Cheukting/mathqa huggingface dataset:
Question (general): in a competitive examination in state a , 6 % candidates got selected from the total appeared candidates . state b had an equal number of candidates appeared and 7 % candidates got selected with 79 more candidates got selected than a . what was the number of candidates appeared from each state ?
Options: a ) 7000 , b ) 7900 , c ) 6000 , d ) 5000 , e ) 4000
Rationale: "state a and state b had an equal number of candidates appeared . in state a , 6 % candidates got selected from the total appeared candidates in state b , 7 % candidates got selected from the total appeared candidates but in state b , 79 more candidates got selected than state a from these , it is clear that 1 % of the total appeared candidates in state b = 79 = > total appeared candidates in state b = 79 x 100 = 7900 = > total appeared candidates in state a = total appeared candidates in state b = 7900"
Answer: b
Question (other): the price ratio of oranges to lemons is 2 : 3 . the price ratio of grapefruits to lemons is 3 : 5 . what is the ratio , by price , of grapefruit to oranges ?
Options: a ) 18 : 20 , b ) 10 : 9 , c ) 2 : 5 , d ) 5 : 2 , e ) 3 : 2
Rationale: let price of lemons be 30 ( since that is common ) so , price of oranges = 20 & price of lemons is = 30 further price of grapefruit will be 6 * 3 = 18 thus price , of grapefruit to oranges = 18 : 20 answer : a
Answer: a
Question (general): 20 carrots on a scale weigh 3.64 kg . when 4 carrots are removed from the scale , the average weight of the 16 carrots is 180 grams . what is the average weight ( in grams ) of the 4 carrots which were removed ?
Options: a ) 160 , b ) 170 , c ) 180 , d ) 190 , e ) 200
Rationale: "16 * 180 = 2880 . the other 4 carrots weigh a total of 760 grams . the average weight is 760 / 4 = 190 grams . the answer is d ."
Answer: d
Question (physics): a can do a particular work in 6 days . b can do the same work in 8 days . a and b signed to do it for rs . 3200 . they completed the work in 3 days with the help of c . how much is to be paid to c ?
Options: a ) rs . 380 , b ) rs . 600 , c ) rs . 420 , d ) rs . 400 , e ) rs . 480
Rationale: "explanation : amount of work a can do in 1 day = 1 / 6 amount of work b can do in 1 day = 1 / 8 amount of work a + b can do in 1 day = 1 / 6 + 1 / 8 = 7 / 24 amount of work a + b + c can do = 1 / 3 amount of work c can do in 1 day = 1 / 3 - 7 / 24 = 1 / 24 work a can do in 1 day : work b can do in 1 day : work c can do in 1 day = 1 / 6 : 1 / 8 : 1 / 24 = 4 : 3 : 1 amount to be paid to c = 3200 × ( 1 / 8 ) = 400 answer : option d"
Answer: d
Question (physics): a train requires 10 seconds to pass a pole while it requires 40 seconds to cross a stationary train which is 300 mtrs long . find the speed of the train .
Options: a ) 36 kmph , b ) 42 kmph , c ) 48 kmph , d ) 52 kmph , e ) 64 kmph
Rationale: "in 10 s the train crosses the pole and in 40 sec the train crosses one more stationary train in 30 sec the train travels a distance of 300 mtrs speed = 300 / 30 = 10 m / s = 10 * 18 / 5 = 36 kmph answer : a"
Answer: a
Question (physics): two trains are running in opposite directions in the same speed . the length of each train is 120 meter . if they cross each other in 4 seconds , the speed of each train ( in km / hr ) is
Options: a ) 42 , b ) 36 , c ) 108 , d ) 120 , e ) 124
Rationale: "explanation : distance covered = 120 + 120 = 240 m time = 4 s let the speed of each train = v . then relative speed = v + v = 2 v 2 v = distance / time = 240 / 4 = 60 m / s speed of each train = v = 60 / 2 = 30 m / s = 30 × 36 / 10 km / hr = 108 km / hr answer : option c"
Answer: c
Question (general): how many multiples of 7 are there between 700 and 1000 , inclusive ?
Options: a ) 43 , b ) 42 , c ) 22 , d ) 21 , e ) 20
Rationale: "there are exactly 301 numbers between 700 to 1000 . . 701 to 800 = 100 801 to 1000 = 200 . . . total 300 numbers , count 700 too . . 301 / 7 = 43 . . . ans option a ."
Answer: a
Question (probability): an unbaised coin is tossed until it shows up the same face in 2 consicative throws wat is the probability that the no of tosses is not more than 4 .
Options: a ) 3 / 4 , b ) 1 / 4 , c ) 7 / 8 , d ) 1 / 8 , e ) 6 / 8
Rationale: using 0 and 1 for head and tail respectively and considering binary system , we find that out of 16 possibilities , 14 are desired options . then probability = 14 / 16 = 7 / 8 answer : c
Answer: c
Question (physics): at a certain bowling alley , it costs $ 0.50 to rent bowling shoes for the day and $ 2 to bowl 1 game . if a person has $ 12.80 and must rent shoes , what is the greatest number of complete games that person can bowl in one day ?
Options: a ) 7 , b ) 8 , c ) 6 , d ) 10 , e ) 11
Rationale: after renting bowling shoes the person is left with $ 12.80 - $ 0.5 = $ 12.30 , which is enough for 12.3 / 2 < 7 = ~ 6 . answer : c .
Answer: c
Question (general): if a * b * c = 130 , b * c * d = 65 , c * d * e = 750 and d * e * f = 250 the ( a * f ) / ( c * d ) = ?
Options: a ) 1 / 2 , b ) 2 / 3 , c ) 3 / 4 , d ) 4 / 3 , e ) none of these
Rationale: "explanation : a â ˆ — b â ˆ — c / b â ˆ — c â ˆ — d = 130 / 65 = > a / d = 2 d â ˆ — e â ˆ — f / c â ˆ — d â ˆ — e = 250 / 750 = > f / c = 1 / 3 a / d * f / c = 2 * 1 / 3 = 2 / 3 answer : b"
Answer: b
Question (physics): a cistern can be filled by a tap in 4 hours while it can be emptied by another tap in 9 hours . if both the taps are opened simultaneously , then after how much time cistern will get filled ?
Options: a ) 7 hours , b ) 7.1 hours , c ) 7.2 hours , d ) 7.3 hours , e ) none of these
Rationale: "explanation : when we have question like one is filling the tank and other is empting it , then we subtraction as , filled in 1 hour = 1 / 4 empties in 1 hour = 1 / 9 net filled in 1 hour = 1 / 4 - 1 / 9 = 5 / 36 so cistern will be filled in 36 / 5 hours i . e . 7.2 hours option c"
Answer: c
Question (general): evaluate : 986 x 237 - 986 x 37
Options: a ) 197600 , b ) 168000 , c ) 278000 , d ) 192700 , e ) none of them
Rationale: "986 x 237 - 986 x 37 = 986 x ( 237 - 37 ) = 986 x 200 = 197200 . answer is d ."
Answer: d
Question (general): what is the sum of the odd integers from 25 to 55 , inclusive ?
Options: a ) 495 , b ) 550 , c ) 555 , d ) 600 , e ) 640
Rationale: "the mean is 40 . sum = mean ( # of elements ) there are 16 odd numbers between 25 - 55 inclusive . 16 * 40 = 640 e"
Answer: e
Question (general): in a class of students , 2 / 3 of the number of girls is equal to 1 / 4 of the total number of students . what is the ratio of boys to girls in the class ?
Options: a ) 1 / 3 , b ) 2 / 3 , c ) 4 / 3 , d ) 5 / 3 , e ) 7 / 3
Rationale: "( 2 / 3 ) g = ( 1 / 4 ) ( b + g ) 8 g = 3 b + 3 g 5 g = 3 b b / g = 5 / 3 . the answer is d ."
Answer: d
Question (gain): a portion of the 85 % solution of chemicals was replaced with an equal amount of 20 % solution of chemicals . as a result , 40 % solution of chemicals resulted . what part of the original solution was replaced ?
Options: a ) 5 / 13 , b ) 6 / 13 , c ) 9 / 13 , d ) 13 / 9 , e ) 13 / 6
Rationale: "let the original amount of 85 percent solution = x and amount replaced be y 0.85 ( x - y ) + 0.2 y = 0.4 x 0.85 x - 0.85 y + 0.2 y = 0.4 x 0.45 x = 0.65 y 9 x = 13 y y = 9 x / 13 so , amount replaced = 9 / 13 of original amount answer : c"
Answer: c
Question (geometry): rain is falling at a rate of 10 centimeters per hour all over north carolina . somewhere downtown in north carolina a group of people are waiting for the rain to stop . if the rain filled a round puddle the with a base area of 300 square centimeters and a depth of 30 centimeters , how long did the people wait for the rain to stop ?
Options: a ) 4 hours
b ) 11 hours
c ) 7 hours 15 minutes
d ) 3 hours
e ) 14 hours
Rationale: answer is : d , 3 hours the volume of the puddle is irrelevant and only height matters since rain fell all over the city . thus , it takes only 30 / 10 = 3 hours of rain to fill the puddle
Answer: d
Question (general): the greatest number which on dividing 1442 and 1816 leaves remainders 12 and 6 respectively , is :
Options: a ) 123 , b ) 127 , c ) 235 , d ) 305 , e ) 10
Rationale: explanation : required number = h . c . f . of ( 1442 - 12 ) and ( 1816 - 6 ) = h . c . f . of 1430 and 1810 = 10 . answer : e
Answer: e
Question (general): if the average ( arithmetic mean ) of x + 1 , x + 3 , and x + 5 is 0 , then x =
Options: a ) – 4 , b ) – 3 , c ) – 2 , d ) – 1 , e ) 0
Rationale: "( x + 1 + x + 3 + x + 5 ) / 3 = 0 = > 3 x + 9 = 0 = > x = - 3 answer b"
Answer: b
Question (physics): a wooden box of dimensions 4 m x 2 m x 4 m is to carry rectangularboxes of dimensions 4 cm x 2 cm x 2 cm . the maximum number ofboxes that can be carried in the wooden box , is
Options: a ) 9800000 , b ) 2000000 , c ) 7500000 , d ) 1200000 , e ) none of these
Rationale: explanation : number = ( 400 * 200 * 400 ) / 4 * 2 * 2 = 2000000 answer : b
Answer: b
Question (gain): find the simple interest on rs . 750 for 9 months at 6 paisa per month ?
Options: a ) rs . 415 , b ) rs . 405 , c ) rs . 450 , d ) rs . 345 , e ) rs . 564
Rationale: "explanation : i = ( 750 * 9 * 6 ) / 100 = 405 answer : option b"
Answer: b
Question (physics): if two projectiles are launched at the same moment from 1182 km apart and travel directly towards each other at 460 km per hour and 525 km per hour respectively , how many minutes will it take for them to meet ?
Options: a ) 68 , b ) 72 , c ) 76 , d ) 80 , e ) 84
Rationale: the projectiles travel a total of 985 km per hour . the time to meet is 1182 / 985 = 1.2 hours = 72 minutes the answer is b .
Answer: b
Question (physics): a and b complete a work in 20 days . a alone can do it in 40 days . if both together can do the work in how many days ?
Options: a ) 1.0875 days , b ) 0.1875 days , c ) 0.0675 days , d ) 0.075 days , e ) 0.0175 days
Rationale: "1 / 20 + 1 / 40 = 0.075 days answer : d"
Answer: d
Question (physics): a metallic sphere of radius 12 cm is melted and drawn into a wire , whose radius of cross section is 8 cm . what is the length of the wire ?
Options: a ) 16 cm , b ) 24 cm , c ) 28 cm , d ) 36 cm , e ) 39 cm
Rationale: "volume of the wire ( in cylindrical shape ) is equal to the volume of the sphere . π ( 8 ) ^ 2 * h = ( 4 / 3 ) π ( 12 ) ^ 3 = > h = 36 cm answer : d"
Answer: d
Question (other): if 0.4 of a number is equal to 0.06 of another number , the ratio of the numbers is :
Options: a ) 2 : 3 , b ) 3 : 4 , c ) 3 : 20 , d ) 20 : 3 , e ) 22 : 1
Rationale: "expl : 0.4 a = 0.06 b - > a / b = 0.06 / 0.40 = 6 / 40 = 3 / 20 : . a : b = 3 : 20 answer : c"
Answer: c
Question (other): a group of people participate in some curriculum , 25 of them practice yoga , 18 study cooking , 10 study weaving , 4 of them study cooking only , 5 of them study both the cooking and yoga , 4 of them participate all curriculums . how many people study both cooking and weaving ?
Options: a ) 1 , b ) 2 , c ) 3 , d ) 4 , e ) 5
Rationale: "both cooking and weaving = 18 - ( 4 + 4 + 5 ) = 5 so , the correct answer is e ."
Answer: e
Question (gain): a $ 500 investment and a $ 1,500 investment have a combined yearly return of 22 percent of the total of the two investments . if the $ 500 investment has a yearly return of 7 percent , what percent yearly return does the $ 1,500 investment have ?
Options: a ) 29 % , b ) 20 % , c ) 27 % , d ) 25 % , e ) 12 %
Rationale: "the equation we can form the question : return on total investment = sum of individual investments ( 500 + 1500 ) ( 22 ) = ( 500 â ˆ — 7 ) + ( 1500 x ) , where x is the return on investment of 1500 . solving the equation , we get x = 27 % ( option c ) answer : c"
Answer: c
Question (general): joe went on a diet 3 months ago when he weighed 222 pounds . if he now weighs 198 pounds and continues to lose at the same average monthly rate , in approximately how many months will he weigh 170 pounds ?
Options: a ) 3 , b ) 3.5 , c ) 4 , d ) 4.5 , e ) 5
Rationale: "222 - 198 = 24 pounds lost in 3 months 24 / 3 = 8 , so joe is losing weight at a rate of 8 pounds per month . . . . in approximately how many months will he weigh 170 pounds ? a simple approach is to just list the weights . now : 198 lbs in 1 month : 190 lbs in 2 months : 182 lbs in 3 months : 174 lbs in 4 months : 166 lbs since 170 pounds is halfway between 174 and 166 , the correct answer must be 3.5 months . answer : b"
Answer: b
Question (physics): two cars are traveling in the same direction along the same route . the red car travels at a constant speed of 40 miles per hour , and the black car is traveling at a constant speed of 50 miles per hour . if the red car is 30 miles ahead of the black car , how many hours will it take the black car to overtake the red car ?
Options: a ) 0.1 , b ) 0.6 , c ) 1 , d ) 1.2 , e ) 3
Rationale: option e 20 + 40 t = 50 t t = 3
Answer: e
Question (gain): in a certain city , 60 percent of the registered voters are democrats and the rest are republicans . in a mayoral race , if 70 percent of the registered voters who are democrats and 20 percent of the registered voters who are republicans are expected to vote for candidate a , what percent of the registered voters are expected to vote for candidate a ?
Options: a ) 50 % , b ) 53 % , c ) 54 % , d ) 55 % , e ) 57 %
Rationale: "say there are total of 100 registered voters in that city . thus 60 are democrats and 40 are republicans . 60 * 0.70 = 42 democrats are expected to vote for candidate a ; 40 * 0.20 = 8 republicans are expected to vote for candidate a . thus total of 42 + 8 = 50 registered voters are expected to vote for candidate a , which is 50 % of the total number of registered voters . answer : a"
Answer: a
Question (other): a boy multiplied 987 by a certain number and obtained 559981 as his answer . if in the answer both 98 are wrong and other digits are correct , then the correct answer would be :
Options: a ) 553681 , b ) 555181 , c ) 555681 , d ) 556581 , e ) 555581
Rationale: "987 = 3 x 7 x 47 . so , the required number must be divisible by each one of 3 , 7 , 47 553681 - - > sum of digits = 28 , not divisible by 3 555181 sum of digits = 25 , not divisible by 3 555681 is divisible by each one of 3 , 7 , 47 . 556581 sum of digits = 30 , not divisible by 7 555581 sum of digits = 29 , not divisible by 3 so the answer is c ."
Answer: c
Question (general): given f ( x ) = 2 x – 3 , for what value of x does 2 * [ f ( x ) ] – 11 = f ( x – 2 ) ?
Options: a ) 2 , b ) 3 , c ) 4 , d ) 5 , e ) 6
Rationale: "2 ( 2 x - 3 ) - 11 = 2 ( x - 2 ) - 3 2 x = 10 x = 5 the answer is d ."
Answer: d
Question (physics): pipe a fills a tank of capacity 750 liters at the rate of 40 liters a minute . another pipe b fills the same tank at the rate of 30 liters a minute . a pipe at the bottom of the tank drains the tank at the rate of 20 liters a minute . if pipe a is kept open for a minute and then closed and pipe b is open for a minute and then closed and then pipe c is open for a minute and then closed and the cycle is repeated , when will the tank be full ?
Options: a ) 45 minutes , b ) 14 minutes , c ) 39 minutes , d ) 40 minutes 20 seconds , e ) none of these
Rationale: "in one cycle they fill 40 + 30 - 20 = 50 liters 750 = 50 * n = > n = 15 here n = number of cycles . total time = 15 * 3 = 45 as in one cycle there are 3 minutes . thus 45 minutes answer : a"
Answer: a
Question (general): the first doughnut is priced at $ 1 and then if you purchase additional doughnuts as dozens then the price is $ 6 / dozen . what is the total number of doughnuts purchased if you paid $ 21 ?
Options: a ) 33 , b ) 35 , c ) 37 , d ) 39 , e ) 41
Rationale: "$ 21 = 3 * $ 6 + $ 3 the number of doughnuts is 3 * 12 + 3 = 39 the answer is d ."
Answer: d
Question (general): all the milk in container a which was filled to its brim was poured into two containers b and c . the quantity of milk in container b was 62.5 % less than the capacity of container a . if 150 liters was now transferred from c to b , then both the containers would have equal quantities of milk . what was the initial quantity of milk in container a ?
Options: a ) 1200 , b ) 1723 , c ) 1129 , d ) 2613 , e ) 1372
Rationale: "a b has 62.5 % or ( 5 / 8 ) of the milk in a . therefore , let the quantity of milk in container a ( initially ) be 8 k . quantity of milk in b = 8 k - 5 k = 3 k . quantity of milk in container c = 8 k - 3 k = 5 k container : a b c quantity of milk : 8 k 3 k 5 k it is given that if 150 liters was transferred from container c to container b , then both the containers would have equal quantities of milk . 5 k - 150 = 3 k + 150 = > 2 k = 300 = > k = 150 the initial quantity of milk in a = 8 k = 8 * 150 = 1200 liters ."
Answer: a
Question (physics): a train traveling at 72 kmph crosses a platform in 30 seconds and a man standing on the platform in 17 seconds . what is the length of the platform in meters ?
Options: a ) 240 meters , b ) 260 meters , c ) 420 meters , d ) 600 meters , e ) can not be determined
Rationale: "speed of the train in metres / sec = 72000 / 3600 = 20 distance travelled by train to cross the platform = 30 * 20 = 600 = length of train + length of platform distance travelled by train to cross the man = 17 * 20 = 340 = length of train length of platform = 600 - 340 = 260 answer : b"
Answer: b
Question (physics): two numbers have a h . c . f of 14 and a product of two numbers is 2562 . find the l . c . m of the two numbers ?
Options: a ) 140 , b ) 150 , c ) 160 , d ) 170 , e ) 183
Rationale: "l . c . m of two numbers is given by ( product of the two numbers ) / ( h . c . f of the two numbers ) = 2562 / 14 = 183 . answer : e"
Answer: e
Question (physics): a can complete a work in 10 days and b can do the same work in 5 days . if a after doing 2 days , leaves the work , find in how many days b will do the remaining work ?
Options: a ) 2 days , b ) 4 days , c ) 6 days , d ) 7 days , e ) 10 days
Rationale: "the required answer = ( 10 - 2 ) * 5 / 10 = 40 / 10 = 4 days answer is b"
Answer: b
Question (general): let the number which when multiplied by 13 is increased by 180 .
Options: a ) 14 , b ) 20 , c ) 15 , d ) 28 , e ) 30
Rationale: "solution let the number be x . then , 13 x - x = 180 ‹ = › 12 x = 180 x ‹ = › 15 . answer c"
Answer: c
Question (geometry): the diagonals of a rhombus are 20 cm and 25 cm . find its area ?
Options: a ) 158 , b ) 129 , c ) 250 , d ) 123 , e ) 117
Rationale: "1 / 2 * 20 * 25 = 250 answer : c"
Answer: c
Question (general): 10 ^ ( 655 ) ã · 10 ^ ( 652 ) = ?
Options: a ) 1 , b ) 100 , c ) 10000 , d ) 100000 , e ) 1000
Rationale: "10 ^ ( 655 ) ã · 10 ^ ( 652 ) = 10 ^ ( 655 - 652 ) = 10 ^ 3 = 1000 answer : e"
Answer: e
Question (physics): if 20 lines are drawn in a plane such that no two of them are parallel and no three are concurrent , then in how many points do they intersect ?
Options: a ) 110 , b ) 130 , c ) 150 , d ) 170 , e ) 190
Rationale: if two lines are not parallel , then they will intersect in exactly one point . lines can be extended infinitely on both ends so somewhere they will intersect with each other if they are not parallel . we are also given that no three lines are concurrent . this means that no three lines intersect at the same point . so every pair of two lines we select will have a unique point of intersection which they will not share with any third line . the number of ways to select 2 lines from 20 lines is 20 c 2 = 190 the answer is e .
Answer: e
Question (general): the jogging track in a sports complex is 1000 meters in circumference . deepak and his wife start from the same point and walk in opposite directions at 20 km / hr and 12 km / hr respectively . they will meet for the first time in ?
Options: a ) 32 min , b ) 40 min , c ) 35 min , d ) 25 min , e ) 20 min
Rationale: "clearly , the two will meet when they are 1000 m apart to be 20 + 12 = 32 km apart , they take 1 hour to be 1000 m apart , they take 32 * 1000 / 1000 = 32 min . answer is a"
Answer: a
Question (gain): an escalator moves towards the top level at the rate of 15 ft . sec and its length is 180 feet . if a person walks on the moving escalator at the rate of 3 feet per second towards the top level , how much time does he take to cover the entire length .
Options: a ) 12 sec , b ) 20 sec , c ) 15 sec , d ) 18 sec , e ) 10 sec
Rationale: "explanation : time taken to cover the entire length = tot . dist / resultant speed = 180 / ( 15 + 3 ) = 10 sec answer : e"
Answer: e
Question (general): a new home buyer pays 4 % annual interest on her first mortgage and 9 % annual interest on her second mortgage . if she borrowed a total of $ 335,000 , 80 % of which was in the first mortgage , what is her approximate monthly interest payment ?
Options: a ) $ 1,395 , b ) $ 1,733 , c ) $ 3,466 , d ) $ 13,333 , e ) $ 20,796
Rationale: "0.04 x + 0.09 y = 335000 [ 1 ] 0.04 x = 0.80 * 335000 = 268000 [ 2 ] 268000 + 0.09 y = 320000 - - > 0.09 y = 67000 [ 3 ] 268000 / 12 = 22333.3333 [ 4 ] 67000 / 12 = 5583.333 [ 5 ] adding [ 4,5 ] we get : 27916 [ 6 ] dividing [ 6 ] / 2 to get an average we get 1.395 , ans a"
Answer: a
Question (physics): a train 200 meters long completely crosses a 300 meters long bridge in 45 seconds . what is the speed of the train is ?
Options: a ) 10 , b ) 20 , c ) 30 , d ) 40 , e ) 50
Rationale: "s = ( 200 + 300 ) / 45 = 500 / 45 * 18 / 5 = 40 answer : d"
Answer: d
Question (gain): john and ingrid pay 30 % and 40 % tax annually , respectively . if john makes $ 56000 and ingrid makes $ 72000 , what is their combined tax rate ?
Options: a ) 32 % , b ) 34.4 % , c ) 35 % , d ) 35.6 % , e ) 36.4 %
Rationale: "( 1 ) when 30 and 40 has equal weight or weight = 1 / 2 , the answer would be 35 . ( 2 ) when 40 has larger weight than 30 , the answer would be in between 35 and 40 . unfortunately , we have 2 answer choices d and e that fit that condition so we need to narrow down our range . ( 3 ) get 72000 / 128000 = 72 / 128 = 9 / 16 . 9 / 16 is a little above 8 / 16 = 1 / 2 . thus , our answer is just a little above 35 . answer : d"
Answer: d
Question (gain): john ' s bank ' s saving amount is decreased 30 % due to loan payment and current balance is rs . 7000 . find the actual balance before deduction ?
Options: a ) 8000 , b ) 8500 , c ) 9000 , d ) 9500 , e ) 10000
Rationale: "cp * ( 70 / 100 ) = 7000 cp = 100 * 100 = > cp = 10000 answer : e"
Answer: e
Question (gain): during a special promotion , a certain filling station is offering a 10 percent discount on gas purchased after the first 6 gallons . if kim purchased 20 gallons of gas , and isabella purchased 25 gallons of gas , then isabella ‟ s total per - gallon discount is what percent of kim ‟ s total per - gallon discount ?
Options: a ) 80 % , b ) 100 % , c ) 109 % , d ) 120 % , e ) 140 %
Rationale: kim purchased 20 gallons of gas . she paid for 6 + 0.9 * 14 = 18.6 gallons , so the overall discount she got was 1.4 / 20 = 7 % . isabella purchased 25 gallons of gas . she paid for 6 + 0.9 * 19 = 23.1 gallons , so the overall discount she got was 1.9 / 25 = 7.6 % . 7.6 is 7.6 / 7 * 100 = 109 % of 7 . answer : c .
Answer: c
Question (other): a farmer with 1,350 acres of land had planted his fields with corn , sugar cane , and tobacco in the ratio of 3 : 2 : 4 , respectively , but he wanted to make more money , so he shifted the ratio to 2 : 2 : 5 , respectively . how many more acres of land were planted with tobacco under the new system ?
Options: a ) 90 , b ) 150 , c ) 270 , d ) 300 , e ) 450
Rationale: "originally ( 4 / 9 ) * 1350 = 600 acres were planted with tobacco . in the new system ( 5 / 9 ) * 1350 = 750 acres were planted with tobacco . thus 750 - 600 = 150 more acres were planted with tobacco . the answer is b ."
Answer: b
Question (general): if two of the 4 expressions x + y , x + 5 y , x - y , and 5 x - y are chosen at random , what is the probability w that their product will be of the form of x ^ 2 - ( by ) ^ 2 , where b is an integer ?
Options: a ) 1 / 2 , b ) 1 / 3 , c ) 1 / 4 , d ) 1 / 5 , e ) w = 1 / 6
Rationale: only ( x + y ) ( x - y ) pair will give the form x ^ 2 - ( by ) ^ 2 the probability of selecting these two pairs are 1 / 4 * 1 / 3 = 1 / 12 , assuming x + y is picked first , then x - y , but x - y can be picked first followed by x + y . so the probability w = 1 / 12 * 2 = 1 / 6 ans e
Answer: e