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 were totally 100 men . 80 are married . 75 have t . v , 85 have radio , 70 have a . c . how many men have t . v , radio , a . c and also married ? | "100 - ( 100 - 80 ) - ( 100 - 75 ) - ( 100 - 85 ) - ( 100 - 70 ) = 100 - 20 - 25 - 15 - 30 = 100 - 90 = 10 answer : a" | a ) 10 , b ) 12 , c ) 13 , d ) 14 , e ) 15 | a | subtract(100, add(add(add(subtract(100, 80), subtract(100, 75)), subtract(100, 85)), subtract(100, 70))) | subtract(n0,n1)|subtract(n0,n2)|subtract(n0,n3)|subtract(n0,n4)|add(#0,#1)|add(#4,#2)|add(#5,#3)|subtract(n0,#6)| | general |
a boy wanted to calculate his speed on his bike . his starting point was 350 meters from the turning point . he made the round trip 5 times in 30 minutes . what was the boy ' s speed in kilometers per hour ? | the distance between the the starting point and the turning point was 350 meters . the boy made the round trip 5 times so that was 10 times he traveled 350 meters . 10 * 350 = 3500 meters or 3.5 km . 30 minutes is half of an hour . divide the 3500 meters in half to put in the right time interval 3500 / 2 = 1750 meters ... | a ) 1.75 , b ) 1 , c ) 2.25 , d ) 2.4 , e ) 3.2 | a | multiply(5, divide(350, const_1000)) | divide(n0,const_1000)|multiply(n1,#0) | physics |
if it is assumed that 60 percent of those who receive a questionnaire by mail will respond and 222 responses are needed , what is the minimum number of questionnaires that should be mailed ? | "let x be the minimum number of questionnaires to be mailed . 0.6 x = 222 x = 370 the answer is b ." | a ) 280 , b ) 370 , c ) 460 , d ) 550 , e ) 640 | b | divide(222, divide(60, const_100)) | divide(n0,const_100)|divide(n1,#0)| | gain |
to deliver an order on time , a company has to make 25 parts a day . after making 25 parts per day for 3 days , the company started to produce 5 more parts per day , and by the last day of work 100 more parts than planned were produced . how many parts the company made ? | "let x be the number of days the company worked . then 25 x is the number of parts they planned to make . at the new production rate they made : 3 β
25 + ( x β 3 ) β
30 = 75 + 30 ( x β 3 ) therefore : 25 x = 75 + 30 ( x β 3 ) β 100 25 x = 75 + 30 x β 90 β 100 190 β 75 = 30 x β 25 115 = 5 x x = 23 so the company worked ... | a ) 675 , b ) 778 , c ) 654 , d ) 412 , e ) 589 | a | add(multiply(divide(subtract(add(multiply(add(25, 5), 3), 100), multiply(25, 3)), 5), 25), 100) | add(n0,n3)|multiply(n0,n2)|multiply(n2,#0)|add(n4,#2)|subtract(#3,#1)|divide(#4,n3)|multiply(n0,#5)|add(n4,#6)| | physics |
what annual installment will discharge a debt of rs . 1092 due in 3 years at 12 % simple interest ? | "let the installment be rs . x if he keeps the total amount for 3 years , he have to pay the interest of rs . ( 1092 * 12 * 3 ) / 100 . but he paid rs . x after 1 year . so he need not to pay interest for rs . x for remaining 2 years . i . e he need not to pay rs . ( x * 12 * 2 ) / 100 . and he paid another rs . x afte... | a ) 442 , b ) 441 , c ) 440 , d ) 320 , e ) 532 | a | multiply(multiply(const_100.0, divide(12, 1092)), 3) | divide(n2,const_100)|multiply(n0,#0)|multiply(n1,#1)| | gain |
how many integerskgreater than 100 and less than 1100 are there such that if the hundreds and the units digits ofkare reversed , the resulting integer is k + 99 ? | numbers will be like 102 = > 201 = 102 + 99 203 = > 302 = 103 + 99 so the hundereth digit and units digit are consecutive where unit digit is bigger than hundred digit . there will be ninet pairs of such numbers for every pair there will 10 numbers like for 12 = > 102 , 112,132 , 142,152 , 162,172 , 182,192 . total = 9... | a ) 50 , b ) 60 , c ) 70 , d ) 80 , e ) 90 | e | add(multiply(divide(100, const_10), multiply(const_2, const_4)), divide(100, const_10)) | divide(n0,const_10)|multiply(const_2,const_4)|multiply(#0,#1)|add(#0,#2) | general |
sandy walked 20 meters towards south . then sandy turned to her left and walked 20 meters . she then turned to her left and walked 20 meters . she then turned to her right and walked 10 meters . what distance is she from the starting point and in which direction ? | "the net distance is 20 + 10 = 30 meters to the east . the answer is e ." | a ) 35 m east , b ) 35 m north , c ) 30 m west , d ) 45 m west , e ) 30 m east | e | add(20, 10) | add(n0,n3)| | physics |
income and expenditure of a person are in the ratio 3 : 2 . if the income of the person is rs . 21000 , then find his savings ? | let the income and the expenditure of the person be rs . 3 x and rs . 2 x respectively . income , 3 x = 21000 = > x = 7000 savings = income - expenditure = 3 x - 2 x = x so , savings = rs . 7000 . answer : b | a ) 6000 , b ) 7000 , c ) 8000 , d ) 9000 , e ) 10000 | b | subtract(21000, multiply(divide(2, 3), 21000)) | divide(n1,n0)|multiply(n2,#0)|subtract(n2,#1) | other |
in how many ways 4 boys and 3 girls can be seated in a row so that they are alternate . | "solution : let the arrangement be , b g b g b g b 4 boys can be seated in 4 ! ways . girl can be seated in 3 ! ways . required number of ways , = 4 ! * 3 ! = 144 . answer : option a" | a ) 144 , b ) 288 , c ) 12 , d ) 256 , e ) none | a | multiply(factorial(4), factorial(3)) | factorial(n0)|factorial(n1)|multiply(#0,#1)| | probability |
the ratio of the radius of two circles is 4 : 3 , and then the ratio of their areas is ? | "r 1 : r 2 = 4 : 3 Ο r 12 : Ο r 22 r 12 : r 22 = 16 : 9 answer : d" | a ) 1 : 8 , b ) 1 : 6 , c ) 1 : 9 , d ) 16 : 9 , e ) 1 : 2 | d | divide(circle_area(4), circle_area(3)) | circle_area(n0)|circle_area(n1)|divide(#0,#1)| | geometry |
in a function , every person shakes hand with every other person . if there was a total of 28 handshakes in the function , how many persons were present in the function ? | suppose there are nn persons present in a function and every person shakes hand with every other person . then , total number of handshakes = nc 2 = n ( n β 1 ) / 2 n ( n β 1 ) = 28 Γ 2 n ( n β 1 ) = 56 n = 8 answer a 8 | a ) 8 , b ) 7 , c ) 2 , d ) 6 , e ) 5 | a | subtract(subtract(28, const_10), const_10) | subtract(n0,const_10)|subtract(#0,const_10) | general |
3 * 16 + 3 * 17 + 3 * 20 + 11 = ? | "3 * 16 + 3 * 17 + 3 * 20 + 11 = 48 + 51 + 60 + 11 = 170 the answer is e ." | a ) 121 , b ) 129 , c ) 138 , d ) 152 , e ) 170 | e | add(add(add(multiply(3, 16), multiply(3, 17)), multiply(3, 20)), 11) | multiply(n0,n1)|multiply(n0,n3)|multiply(n0,n5)|add(#0,#1)|add(#3,#2)|add(n6,#4)| | general |
if x = - 2 and y = - 4 , what is the value of 5 ( x - y ) ^ 2 - xy ? | "x = - 2 and y = - 4 x - y = - 2 - ( - 4 ) = - 2 + 4 = 2 x * y = - 2 * - 4 = 8 now we apply it in the equation 5 ( x - y ) ^ 2 - xy = 5 ( 2 ) ^ 2 - 8 = = > 5 * 4 - 8 = 20 - 8 = 12 answer : a" | a ) 12 , b ) 13 , c ) 15 , d ) 18 , e ) 22 | a | subtract(multiply(power(subtract(negate(2), negate(4)), 2), 5), multiply(negate(2), negate(4))) | negate(n0)|negate(n1)|multiply(#0,#1)|subtract(#0,#1)|power(#3,n3)|multiply(n2,#4)|subtract(#5,#2)| | general |
on the number line , if x is halfway between - 8 and 4 , and if y is halfway between - 4 and 6 , what number is halfway between x and y ? | "x = - 2 and y = 1 . the answer is b ." | a ) - 1.5 , b ) - 0.5 , c ) 0.5 , d ) 1.5 , e ) 2.5 | b | add(negate(8), 4) | negate(n0)|add(n1,#0)| | general |
a train speeds past a pole in 15 sec and a platform 120 m long in 25 sec , its length is ? | "let the length of the train be x m and its speed be y m / sec . then , x / y = 15 = > y = x / 15 ( x + 120 ) / 25 = x / 15 = > x = 180 m . answer : option e" | a ) 100 , b ) 150 , c ) 160 , d ) 170 , e ) 180 | e | multiply(120, subtract(const_2, const_1)) | subtract(const_2,const_1)|multiply(n1,#0)| | physics |
a library has an average of 660 visitors on sundays and 240 on other days . the average number of visitors per day in a month of 30 days beginning with a sunday is : | "since the month begins with sunday , to there will be five sundays in the month average required = ( 660 x 5 + 240 x 25 ) / 30 ) = 310 answer : option d" | a ) 250 , b ) 276 , c ) 280 , d ) 310 , e ) none | d | divide(add(multiply(add(floor(divide(30, add(const_3, const_4))), const_1), 660), multiply(subtract(30, add(floor(divide(30, add(const_3, const_4))), const_1)), 240)), 30) | add(const_3,const_4)|divide(n2,#0)|floor(#1)|add(#2,const_1)|multiply(n0,#3)|subtract(n2,#3)|multiply(n1,#5)|add(#4,#6)|divide(#7,n2)| | general |
mr . riddle invested in fund x and fund y . the total amount she invested , in both funds combined , was $ 200000 . in one year , fund x paid 43 % and fund y paid 28 % . the interest earned in fund y was exactly $ 200 greater than the interest earned in fund x . how much did ms . tom invest in fund x ? | x + y = 200000 0.28 y = 0.43 a + 300 take away decimals first : 28 y + 43 x + 20000 isolate first equation to solve for x ( your goal ) : y = 200000 - y plug in for b : 28 ( 200000 - x ) = 43 x + 30000 5 , 600000 - 28 x = 43 x + 30000 5 , 570000 = 71 x 5 , 570000 / 71 = x 5 , 570000 / 71 = x x = 78 , 450.70 = answer ch... | a ) 43 , 870.34 , b ) 56 , 876.45 , c ) 77 , 789.45 , d ) 78 , 450.70 , e ) 87 , 987.34 | d | add(divide(divide(multiply(subtract(divide(multiply(200000, 28), const_100), 200), const_100), add(43, 28)), const_100), subtract(const_100, const_10)) | add(n1,n2)|multiply(n0,n2)|subtract(const_100,const_10)|divide(#1,const_100)|subtract(#3,n3)|multiply(#4,const_100)|divide(#5,#0)|divide(#6,const_100)|add(#7,#2) | gain |
at the faculty of aerospace engineering , 312 students study random - processing methods , 232 students study scramjet rocket engines and 114 students study them both . if every student in the faculty has to study one of the two subjects , how many students are there in the faculty of aerospace engineering ? | 312 + 232 - 114 ( since 112 is counted twice ) = 430 c is the answer | a ) 438 , b ) 436 , c ) 430 , d ) 442 , e ) 444 | c | add(subtract(312, divide(114, const_2)), subtract(232, divide(114, const_2))) | divide(n2,const_2)|subtract(n0,#0)|subtract(n1,#0)|add(#1,#2) | other |
two boats are heading towards each other at constant speeds of 5 miles / hr and 25 miles / hr respectively . they begin at a distance 20 miles from each other . how far are they ( in miles ) one minute before they collide ? | "the question asks : how far apart will they be 1 minute = 1 / 60 hours before they collide ? since the combined rate of the boats is 5 + 25 = 30 mph then 1 / 60 hours before they collide they ' ll be rate * time = distance - - > 30 * 1 / 60 = 1 / 2 miles apart . answer : d ." | a ) 1 / 12 , b ) 5 / 12 , c ) 1 / 6 , d ) 1 / 2 , e ) 1 / 5 | d | divide(add(25, 5), const_60) | add(n0,n1)|divide(#0,const_60)| | physics |
excluding stoppages , the speed of a train is 45 kmph and including stoppages it is 32 kmph . of how many minutes does the train stop per hour ? | "explanation : t = 13 / 45 * 60 = 17 answer : option a" | a ) 17 , b ) 83 , c ) 12 , d ) 83 , e ) 28 | a | subtract(const_60, multiply(const_60, divide(32, 45))) | divide(n1,n0)|multiply(#0,const_60)|subtract(const_60,#1)| | physics |
a and b together can do a piece of work in 8 days . if a alone can do the same work in 12 days , then b alone can do the same work in ? | b = 1 / 8 β 1 / 2 = 1 / 24 = > 24 days answer : c | a ) 49 , b ) 99 , c ) 24 , d ) 88 , e ) 21 | c | inverse(subtract(inverse(8), inverse(12))) | inverse(n0)|inverse(n1)|subtract(#0,#1)|inverse(#2)| | physics |
company z has 48 employees . if the number of employees having birthdays on wednesday is more than the number of employees having birthdays on any other day of the week , each of which have same number of birth - days , what is the minimum number of employees having birthdays on wednesday . | "say the number of people having birthdays on wednesday is x and the number of people having birthdays on each of the other 6 days is y . then x + 6 y = 48 . now , plug options for x . only a and e give an integer value for y . but only for e x > y as needed . answer : e ." | a ) 6 , b ) 7 , c ) 8 , d ) 9 , e ) 12 | e | add(const_4, add(floor(divide(48, add(const_4, const_3))), const_1)) | add(const_3,const_4)|divide(n0,#0)|floor(#1)|add(#2,const_1)|add(#3,const_4)| | general |
in a fuel station the service costs $ 2.05 per car , every liter of fuel costs 0.6 $ . assuming that you fill up 3 mini - vans and 2 trucks , how much money will the fuel cost to all the cars owners total , if a mini - van ' s tank is 65 liters and a truck ' s tank is 120 % bigger and they are all empty - ? | "mini van cost = 65 * 0.6 + 2.05 truck capacity = 65 ( 1 + 120 / 100 ) = 143 lts . cost of truck = 143 + 0.6 + 2.05 total cost = 3 * 41.05 ( car ) + 2 * 87.85 ( truck ) = 298.85 answer : d" | a ) 122.6 $ , b ) 128.9 $ , c ) 243.7 $ , d ) 298.85 $ , e ) 312.12 $ | d | add(multiply(multiply(add(65, divide(multiply(65, 120), const_100)), 2), 0.6), multiply(multiply(65, 3), 0.6)) | multiply(n4,n5)|multiply(n2,n4)|divide(#0,const_100)|multiply(n1,#1)|add(n4,#2)|multiply(n3,#4)|multiply(n1,#5)|add(#6,#3)| | general |
a two - digit number is such that the product of the digits is 8 . when 18 is added to the number , then the digits are reversed . the number is : | "answer : option b let the ten ' s and unit ' s digit be x and 8 / x respectively . then , ( 10 x + 8 / x ) + 18 = 10 * 8 / x + x 9 x 2 + 18 x - 72 = 0 x 2 + 2 x - 8 = 0 ( x + 4 ) ( x - 2 ) = 0 x = 2 so , ten ' s digit = 2 and unit ' s digit = 4 . hence , required number = 24 ." | a ) 32 , b ) 24 , c ) 12 , d ) 7 , e ) 45 | b | divide(18, subtract(const_10, const_1)) | subtract(const_10,const_1)|divide(n1,#0)| | general |
by selling 95 pens , a trader gains the cost of 19 pens . find his gain percentage ? | "let the cp of each pen be rs . 1 . cp of 95 pens = rs . 95 profit = cost of 19 pens = rs . 19 profit % = 19 / 95 * 100 = 20 % answer : a" | a ) 20 % , b ) 21 % , c ) 22 % , d ) 23 % , e ) 24 % | a | multiply(divide(19, 95), const_100) | divide(n1,n0)|multiply(#0,const_100)| | gain |
there are 193 items that are members of set u . of these items , 41 are members of set b , 59 are not members of either of set a or set b , and 23 are members of both sets a and b . how many of the members of set u are members of set a ? | "you had the answer almost right . the x = 93 refers to only set a . however what ' s being asked is how many members are part of set a . this will include : 1 . only set a 2 . set a and set b so the answer is set a = 93 + set ab = 93 + 23 = 116 a" | a ) 116 , b ) 85 , c ) 94 , d ) 98 , e ) 108 | a | subtract(add(subtract(193, 59), 23), 41) | subtract(n0,n2)|add(n3,#0)|subtract(#1,n1)| | other |
a machine can filled a tank in 25 minutes and another machine can empty it in 50 minutes . if the tank is already half full and both the taps are opened together , then the tank is filled in how many minutes ? | t = 1 / 2 ( 25 * 50 / 50 - 25 ) = 25 minutes tank is filled in 25 minutes answer is a | a ) 25 min , b ) 20 min , c ) 10 min , d ) 15 min , e ) 30 min | a | divide(divide(const_1, subtract(divide(const_1, 25), divide(const_1, 50))), const_2) | divide(const_1,n0)|divide(const_1,n1)|subtract(#0,#1)|divide(const_1,#2)|divide(#3,const_2) | physics |
a hall 36 m long and 15 m broad is to be paved with stones , each measuring 8 dm by 5 dm . the number of stones required is : | "area of the hall = 3600 * 1500 area of each stone = ( 80 * 50 ) therefore , number of stones = ( 3600 * 1500 / 80 * 50 ) = 1350 answer : e" | a ) 180 , b ) 1800 , c ) 18 , d ) 18000 , e ) 1350 | e | divide(multiply(36, 15), divide(multiply(8, 5), const_100)) | multiply(n0,n1)|multiply(n2,n3)|divide(#1,const_100)|divide(#0,#2)| | physics |
at company x , senior sales representatives visit the home office once every 16 days , and junior sales representatives visit the home office once every 12 days . the number of visits that a junior sales representative makes in a 2 - year period is approximately what percent greater than the number of visits that a sen... | each 48 - day period , senior representatives visit the home office 3 times while junior representatives visit 4 times , thus 33 % more . the answer is c . | a ) 10 % , b ) 25 % , c ) 33 % , d ) 50 % , e ) 67 % | c | multiply(add(const_1, const_10), subtract(subtract(16, 12), const_1)) | add(const_1,const_10)|subtract(n0,n1)|subtract(#1,const_1)|multiply(#0,#2) | general |
in n is a positive integer less than 200 , and 14 n / 60 is an integer , then n has how many different positive prime factors q ? | "i like to put the numbers in prime factors so it is easier and faster to visualize . 14 * n / 60 if we write the factors of 14 - - > 2 , 7 , and the factors of 60 - - > 2 , 2 , 3 , 5 , we have ( 2 * 7 * n ) / ( 2 ^ 2 * 3 * 5 ) simplifying 7 * n / ( 2 * 3 * 5 ) the only way the equation above has an integer value is if... | a ) 2 , b ) 3 , c ) 5 , d ) 6 , e ) 8 | b | add(divide(add(const_1, const_4), divide(divide(divide(60, const_2), const_2), const_3)), const_2) | add(const_1,const_4)|divide(n2,const_2)|divide(#1,const_2)|divide(#2,const_3)|divide(#0,#3)|add(#4,const_2)| | general |
the two lines y = x and x = - 9 intersect on the coordinate plane . what is the value of the area of the figure formed by the intersecting lines and the x - axis ? | the point of intersection is ( - 9 , - 9 ) . the triangle has a base of length 9 and a height of 9 . area = ( 1 / 2 ) * base * height = ( 1 / 2 ) * 9 * 9 = 40.5 the answer is c . | a ) 32.5 , b ) 36.5 , c ) 40.5 , d ) 44.5 , e ) 48.5 | c | divide(multiply(9, 9), const_2) | multiply(n0,n0)|divide(#0,const_2) | general |
at a certain food stand , the price of each apple is 40 Β’ and the price of each orange is 60 Β’ . mary selects a total of 10 apples and oranges from the food stand , and the average ( arithmetic mean ) price of the 10 pieces of fruit is 54 Β’ . how many oranges must mary put back so that the average price of the pieces o... | "if the average price is 54 , then mary has 7 oranges and 3 apples ( a ratio of 7 : 3 ) . for the average price to be 50 , the ratio should be 1 : 1 . mary must put back 4 oranges . the answer is d ." | a ) 1 , b ) 2 , c ) 3 , d ) 4 , e ) 5 | d | divide(subtract(add(multiply(divide(subtract(multiply(60, 10), multiply(54, 10)), subtract(60, 40)), 40), multiply(subtract(10, divide(subtract(multiply(60, 10), multiply(54, 10)), subtract(60, 40))), 60)), multiply(50, 10)), subtract(60, 50)) | multiply(n1,n2)|multiply(n2,n4)|multiply(n2,n5)|subtract(n1,n0)|subtract(n1,n5)|subtract(#0,#1)|divide(#5,#3)|multiply(n0,#6)|subtract(n2,#6)|multiply(n1,#8)|add(#7,#9)|subtract(#10,#2)|divide(#11,#4)| | general |
a store has 10 bottles of juice , including 5 bottles of apple juice . in the evening , 6 bottles of juice are sold one by one . what is the probability of selling 4 bottles of apple juice among the 6 bottles ? assume that every bottle has an equal chance of being bought . | "the total number of ways to sell 6 bottles from 10 is 10 c 6 = 210 . the number of ways to sell 4 bottles of apple juice is 5 c 4 * 5 c 2 = 5 * 10 = 50 p ( selling 4 bottles of apple juice ) = 50 / 210 = 5 / 21 the answer is d ." | a ) 2 / 7 , b ) 3 / 11 , c ) 4 / 15 , d ) 5 / 21 , e ) 6 / 25 | d | divide(choose(5, 4), choose(10, 5)) | choose(n1,n3)|choose(n0,n1)|divide(#0,#1)| | probability |
a student got 71 % in math and 81 % in history . to get an overall average of 75 % , how much should the student get in the third subject ? | "71 + 81 + x = 3 * 75 x = 73 the answer is a ." | a ) 63 % , b ) 75 % , c ) 77 % , d ) 79 % , e ) 81 % | a | subtract(multiply(const_3, 75), add(71, 81)) | add(n0,n1)|multiply(n2,const_3)|subtract(#1,#0)| | general |
m and n are the x and y coordinates , respectively , of a point in the coordinate plane . if the points ( m , n ) and ( m + p , n + 9 ) both lie on the line defined by the equation x = ( y / 3 ) - ( 2 / 5 ) , what is the value of p ? | "x = ( y / 3 ) - ( 2 / 5 ) , and so y = 3 x + 6 / 5 . the slope is 3 . ( n + 9 - n ) / ( m + p - m ) = 3 p = 3 the answer is c ." | a ) 1 , b ) 2 , c ) 3 , d ) 4 , e ) 5 | c | divide(9, 3) | divide(n0,n1)| | general |
at an international conference , β red β world countries and β blue β world countries are the only participants . the ratio of β red β world participants to β blue β world participants is 5 : 5 . if one - third of β red β world participants are left - handed and two - thirds of β blue β world participants are left - ha... | "red : blue = 5 : 5 let red = 5 x and blue = 5 x 1 / 3 of red are left handed = > 1 / 3 * 5 x = 5 x / 3 red left handed 2 / 3 of blue are left handed = > 2 / 3 * 5 x = 10 x / 3 blue left handed fraction of participants who are left handed = total left handed / total participants = ( red left handed + blue left handed )... | a ) 1 / 4 , b ) 1 / 8 , c ) 1 / 6 , d ) 1 / 2 , e ) 1 | d | divide(add(multiply(5, const_0_33), multiply(5, divide(const_2, const_3))), add(5, 5)) | add(n0,n1)|divide(const_2,const_3)|multiply(n0,const_0_33)|multiply(n1,#1)|add(#2,#3)|divide(#4,#0)| | other |
what is the remainder when 42 * 49 is divided by 8 ? | "we can make use of the rule : remainder of { ( a * b ) / n } } = remainder of ( a / n ) * remainder of ( b / n ) here remainder of { 42 * 49 ) / 8 } } = remainder of ( 42 / 8 ) * remainder of ( 49 / 8 ) = 2 * 1 = 2 answer : b" | a ) 1 , b ) 2 , c ) 4 , d ) 5 , e ) 7 | b | subtract(divide(8, const_2), multiply(42, 42)) | divide(n2,const_2)|multiply(n0,n0)|subtract(#0,#1)| | general |
1 + 2 + 3 + . . . + 12 = ? | 1 + 2 + 3 + β― + n = β n = n ( n + 1 ) / 2 1 + 2 + 3 + β― + 12 = n ( n + 1 ) / 2 = ( 12 ( 12 + 1 ) ) / 2 = ( 12 Γ 13 ) / 2 = 6 Γ 13 = 78 answer is c | a ) 76 , b ) 68 , c ) 78 , d ) 66 , e ) 67 | c | divide(multiply(12, add(12, 1)), 2) | add(n0,n3)|multiply(n3,#0)|divide(#1,n1) | general |
the largest 4 digit number exactly divisible by 77 is ? | "largest 4 - digit number = 9999 77 ) 9999 ( 129 9933 answer : b" | a ) 9935 , b ) 9933 , c ) 9944 , d ) 9954 , e ) 9960 | b | square_area(const_pi) | square_area(const_pi)| | general |
a room of 6 m 44 cm long and 3 m 00 cm broad is to be paved with square tiles . find the least number of square tiles required to cover the floor . | "explanation : area of the room = 644 * 300 sq cm size of largest square tile = h . c . f of 644 cm and 300 cm = 4 cm area of 1 tile = 4 * 4 sq cm no . of tiles required = ( 644 * 300 ) / ( 4 * 4 ) = 12075 answer : d ) 12075" | a ) 12076 , b ) 12070 , c ) 12077 , d ) 12075 , e ) 12074 | d | divide(multiply(add(multiply(6, const_100), 44), add(multiply(3, const_100), 00)), power(divide(add(multiply(6, const_100), 44), power(const_2, const_4)), const_2)) | multiply(n0,const_100)|multiply(n2,const_100)|power(const_2,const_4)|add(n1,#0)|add(n3,#1)|divide(#3,#2)|multiply(#3,#4)|power(#5,const_2)|divide(#6,#7)| | physics |
7 people average age is 30 . youngest person age is 6 . find average of the people when youngest was born . | "average age of people = 30 so have total age = 210 before 7 years we have to deduct each person age by seven years 210 - 42 = 161 so average age would be 161 / 7 = 24 answer : b" | a ) 23 , b ) 24 , c ) 25 , d ) 26 , e ) 27 | b | divide(subtract(multiply(30, 7), multiply(6, 7)), 7) | multiply(n0,n1)|multiply(n0,n2)|subtract(#0,#1)|divide(#2,n0)| | general |
if 4 men can reap 40 acres of land in 15 days , how many acres of land can 16 men reap in 30 days ? | "4 men 40 acres 15 days 16 men ? 30 days 40 * 16 / 4 * 30 / 15 40 * 4 * 2 40 * 8 = 320 answer : a" | a ) 320 , b ) 240 , c ) 369 , d ) 489 , e ) 125 | a | multiply(40, multiply(divide(16, 4), divide(30, 15))) | divide(n3,n0)|divide(n4,n2)|multiply(#0,#1)|multiply(n1,#2)| | physics |
in the excel manufacturing company , 46 percent of the employees are men . if 60 percent of the employees are unionized and 70 percent of these are men , what percent of the non - union employees are women ? | lets say there are total 100 employees then men = 46 & women = 54 unionized emp = 60 & non unionized emp = 40 men unionized = . 7 * 60 = 42 women unionized = 18 women non - unionized = 54 - 18 = 36 percentage of women non unionized = 36 / 40 * 100 = 90 % the answer is option a | a ) 90 % , b ) 87.5 % , c ) 66.7 % , d ) 50 % , e ) 36 % | a | multiply(divide(subtract(subtract(const_100, 46), subtract(60, multiply(divide(70, const_100), 60))), subtract(const_100, 60)), const_100) | divide(n2,const_100)|subtract(const_100,n0)|subtract(const_100,n1)|multiply(n1,#0)|subtract(n1,#3)|subtract(#1,#4)|divide(#5,#2)|multiply(#6,const_100) | general |
a library branch originally contained 18360 volumes , 30 % of which were fiction novels . 1 / 3 of the volumes were transferred to another location and 1 / 4 of the volumes transferred were fiction novels . what percent of the remaining collection was fiction novels ? | "fiction novels = 5,508 transferred to another location = 6,120 transferred fiction novels = 1,530 non transferred fiction novels = 3,978 percent of the remaining collection was fiction novels = 3978 / ( 18360 - 6120 ) * 100 = > 32.5 % hence answer will be ( e )" | a ) 2.5 % , b ) 17.67 % , c ) 28.3 % , d ) 45.2 % , e ) 32.5 % | e | multiply(divide(multiply(divide(30, const_100), subtract(1, divide(1, 4))), subtract(1, divide(1, 3))), const_100) | divide(n1,const_100)|divide(n2,n5)|divide(n2,n3)|subtract(n2,#1)|subtract(n2,#2)|multiply(#0,#3)|divide(#5,#4)|multiply(#6,const_100)| | gain |
a man was asked to state his age in years . his reply was , ` ` take my age 6 years hence , multiply it by 6 and subtract 6 times my age 6 years ago and you will know how old i am . ' ' what was the age of the person ? | explanation : let the present age of person be x years . then , 6 ( x + 6 ) - 6 ( x - 6 ) = x < = > ( 6 x + 36 ) - ( 6 x - 36 ) = x < = > x = 72 . . answer : c | a ) 18 , b ) 92 , c ) 72 , d ) 26 , e ) 19 | c | multiply(add(6, 6), 6) | add(n0,n0)|multiply(n0,#0) | general |
if the average ( arithmetic mean ) of x and y is 40 , and z β x = 60 , what is the average of y and z ? | "x + y / 2 = 40 = > x + y = 80 x = z - 60 . . . sub this value z - 60 + y = 80 = > z + y = 140 = > z + y / 2 = 70 . answer : d" | a ) 20 , b ) 50 , c ) 65 , d ) 70 , e ) 140 | d | subtract(multiply(60, const_2), multiply(40, const_2)) | multiply(n1,const_2)|multiply(n0,const_2)|subtract(#0,#1)| | general |
find the simple interest on rs . 235 for 3 months at 8 paisa per month ? | "explanation : i = ( 235 * 3 * 8 ) / 100 = 56.4 answer : option b" | a ) s . 57.8 , b ) s . 56.4 , c ) s . 29.3 , d ) s . 33 , e ) s . 74 | b | multiply(235, divide(3, const_100)) | divide(n1,const_100)|multiply(n0,#0)| | gain |
a , b and c started a business with capitals of rs . 8000 , rs . 10000 and rs . 12000 respectively . at the end of the year , the profit share of b is rs . 1800 . the difference between the profit shares of a and c is ? | "ratio of investments of a , b and c is 8000 : 10000 : 12000 = 4 : 5 : 6 and also given that , profit share of b is rs . 1800 = > 5 parts out of 15 parts is rs . 1800 now , required difference is 6 - 4 = 2 parts required difference = 2 / 5 ( 1800 ) = rs . 720 answer : a" | a ) 720 , b ) 266 , c ) 155 , d ) 600 , e ) 441 | a | multiply(subtract(divide(12000, 10000), divide(8000, 10000)), 1800) | divide(n2,n1)|divide(n0,n1)|subtract(#0,#1)|multiply(n3,#2)| | gain |
the length of a bridge in meters , which a train 120 - meters long and traveling at 45 km / hr can cross in 30 seconds is ? | "45 km / h = 45000 m / 3600 s = 12.5 m / s in 30 seconds , the train can go 30 ( 12.5 ) = 375 meters let x be the length of the bridge . x + 120 = 375 meters x = 255 meters the answer is a ." | a ) 255 , b ) 285 , c ) 315 , d ) 345 , e ) 375 | a | subtract(multiply(divide(multiply(45, const_1000), const_3600), 30), 120) | multiply(n1,const_1000)|divide(#0,const_3600)|multiply(n2,#1)|subtract(#2,n0)| | physics |
of 70 players on a football team , 49 are throwers . the rest of the team is divided so one third are left - handed and the rest are right handed . assuming that all throwers are right handed , how many right - handed players are there total ? | total = 70 thrower = 49 rest = 70 - 49 = 21 left handed = 21 / 3 = 7 right handed = 14 if all thrower are right handed then total right handed is 49 + 14 = 63 so c . 63 is the right answer | a ) 54 , b ) 59 , c ) 63 , d ) 71 , e ) 92 | c | add(multiply(subtract(const_1, divide(const_1, const_3)), subtract(70, 49)), 49) | divide(const_1,const_3)|subtract(n0,n1)|subtract(const_1,#0)|multiply(#2,#1)|add(n1,#3) | general |
jack has two dice , one has 6 equally probable sides , labeled 1 , 2 , 3 , 4 , 5 , 6 , and the other has 7 equally probable sides , labeled 1 , 2 , 3 , 4 , 5 , 6 , 7 . if jack rolls both dice what is the probability that both of the numbers will be 3 ? | method - 1 probability that the number on first die is 3 = 1 / 6 probability that the number on second die is 3 = 1 / 7 probability that both dice result in odd numbers = ( 1 / 6 ) * ( 1 / 7 ) = 1 / 42 answer : option d | a ) 3 / 14 , b ) 2 / 7 , c ) 1 / 3 , d ) 1 / 42 , e ) 12 / 21 | d | multiply(divide(const_1, 6), divide(const_1, 7)) | divide(const_1,n0)|divide(const_1,n7)|multiply(#0,#1) | other |
a number divided by 44 leaves remainder 12 what is the remainder when same number divided by 12 | "add 44 + 12 = 56 now 56 divided by 12 so we get 8 as reaminder answer : b" | a ) 7 , b ) 8 , c ) 9 , d ) 10 , e ) 11 | b | divide(subtract(12, 12), subtract(12, 12)) | subtract(n1,n2)|divide(#0,#0)| | general |
a person walks at a speed of 4 km / hr and runs at a speed of 8 km / hr . how many hours will the person require to cover a distance of 16 km , if the person completes half of the distance by walking and the other half by running ? | time = 8 / 4 + 8 / 8 = 3 hours the answer is c . | a ) 2 , b ) 2.5 , c ) 3 , d ) 3.5 , e ) 4 | c | add(divide(divide(16, const_2), 4), divide(divide(16, const_2), 8)) | divide(n2,const_2)|divide(#0,n0)|divide(#0,n1)|add(#1,#2) | physics |
change the below lagarithm log 255 = 1 / 2 to exponential form | solution : log 255 = 251 / 2 = 5 answer is a | a ) 5 , b ) 8 , c ) 7 , d ) 10 , e ) 11 | a | subtract(subtract(subtract(subtract(255, const_100), const_100), multiply(const_10, const_4)), const_10) | multiply(const_10,const_4)|subtract(n0,const_100)|subtract(#1,const_100)|subtract(#2,#0)|subtract(#3,const_10) | general |
the length of a rectangle is twice its breadth . if its length is decreased by 5 cm and breadth is increased by 5 cm , the area of the rectangle is increased by 75 sq . cm . find the length of the rectangle ? | "let the breadth of the given rectangle be x then length is 2 x . thus area of the given rect is \ fn _ jvn { \ color { black } 2 x ^ { 2 } } after dec 5 cm from length and inc 5 cm breadth , new lenght becomes 2 x - 5 and breadth is x + 5 . thus new area = ( 2 x - 5 ) ( x + 5 ) = \ fn _ jvn { \ color { black } 2 x ^ {... | a ) 10 cm , b ) 40 cm , c ) 20 cm , d ) 30 cm , e ) 50 cm | b | divide(const_100, const_3) | divide(const_100,const_3)| | geometry |
by selling 16 pencils for a rupee a man loses 10 % . how many for a rupee should he sell in order to gain 20 % ? | "90 % - - - 16 120 % - - - ? 90 / 120 * 16 = 12 answer : c" | a ) 8 , b ) 9 , c ) 12 , d ) 89 , e ) 81 | c | multiply(divide(const_1, multiply(add(const_100, 20), divide(const_1, subtract(const_100, 10)))), 16) | add(n2,const_100)|subtract(const_100,n1)|divide(const_1,#1)|multiply(#0,#2)|divide(const_1,#3)|multiply(n0,#4)| | gain |
if it takes a machine 2 β 3 minute to produce one item , how many items will it produce in 1 hours ? | "1 item takes 2 / 3 min so it takes 60 min to produce x 2 x / 3 = 60 the x = 90 answer : c" | a ) 1 β 3 , b ) 4 β 3 , c ) 90 , d ) 120 , e ) 180 | c | divide(multiply(1, const_60), divide(2, 3)) | divide(n0,n1)|multiply(n2,const_60)|divide(#1,#0)| | physics |
a batsman makes a score of 65 runs in the 17 th inning and thus increases his average by 3 . find his average after 17 th inning . | let the average after 17 th inning = x . then , average after 16 th inning = ( x β 3 ) . β΄ 16 ( x β 3 ) + 65 = 17 x or x = ( 65 β 48 ) = 17 . answer a | a ) 17 , b ) 39 , c ) 42 , d ) 45 , e ) none of the above | a | add(subtract(65, multiply(17, 3)), 3) | multiply(n1,n2)|subtract(n0,#0)|add(n2,#1) | general |
an article is bought for rs . 675 and sold for rs . 1200 , find the gain percent ? | "675 - - - - 525 100 - - - - ? = > = 78 % answer : c" | a ) 87 % , b ) 88 % , c ) 78 % , d ) 75 % , e ) 73 % | c | subtract(const_100, divide(multiply(1200, const_100), 675)) | multiply(n1,const_100)|divide(#0,n0)|subtract(const_100,#1)| | gain |
the distance between two cities a and b is 1410 km . a train starts from a at 8 a . m . and travel towards b at 60 km / hr . another train starts from b at 9 a . m and travels towards a at 75 km / hr . at what time do they meet ? | "explanation : suppose they meet x hrs after 8 a . m then , [ distance moved by first in x hrs ] + [ distance moved by second in ( x - 1 ) hrs ] = 1410 . therefore , 60 x + 75 ( x - 1 ) = 1410 . = > x = 3 . so , they meet at ( 8 + 11 ) i . e , 7 pm . answer : b" | a ) 09 pm , b ) 07 pm , c ) 11 pm , d ) 05 am , e ) 03 am | b | add(divide(add(1410, 75), add(60, 75)), 8) | add(n0,n4)|add(n2,n4)|divide(#0,#1)|add(n1,#2)| | physics |
tom opened a shop investing rs . 3000 . jose joined him 2 months later , investing rs . 4000 . they earned a profit of rs . 4230 after completion of one year . what will be jose ' s share of profit ? | "sol = ~ s - so anju β s share = [ 5 / 9 ] x 4230 = 2350 d" | a ) 2000 , b ) 2200 , c ) 2309 , d ) 2350 , e ) 3250 | d | multiply(4230, subtract(const_1, divide(multiply(3000, multiply(2, multiply(2, const_3))), add(multiply(4000, subtract(multiply(2, multiply(2, const_3)), 2)), multiply(3000, multiply(2, multiply(2, const_3))))))) | multiply(n1,const_3)|multiply(#0,n1)|multiply(n0,#1)|subtract(#1,n1)|multiply(n2,#3)|add(#4,#2)|divide(#2,#5)|subtract(const_1,#6)|multiply(n3,#7)| | gain |
a student got twice as many sums wrong as he got right . if he attempted 54 sums in all , how many did he solve correctly ? | "explanation : suppose the boy got x sums right and 2 x sums wrong . then , x + 2 x = 54 3 x = 54 x = 18 . answer : c" | a ) 12 , b ) 16 , c ) 18 , d ) 24 , e ) 26 | c | divide(54, add(const_1, const_2)) | add(const_1,const_2)|divide(n0,#0)| | general |
the instructions state that deepthi needs 4 / 17 square yards of one type of material and 3 / 10 square yards of another type of material for a project . she buys exactly that amount . after finishing the project , however , she has 9 / 30 square yards left that she did not use . what is the total amount of square yard... | total bought = 4 / 17 + 3 / 10 left part 9 / 30 - - - > 3 / 10 so used part 4 / 17 + 3 / 10 - 3 / 10 = 4 / 17 answer : b | a ) 1 / 12 , b ) 4 / 17 , c ) 2 / 3 , d ) 1 1 / 9 , e ) 2 1 / 9 | b | subtract(add(divide(4, 17), divide(const_3, const_10)), divide(9, 30)) | divide(n0,n1)|divide(const_3,const_10)|divide(n4,n5)|add(#0,#1)|subtract(#3,#2) | general |
a certain city with a population of 108,000 is to be divided into 11 voting districts , and no district is to have a population that is more than 10 percent greater than the population of any other district what is the minimum possible population that the least populated district could have ? | "let x = number of people in smallest district x * 1.1 = number of people in largest district x will be minimised when the number of people in largest district is maximised 10 * x * 1.1 = 11 x = total number of people in other districts so we have 11 x + x = 108 k x = 9,000 answer : c" | a ) a ) 10,700 , b ) b ) 10,800 , c ) c ) 9,000 , d ) d ) 11,000 , e ) e ) 11,100 | c | multiply(multiply(const_4, const_2), const_100) | multiply(const_2,const_4)|multiply(#0,const_100)| | general |
company p had 15 percent more employees in december than it had in january . if company p had 470 employees in december , how many employees did it have in january ? | "d = number of employees in december j = number of employees in january j x 1.15 = d j x 1.15 = 470 j = 470 / 1.15 j = 47,000 / 115 = 408 thus b is the correct answer ." | a ) 391 , b ) 408 , c ) 410 , d ) 423 , e ) 445 | b | divide(470, add(const_1, divide(15, const_100))) | divide(n0,const_100)|add(#0,const_1)|divide(n1,#1)| | gain |
a , b and c can do a piece of work in 5 days , 10 days and 15 days respectively . how long will they taken , if all the three work together ? | "1 / 5 + 1 / 10 + 1 / 15 = 11 / 30 = > 30 / 11 = > 2 8 / 11 days answer : c" | a ) 2 , b ) 4 , c ) 2 8 / 11 , d ) 67 , e ) 9 | c | inverse(add(inverse(15), add(inverse(5), inverse(10)))) | inverse(n0)|inverse(n1)|inverse(n2)|add(#0,#1)|add(#3,#2)|inverse(#4)| | physics |
two unbiased coins are tossed . find the probability of getting at most one head ? | "s = { hh , ht , th , tt } e = event of getting at most one head e = { tt , ht , th } p ( e ) = 3 / 4 answer is b" | a ) 1 / 2 , b ) 3 / 4 , c ) 2 / 5 , d ) 2 / 3 , e ) 1 / 4 | b | negate_prob(divide(const_1, power(const_2, const_3))) | power(const_2,const_3)|divide(const_1,#0)|negate_prob(#1)| | probability |
find the annual income derived by investing $ 6800 in 60 % stock at 136 . | "by investing $ 136 , income obtained = $ 60 . by investing $ 6800 , income obtained = $ [ ( 60 / 136 ) * 6800 ] = $ 3000 . answer b ." | a ) 550 , b ) 3000 , c ) 250 , d ) 300 , e ) 400 | b | divide(multiply(6800, 60), 136) | multiply(n0,n1)|divide(#0,n2)| | gain |
when positive integer x is divided by positive integer y , the result is 59.32 . what is the sum w of all possible 2 - digit remainders for x / y ? | "ans b 616 . . . remainders = . 32 = 32 / 100 = 8 / 25 = 16 / 50 and so on . . so two digit remainders are 16 + 24 + 32 + . . . . + 96 . . w = 8 ( 2 + 3 + 4 . . . . + 12 ) = 616" | a ) 560 , b ) 616 , c ) 672 , d ) 728 , e ) 784 | b | divide(59.32, subtract(2, floor(2))) | floor(n1)|subtract(n1,#0)|divide(n0,#1)| | general |
jerry β s average ( arithmetic mean ) score on the first 3 of 4 tests is 81 . if jerry wants to raise his average by 2 points , what score must he earn on the fourth test ? | "total score on 3 tests = 81 * 3 = 243 jerry wants the average to be = 83 hence total score on 4 tests should be = 83 * 4 = 332 score required on the fourth test = 332 - 243 = 89 option b" | a ) 87 , b ) 89 , c ) 90 , d ) 93 , e ) 95 | b | subtract(multiply(4, add(81, 2)), multiply(81, 3)) | add(n2,n3)|multiply(n0,n2)|multiply(n1,#0)|subtract(#2,#1)| | general |
a rectangular field is to be fenced on three sides leaving a side of 20 feet uncovered . if the area of the field is 390 sq . feet , how many feet of fencing will be required ? | given that length and area , so we can find the breadth . length x breadth = area 20 x breadth = 390 breadth = 19.5 feet area to be fenced = 2 b + l = 2 ( 19.5 ) + 20 = 59 feet answer : b | ['a ) 34', 'b ) 59', 'c ) 68', 'd ) 88', 'e ) 92'] | b | add(multiply(divide(390, 20), const_2), 20) | divide(n1,n0)|multiply(#0,const_2)|add(n0,#1) | geometry |
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 = 2000 : 8000 - - - - - > 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 : a" | a ) 20 % , b ) 25 % , c ) 50 % , d ) 60 % , e ) 27 % | a | divide(multiply(2,000, const_100), add(add(multiply(const_2, const_1000), const_100), 2,000)) | multiply(n0,const_100)|multiply(const_1000,const_2)|add(#1,const_100)|add(n0,#2)|divide(#0,#3)| | general |
what is the smallest positive integer that can be multiplied by 1,008 to make it a perfect square ? | 1008 = 2 ^ 4 x 3 ^ 2 x 7 . therefore the smallest integer to multiplied to 1008 to make it a perfect square is 7 . answer d . | ['a ) 2', 'b ) 3', 'c ) 5', 'd ) 7', 'e ) 11'] | d | add(const_3, const_4) | add(const_3,const_4) | geometry |
how many factors of 660 are odd numbers greater than 1 ? | when factorized , 660 has 5 prime factors . of these prime factors 4 are odd and 1 is even . hence total number of odd factors is 2 * 2 * 2 * 2 ( 16 ) , which includes 1 . the total number of odd factors greater than 1 are 15 . ( option e ) | a ) 3 , b ) 4 , c ) 5 , d ) 6 , e ) 15 | e | divide(660, multiply(const_10, const_2)) | multiply(const_10,const_2)|divide(n0,#0)| | other |
a palindrome is a number that reads the same front - to - back as it does back - to - front ( e . g . 202 , 575 , 1991 , etc . ) p is the smallest integer greater than 300 that is both a prime and a palindrome . what is the sum of the digits of p ? | given that p is smallest integer greater than 300 - assume there is a 3 - digit that satisfies the above conditions . let the number be xyx ; question asks us the values of 2 x + y we can straight away cross out options a ) and d ) - sum of digits 3 or 6 implies it is divisible by 3 - - - > we know that p is a prime nu... | a ) 3 , b ) 4 , c ) 5 , d ) 6 , e ) 7 | d | add(const_3, const_3) | add(const_3,const_3) | general |
a sucrose solution contains 10 grams of sucrose per 100 cubic centimeters of solution . if 60 cubic centimeters of the solution were poured into an empty container , how many grams of sucrose would be in the container ? | we are given that a sucrose solution contains 10 grams of sucrose per 100 cubic centimeters of solution . since we are dealing with a solution , we know that the grams of sucrose is proportional to the number of cubic centimeters of solution . thus , to determine how many grams of sucrose would be in the container when... | ['a ) 4.00', 'b ) 6.00', 'c ) 5.50', 'd ) 6.50', 'e ) 6.75'] | b | divide(multiply(60, 10), 100) | multiply(n0,n2)|divide(#0,n1) | physics |
a crate measures 6 feet by 8 feet by 12 feet on the inside . a stone pillar in the shape of a right circular cylinder must fit into the crate for shipping so that it rests upright when the crate sits on at least one of its six sides . what is the radius , in feet , of the pillar with the largest volume that could still... | "we can find the radius of all the three cases of cylinders . the only crux to find the answer faster is that : voulme is pi * r ^ 2 * h . the volume is a function of r ^ 2 . so r has to be the highest to find the largest volume . so r = 6 for the surface 8 * 12 face . volume = 216 pi answer c" | a ) 2 , b ) 4 , c ) 6 , d ) 8 , e ) 12 | c | divide(divide(multiply(multiply(8, 12), 6), 12), 8) | multiply(n1,n2)|multiply(n0,#0)|divide(#1,n2)|divide(#2,n1)| | geometry |
a man can row downstream at 20 kmph and upstream at 12 kmph . find the speed of the man in still water and the speed of stream respectively ? | "explanation : let the speed of the man in still water and speed of stream be x kmph and y kmph respectively . given x + y = 20 - - - ( 1 ) and x - y = 12 - - - ( 2 ) from ( 1 ) & ( 2 ) 2 x = 32 = > x = 16 , y = 4 . answer : option c" | a ) 13 , 3 , b ) 12 , 6 , c ) 16 , 4 , d ) 14 , 4 , e ) none of these | c | divide(divide(add(20, 12), const_2), const_2) | add(n0,n1)|divide(#0,const_2)|divide(#1,const_2)| | physics |
a and b go around a circular track of length 1200 m on a cycle at speeds of 36 kmph and 54 kmph . after how much time will they meet for the first time at the starting point ? | "time taken to meet for the first time at the starting point = lcm { length of the track / speed of a , length of the track / speed of b } = lcm { 1200 / ( 36 * 5 / 18 ) , 1200 / ( 54 * 5 / 18 ) } = lcm ( 120 , 80 ) = 240 sec . answer : a" | a ) 240 sec , b ) 165 sec , c ) 186 sec , d ) 167 sec , e ) 168 sec | a | divide(1200, subtract(multiply(54, const_0_2778), multiply(36, const_0_2778))) | multiply(n2,const_0_2778)|multiply(n1,const_0_2778)|subtract(#0,#1)|divide(n0,#2)| | physics |
if the number is decreased by 5 and divided by 7 the result is 7 . what would be the result if 24 is subtracted and divided by 10 ? | "explanation : let the number be x . then , ( x - 5 ) / 7 = 7 = > x - 5 = 49 x = 54 . : ( x - 24 ) / 10 = ( 54 - 24 ) / 10 = 3 answer : option e" | a ) 4 , b ) 7 , c ) 8 , d ) 5 , e ) 3 | e | divide(subtract(add(multiply(7, 7), 5), 24), 10) | multiply(n1,n1)|add(n0,#0)|subtract(#1,n3)|divide(#2,n4)| | general |
tom read a book containing 560 pages by reading the same number of pages each day . if he would have finished the book 5 days earlier by reading 16 pages a day more , how many days did tom spend reading the book ? | "actually u can set up 2 equation p - - stands for the pages d - - stands for the days 1 ) p * d = 560 ( we want to find the days , sop = 560 / d ) 2 ) ( p + 16 ) ( d - 5 ) = 560 = > pd - 5 p + 16 d - 80 = 560 as the 1 ) stated u can put 1 ) into 2 ) = > 560 - 5 p + 16 d - 80 = 560 = > 16 d - 5 p = 80 put the bold one ... | a ) 19 , b ) 18 , c ) 9.12 , d ) 20 , e ) none | c | divide(subtract(sqrt(add(multiply(multiply(16, 5), const_4), power(16, const_2))), 16), const_2) | multiply(n1,n2)|power(n2,const_2)|multiply(#0,const_4)|add(#2,#1)|sqrt(#3)|subtract(#4,n2)|divide(#5,const_2)| | general |
john bought 9.25 m of cloth for $ 407 . find the cost price per metre . | "cloth bought by john = 9.25 m cost of 9.25 m = $ 407 cost per metre = 407 Γ· 9.25 the cost of the cloth per metre = $ 44 answers : d" | a ) 46 , b ) 47 , c ) 58 , d ) 44 , e ) 54 | d | divide(407, 9.25) | divide(n1,n0)| | physics |
how many pieces can a square pizza be cut into by making 6 linear cuts ? | "1 cut makes 2 pieces a second cut can make 4 pieces by cutting through both pieces a third cut can make 7 pieces by cutting through 3 of the pieces a fourth cut can make 11 pieces by cutting through 4 of the pieces a fifth cut can make 16 pieces by cutting through 5 of the pieces a sixth cut can make 22 pieces by cutt... | a ) 20 , b ) 21 , c ) 22 , d ) 23 , e ) 24 | c | subtract(multiply(6, const_3), const_1) | multiply(n0,const_3)|subtract(#0,const_1)| | geometry |
on the xy - plane , each point on circle c has coordinates such that x 0 and y 0 . if the center of circle c is the point ( 3 ; 9 ) , what is the maximum possible area of c ? | i think that theintentof this question is that the circle will have no co - ordinates that fit the following 2 forms : ( 0 , y ) or ( x , 0 ) . in real basic terms , this circle will neither touch ( nor cross ) the x - axis nor will it touch ( nor cross ) the y - axis . with a center at ( 3,8 ) , the longest possible r... | a ) 6 , b ) 9 , c ) 24 , d ) 32 , e ) 64 | c | subtract(add(power(3, const_2), power(const_4, const_2)), const_2) | power(n2,const_2)|power(const_4,const_2)|add(#0,#1)|subtract(#2,const_2) | geometry |
if 10 gallons of grape juice are added to 40 gallons of a mixture , which contains 30 percent grape juice then what percent of the resulting mixture is grape juice ? | "official solution : if we start with 40 gallons of a mixture that is 10 % grape juice , then we have : 40 Γ 0.30 = 12 gallons of grape juice . 40 Γ 0.70 = 28 gallons of other components . if we add 10 gallons of grape juice , we will end up with 24 gallons of grape juice and 36 gallons of other components , and we wil... | a ) 14 % , b ) 25 % , c ) 48 % , d ) 34 % , e ) 50 % | c | multiply(divide(add(multiply(divide(30, const_100), 40), 10), add(40, 10)), const_100) | add(n0,n1)|divide(n2,const_100)|multiply(n1,#1)|add(n0,#2)|divide(#3,#0)|multiply(#4,const_100)| | general |
in a school 10 % of the boys are same in number as 1 / 5 th of the girls . what is the ratio of boys to the girls in the school ? | 10 % of b = 1 / 5 g 10 b / 100 = g / 5 b = g / 2 b / g = 1 / 2 b : g = 1 : 2 answer is c | a ) 5 : 2 , b ) 2 : 3 , c ) 1 : 2 , d ) 3 : 7 , e ) 2 : 5 | c | divide(divide(10, const_100), divide(1, 5)) | divide(n0,const_100)|divide(n1,n2)|divide(#0,#1) | other |
in a certain parallelogram the degree measure of one angle exceeds that of the other by 40 what is the degree measure of the smaller angle ? | "in a parallelogram opposite angles are equal and the angles at each side are supplementary to each other ( supplementary angles are two angles that add up to 180 Β° ) . given : x + ( x + 40 ) = 180 - - > x = 70 . answer : a ." | a ) 70 , b ) 80 , c ) 85 , d ) 90 , e ) 95 | a | divide(subtract(divide(const_3600, const_10), multiply(40, const_2)), const_4) | divide(const_3600,const_10)|multiply(n0,const_2)|subtract(#0,#1)|divide(#2,const_4)| | geometry |
a farmer built a fence around his square plot . he used 27 fence poles on each side of the square . how many poles did he need altogether ? | one side = 2 corners ( 1 nd 1 each ) plus 25 . . . 1 25 1 25 25 1 25 1 der 4 ans = 25 * 4 + 4 = 104 answer : b | ['a ) 100', 'b ) 104', 'c ) 108', 'd ) 112', 'e ) none of these'] | b | add(multiply(subtract(27, const_2), const_4), const_4) | subtract(n0,const_2)|multiply(#0,const_4)|add(#1,const_4) | geometry |
if one positive integer is greater than another positive integer by 4 , and the difference of their cubes is 208 , what is their sum ? | "1 ^ 3 = 1 2 ^ 3 = 8 3 ^ 3 = 27 4 ^ 3 = 64 5 ^ 3 = 125 6 ^ 3 = 216 the two numbers are 2 and 6 . the answer is a ." | a ) 8 , b ) 10 , c ) 12 , d ) 14 , e ) 16 | a | add(divide(add(power(4, 4), sqrt(add(power(power(4, 4), const_2), power(subtract(208, power(4, 4)), const_2)))), multiply(power(4, const_2), const_2)), subtract(divide(add(power(4, 4), sqrt(add(power(power(4, 4), const_2), power(subtract(208, power(4, 4)), const_2)))), multiply(power(4, const_2), const_2)), 4)) | power(n0,n0)|power(n0,const_2)|multiply(#1,const_2)|power(#0,const_2)|subtract(n1,#0)|power(#4,const_2)|add(#3,#5)|sqrt(#6)|add(#0,#7)|divide(#8,#2)|subtract(#9,n0)|add(#9,#10)| | general |
if s = { 1 , 2 , 3 , 4 , 5 , 6 , 7 } , how much less is the mean of the numbers in s than the median of the numbers in s ? | "mean = ( 1 + 2 + 3 + 4 + 5 + 6 + 7 ) / 7 = 4 median = 4 difference = 4 - 4 = 0 option a" | a ) 0 , b ) 1 , c ) 2 , d ) 3 , e ) 4 | a | multiply(divide(add(add(add(add(add(2, 1), 3), 4), 5), 6), add(const_2, const_4)), divide(add(3, 4), const_2)) | add(n0,n1)|add(const_2,const_4)|add(n2,n3)|add(n2,#0)|divide(#2,const_2)|add(n3,#3)|add(n4,#5)|add(n5,#6)|divide(#7,#1)|multiply(#8,#4)| | general |
45 x ? = 40 % of 900 | "answer let 45 x a = ( 40 x 900 ) / 100 β΄ a = ( 40 x 9 ) / 45 = 8 correct option : e" | a ) 16.2 , b ) 4 , c ) 5 , d ) 500 , e ) 8 | e | divide(multiply(divide(40, const_100), 900), 45) | divide(n1,const_100)|multiply(n2,#0)|divide(#1,n0)| | general |
ramu bought an old car for rs . 42000 . he spent rs . 13000 on repairs and sold it for rs . 64900 . what is his profit percent ? | "total cp = rs . 42000 + rs . 13000 = rs . 55000 and sp = rs . 64900 profit ( % ) = ( 64900 - 55000 ) / 55000 * 100 = 18 % answer : c" | a ) 22 , b ) 77 , c ) 18 , d ) 77 , e ) 65 | c | multiply(divide(subtract(64900, add(42000, 13000)), add(42000, 13000)), const_100) | add(n0,n1)|subtract(n2,#0)|divide(#1,#0)|multiply(#2,const_100)| | gain |
a honey bee flies for 10 seconds , from a daisy to a rose . it immediately continues to a poppy , flying for 6 additional seconds . the distance the bee passed , flying from the daisy to the rose is 8 meters longer than the distance it passed flying from the rose to the poppy . the bee flies to the poppy at 3 meters pe... | let the speed be ' s ' and let the distance between rose and poppy be ' x ' the problem boils down to : rose to poppy : s + 3 = x / 6 - - - - - - - 1 daisy to rose : s = ( x + 8 ) / 10 - - - - - - 2 so from 1 we can re write x as x = 6 s + 18 substitute the value of x in 2 gives us s = 2.6 m / s a | a ) 2.6 , b ) 5.6 , c ) 6.3 , d ) 8 , e ) 10 | a | divide(add(multiply(6, 3), 8), 10) | multiply(n1,n3)|add(n2,#0)|divide(#1,n0) | physics |
of the female students at barkely university , 5 / 6 are on the honor roll . of the male students , 2 / 3 are on the honor roll . if 3 / 5 of the students are female , what is ratio of male to female students on honor roll ? | "let the total students be 30 given 3 / 5 of the students are females = 18 then males = 2 / 5 = 12 5 / 6 of the females are on honor roll = 15 males on the honor roll = 2 / 3 = 8 ratio of m : f students on honor roll = 8 / 15 b" | a ) 5 / 9 , b ) 8 / 15 , c ) 23 / 30 , d ) 43 / 60 , e ) 53 / 90 | b | divide(add(multiply(multiply(5, 2), const_2.0), 3), multiply(2, multiply(3, 5))) | multiply(n0,n2)|multiply(n0,n3)|multiply(n2,#0)|multiply(n4,#1)|add(n2,#2)|divide(#4,#3)| | other |
if in a race of 90 m , a covers the distance in 20 seconds and b in 25 seconds , then a beats b by : | explanation : the difference in the timing of a and b is 5 seconds . hence , a beats b by 5 seconds . the distance covered by b in 5 seconds = ( 90 * 5 ) / 25 = 18 m hence , a beats b by 18 m . answer e | a ) 20 m , b ) 16 m , c ) 11 m , d ) 10 m , e ) 18 m | e | multiply(divide(subtract(25, 20), 25), 90) | subtract(n2,n1)|divide(#0,n2)|multiply(n0,#1) | physics |
the sum of all two digit numbers divisible by 9 is | required numbers are 18,27 . . . . . 99 this is an a . p . in which a = 18 , d = 9 and l = 99 . let the number of terms in it be n . then t = 99 so a + ( n - 1 ) d = 99 . 18 + ( n - 1 ) * 9 = 99 , 18 + 9 n - 9 = 99 9 + 9 n = 99 9 n = 99 - 9 n = 90 / 9 then n = 10 . required sum = n / 2 ( a + l ) = 10 / 2 ( 18 + 99 ) = ... | a ) 910 , b ) 585 , c ) 785 , d ) 685 , e ) 885 | b | add(add(add(add(add(add(add(add(add(add(9, 9), add(add(9, 9), 9)), add(add(add(9, 9), 9), 9)), add(add(add(add(9, 9), 9), 9), 9)), add(add(add(add(add(9, 9), 9), 9), 9), 9)), add(add(add(add(add(add(9, 9), 9), 9), 9), 9), 9)), add(add(add(add(add(add(add(9, 9), 9), 9), 9), 9), 9), 9)), add(add(add(add(add(add(add(add(9... | add(n0,n0)|add(n0,#0)|add(#0,#1)|add(n0,#1)|add(#2,#3)|add(n0,#3)|add(#4,#5)|add(n0,#5)|add(#6,#7)|add(n0,#7)|add(#8,#9)|add(n0,#9)|add(#10,#11)|add(n0,#11)|add(#12,#13)|add(n0,#13)|add(#14,#15)|add(n0,#15)|add(#16,#17) | general |
find the least number must be subtracted from 899830 so that remaining no . is divisible by 16 ? | "on dividing 899830 by 16 we get the remainder 6 , so 6 should be subtracted d" | a ) 5 , b ) 8 , c ) 7 , d ) 6 , e ) 9 | d | subtract(899830, multiply(floor(divide(899830, 16)), 16)) | divide(n0,n1)|floor(#0)|multiply(n1,#1)|subtract(n0,#2)| | general |
at 3 : 40 , the hour hand and the minute hand of a clock form an angle of : | angle traced by hour hand in 12 hrs . = 360 Γ’ Β° . abgle traced it in 11 / 3 hrs = ( 360 / 12 * 11 / 3 ) = 110 angle traced by min hand in 60 min = 360 angle traced by it in 40 min = ( 360 / 60 * 40 ) = 240 req ( 240 - 110 ) = 130 d | a ) 130 , b ) 125 , c ) 140 , d ) 154 , e ) 145 | a | subtract(multiply(multiply(multiply(const_60, const_3), const_2), divide(40, const_60)), multiply(divide(divide(multiply(multiply(const_60, const_3), const_2), const_3), const_4), add(divide(40, const_60), 3))) | divide(n1,const_60)|multiply(const_3,const_60)|add(n0,#0)|multiply(#1,const_2)|divide(#3,const_3)|multiply(#0,#3)|divide(#4,const_4)|multiply(#2,#6)|subtract(#5,#7) | physics |
express 60 mps in kmph ? | "60 * 18 / 5 = 216 kmph answer : c" | a ) 200 , b ) 182 , c ) 216 , d ) 127 , e ) 400 | c | multiply(divide(60, const_1000), const_3600) | divide(n0,const_1000)|multiply(#0,const_3600)| | physics |
set a : { 1 , 3 , 4 , 6 , 9 , 12 , 15 } if 3 numbers are randomly selected from set a without replacement , what is the probability that the sum of the 3 numbers is divisible by 3 ? | probability of an event = ( # of favorable outcomes ) / ( total # of outcomes ) . there are 5 numbers you can choose from ( 3 , 6 , 9 , 12 , 15 ) so that the sum to be divisible by 3 and there are total of 7 numbers so p = c 35 c 37 = 27 p = c 53 c 73 = 27 . answer : b . | a ) 3 / 14 , b ) 2 / 7 , c ) 9 / 14 , d ) 5 / 7 , e ) 11 / 14 | b | divide(divide(factorial(add(4, 1)), multiply(factorial(subtract(add(4, 1), 3)), factorial(3))), divide(factorial(add(4, 3)), multiply(factorial(4), factorial(3)))) | add(n0,n2)|add(n1,n2)|factorial(n1)|factorial(n2)|factorial(#0)|factorial(#1)|multiply(#3,#2)|subtract(#0,n1)|divide(#5,#6)|factorial(#7)|multiply(#9,#2)|divide(#4,#10)|divide(#11,#8) | general |
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