regisss/math_qa huggingface dataset:
Problem: the pinedale bus line travels at an average speed of 60 km / h , and has stops every 5 minutes along its route . yahya wants to go from his house to the pinedale mall , which is 9 stops away . how far away , in kilometers , is pinedale mall away from yahya ' s house ?
Options: a ) 20 km , b ) 30 km , c ) 45 km , d ) 50 km , e ) 60 km
Rationale: "number of stops in an hour : 60 / 5 = 12 distance between stops : 60 / 12 = 5 km distance between yahya ' s house and pinedale mall : 5 x 9 = 45 km imo , correct answer is ` ` c . ' '"
Answer: c
Problem: in a certain warehouse , 50 percent of the packages weigh less than 75 pounds , and a total of 48 packages weigh less than 25 pounds . if 80 percent of the packages weigh at least 25 pounds , how many of the packages weigh at least 25 pounds but less than 75 pounds ?
Options: a ) 8 , b ) 64 , c ) 72 , d ) 102 , e ) 144
Rationale: "if 80 % of the packages weigh at least 25 pounds this means that 20 % of the packages weigh less than 25 pounds let t = total number of packages so , 20 % of t = # of packages that weigh less than 25 pounds 48 packages weigh less than 25 pounds great . so , 20 % of t = 48 rewrite to get : 0.2 t = 48 solve : t = 240 50 % of the packages weigh less than 75 pounds so , 50 % oft = number of packages that weigh less than 75 pounds 50 % of 240 = 120 , so 120 packages weigh less than 75 pounds of those 120 packages that weigh less than 75 pounds , 48 packages weigh less than 25 pounds . so , the number of packages that weight between 25 and 75 pounds = 120 - 48 = 72 = c"
Answer: c
Problem: in one hour , a boat goes 11 km along the stream and 5 km against the stream . the speed of the boat in still water ( in km / hr ) is :
Options: a ) 3 , b ) 5 , c ) 8 , d ) 9 , e ) 10
Rationale: "solution speed in still water = 1 / 2 ( 11 + 5 ) kmph . = 8 kmph . answer c"
Answer: c
Problem: the ratio of the cost price and the selling price is 4 : 5 . the profit percent is ?
Options: a ) 17 , b ) 56 , c ) 25 , d ) 28 , e ) 12
Rationale: "let c . p . = rs . 4 x . then , s . p . = rs . 5 x gain = ( 5 x - 4 x ) = rs . x gain % = ( x * 100 ) / 4 x = 25 % . answer : c"
Answer: c
Problem: if 45 % of a class averages 100 % on a test , 50 % of the class averages 78 % on the test , and the remainder of the class averages 65 % on the test , what is the overall class average ? ( round final answer to the nearest percent ) .
Options: a ) 86 % , b ) 87 % , c ) 88 % , d ) 89 % , e ) 90 %
Rationale: "this question is a weighted average question with a series of dependent variables . the remaining portion of the class represents 100 % - 45 % - 50 % = 5 % of the class converting the portions of the class population to decimal weights , we find : class average = 0.45 x 100 + 0.50 x 78 + 0.05 x 63 = 87.15 the class average ( rounded ) is 87 % final answer b ) 87 %"
Answer: b
Problem: of the votes cast on a certain proposal , 62 more were in favor of the proposal than were against it . if the number of votes against the proposal was 40 percent of the total vote , what was the total number of votes cast ? ( each vote cast was either in favor of the proposal or against it . )
Options: a ) 280 , b ) 290 , c ) 300 , d ) 310 , e ) 320
Rationale: let x be the total number of votes cast . 0.6 x = 0.4 x + 62 0.2 x = 62 x = 310 the answer is d .
Answer: d
Problem: how many of the integers between 20 and 80 are even ?
Options: a ) 21 , b ) 30 , c ) 11 , d ) 10 , e ) 9
Rationale: "number start between 20 to 80 is 60 numbers half of them is even . . which is 30 answer : b"
Answer: b
Problem: if a and b are positive integers , and a = 5 b + 20 , the greatest common divisor of a and b can not be
Options: a ) 2 , b ) 4 , c ) 5 , d ) 6 , e ) 10
Rationale: if b is 2 , 4 , 5 , or 10 , then gcd of a and b is 2 , 4 , 5 , and 10 respectively . so , by poe the answer must be d . still : if b is a multiple of 6 , then a is 20 greater than a multiple of 6 , so not a multiple of 6 , so both of them can not be divisive by 6 . answer : d .
Answer: d
Problem: what is the value of ( 44444445 * 88888885 * 44444442 + 44444438 ) / 44444444 ^ 2
Options: a ) 88888883 , b ) 88888827 , c ) 16992677 , d ) 88888237 , e ) 88888182
Rationale: "ans : a let x = 44444444 ( x + 1 ) × ( 2 x − 3 ) × ( x − 2 ) + ( x − 6 ) x 2 ( x + 1 ) × ( 2 x − 3 ) × ( x − 2 ) + ( x − 6 ) x 2 ( x 2 − x − 2 ) × ( 2 x − 3 ) + ( x − 6 ) x 2 ( x 2 − x − 2 ) × ( 2 x − 3 ) + ( x − 6 ) x 2 2 x 3 − 2 x 2 − 4 x − 3 x 2 + 3 x + 6 + x − 6 x 22 x 3 − 2 x 2 − 4 x − 3 x 2 + 3 x + 6 + x − 6 x 2 2 x 3 − 5 x 2 x 2 = 2 x − 52 x 3 − 5 x 2 x 2 = 2 x − 5 substituting the value of x in 2 x - 5 , we get 88888883 answer : a"
Answer: a
Problem: find the greatest number which leaves the same remainder when it divides 21 , 57 and 105 .
Options: a ) 18 , b ) 8 , c ) 12 , d ) 16 , e ) none of these
Rationale: "105 - 57 = 48 57 - 21 = 36 105 - 21 = 84 the h . c . f of 36 , 48 and 84 is 12 . answer : c"
Answer: c
Problem: at a summer camp with 2100 participants , 1 / 2 of the campers are aged 8 to 12 . next year , the number of campers aged 8 to 12 will increase by 1 / 3 . after this change , what percentage of the total 2100 campers will the 8 - to 12 - year - olds represent ?
Options: a ) 62 , b ) 68 , c ) 66 , d ) 64 , e ) 66 2 / 3
Rationale: "total - 2100 participants campers are aged 8 to 12 = ( 1 / 2 ) * 2100 = 1050 next year , campers are aged 8 to 12 = ( 4 / 3 ) * 1050 = 1400 percentage = ( 1400 / 2100 ) * 100 = 66 2 / 3 % answer : option e"
Answer: e
Problem: express 35 mps in kmph ?
Options: a ) 122 , b ) 188 , c ) 126 , d ) 140 , e ) 124
Rationale: "35 * 18 / 5 = 126 kmph answer : c"
Answer: c
Problem: the area of a square field 3136 sq m , if the length of cost of drawing barbed wire 3 m around the field at the rate of rs . 2.50 per meter . two gates of 1 m width each are to be left for entrance . what is the total cost ?
Options: a ) s . 1014 , b ) s . 1140 , c ) s . 999 , d ) s . 1665 , e ) s . 1020
Rationale: "a 2 = 3136 = > a = 56 56 * 4 * 3 = 672 – 6 = 666 * 2.5 = 1665 answer : d"
Answer: d
Problem: what is the area inscribed by the lines y = 4 , x = 2 , y = 6 - 2 x on an xy - coordinate plane ?
Options: a ) a ) 1 , b ) b ) 2 , c ) c ) 4 , d ) d ) 6 , e ) e ) 8
Rationale: "first , let ' s graph the lines y = 4 and x = 2 at this point , we need to find the points where the line y = 6 - 2 x intersects the other two lines . for the vertical line , we know that x = 2 , so we ' ll plug x = 2 into the equation y = 6 - 2 x to get y = 6 - 2 ( 2 ) = 2 perfect , when x = 2 , y = 2 , so one point of intersection is ( 2,2 ) for the horizontal line , we know that y = 4 , so we ' ll plug y = 4 into the equation y = 6 - 2 x to get 4 = 6 - 2 x . solve to get : x = 1 so , when y = 4 , x = 1 , so one point of intersection is ( 1,4 ) now add these points to our graph and sketch the line y = 6 - 2 x at this point , we can see that we have the following triangle . the base has length 1 and the height is 2 area = ( 1 / 2 ) ( base ) ( height ) = ( 1 / 2 ) ( 1 ) ( 2 ) = 1 answer : a"
Answer: a
Problem: there are 690 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 ?
Options: a ) 75 , b ) 100 , c ) 115 , d ) 175 , e ) 225
Rationale: female = x male = 690 - x x / 2 + 690 - x / 4 = 1 / 3 * ( 690 ) = 230 x = 230 x / 2 = 115 is supposed to be the answer m is missing something correct option c
Answer: c
Problem: find the area of a parallelogram with base 20 cm and height 40 cm ?
Options: a ) 100 cm 2 , b ) 250 cm 2 , c ) 800 cm 2 , d ) 296 cm 2 , e ) 456 cm 2
Rationale: "area of a parallelogram = base * height = 20 * 40 = 800 cm 2 answer : c"
Answer: c
Problem: in a garden , there are 10 rows and 14 columns of mango trees . the distance between the two trees is 2 metres and a distance of one metre is left from all sides of the boundary of the garden . the length of the garden is
Options: a ) 20 m , b ) 22 m , c ) 24 m , d ) 26 m , e ) 28 m
Rationale: "explanation : each row contains 14 plants . there are 13 gapes between the two corner trees ( 13 x 2 ) metres and 1 metre on each side is left . therefore length = ( 26 + 2 ) m = 28 m . answer : e"
Answer: e
Problem: a can do a piece of work in 6 hours ; b and c together can do it in 4 hours , which a and c together can do it in 3 hours . how long will b alone take to do it ?
Options: a ) 8 hours , b ) 6 hours , c ) 14 hours , d ) 12 hours , e ) 5 hours
Rationale: "a ' s 1 hour work = 1 / 6 ; ( b + c ) ' s 1 hour work = 1 / 4 ; ( a + c ) ' s 1 hour work = 1 / 3 ( a + b + c ) ' s 1 hour work = ( 1 / 4 + 1 / 6 ) = 5 / 12 b ' s 1 hour work = ( 5 / 12 - 1 / 3 ) = 1 / 12 b alone will take 12 hours to do the work . answer : d"
Answer: d
Problem: a train 250 m long running at 72 kmph crosses a platform in 30 sec . what is the length of the platform ?
Options: a ) 350 m , b ) 200 m , c ) 250 m , d ) 270 m , e ) 300 m
Rationale: "d = 72 * 5 / 18 = 30 = 600 â € “ 250 = 350 m answer : a"
Answer: a
Problem: 4 shepherds were watching over the flocks and they were commenting on how many sheep they each had . if ram had 3 more sheep than he would have one less than rahul . wheras akar has the same number as the other 3 shepherds put togeher . if john had 3 less sheep he would have exactly trile the number of ram . if they were evenly distributed if they would each have 11 seep how many sheep did ram have ?
Options: a ) 2 , b ) 3 , c ) 4 , d ) 5 , e ) 6
Rationale: akar has = ram + rahul + john after evenly distribution each has 11 . so , total no . is 44 so , akar has = 22 & ram + rahul + john = 22 also ram = rahul - 4 & john - 3 = 3 * ram solving these we get the sol . answer : b
Answer: b