0,const_100)|divide(n1,const_100)|add(#0,const_1)|add(#1,const_1)|multiply(#2,#3)|divide(n2,#4)| | gain |
by weight , liquid x makes up 0.8 percent of solution a and 1.8 percent of solution b . if 300 grams of solution a are mixed with 700 grams of solution b , then liquid x accounts for what percent of the weight of the resulting solution ? | "i think there is a typo in question . it should have been ` ` by weight liquid ' x ' makes up . . . . . ` ` weight of liquid x = 0.8 % of weight of a + 1.8 % of weight of b when 300 gms of a and 700 gms of b is mixed : weight of liquid x = ( 0.8 * 300 ) / 100 + ( 1.8 * 700 ) / 100 = 15 gms % of liquid x in resultant m... | a ) 1.5 % , b ) 1.9 % , c ) 10 % , d ) 15 % , e ) 19 % | a | divide(add(multiply(300, 0.8), multiply(700, 1.8)), const_1000) | multiply(n0,n2)|multiply(n1,n3)|add(#0,#1)|divide(#2,const_1000)| | gain |
two pipes a and b can fill a tank in 10 hour and 15 hours respectively . if both the pipes are opened simultaneously , how much time will be taken to fill the tank ? | "part filled by a in 1 hour = 1 / 10 part filled by b in 1 hour = 1 / 15 part filled by a + b in 1 hour = 1 / 10 + 1 / 15 = 1 / 6 both the pipes will together will fill the tank in 6 hours . answer is b" | a ) 2 hrs , b ) 6 hrs , c ) 5 hrs , d ) 4 hrs , e ) 1 hr | b | divide(const_1, add(divide(const_1, 10), divide(const_1, 15))) | divide(const_1,n0)|divide(const_1,n1)|add(#0,#1)|divide(const_1,#2)| | physics |
if x # y is defined to equal x ^ 2 / y for all x and y , then ( - 1 # 3 ) # 3 = | "( - 1 ) ^ 2 / 3 = 1 / 3 ( 1 / 3 ) ^ 2 / 3 = 1 / 27 so c is my answer" | a ) 4 / 3 , b ) 1 / 3 , c ) 1 / 27 , d ) - 1 / 12 , e ) - 4 / 3 | c | divide(power(divide(power(negate(1), 2), 2), 2), negate(3)) | negate(n1)|negate(n3)|power(#0,n0)|divide(#2,n0)|power(#3,n0)|divide(#4,#1)| | general |
how many integers between 362,855 and 852,755 have tens digit 1 and units digit 3 ? | "there is one number in hundred with 1 in the tens digit and 3 in the units digit : 13 , 113 , 213 , 313 , . . . the difference between 362,855 and 852,755 is 852,755 - 362,855 = 489,900 - one number per each hundred gives 133,900 / 100 = 4,889 numbers . answer : c ." | a ) 4,888 , b ) 4,898 , c ) 4,889 , d ) 4,869 , e ) 4,896 | c | subtract(852,755, add(add(multiply(const_2, const_100), multiply(add(const_3, const_4), const_10)), const_2)) | add(const_3,const_4)|multiply(const_100,const_2)|multiply(#0,const_10)|add(#1,#2)|add(#3,const_2)|subtract(n1,#4)| | general |
a train covers a distance of 12 km in 10 min . if it takes 15 sec to pass a telegraph post , then the length of the train is ? | "speed = ( 12 / 10 * 60 ) km / hr = ( 72 * 5 / 18 ) m / sec = 20 m / sec . length of the train = 20 * 15 = 300 m . answer : b" | a ) 250 m , b ) 300 m , c ) 120 m , d ) 200 m , e ) 166 m | b | divide(12, subtract(divide(12, 10), 15)) | divide(n0,n1)|subtract(#0,n2)|divide(n0,#1)| | physics |
two right circular cylinders of equal volumes have their heights in the ratio 1 : 2 . find the ratio of their radii . | explanation : let their heights be h and 2 h and radii be r and r respectively then . π r 2 h = π r 2 ( 2 h ) = > r 2 / r 2 = 2 h / h = 2 / 1 = > r / r = √ 2 / 1 = > r : r = √ 2 : 1 answer is c | ['a ) √ 3 : 1', 'b ) √ 7 : 1', 'c ) √ 2 : 1', 'd ) 2 : 1', 'e ) 3 : 1'] | c | sqrt(2) | sqrt(n1) | geometry |
a certain country had a total annual expenditure of $ 4.8 x 10 ^ 11 last year . if the population of the country was 240 million last year , what was the per capita expenditure ? | "total expenditure / population = per capita expenditure hence , ( 4,8 x 10 ^ 11 ) / 240 000 000 = ( 4,8 x 10 ^ 11 ) / ( 2,4 x 10 ^ 8 ) = 2 x 10 ^ ( 11 - 8 ) = 2 x 10 ^ 3 = 2000 . answer is c ." | a ) $ 500 , b ) $ 1,000 , c ) $ 2,000 , d ) $ 3,000 , e ) $ 5,000 | c | divide(multiply(4.8, power(10, 11)), multiply(240, power(10, add(const_4, const_2)))) | add(const_2,const_4)|power(n1,n2)|multiply(n0,#1)|power(n1,#0)|multiply(n3,#3)|divide(#2,#4)| | general |
a waitress ' s income consists of her salary and tips . during one week , her tips were 2 / 4 of her salary . what fraction of her income for the week came from tips ? | "her tips were 2 / 4 of her salary . let ' s say her salary = $ 4 this mean her tips = ( 2 / 4 ) ( $ 4 ) = $ 2 so , her total income = $ 4 + $ 2 = $ 6 what fraction of her income for the week came from tips $ 2 / $ 6 = 1 / 3 = c" | a ) 1 / 9 , b ) 1 / 6 , c ) 1 / 3 , d ) 4 / 9 , e ) 5 / 9 | c | divide(2, add(2, 4)) | add(n0,n1)|divide(n0,#0)| | general |
what is the sum of all even numbers from 1 to 601 ? | "explanation : 600 / 2 = 300 300 * 301 = 90300 answer : c" | a ) 122821 , b ) 281228 , c ) 90300 , d ) 122850 , e ) 128111 | c | divide(multiply(1, 601), const_4) | multiply(n0,n1)|divide(#0,const_4)| | general |
60 percent of movie theatres in town x have 3 screens or less . 20 % of those theatres sell an average of more than $ 200 worth of popcorn per showing . 56 percent of all the movie theatres in town x sell $ 300 or less of popcorn per showing . what percent of all the stores on the street have 4 or more screens and sell... | "lets take numbers here . assume that the total number of movie theaters in the town = 100 then number of movie theaters with 3 screens or less = 60 = > number of movie theaters with 4 screens or more = 40 movie theaters with 3 screens or less selling popcorn at more than $ 200 = 20 % of 60 = 12 number of movie theater... | a ) 12 , b ) 18 , c ) 32 , d ) 40 , e ) 44 | b | multiply(divide(20, 300), multiply(divide(20, const_100), 200)) | divide(n2,n7)|multiply(n5,#0)|multiply(#0,#1)| | general |
in a certain pond , 70 fish were caught , tagged , and returned to the pond . a few days later , 50 fish were caught again , of which 2 were found to have been tagged . if the percent of tagged fish in the second catch approximates the percent of tagged fish in the pond , what is the approximate number of fish in the p... | "this is a rather straight forward ratio problem . 1 . 70 fish tagged 2 . 2 out of the 50 fish caught were tagged thus 2 / 50 2 / 50 = 70 / x thus , x = 1750 think of the analogy : 2 fish is to 50 fish as 50 fish is to . . . ? you ' ve tagged 50 fish and you need to find what that comprises as a percentage of the total... | a ) 400 , b ) 625 , c ) 1,750 , d ) 2,500 , e ) 10,000 | c | divide(70, divide(2, 50)) | divide(n2,n1)|divide(n0,#0)| | gain |
there are 990 male and female participants in a meeting . half the female participants and one - quarter of the male participants are democrats . one - third of all the participants are democrats . how many of the democrats are female ? | "female = x male = 990 - x x / 2 + 990 - x / 4 = 1 / 3 * ( 990 ) = 330 x = 330 x / 2 = 165 is supposed to be the answer m is missing something correct option e" | a ) 75 , b ) 100 , c ) 125 , d ) 175 , e ) 165 | e | divide(subtract(multiply(divide(990, const_3), const_4), 990), const_2) | divide(n0,const_3)|multiply(#0,const_4)|subtract(#1,n0)|divide(#2,const_2)| | general |
5 years ago amith was 3 times as old as his daughter and 10 years hence , he will be two times as old as his daughter . then amith ’ s current age is , | d 20 amith ’ s age = a and daughter ’ s age = b then , a – 5 = 3 ( b – 5 ) = > a – 3 b + 10 = 0 … … ( 1 ) and , a + 10 = 2 ( a + 10 ) = > a – 2 b – 10 = 0 … … ( 2 ) solving the 2 eqns , we will get a = 50 , b = 20 . therefore , amith ’ s age is 50 and his daughter ’ s age is 20 | a ) 10 , b ) 50 , c ) 40 , d ) 20 , e ) 60 | d | add(multiply(5, 3), 5) | multiply(n0,n1)|add(n0,#0) | general |
at a tanning salon , customers are charged $ 10 for their first visit in a calendar month and $ 7 for each visit after that in the same calendar month . in the last calendar month , 100 customers visited the salon , of which 30 made a second visit , and 10 made a third visit . all other customers made only one visit . ... | "i get b . this question seems too straightforward for 600 + . am i missing something ? 100 first - time visits - - > 100 ( 10 ) = $ 1000 30 + 10 = 40 subsequent visits - - > 40 ( 7 ) = $ 280 total revenue : 1000 + 280 = $ 1280 the answer is b ." | a ) $ 1220 , b ) $ 1280 , c ) $ 1300 , d ) $ 1340 , e ) $ 1880 | b | add(multiply(add(10, 7), 30), multiply(subtract(100, 30), 10)) | add(n0,n1)|subtract(n2,n3)|multiply(n3,#0)|multiply(n0,#1)|add(#2,#3)| | physics |
a retailer buys a radio for rs 232 . his overhead expenses are rs 15 . he sellis the radio for rs 300 . the profit percent of the retailer is | explanation : cost price = ( 232 + 15 ) = 247 sell price = 300 gain = ( 53 / 247 ) * 100 = 21.4 % . answer : c | a ) 10 % , b ) 50 % , c ) 21.4 % , d ) 52 % , e ) none of these | c | subtract(multiply(divide(300, add(232, 15)), const_100), const_100) | add(n0,n1)|divide(n2,#0)|multiply(#1,const_100)|subtract(#2,const_100) | gain |
a batch of cookies was divided among 3 tins : 2 / 3 of all the cookies were placed in either the blue tin or the green tin , and the rest were placed in the red tin . if 1 / 4 of all the cookies were placed in the blue tin , what fraction q of the cookies that were placed in the other tins were placed in the green tin ... | blue tin or red tin : 2 / 3 ( n ) red tin : ( 1 / 3 ) n blue tin : ( 1 / 4 ) n what the last statment meant , is it wants this fraction : ( # of cookies in green tin ) / ( # of cookies in red and green tin ) # of cookies in green tin = 2 n / 3 - n / 4 = 8 n - 3 n / 12 = 5 n / 12 # of cookies in red and green tin = n / ... | a ) 15 / 2 , b ) 9 / 4 , c ) 5 / 9 , d ) 7 / 5 , e ) 9 / 7 | c | divide(multiply(subtract(divide(2, 3), divide(1, 4)), const_12), add(divide(const_12, 3), multiply(subtract(divide(2, 3), divide(1, 4)), const_12))) | divide(n1,n0)|divide(n3,n4)|divide(const_12,n0)|subtract(#0,#1)|multiply(#3,const_12)|add(#2,#4)|divide(#4,#5) | general |
aaron will jog from home at 3 miles per hour and then walk back home by the same route at 6 miles per hour . how many miles from home can aaron jog so that he spends a total of 3 hours jogging and walking ? | "xyt / ( x + y ) x = 3 , y = 6 , t = 3 3 * 6 * 3 / 3 + 6 = 54 / 9 = 6 answer : b" | a ) 3 , b ) 6 , c ) 2 , d ) 5 , e ) 8 | b | divide(multiply(multiply(3, 6), 3), multiply(3, 6)) | multiply(n0,n1)|multiply(n2,#0)|divide(#1,#0)| | physics |
a man engaged a servant on the condition that he would pay him rs . 710 and a uniform after a year service . he served only for 8 months and got rs . 460 and a uniform . find the price of the uniform ? | "8 / 12 = 2 / 3 * 710 = 473.33 460.00 - - - - - - - - - - - - - - - 13.33 1 / 3 uniform 13.33 1 - - - - - - - - - - - - - - - ? = > rs . 40 answer : a" | a ) rs . 40 , b ) rs . 30 , c ) rs . 25 , d ) rs . 20 , e ) rs . 45 | a | multiply(divide(subtract(multiply(8, 710), multiply(multiply(const_3, const_4), 460)), multiply(multiply(const_3, const_4), const_1)), const_4) | multiply(n0,n1)|multiply(const_3,const_4)|multiply(n2,#1)|multiply(#1,const_1)|subtract(#0,#2)|divide(#4,#3)|multiply(#5,const_4)| | general |
the cricket team of 11 members is 26 yrs old & the wicket keeper is 3 yrs older . if the ages ofthese 2 are excluded , the average age of theremaining players is 1 year less than the average age of the whole team . what is the average age of the team ? | "let the average age of the whole team be x years . 11 x - ( 26 + 29 ) = 9 ( x - 1 ) = > 11 x - 9 x = 46 = > 2 x = 46 = > x = 23 . so , average age of the team is 23 years . c" | a ) 19 , b ) 21 , c ) 23 , d ) 25 , e ) 27 | c | divide(subtract(add(add(26, 3), 26), subtract(11, 2)), subtract(11, subtract(11, 2))) | add(n1,n2)|subtract(n0,n3)|add(n1,#0)|subtract(n0,#1)|subtract(#2,#1)|divide(#4,#3)| | general |
a student has to obtain 33 % of the total marks to pass . he got 125 marks and failed by 73 marks . the maximum marks are ? | "let the maximum marks be x then , 33 % of x = 125 + 73 33 x / 100 = 198 x = 600 answer is d" | a ) 450 , b ) 300 , c ) 500 , d ) 600 , e ) 175 | d | divide(add(125, 73), divide(33, const_100)) | add(n1,n2)|divide(n0,const_100)|divide(#0,#1)| | general |
a ratio between two numbers is 3 : 4 and their l . c . m . is 180 . the first number is | "sol . let the required numbers be 3 x and 4 x . then , their l . c . m . is 12 x . ∴ 12 x = 180 ⇔ x = 15 . hence , the first number is 45 . answer b" | a ) 60 , b ) 45 , c ) 20 , d ) 15 , e ) none | b | multiply(divide(180, multiply(3, 4)), 3) | multiply(n0,n1)|divide(n2,#0)|multiply(n0,#1)| | other |
mike , jim and bob are all professional fisherman . mike can catch 30 fish in one hour , jim can catch twice as much and bob can catch 50 % more than jim . if the 3 started to fish together and after 40 minutes mike and bob left , how many fish did the 3 fishermen catch in one hour ? | all of them catch fishes in relation to number 30 . . . . 2 / 3 * 30 + 2 * 30 + 2 * 1.5 * 30 * 2 / 3 = 140 answer is c | a ) 110 , b ) 120 , c ) 140 , d ) 130 , e ) 112 | c | subtract(add(multiply(3, 40), 50), 30) | multiply(n2,n3)|add(n1,#0)|subtract(#1,n0) | physics |
in a certain game of dice , the player ’ s score is determined as a sum of two throws of a single die . the player with the highest score wins the round . if more than one player has the highest score , the winnings of the round are divided equally among these players . if john plays this game against 22 other players ... | "to guarantee that john will get some monetary payoff he must score the maximum score of 6 + 6 = 12 , because if he gets even one less than that so 11 , someone can get 12 and john will get nothing . p ( 12 ) = 1 / 6 ^ 2 = 1 / 36 . answer : d ." | a ) 41 / 50 , b ) 1 / 221 , c ) 1 / 216 , d ) 1 / 36 , e ) 1 / 42 | d | divide(const_1, power(subtract(divide(22, const_3), const_1), const_2)) | divide(n0,const_3)|subtract(#0,const_1)|power(#1,const_2)|divide(const_1,#2)| | general |
it was calculated that 75 men could complete a piece of work in 10 days . when work was scheduled to commence , it was found necessary to send 25 men to another project . how much longer will it take to complete the work ? | "one day work = 1 / 10 one man ’ s one day work = 1 / ( 10 * 75 ) now : no . of workers = 50 one day work = 50 * 1 / ( 10 * 75 ) the total no . of days required to complete the work = ( 75 * 10 ) / 50 = 15 answer : e" | a ) 10 days . , b ) 20 days . , c ) 25 days . , d ) 12.5 days . , e ) 15 days . | e | multiply(10, divide(75, 25)) | divide(n0,n2)|multiply(n1,#0)| | physics |
two equally sized jugs full of water are each emptied into two separate unequally sized empty jugs , x and y . now , jug x is 1 / 7 full , while jug y is 2 / 3 full . if water is poured from jug x into jug y until jug y is filled , what fraction of jug x then contains water ? | suppose the water in each jug is l liters cx x ( 1 / 7 ) = l cx = 7 l liters cx is capacity of x cy x ( 2 / 3 ) = l cy = 3 l / 2 liters cy is capacity of y now , y is 3 l / 2 - l empty = l / 2 empty so , we can put only l / 2 water in jug y from jug x jug x ' s remaining water = l - l / 2 = l / 2 fraction of x which co... | a ) 0 , b ) 1 / 14 , c ) 2 / 15 , d ) 1 / 10 , e ) 2 / 10 | b | multiply(divide(1, 7), divide(subtract(const_1, divide(2, 3)), divide(2, 3))) | divide(n0,n1)|divide(n2,n3)|subtract(const_1,#1)|divide(#2,#1)|multiply(#0,#3) | general |
a grocery store bought some mangoes at a rate of 4 for a dollar . they were separated into two stacks , one of which was sold at a rate of 3 for a dollar and the other at a rate of 6 for a dollar . what was the ratio of the number of mangoes in the two stacks if the store broke even after having sold all of its mangoes... | "the cost price of a mango = 1 / 4 dollars . the selling price of a mango from the first stack = 1 / 3 dollars - - > the profit from one mango = 1 / 3 - 1 / 4 = 1 / 12 dollars . the selling price of a mango from the second stack = 1 / 6 dollars - - > the loss from one mango = 1 / 3 - 1 / 6 = 1 / 6 dollars . the profit ... | a ) 1 : 4 , b ) 1 : 5 , c ) 2 : 3 , d ) 1 : 2 , e ) 1 : 2 | e | divide(subtract(divide(const_1, 3), divide(const_1, 4)), subtract(divide(const_1, 4), divide(const_1, multiply(const_2, const_4)))) | divide(const_1,n1)|divide(const_1,n0)|multiply(const_2,const_4)|divide(const_1,#2)|subtract(#0,#1)|subtract(#1,#3)|divide(#4,#5)| | other |
if the weight of 13 meters long rod is 13.4 kg . what is the weight of 6 meters long rod ? | answer ∵ weight of 13 m long rod = 13.4 kg ∴ weight of 1 m long rod = 13.4 / 13 kg ∴ weight of 6 m long rod = 13.4 x 6 / 13 = 6.18 kg option : d | a ) 7.2 kg . , b ) 10.8 kg . , c ) 12.4 kg . , d ) 6.18 kg , e ) none | d | divide(multiply(6, 13.4), 13) | multiply(n1,n2)|divide(#0,n0) | physics |
if each side of a rectangle is increased by 50 % with the length being double the width , find the percentage change in its area ? | "area = 2 a x a new length = 250 a / 100 = 5 a / 2 new width = 150 a / 100 = 3 a / 2 new area = ( 5 a x 3 a ) / ( 2 x 2 ) = ( 15 a ² / 4 ) increased area = = ( 15 a ² / 4 ) - a ² increase % = [ ( 11 a ² / 4 ) x ( 1 / a ² ) x 100 ] % = 275 % answer : e" | a ) 284 % , b ) 276 % , c ) 265.25 % , d ) 284.5 % , e ) 275 % | e | multiply(subtract(power(multiply(divide(50, 50), const_2), const_2), const_1), const_100) | divide(n0,n0)|multiply(#0,const_2)|power(#1,const_2)|subtract(#2,const_1)|multiply(#3,const_100)| | geometry |
the length of a room is 5.5 m and width is 3.75 m . find the cost of paying the floor by slabs at the rate of rs . 800 per sq . metre | "explanation : area = 5.5 × 3.75 sq . metre . cost for 1 sq . metre . = rs . 800 hence total cost = 5.5 × 3.75 × 800 = 5.5 × 3000 = rs . 16500 answer : b ) rs . 16500" | a ) 22488 , b ) 16500 , c ) 27889 , d ) 23778 , e ) 29982 | b | multiply(800, multiply(5.5, 3.75)) | multiply(n0,n1)|multiply(n2,#0)| | physics |
if the area of a circle decreases by 25 % , then the radius of a circle decreases by | "if area of a circle decreased by x % then the radius of a circle decreases by ( 100 − 10 √ 100 − x ) % = ( 100 − 10 √ 100 − 25 ) % = ( 100 − 10 √ 75 ) % = 100 - 87 = 13 % answer a" | a ) 13 % , b ) 18 % , c ) 36 % , d ) 64 % , e ) none of these | a | multiply(subtract(const_1, sqrt(divide(subtract(const_100, 25), const_100))), const_100) | subtract(const_100,n0)|divide(#0,const_100)|sqrt(#1)|subtract(const_1,#2)|multiply(#3,const_100)| | geometry |
alfred buys an old scooter for $ 4700 and spends $ 1000 on its repairs . if he sells the scooter for $ 5800 , his gain percent is ? | "c . p . = 4700 + 1000 = $ 5700 s . p . = $ 5800 gain = 5800 - 5700 = $ 100 gain % = 100 / 5700 * 100 = 1.75 % answer is c" | a ) 5.45 % , b ) 6.23 % , c ) 1.75 % , d ) 8.12 % , e ) 10 % | c | multiply(divide(subtract(5800, add(4700, 1000)), add(4700, 1000)), const_100) | add(n0,n1)|subtract(n2,#0)|divide(#1,#0)|multiply(#2,const_100)| | gain |
find the average of all the numbers between 11 and 36 which are divisible by 5 . | "explanation : average = ( 15 + 20 + 25 + 30 + 35 ) / 5 = 125 / 5 = 25 answer : a" | a ) 25 , b ) 77 , c ) 20 , d ) 28 , e ) 10 | a | divide(add(add(11, const_4), subtract(36, const_4)), const_2) | add(n0,const_4)|subtract(n1,const_4)|add(#0,#1)|divide(#2,const_2)| | general |
how many e ways can jason sit with his 5 friends in a row of 6 seats with an aisle on either side of the row , if jason insists on sitting next to one of the aisles ? | jason can select his seat in 2 ways ( two aisles ) his 1 st of 4 friends have 5 seats to select = > his 2 nd of remaining 3 friends will have 4 seat to chose from . . . and so on total ways e = > 2 * 5 * 4 * 3 * 2 * 1 = 240 . b | a ) 120 , b ) 240 , c ) 360 , d ) 540 , e ) 720 | b | multiply(factorial(5), const_2) | factorial(n0)|multiply(#0,const_2) | general |
56 : 65 : : 68 : ? | "ans 86 reverse of 68 answer : c" | a ) 49 , b ) 84 , c ) 86 , d ) 64 , e ) 56 | c | multiply(68, divide(56, 65)) | divide(n0,n1)|multiply(n2,#0)| | general |
in the biology lab of ` ` jefferson ' ' high school there are 0.037 * 10 ^ 5 germs , equally divided among 148000 * 10 ^ ( - 3 ) petri dishes . how many germs live happily in a single dish ? | "0.037 * 10 ^ 5 can be written as 3700 148000 * 10 ^ ( - 3 ) can be written as 148 required = 3700 / 148 = 25 answer : b" | a ) 10 , b ) 25 , c ) 35 , d ) 40 , e ) 55 | b | divide(multiply(multiply(const_1000, const_100), 0.037), divide(148000, const_1000)) | divide(n3,const_1000)|multiply(const_100,const_1000)|multiply(n0,#1)|divide(#2,#0)| | general |
the sum of ages of 5 children born 1.5 years different each is 50 years . what is the age of the elder child ? | "let the ages of children be x , ( x + 1.5 ) , ( x + 3 ) , ( x + 4.5 ) and ( x + 6 ) years . then , x + ( x + 1.5 ) + ( x + 3 ) + ( x + 4.5 ) + ( x + 6 ) = 50 5 x = 35 x = 7 . x + 6 = 7 + 6 = 13 answer : e" | a ) 8 , b ) 9 , c ) 10 , d ) 16 , e ) 13 | e | divide(add(add(add(add(1.5, const_4), add(1.5, const_4)), add(const_4, const_4)), 50), 5) | add(n1,const_4)|add(const_4,const_4)|add(#0,#0)|add(#2,#1)|add(n2,#3)|divide(#4,n0)| | general |
what is the average ( arithmetic mean ) of all multiples of 10 from 10 to 100 inclusive ? | "this question can be solved with the average formula and ' bunching . ' we ' re asked for the average of all of the multiples of 10 from 10 to 100 , inclusive . to start , we can figure out the total number of terms rather easily : 1 ( 10 ) = 10 2 ( 10 ) = 20 . . . 10 ( 10 ) = 100 so we know that there are 10 total nu... | a ) 190 , b ) 195 , c ) 200 , d ) 205 , e ) 55 | e | divide(divide(multiply(add(10, 100), add(divide(subtract(100, 10), 10), const_1)), const_2), add(divide(subtract(100, 10), 10), const_1)) | add(n0,n2)|subtract(n2,n0)|divide(#1,n0)|add(#2,const_1)|multiply(#0,#3)|divide(#4,const_2)|divide(#5,#3)| | general |
a cistern can be filled by a tap in 4 hours while it can be emptied by another tap in 5 hours . if both the taps are opened simultaneously , then after how much time will the cistern get filled ? | "net part filled in 1 hour = ( 1 / 4 - 1 / 5 ) = 1 / 20 the cistern will be filled in 20 / 1 hrs i . e . , 20 hrs . answer : b" | a ) 7.5 , b ) 20 , c ) 30 , d ) 32 , e ) 40 | b | divide(const_1, subtract(divide(const_1, 4), divide(const_1, 5))) | divide(const_1,n0)|divide(const_1,n1)|subtract(#0,#1)|divide(const_1,#2)| | physics |
what is the sum of all 3 digit numbers that leave a remainder of ' 2 ' when divided by 4 ? | "find the number , upon sum of 3 digits of a number gives a reminder 2 when it is divided by 4 seeing the options after dividing and finding the reminder of 2 my answer was a" | a ) 123,750 , b ) 164,850 , c ) 164,749 , d ) 149,700 , e ) 156,720 | a | multiply(divide(add(divide(subtract(subtract(const_1000, 3), add(add(multiply(multiply(3, 3), const_10), multiply(3, 3)), 3)), 4), const_1), 2), add(subtract(const_1000, 3), add(add(multiply(multiply(3, 3), const_10), multiply(3, 3)), 3))) | multiply(n0,n0)|subtract(const_1000,n0)|multiply(#0,const_10)|add(#2,#0)|add(n0,#3)|add(#4,#1)|subtract(#1,#4)|divide(#6,n2)|add(#7,const_1)|divide(#8,n1)|multiply(#5,#9)| | general |
in an election a candidate who gets 60 % of the votes is elected by a majority of 1200 votes . what is the total number of votes polled ? | "let the total number of votes polled be x then , votes polled by other candidate = ( 100 - 60 ) % of x = 40 % of x 60 % of x - 40 % of x = 1200 20 x / 100 = 1200 x = 1200 * 100 / 20 = 6000 answer is e" | a ) 4500 , b ) 5200 , c ) 6900 , d ) 7520 , e ) 6000 | e | divide(1200, divide(subtract(60, subtract(const_100, 60)), const_100)) | subtract(const_100,n0)|subtract(n0,#0)|divide(#1,const_100)|divide(n1,#2)| | gain |
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 $ 5000 in a long term bond that pays 8 percent interest , compounded annually , what will be the approximate total amount of investment 18 years later , whe... | "since investment doubles in 70 / r years then for r = 8 it ' ll double in 70 / 8 = ~ 9 years ( we are not asked about the exact amount so such an approximation will do ) . thus in 18 years investment will double twice and become ( $ 5,000 * 2 ) * 2 = $ 20,000 ( after 9 years investment will become $ 5,000 * 2 = $ 10,0... | a ) $ 20000 , b ) $ 15000 , c ) $ 12000 , d ) $ 10000 , e ) $ 9000 | a | multiply(multiply(5000, const_2), const_2) | multiply(n1,const_2)|multiply(#0,const_2)| | general |
tomeka is playing a dice game . if she rolls the same number on her second roll as she rolls on her first , she wins . each roll is with two , fair , 6 - sided dice . if tomeka rolled a 7 on her first roll , what is the probability that she will win on her second roll ? | there are 6 ways to roll a seven : 1 and 6 , 6 and 1 , 2 and 5 , 5 and 2 , 3 and 4 , 4 and 3 . there are 6 * 6 = 36 ways to roll two six - sided dice . thus the probability of winning by rolling a seven on the second roll given a seven on the first roll is 6 / 36 = 1 / 6 c | a ) 1 / 4 , b ) 1 / 5 , c ) 1 / 6 , d ) 1 / 9 , e ) 1 / 12 | c | divide(6, multiply(6, 6)) | multiply(n0,n0)|divide(n0,#0) | probability |
a company has 15 managers and 75 associates . the 15 managers have an average salary of $ 90000 . the 75 associates have an average salary of $ 30000 . what is the average salary for the company ? | another method is to get ratios say 30000 = a and we know the # of people are in 1 : 5 ratio average = ( 3 a * 1 + a * 5 ) / 6 = 8 a / 6 = 40000 answer is b . $ 40,000 | a ) $ 35,000 , b ) $ 40,000 , c ) $ 55,000 , d ) $ 65,000 , e ) $ 75,000 | b | divide(add(multiply(15, 90000), multiply(75, 30000)), add(15, 75)) | add(n0,n1)|multiply(n0,n3)|multiply(n1,n5)|add(#1,#2)|divide(#3,#0) | general |
a man can row upstream at 37 kmph and downstream at 53 kmph , and then find the speed of the man in still water ? | "us = 37 ds = 53 m = ( 53 + 37 ) / 2 = 45 answer : e" | a ) 29 , b ) 92 , c ) 30 , d ) 32 , e ) 45 | e | divide(add(37, 53), const_2) | add(n0,n1)|divide(#0,const_2)| | physics |
a certain car dealership sells economy cars , luxury cars , and sport utility vehicles . the ratio of economy to luxury cars is 3 : 2 . the ratio of economy cars to sport utility vehicles is 5 : 4 . what is the ratio of luxury cars to sport utility vehicles ? | "the ratio of economy to luxury cars is 3 : 2 - - > e : l = 3 : 2 = 15 : 10 . the ratio of economy cars to sport utility vehicles is 5 : 4 - - > e : s = 5 : 4 = 15 : 12 . thus , l : s = 10 : 12 . answer : d ." | a ) 9 : 8 , b ) 8 : 9 , c ) 3 : 2 , d ) 10 : 12 , e ) 1 : 2 | d | divide(divide(multiply(const_4, const_3.0), multiply(4, 4)), divide(multiply(4, const_4), multiply(2, const_4))) | multiply(const_3.0,const_4)|multiply(n3,n3)|multiply(n1,const_4)|divide(#0,#1)|divide(#0,#2)|divide(#3,#4)| | other |
in a certain apartment building , there are one - bedroom and two - bedroom apartments . the rental prices of the apartment depend on a number of factors , but on average , two - bedroom apartments have higher rental prices than do one - bedroom apartments . let m be the average rental price for all apartments in the b... | "ratio of 2 bedroom apartment : 1 bedroom apartment = 1500 : 6000 - - - - - > 1 : 4 let total number of apartments be x no . of 2 bedroom apartment = ( 1 / 5 ) * x percentage of apartments in the building are two - bedroom apartments - - - - > ( 1 / 5 ) * 100 - - - > 20 % answer : d" | a ) 40 % , b ) 35 % , c ) 30 % , d ) 20 % , e ) 28 % | d | divide(multiply(1,500, const_100), add(add(multiply(const_2, const_1000), const_100), 1,500)) | multiply(n0,const_100)|multiply(const_1000,const_2)|add(#1,const_100)|add(n0,#2)|divide(#0,#3)| | general |
solve below question 2 x - 1 = 17 | 1 . add 1 to both sides : 2 x - 1 + 1 = 17 + 1 2 . simplify both sides : 2 x = 18 3 . divide both sides by 2 : 4 . simplify both sides : x = 9 e | a ) - 8 , b ) - 9 , c ) - 5 , d ) - 4 , e ) 9 | e | divide(negate(add(17, 1)), 2) | add(n1,n2)|negate(#0)|divide(#1,n0)| | general |
john and jane went out for a dinner and they ordered the same dish . both used a 10 % discount coupon . john paid a 15 % tip over the original price of the dish , while jane paid the tip over the discounted price for the coupon . if john paid $ 0.54 more than jane , what was the original price of the dish ? | "the difference between the amounts john paid and jane paid is the deference between 15 % of p and 15 % of 0.9 p : 0.15 p - 0.15 * 0.9 p = 0.54 - - > 15 p - 13.5 p = 54 - - > p = 36 . answer : c ." | a ) 24 , b ) 34.8 , c ) 36 , d ) 42 , e ) 84 | c | divide(0.54, subtract(divide(15, const_100), multiply(subtract(const_1, divide(10, const_100)), divide(15, const_100)))) | divide(n1,const_100)|divide(n0,const_100)|subtract(const_1,#1)|multiply(#0,#2)|subtract(#0,#3)|divide(n2,#4)| | gain |
80 % of 5 / 8 = | "should be simple . 0.8 * 5 / 8 = 4 / 8 = 1 / 2 = 0.5 correct option : b" | a ) 0.2 , b ) 0.5 , c ) 0.6 , d ) 0.75 , e ) 1.0 | b | divide(multiply(divide(multiply(8, 5), const_100), 80), const_100) | multiply(n1,n2)|divide(#0,const_100)|multiply(n0,#1)|divide(#2,const_100)| | general |
if n is a positive integer and n ^ 2 is divisible by 72 , then the largest positive integer t that must divide n is ? | "q : if n is a positive integer and n ^ 2 is divisible by 72 , then the largest positive integer t that must divide n is : a 6 , b 12 , c 24 , d 36 , e 48 n ^ 2 is divisible by 72 , but it must also be greater than 72 . if n is an integer , then n ^ 2 must be a perfect square . the factorization of 72 is ( 8 ) ( 9 ) , ... | a ) 6 , b ) 12 , c ) 24 , d ) 36 , e ) 48 | b | multiply(sqrt(divide(72, 2)), 2) | divide(n1,n0)|sqrt(#0)|multiply(n0,#1)| | general |
angelina walked 720 meters from her home to the grocery at a constant speed . she then walked 480 meters to the gym at double the speed . she spent 40 seconds less on her way from the grocery to the gym than on her way from home to the grocery . what was angelina ' s speed , in meters per second , from the grocery to t... | "let the speed be x . . . so time taken from home to grocery = 720 / x . . the speed to gym = 2 x . . so time taken = 480 / 2 x = 240 / x . . its given 720 / x - 240 / x = 40 . . 480 / x = 40 . . x = 12 m / secs . . so grocery to gym = 2 * 12 = 24 m / s . . . e" | a ) 2 , b ) 3 , c ) 4 , d ) 6 , e ) 24 | e | multiply(divide(subtract(720, divide(480, const_2)), 40), const_2) | divide(n1,const_2)|subtract(n0,#0)|divide(#1,n2)|multiply(#2,const_2)| | physics |
the average age of 15 students of a class is 15 years . out of these , the average age of 5 students is 14 years and that of the other 9 students is 16 years . tee age of the 15 th student is : | "age of the 15 th student = [ 15 * 15 - ( 14 * 5 + 16 * 9 ) ] = ( 225 - 214 ) = 11 years . answer a" | a ) 11 , b ) 14 , c ) 15 , d ) 13 , e ) 18 | a | subtract(multiply(15, 15), add(multiply(5, 14), multiply(9, 16))) | multiply(n0,n0)|multiply(n2,n3)|multiply(n4,n5)|add(#1,#2)|subtract(#0,#3)| | general |
john and peter are among the 9 players a volleyball coach can choose from to field a 6 - player team . if all 6 players are chosen at random , what is the probability of choosing a team that includes john and peter ? | the total possible ways of selecting a 6 - member team is 9 c 6 = 84 the possible ways which include john and peter is 7 c 4 = 35 the probability of choosing both john and peter is 35 / 84 = 5 / 12 the answer is c . | a ) 3 / 10 , b ) 4 / 11 , c ) 5 / 12 , d ) 6 / 13 , e ) 7 / 15 | c | divide(divide(factorial(subtract(9, const_2)), multiply(factorial(subtract(6, const_2)), factorial(subtract(subtract(9, const_2), subtract(6, const_2))))), divide(factorial(9), multiply(factorial(6), factorial(subtract(9, 6))))) | factorial(n0)|factorial(n1)|subtract(n0,const_2)|subtract(n1,const_2)|subtract(n0,n1)|factorial(#2)|factorial(#3)|factorial(#4)|subtract(#2,#3)|factorial(#8)|multiply(#1,#7)|divide(#0,#10)|multiply(#6,#9)|divide(#5,#12)|divide(#13,#11) | probability |
a certain company has records stored with a record storage firm in 15 - inch by 12 - inch by 10 - inch boxes . the boxes occupy 1.08 million cubic inches of space . if the company pays $ 0.6 per box per month for the record storage , what is the total amount that the company pays each month for record storage ? | "volume per box : 15 x 12 x 10 = 1,800 total volume : 1 , 080,000 number of boxes : total volume / volume per box = 1 , 080,000 / 1,800 = 600 price per month : number of boxes * price per box = 600 * 0.6 = 360 answer : e" | a ) a . 150 , b ) b . 300 , c ) c . 600 , d ) d . 1,200 , e ) e . 360 | e | multiply(0.6, divide(1.08, divide(divide(divide(multiply(multiply(15, 12), 10), const_100), const_100), const_100))) | multiply(n0,n1)|multiply(n2,#0)|divide(#1,const_100)|divide(#2,const_100)|divide(#3,const_100)|divide(n3,#4)|multiply(n4,#5)| | general |
how many diagonals does a 62 - sided convex polygon have ? | "a 62 - sided convex polygon has 62 vertices . if we examine a single vertex , we can see that we can connect it with 59 other vertices to create a diagonal . note that we ca n ' t connect the vertex to itself and we ca n ' t connect it to its adjacent vertices , since this would not create a diagonal . if each of the ... | a ) 1829 , b ) 2356 , c ) 3458 , d ) 3843 , e ) 4820 | a | divide(factorial(62), multiply(factorial(subtract(62, const_2)), factorial(const_2))) | factorial(n0)|factorial(const_2)|subtract(n0,const_2)|factorial(#2)|multiply(#3,#1)|divide(#0,#4)| | general |
if y > 0 , ( 8 y ) / 20 + ( 3 y ) / 10 is what percent of y ? | "can be reduced to 4 y / 10 + 3 y / 10 = 7 y / 10 = 70 % answer d" | a ) 40 % , b ) 50 % , c ) 60 % , d ) 70 % , e ) 80 % | d | multiply(const_100, add(divide(8, 20), divide(3, 10))) | divide(n1,n2)|divide(n3,n4)|add(#0,#1)|multiply(#2,const_100)| | general |
how many kg of pure salt must be added to 30 kg of 2 % solution of salt and water to increase it to a 10 % solution ? | "amount salt in 30 kg solution = 2 * 30 / 100 = 0.6 kg let x kg of pure salt be added then ( 0.6 + x ) / ( 30 + x ) = 10 / 100 60 + 100 x = 300 + 10 x 90 x = 240 x = 8 / 3 answer is a" | a ) 8 / 3 , b ) 9 / 7 , c ) 7 / 4 , d ) 5 / 2 , e ) 6 / 7 | a | divide(subtract(10, 2), subtract(const_1, divide(10, 30))) | divide(n2,n0)|subtract(n2,n1)|subtract(const_1,#0)|divide(#1,#2)| | general |
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