Cheukting/mathqa huggingface dataset:
Question (gain): albert buys 4 horses and 9 cows for rs . 13,400 . if he sells the horses at 10 % profit and the cows at 20 % profit , then he earns a total profit of rs . 1880 . the cost of a horse is :
Options: a ) rs . 2007 , b ) rs . 2000 , c ) rs . 2089 , d ) rs . 2067 , e ) rs . 2098
Rationale: "let c . p . of each horse be rs . x and c . p . of each cow be rs . y . then , 4 x + 9 y = 13400 - - ( i ) and , 10 % of 4 x + 20 % of 9 y = 1880 2 / 5 x + 9 / 5 y = 1880 = > 2 x + 9 y = 9400 - - ( ii ) solving ( i ) and ( ii ) , we get : x = 2000 and y = 600 . cost price of each horse = rs . 2000 . answer : b"
Answer: b
Question (physics): two motor bikes cover the same distance at the speed of 60 and 64 kmps respectively . find the distance traveled by them if the slower bike takes 1 hour more than the faster bike ?
Options: a ) 860 km , b ) 870 km , c ) 960 km , d ) 260 km , e ) 840 km
Rationale: explanation : 60 ( x + 1 ) = 64 x x = 15 60 x 16 = 960 km answer : c
Answer: c
Question (geometry): the edge of a cube is 7 a cm . find its surface ?
Options: a ) 24 a 8
b ) 24 a 4
c ) 24 a 1
d ) 24 a 2
e ) 294 a 2
Rationale: 6 a 2 = 6 * 7 a * 7 a = 294 a 2 answer : e
Answer: e
Question (general): if x < y < z and y - x > 5 , where x is an even integer and y and z are odd integers , what is the least possible value s of z - x ?
Options: a ) 6 , b ) 7 , c ) 8 , d ) 9 , e ) 10
Rationale: "x < y < z to find the least possible value for z - x ; we need to find the values for z and x that can be closest to each other . if x is some even number , then what could be minimum possible odd z . if x is some even number y - x > 5 ; y > x + 5 ; minimum value for y = x + 5 + 2 = x + 7 [ note : x + 5 is as even + odd = odd and nearest odd greater than x + 5 is x + 5 + 2 ] minimum value for z = y + 2 = x + 7 + 2 = x + 9 [ note : z = y + 2 because both z and y are odd . difference between two odd numbers is 2 ] s = z - x = x + 9 - x = 9 ans : d"
Answer: d
Question (general): if renee earns a raise of between 5 % and 10 % , non - inclusive , by what fraction could her salary have increased ?
Options: a ) 1 / 4 , b ) 1 / 5 , c ) 1 / 10 , d ) 2 / 25 , e ) 1 / 20
Rationale: 5 % is 5 / 100 = 1 / 20 10 % is 10 / 100 = 1 / 10 the increase must be greater than 1 / 20 and less than 1 / 10 . 1 / 4 , 1 / 5 , and 1 / 10 are not less than 1 / 10 . 1 / 20 is not greater than 1 / 20 . the only option left is 2 / 25 , which is in the specified range . answer : d
Answer: d
Question (gain): a merchant sells an item at a 20 % discount , but still makes a gross profit of 20 percent of the cost . what percent r of the cost would the gross profit on the item have been if it had been sold without the discount ?
Options: a ) 20 % , b ) 40 % , c ) 50 % , d ) 60 % , e ) 75 %
Rationale: "let the market price of the product is mp . let the original cost price of the product is cp . selling price ( discounted price ) = 100 % of mp - 20 % mp = 80 % of mp . - - - - - - - - - - - - - - - - ( 1 ) profit made by selling at discounted price = 20 % of cp - - - - - - - - - - - - - - ( 2 ) apply the formula : profit r = selling price - original cost price = > 20 % of cp = 80 % of mp - 100 % cp = > mp = 120 cp / 80 = 3 / 2 ( cp ) now if product is sold without any discount , then , profit = selling price ( without discount ) - original cost price = market price - original cost price = mp - cp = 3 / 2 cp - cp = 1 / 2 cp = 50 % of cp thus , answer should bec ."
Answer: c
Question (general): in δ pqs above , if pq = 5 and ps = 6 , then
Options: a ) 9 / 4 , b ) 12 / 5 , c ) 16 / 5 , d ) 30 / 7 , e ) 50 / 3
Rationale: "there are two ways to calculate area of pqs . area remains same , so both are equal . 5 * 6 / 2 = pr * 7 / 2 pr = 30 / 7 d"
Answer: d
Question (gain): in a graduate physics course , 70 percent of the students are male and 30 percent of the students are married . if two - sevenths of the male students are married , what fraction of the male students is single ?
Options: a ) 2 / 7 , b ) 1 / 3 , c ) 1 / 2 , d ) 2 / 3 , e ) 5 / 7
Rationale: "let assume there are 100 students of which 70 are male and 30 are females if 30 are married then 70 will be single . now its given that two - sevenths of the male students are married that means 2 / 7 of 70 = 20 males are married if 30 is the total number of students who are married and out of that 20 are males then the remaining 10 will be females who are married . total females = 70 married males = 20 then single males = 70 - 20 = 50 we need to find the fraction of male students who are single i . e single male students / total male student = 50 / 70 = 5 / 7 [ e ]"
Answer: e
Question (physics): johnny travels a total of one hour to and from school . on the way there he jogs at 4 miles per hour and on the return trip he gets picked up by the bus and returns home at 20 miles per hour . how far is it to the school ?
Options: a ) 2 miles , b ) 6.6 miles , c ) 4.8 miles , d ) 8 miles , e ) 10 miles
Rationale: "answer : b ) 6.6 miles . average speed for round trip = 2 * a * b / ( a + b ) , where a , b are speeds so , average speed was = 2 * 4 * 20 / ( 4 + 20 ) = 6.6 m / hr the distance between schoolhome should be half of that . ie . 6.6 miles answer b"
Answer: b
Question (physics): an engine moves at the speed of 90 kmph without any coaches attached to it . speed of the train reduces at the rate that varies directly as the square root of the number of coaches attached . when 4 coaches are attached speed decreases to 78 kmph . what will be the speed of train when 16 coaches are attached .
Options: a ) 66 , b ) 72 , c ) 80 , d ) 68 , e ) 73
Rationale: "1 . no . of coaches = 4 sqr root = 2 speed decreases by 12 12 = k * 2 k = 6 no . of coaches = 16 swr root = 4 decrease = 4 * 6 = 24 new speed = 90 - 24 = 66 a"
Answer: a
Question (gain): at what rate percent of simple interest will a sum of money double itself in 77 years ?
Options: a ) 6.54 % , b ) 2.54 % , c ) 8 . 2 % , d ) 4.94 % , e ) 1.29 %
Rationale: let sum = x . then , s . i . = x . rate = ( 100 * s . i . ) / ( p * t ) = ( 100 * x ) / ( x * 77 ) = 100 / 77 = 1.29 % answer : e
Answer: e
Question (general): what is the value of 10 ^ 7 - 6 ^ 5 ?
Options: a ) 99 , 91,223 , b ) 99 , 92,224 , c ) 99 , 94,265 , d ) 99 , 95,300 , e ) 99 , 96,307
Rationale: "as 10 ^ n will always have last digit as 0 and 6 ^ n will always as last digit 6 . . hence difference of such sum should always be ending with 4 and there is only on option . . answer b"
Answer: b
Question (general): dacid obtained 73 , 69 , 92 , 64 and 82 marks ( out of 100 ) in english , mathematics , physics , chemistry and biology . what are his average marks ?
Options: a ) 79 , b ) 99 , c ) 88 , d ) 88 , e ) 76
Rationale: "average = ( 73 + 69 + 92 + 64 + 82 ) / 5 = 380 / 5 = 76 answer : e"
Answer: e
Question (general): in may mrs lee ' s earnings were 60 percent of the lee family ' s total income . in june mrs lee earned 30 percent more than in may . if the rest of the family ' s income was the same both months , then , in june , mrs lee ' s earnings were approximately what percent of the lee family ' s total income ?
Options: a ) 64 % , b ) 66 % , c ) 72 % , d ) 76 % , e ) 80 %
Rationale: "let in may lee family ' s total income = 100 in may mrs lee ' s income = 60 in may rest of the family ' s income = 40 in june mrs lees income = 60 * 130 / 100 = 78 in june total income = 78 + 40 = 118 % of mrs lee ' s income = 72 / 112 = 66.10 ( b )"
Answer: b
Question (physics): r and s together can plough a field in 10 hours but by himself r requires 15 hours . how long would s take to plough the same field ?
Options: a ) 24 hours , b ) 5 hours , c ) 10 hours , d ) 15 hours , e ) 20 hours
Rationale: f r and s together can do a piece of work in x days and r alone can do the same work in y days , then s alone can do the same work in x y / y â € “ x days . the no . of hours required by s = 10 ã — 20 / 20 â € “ 10 = 200 / 10 = 20 hours e
Answer: e
Question (geometry): the area of a square is equal to five times the area of a rectangle of dimensions 60 cm * 12 cm . what is the perimeter of the square ?
Options: a ) 289 cm , b ) 800 cm , c ) 829 cm , d ) 288 cm , e ) 240 cm
Rationale: "area of the square = s * s = 5 ( 60 * 12 ) = > s = 60 = 60 cm perimeter of the square = 4 * 60 = 240 cm . answer : e"
Answer: e
Question (general): 36 is divided in 2 parts such that 8 times the first part added to 3 times the second part makes 203 . what is the first part ?
Options: a ) 19 , b ) 88 , c ) 267 , d ) 26 , e ) 28
Rationale: explanation : let the first part be x . 8 x + 3 ( 36 – x ) = 203 8 x + 108 – 3 x = 203 5 x + 108 = 203 5 x = 95 x = 19 answer : a
Answer: a
Question (general): roy is now 8 years older than julia and half of that amount older than kelly . if in 2 years , roy will be twice as old as julia , then in 2 years what would be roy ’ s age multiplied by kelly ’ s age ?
Options: a ) 160 , b ) 168 , c ) 176 , d ) 184 , e ) 192
Rationale: "r = j + 8 = k + 4 r + 2 = 2 ( j + 2 ) ( j + 8 ) + 2 = 2 j + 4 j = 6 r = 14 k = 10 in 2 years ( r + 2 ) ( k + 2 ) = 16 * 12 = 192 the answer is e ."
Answer: e
Question (geometry): the radius of a cylindrical vessel is 5 cm and height is 3 cm . find the whole surface of the cylinder ?
Options: a ) 251.4 sq cm , b ) 220 sq cm , c ) 440 sq cm , d ) 132 sq cm , e ) 138 sq cm
Rationale: "r = 5 h = 3 2 π r ( h + r ) = 2 * 22 / 7 * 5 ( 8 ) = 251.4 answer : a"
Answer: a
Question (physics): mike works at a science lab that conducts experiments on bacteria . the population of the bacteria multiplies at a constant rate , and his job is to notate the population of a certain group of bacteria each hour . at 1 p . m . on a certain day , he noted that the population was 500 and then he left the lab . he returned in time to take a reading at 4 p . m . , by which point the population had grown to 62,500 . now he has to fill in the missing data for 2 p . m . and 3 p . m . what was the population at 3 p . m . ?
Options: a ) 13000 , b ) 12500 , c ) 13500 , d ) 14000 , e ) 15000
Rationale: let the rate be x , then population of the bacteria after each hour can be given as 500,500 x , 500 ( x ^ 2 ) , 500 ( x ^ 3 ) now population at 4 pm = 62,500 thus we have 500 ( x ^ 3 ) = 62,500 = 125 thus x = 5 therefore population at 3 pm = 500 ( 25 ) = 12500 answer : b
Answer: b
Question (general): the average weight of a group of boys is 20 kg . after a boy of weight 35 kg joins the group , the average weight of the group goes up by 1 kg . find the number of boys in the group originally ?
Options: a ) 12 , b ) 14 , c ) 18 , d ) 24 , e ) 10
Rationale: "let the number off boys in the group originally be x . total weight of the boys = 20 x after the boy weighing 35 kg joins the group , total weight of boys = 20 x + 35 so 20 x + 35 = 21 ( x + 1 ) = > x = 14 . answer : b"
Answer: b
Question (physics): at a certain bowling alley , it costs $ 0.50 to rent bowling shoes for the day and $ 1.75 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 ) 9 , 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 / 1.75 = 7.02 - > ~ 7 . answer : a ."
Answer: a
Question (other): the ratio of number of boys and girls in a school is 3 : 5 . if there are 320 students in the school , find the number of girls in the school ?
Options: a ) 150 , b ) 250 , c ) 300 , d ) 200 , e ) 280
Rationale: "let the number of boys and girls be 3 x and 5 x total students = 320 number of girls in the school = 5 * 320 / 8 = 200 answer is d"
Answer: d
Question (general): the arithmetic mean and standard deviation of a certain normal distribution are 14.5 and 1.5 , respectively . what value is exactly 2 standard deviations less than the mean ?
Options: a ) 10.5 , b ) 11 , c ) 11.5 , d ) 12 , e ) 12.5
Rationale: "the value which isexactlytwo sd less than the mean is : mean - 2 * sd = 14.5 - 2 * 1.5 = 11.5 . answer : c ."
Answer: c
Question (physics): a girl sitting in a train which is travelling at 100 kmph observes that a goods train travelling in a opposite direction , takes 6 seconds to pass him . if the goods train is 560 m long , find its speed .
Options: a ) 230 , b ) 232 , c ) 234 , d ) 236 , e ) 238
Rationale: "relative speed = ( 560 / 6 ) m / s = ( 560 / 6 ) * ( 18 / 5 ) = 336 kmph speed of goods train = 336 - 100 = 236 kmph answer is e"
Answer: e
Question (general): the average age of 15 students of a class is 15 years . out of these , the average age of 4 students is 14 years and that of the other 9 students is 16 years . tee age of the 15 th student is ?
Options: a ) 20 years , b ) 22 years , c ) 24 years , d ) 25 years , e ) 27 years
Rationale: "age of the 15 th student = [ 15 * 15 - ( 14 * 4 + 16 * 9 ) ] = ( 225 - 200 ) = 25 years . answer : d"
Answer: d
Question (physics): a can do a piece of work in 10 days and b alone can do it in 15 days . how much time will both take to finish the work ?
Options: a ) 2 days , b ) 7 days , c ) 6 days , d ) 9 days , e ) 3 days
Rationale: "c 6 days time taken to finish the job = xy / ( x + y ) = 10 x 15 / ( 10 + 15 ) = 150 / 25 = 6 days"
Answer: c
Question (general): in a class of 25 students in an examination in maths 5 students scored 95 marks each , 3 get zero each and the average of the rest was 45 . what is the average of the whole class ?
Options: a ) a ) 47 , b ) b ) 45.6 , c ) c ) 44 , d ) d ) 48 , e ) e ) 49.6
Rationale: "explanation : total marks obtained by a class of 25 students = 5 * 95 + 3 * 0 + 17 * 45 = 1240 average marks of whole class = 1240 / 25 = 49.6 answer : option e"
Answer: e
Question (general): if | 20 x - 10 | = 190 , then find the product of the values of x ?
Options: a ) - 45 , b ) 50 , c ) - 62 , d ) 35 , e ) - 90
Rationale: "| 20 x - 10 | = 190 20 x - 10 = 190 or 20 x - 10 = - 190 20 x = 200 or 20 x = - 180 x = 10 or x = - 9 product = - 9 * 10 = - 90 answer is e"
Answer: e
Question (general): how many positive integers between 1 and 400 are there such that they are multiples of 25 ?
Options: a ) 12 , b ) 13 , c ) 16 , d ) 15 , e ) 11
Rationale: "multiples of 25 = 25 , 50,75 , - - - - - 400 number of multiples of 25 = > 25 * 16 = 400 answer is c"
Answer: c
Question (general): if the range w of the 6 numbers 4 , 314 , 710 and x is 12 , what is the difference between the greatest possible value of x and least possible value of x ?
Options: a ) 0 , b ) 2 , c ) 12 , d ) 13 , e ) 15
Rationale: the range w of a set is the difference between the largest and smallest elements of a set . without x , the difference between the largest and smallest elements of a set is 14 - 3 = 11 < 12 , which means that in order 12 to be the range of the set x must be either the smallest element so that 14 - x = 12 - - - > x = 2 or x must the largest element so that x - 3 = 12 - - > x = 15 . the the difference between the greatest possible value of x and least possible value of x is 15 - 2 = 13 . answer : d .
Answer: d
Question (general): how many 7 digit number contain number 3 ?
Options: a ) 2748472 , b ) 3748472 , c ) 4748472 , d ) 5748472 , e ) 6748472
Rationale: "total 7 digit no . = 9 * 10 * 10 * 10 * 10 * 10 * 10 = 9000000 not containing 3 = 8 * 9 * 9 * 9 * 9 * 9 * 9 = 4251528 total 7 digit number contain 3 = 9000 - 4251528 = 4748472 answer : c"
Answer: c
Question (gain): the sale price of an article including the sales tax is rs . 616 . the rate of sales tax is 10 % . if the shopkeeper has made a profit of 18 % , then the cost price of the article is :
Options: a ) 500 , b ) 474.6 , c ) 222 , d ) 297 , e ) 111
Rationale: "explanation : 110 % of s . p . = 616 s . p . = ( 616 * 100 ) / 110 = rs . 560 c . p = ( 100 * 560 ) / 118 = rs . 474.6 answer : b"
Answer: b
Question (general): how many integers from 10 to 180 , inclusive , are divisible by 3 but not divisible by 7 ?
Options: a ) 45 , b ) 49 , c ) 50 , d ) 52 , e ) 56
Rationale: "we should find # of integers divisible by 3 but not by 3 * 7 = 21 . # of multiples of 21 in the range from 10 to 180 , inclusive is ( 168 - 21 ) / 21 + 1 = 8 ; 57 - 8 = 49 . answer : b ."
Answer: b
Question (physics): 12 men work 8 hours per day to complete the work in 10 days . to complete the same work in 8 days , working 15 hours a day , the number of men required
Options: a ) 8 days , b ) 3 days , c ) 7 days , d ) 5 days , e ) 6 days
Rationale: "that is , 1 work done = 12 × 8 × 10 then , 12 8 × 10 = ? × 15 × 8 ? ( i . e . no . of men required ) = 12 × 8 × 10 / 15 × 10 = 8 days . a"
Answer: a
Question (general): if x is an integer and 2.134 × 10 ^ x is less than 220,000 , what is the greatest possible value for x ?
Options: a ) 7 , b ) 6 , c ) 5 , d ) 4 , e ) 3
Rationale: "x is an integer and 2.134 × 10 x is less than 220,000 , what is the greatest possible value for x ? for 2.134 × 10 x is less than 220,000 to remain true , the greatest number is 213,400 , which makes x = 5 c . 5"
Answer: c
Question (general): calculate 469157 x 9999 = ?
Options: a ) 4586970843 , b ) 4686970743 , c ) 4691100843 , d ) 4586870843 , e ) none
Rationale: "answer 469157 x 9999 = 469157 x ( 10000 - 1 ) = 4691570000 - 469157 = 4691100843 . option : c"
Answer: c
Question (geometry): the area of a square field is 400 km 2 . how long will it take for a horse to run around at the speed of 20 km / h ?
Options: a ) 12 h , b ) 10 h , c ) 4 h , d ) 6 h , e ) none of these
Rationale: explanation area of field = 400 km 2 . then , each side of field = √ 400 = 20 km distance covered by the horse = perimeter of square field = 20 × 4 = 80 km ∴ time taken by horse = distances / peed = 80 / 20 = 4 h answer c
Answer: c
Question (general): there are 10 dozen mangoes in a box . if there are 36 such boxes , how many mangoes are there in all the boxes together ?
Options: a ) 516 , b ) 3096 , c ) 6192 , d ) 628 , e ) 4320
Rationale: number of mangoes = 12 dozens = 12 × 10 = 120 ∴ number of mangoes in 36 boxes = 36 × 120 = 4320 answer e
Answer: e
Question (other): if a and b are in the ratio 3 : 4 , and b and c in the ratio 12 : 13 , then a and c will be in the ratio
Options: a ) 3 : 13 , b ) 9 : 13 , c ) 36 : 13 , d ) 13 : 9 , e ) none
Rationale: solution : ( a / b ) * ( b / c ) = ( 3 / 4 ) * ( 12 / 13 ) ; or , a / b = 36 / 39 = 9 : 13 . answer : option b
Answer: b
Question (general): the sum of a number and the number preceding it is 33 . by how much is two less than 6 times the number ?
Options: a ) 196 , b ) 94 , c ) 90 , d ) 100 , e ) 120
Rationale: two numbers must be 16 and 17 16 + 17 = 33 required number is 17 six times of this number = 6 * 17 = 102 two less than 102 = 102 - 2 = 100 answer : d
Answer: d
Question (general): 4,18 , 100,294 , ___
Options: a ) 1000 , b ) 1100 , c ) 1210 , d ) 1452 , e ) 1552
Rationale: "2 ^ 3 - 2 ^ 2 = 4 ; 3 ^ 3 - 3 ^ 2 = 18 ; 5 ^ 3 - 5 ^ 2 = 100 ; 7 ^ 3 - 7 ^ 2 = 294 ; so , 11 ^ 3 - 11 ^ 2 = 1210 answer : c"
Answer: c
Question (other): a bag holds 5 red marbles and 5 green marbles . if you removed two randomly selected marbles from the bag , without replacement , what is the probability that both would be red ?
Options: a ) 1 / 6 , b ) 2 / 5 , c ) 3 / 10 , d ) 2 / 9 , e ) 1 / 2
Rationale: "probability of selecting first red marble = 5 / 10 probability of selecting second red marble without replacement = 4 / 9 final probability = 5 / 10 * 4 / 9 = 2 / 9 the correct answer is d ."
Answer: d
Question (general): what is the smallest integer x for which 27 ^ x > 3 ^ 24 ?
Options: a ) 7 , b ) 8 , c ) 9 , d ) 10 , e ) 12
Rationale: "27 ^ x > 3 ^ 24 converting into the same bases : 27 ^ x > 27 ^ 8 therefore for the equation to hold true , x > 8 or x = 9 option c"
Answer: c
Question (physics): a man can row downstream at 16 kmph and upstream at 12 kmph . find the speed of the man in still water .
Options: a ) 14 , b ) 13 , c ) 12 , d ) 16 , e ) 15
Rationale: "let the speed of the man in still water and speed of stream be x kmph and y kmph respectively . given x + y = 16 - - - ( 1 ) and x - y = 12 - - - ( 2 ) from ( 1 ) & ( 2 ) 2 x = 28 = > x = 14 , y = 2 . answer : a"
Answer: a
Question (gain): a shopkeeper sold an article offering a discount of 4 % and earned a profit of 38 % . what would have been the percentage of profit earned if no discount was offered ?
Options: a ) 24 , b ) 28 , c ) 30 , d ) 32 , e ) 44
Rationale: "let c . p . be rs . 100 . then , s . p . = rs . 138 let marked price be rs . x . then , 96 / 100 x = 138 x = 13800 / 96 = rs . 143.75 now , s . p . = rs . 143.75 , c . p . = rs . 100 profit % = 44 % . answer : e"
Answer: e
Question (physics): two trains of length 160 m and 320 m are running towards each other on parallel lines at 42 kmph and 30 kmph respectively . in what time will they be clear of each other from the moment they meet ?
Options: a ) 10 sec , b ) 32 sec , c ) 82 sec , d ) 24 sec , e ) 89 sec
Rationale: "relative speed = ( 42 + 30 ) * 5 / 18 = 4 * 5 = 20 mps . distance covered in passing each other = 160 + 320 = 480 m . the time required = d / s = 480 / 20 = 24 sec . answer : d"
Answer: d
Question (general): solve ( 0.76 × 0.76 × 0.76 − 0.008 ) / ( 0.76 × 0.76 + 0.76 × 0.2 + 0.04 )
Options: a ) 0.56 , b ) 0.62 , c ) 0.5 , d ) 0.48 , e ) 0.52
Rationale: 0.56 option ' a '
Answer: a
Question (physics): what is the maximum area that can be enclosed by a wire 44 cm long ?
Options: a ) 77
b ) 154
c ) 308
d ) 318
e ) none of these
Rationale: perimeter of circle = 2 * 22 / 7 * r = 44 cm from this r = 7 then area of circle = 22 / 7 * r ^ 2 = 154 answer : b
Answer: b
Question (general): if the average ( arithmetic mean ) of 2 x , 4 x , and 8 x is 140 , what is the value of x ?
Options: a ) 20 , b ) 30 , c ) 15 , d ) 33 , e ) 31
Rationale: "am of 2 x , 4 x and 8 x = 2 x + 4 x + 8 x / 3 = 14 x / 3 given that 14 x / 3 = 140 x = 30 answer is b"
Answer: b
Question (general): if the probability of rain on any given day in chicago during the summer is 50 % , independent of what happens on any other day , what is the probability of having exactly 3 rainy days from july 4 through july 10 inclusive ?
Options: a ) 7 / 32 , b ) 11 / 64 , c ) 35 / 128 , d ) 49 / 128 , e ) 65 / 128
Rationale: "one possible case is : rainy - rainy - rainy - not rainy - not rainy - not rainy - not rainy . the probability of this case is ( 1 / 2 ) ^ 7 = 1 / 128 the number of possible cases is 7 c 3 = 35 . p ( exactly 3 rainy days ) = 35 * 1 / 128 = 35 / 128 the answer is c ."
Answer: c
Question (general): what is the positive difference between the sum of the squares of the first 5 positive integers and the sum of the prime numbers between the first square and fourth square ?
Options: a ) 11 , b ) 12 , c ) 13 , d ) 14 , e ) 15
Rationale: "forget conventional ways of solving math questions . in ps , ivy approach is the easiest and quickest way to find the answer . the sum of the squares of the first 4 positive integers = 1 ^ 2 + 2 ^ 2 + 3 ^ 2 + 4 ^ 2 + 5 ^ 2 = 55 the sum of the prime numbers between the first square ( = 1 ) and fourth square ( = 16 ) = 2 + 3 + 5 + 7 + 11 + 13 = 41 . so the difference between 41 and 55 is 14 . so the answer is ( d ) ."
Answer: d
Question (general): find the value of 80641 x 9999 = m ?
Options: a ) 807518799 , b ) 806436469 , c ) 807538799 , d ) 806329359 , e ) 817431046
Rationale: "80641 x 9999 = 80641 x ( 10000 - 1 ) = 80641 x 10000 - 80641 x 1 = 806410000 - 80641 = 806329359 d"
Answer: d
Question (general): 3889 + 12.952 – ? = 3854.002
Options: a ) 47.095 , b ) 47.752 , c ) 47.932 , d ) 47.95 , e ) none
Rationale: explanation let 3889 + 12.952 – x = 3854.002 . then x = ( 3889 + 12.952 ) – 3854.002 = 3901.952 – 3854.002 = 47.95 . answer d
Answer: d