Cheukting/mathqa huggingface dataset:
Question (physics): a space shuttle orbits the earth at about 6 kilometers per second . this speed is equal to how many kilometers per hour ?
Options: a ) 480 , b ) 2,880 , c ) 21,600 , d ) 28,800 , e ) 48,000
Rationale: seconds in 1 hours : 60 s in 1 min 60 min in 1 hr 60 * 60 = 3600 sec in 1 hr 6 * 3600 = 21,600 answer : c
Answer: c
Question (probability): a father purchased dress for his 3 daughters . the dresses are of same color but diff size and they are kept in dark room . what is probability that all the 3 will not choose there own dress ?
Options: a ) 1 / 3 , b ) 2 / 3 , c ) 1 / 2 , d ) 3 / 4 , e ) 3 / 7
Rationale: explanation : let 1 st girl come and she choose wrong dress so probability of that girl to choose wrong dress out of 3 is = 2 / 3 . now 2 nd girl come nd she choose wrong dress so probability of that girl to choose wrong dress out of 2 is 1 / 2 . now for 3 rd girl probability is 1 to choose wrong dress . so probability tht all the 3 wil not choose der own dress is = 2 / 3 * 1 / 2 * 1 = 1 / 3 . hence ( a ) is the correct answer . answer : a
Answer: a
Question (general): a man has some hens and cows . if the number of heads be 48 and the number of feet equals 144 , then the number of hens will be :
Options: a ) 22 , b ) 23 , c ) 24 , d ) 26 , e ) 28
Rationale: "let hens be x and cows be y now , feet : x * 2 + y * 4 = 144 heads : x * 1 + y * 1 = 48 implies , 2 x + 4 y = 144 and x + y = 48 solving these two equations , we get x = 24 and y = 24 therefore , hens are 26 . answer : c"
Answer: c
Question (general): a batsman in his 10 th innings makes a score of 60 , and thereby increases his average by 3 . what is his average after the 10 th innings ? he had never been ’ not out ’ .
Options: a ) 47 , b ) 37 , c ) 39 , d ) 43 , e ) 33
Rationale: "average score before 10 th innings = 60 - 3 × 10 = 30 average score after 10 th innings = > 30 + 3 = 33 answer : e"
Answer: e
Question (geometry): the radius of a cylinder is 10 m , height 14 m . the volume of the cylinder is :
Options: a ) 2200 , b ) 5500 , c ) 3300 , d ) 1100 , e ) 4400
Rationale: "cylinder volume = π r ( power 2 ) h = 22 / 7 × 10 × 10 × 14 = 4400 m ( power 3 ) answer is e ."
Answer: e
Question (gain): at what price must an article costing rs . 47.50 be marked in order that after deducting 5 % from the list price . it may be sold at a profit of 30 % on the cost price ?
Options: a ) 62.5 , b ) 62.3 , c ) 65 , d ) 62.2 , e ) 62.9
Rationale: "cp = 47.50 sp = 47.50 * ( 130 / 100 ) = 61.75 mp * ( 95 / 100 ) = 61.75 mp = 65 answer : c"
Answer: c
Question (other): income and expenditure of a person are in the ratio 5 : 3 . if the income of the person is rs . 10000 , then find his savings ?
Options: a ) rs . 4000 , b ) rs . 3603 , c ) rs . 3639 , d ) rs . 3632 , e ) rs . 3602
Rationale: "let the income and the expenditure of the person be rs . 5 x and rs . 3 x respectively . income , 5 x = 10000 = > x = 2000 savings = income - expenditure = 5 x - 3 x = 2 x so , savings = rs . 2 * 2000 = rs . 4000 answer : a"
Answer: a
Question (geometry): in a triangle , one side is 6 cm and another side is 8 cm . which of the following can be the perimeter of the triangle ?
Options: a ) 22 .
b ) 25 .
c ) 30 .
d ) 32 .
e ) 34 .
Rationale: given : one side is 6 cm and another side is 8 cm . so the 3 rd side will be > 3 and < 15 . thus the perimeter will be : 18 < perimeter < 30 . only option satisfying this condition is 22 . hence a .
Answer: a
Question (other): in 50 l can , milk and water in the ratio of 3 : 1 . if the ratio has made 1 : 3 then the quantity of water that has to be added further is ?
Options: a ) 100 , b ) 120 , c ) 90 , d ) 80 , e ) 70
Rationale: 100 litre water is to be added . let ' x ' liter water is to be added more . then 1 / 3 = 37.5 / ( 12.5 + x ) x = 100 answer : a
Answer: a
Question (general): find the sum of all 4 digit numbers formed using digits 1,2 , 5,6 .
Options: a ) 93324 , b ) 92324 , c ) 93424 , d ) 93424 , e ) 93824
Rationale: "( n - 1 ) ! * ( 111 . . . n ) * ( sum of the digits ) = ( 4 - 1 ) ! * 1111 * ( 1 + 2 + 5 + 6 ) = 93324 answer : a"
Answer: a
Question (general): 8.036 divided by 0.04 gives :
Options: a ) 200.9 , b ) 2.06 , c ) 20.06 , d ) 100.9 , e ) 200.6
Rationale: "= 8.036 / 0.04 = 803.6 / 4 = 200.9 answer is a ."
Answer: a
Question (gain): the simple interest on rs . 20 for 6 months at the rate of 5 paise per rupeeper month is
Options: a ) 1.2 , b ) 1.4 , c ) 6 , d ) 7 , e ) none
Rationale: "sol . s . i . = rs . [ 20 * 5 / 100 * 6 ] = rs . 6 answer c"
Answer: c
Question (general): tom has travelling to 7 cities . gasoline prices varied from city to city . what is the median gasoline price ?
Options: a ) $ 1 , b ) $ 1.84 , c ) $ 1.98 , d ) $ 2.34 , e ) $ 2.56
Rationale: ordering the data from least to greatest , we get : $ 1.61 , $ 1.75 , $ 1.79 , $ 1.84 , $ 1.96 , $ 2.09 , $ 2.11 the median gasoline price is $ 1.84 . ( there were 3 states with higher gasoline prices and 3 with lower prices . ) b
Answer: b
Question (general): if n is an integer and 102 n ^ 2 is less than or equal to 8100 , what is the greatest possible value of n ?
Options: a ) 7 , b ) 8 , c ) 9 , d ) 10 , e ) 11
Rationale: "102 * n ^ 2 < = 8100 n ^ 2 < = 8100 / 102 which will be less than 81 since 8100 / 100 = 81 which is the square of 9 next closest value of n where n ^ 2 < = 81 is 8 ans b"
Answer: b
Question (gain): 4 mat - weavers can weave 4 mats in 4 days . at the same rate , how many mats would be woven by 12 mat - weavers in 12 days ?
Options: a ) 25 , b ) 19 , c ) 39 , d ) 61 , e ) 36
Rationale: "let the required number of bottles be x . more weavers , more mats ( direct proportion ) more days , more mats ( direct proportion ) wavers 4 : 12 : : 4 : x days 4 : 12 4 * 4 * x = 12 * 12 * 4 x = ( 12 * 12 * 4 ) / ( 4 x 4 ) x = 36 . answer is e ."
Answer: e
Question (physics): if 3 people can do 3 times of a particular work in 3 days , then how many days would it take 6 people to do 6 times of that particular work ?
Options: a ) 1 , b ) 2 , c ) 3 , d ) 6 , e ) 9
Rationale: "3 people can do the work one time in one day . 1 person can do 1 / 3 of the work in one day . 6 people can do 6 / 3 of the work in one day . 6 people can do 6 times the work in 3 days . the answer is c ."
Answer: c
Question (general): if 4 xz + yw = 7 and xw + yz = 14 , what is the value of the expression ( 2 x + y ) ( 2 z + w ) ?
Options: a ) 9 . , b ) 12 . , c ) 35 . , d ) 16 . , e ) 18 .
Rationale: "( 2 x + y ) * ( 2 z + w ) = 7 + 2 ( 14 ) = 35 answer : c"
Answer: c
Question (physics): a , b , k start from the same place and travel in the same direction at speeds of 30 km / hr , 40 km / hr , 120 km / hr respectively . b starts two hours after a . if b and k overtake a at the same instant , how many hours after a did k start ?
Options: a ) 3 , b ) 4 , c ) 6 , d ) 8 , e ) 10
Rationale: "in 2 hours , a travels 60 km . b can catch a at a rate of 10 km / hr , so b catches a 6 hours after b starts . so a and b both travel a distance of 240 km . c needs 2 hours to travel 240 km , so c leaves 6 hours after a . the answer is c ."
Answer: c
Question (physics): a river 3 m deep and 55 m wide is flowing at the rate of 1 kmph the amount of water that runs into the sea per minute is ?
Options: a ) 2338.9 , b ) 2748.9 , c ) 2148.9 , d ) 2745.9 , e ) 2718.9
Rationale: "rate of water flow - 1 kmph - - 1000 / 60 - - 16.66 m / min depth of river - - 3 m width of river - - 55 m vol of water per min - - 16.66 * 3 * 55 - - - 2748.9 answer b"
Answer: b
Question (general): in x - y plane , there is a right triangle abc ( ∠ b = 90 o ) . if the length of ac is 100 and the slope of line segment ac is 4 / 3 , what is the length of ab ?
Options: a ) 12 , b ) 18 , c ) 24 , d ) 28 , e ) 80
Rationale: slope = change in vertical direction / change in horizontal direction = 4 / 3 change in vertical direction = 4 x = ab change in horizontal direction = 3 x = bc ab ^ 2 + bc ^ 2 = 100 ^ 2 16 x ^ 2 + 9 x ^ 2 = 10000 25 x ^ 2 = 400 x ^ 2 = 400 x = 20 therefore ab = 20 * 4 = 80 answer : e
Answer: e
Question (general): what is the remainder when 14,451 × 15,651 × 16,788 is divided by 5 ?
Options: a ) 1 , b ) 2 , c ) 4 , d ) 3 , e ) 5
Rationale: "only the unit ' s digit of the product will decide the remainder when divided by 5 . hence , 1 * 1 * 8 = will give units digit as 8 so , whatever be the number , if it ends in 8 , the remainder after dividing with 5 will be 3 . optiond"
Answer: d
Question (gain): a dishonest dealer professes to sell goods at the cost price but uses a weight of 850 grams per kg , what is his percent ?
Options: a ) 25 % , b ) 17 % , c ) 29 % , d ) 55 % , e ) 45 %
Rationale: "850 - - - 150 100 - - - ? = > 17.64 % answer : b"
Answer: b
Question (other): a bag contains 7 red , 9 blue and 5 green balls . if 3 balls are picked at random , what is the probability that both are red ?
Options: a ) 2 / 21 , b ) 3 / 41 , c ) 5 / 26 , d ) 1 / 38 , e ) 5 / 32
Rationale: "p ( both are red ) , = 7 c 3 / 21 c 3 = ( 7 * 6 * 5 ) / 21 * 20 * 19 = 1 / 38 d"
Answer: d
Question (general): 40 is divided into two parts in such a way that seventh part of first and ninth part of second are equal . find the smallest part ?
Options: a ) 13.2 , b ) 17.5 , c ) 12.8 , d ) 34.25 , e ) 31.25
Rationale: "x / 7 = y / 9 = > x : y = 7 : 9 7 / 16 * 40 = 17.5 answer : b"
Answer: b
Question (general): hammers and wrenches are manufactured at a uniform weight per hammer and a uniform weight per wrench . if the total weight of two hammers and three wrenches is one - third that of 8 hammers and 4 wrenches , then the total weight of one wrench is how many times that of one hammer ?
Options: a ) 1 / 2 , b ) 2 / 5 , c ) 1 , d ) 3 / 2 , e ) 2
Rationale: "x b é the weight of a hammer and y be the weight of a wrench . ( 2 x + 3 y ) = 1 / 3 * ( 8 x + 4 y ) 3 ( 2 x + 3 y ) = ( 8 x + 4 y ) 6 x + 9 y = 8 x + 4 y 5 y = 2 x y = 2 x / 5 ans - b"
Answer: b
Question (physics): a man can row at 5 kmph in still water . if the velocity of the current is 1 kmph and it takes him 1 hour to row to a place and come back . how far is that place .
Options: a ) . 4 km , b ) 1.4 km , c ) 2.4 km , d ) 3.4 km , e ) none of these
Rationale: "explanation : let the distance is x km rate downstream = 5 + 1 = 6 kmph rate upstream = 5 - 1 = 4 kmph then x / 6 + x / 4 = 1 [ because distance / speed = time ] = > 2 x + 3 x = 12 = > x = 12 / 5 = 2.4 km option c"
Answer: c
Question (other): in a certain school , the ratio of boys to girls is 5 to 13 . if there are 80 more girls than boys , how many boys are there ?
Options: a ) 27 , b ) 36 , c ) 45 , d ) 50 , e ) 117
Rationale: "the ratio of b to g is 5 : 13 and the other data point is g are more than boys by 80 . . . looking at the ratio we can say that the 8 ( 13 - 5 ) extra parts caused this diff of 80 . so 1 part corresponds to 80 / 8 = 10 and so 5 parts correspond to 5 * 10 = 50 . d"
Answer: d
Question (gain): a reduction in the price of petrol by 10 % enables a motorist to buy 5 gallons more for $ 300 . find the original price of petrol ?
Options: a ) $ 11 , b ) $ 5 , c ) $ 45 , d ) $ 400 , e ) $ 6.6
Rationale: "price decreased by 10 % , so 9 / 10 times , which means that original gallons bought increased 10 / 9 times . since this increase equals to 5 gallons then 45 gallons were bought originally ( 45 * 10 / 9 = 50 - - > increase 5 gallons ) . hence original price was 300 / 45 = $ 6.6 answer : e ."
Answer: e
Question (general): it costs a publishing company 50000 dollars to make books . the 50000 is a fixed cost or a cost that can not change . to help the publishing company sell the books , a marketing company charges 4 dollars for each book sold . if the company charges 9 dollars per book , how many books should they sell to break even ?
Options: a ) 100 , b ) 1000 , c ) 10000 , d ) 100000 , e ) none
Rationale: let c be the cost of producing and selling x books let r be the revenue made for selling x books r = selling price of 1 book × number of books sold r = 9 x c = fixed cost + variable cost variable cost = fee charged for 1 book × number of books sold variable cost = 4 x c = 50000 + 4 x r = c 9 x = 50000 + 4 x 9 x - 4 x = 50000 + 4 x - 4 x 5 x = 50000 x = 10000 since 5 × 10000 = 50000 the break even point is to sell 10000 books . answer c
Answer: c
Question (general): a certain characteristic in a large population has a distribution that is symmetric about the mean m . if 68 % of the distribution lies one standard deviation s of the mean , what percent of the distribution is less than m + s ?
Options: a ) 16 % , b ) 32 % , c ) 48 % , d ) 84 % , e ) 92 %
Rationale: "16 % ________________________________________________ m + s 34 % ________________________________________________ m 34 % ________________________________________________ m - s 16 % since 68 % lies one standard deviation from mean m , = > 50 % of 68 % lies on either side as it is symmetric about m . thus 16 % lie below m - s and 16 % lie above m + s now below m + s = 16 + 34 + 34 = 84 % hence d"
Answer: d
Question (gain): sam invested rs . 6000 @ 10 % per annum for one year . if the interest is compounded half - yearly , then the amount received by sam at the end of the year will be ?
Options: a ) 5300.0 , b ) 24580.0 , c ) 16537.5 , d ) 7120.0 , e ) 6615.0
Rationale: p = rs . 6000 ; r = 10 % p . a . = 5 % per half - year ; t = 1 year = 2 half - year amount = [ 6000 * ( 1 + 5 / 100 ) 2 ] = ( 6000 * 21 / 20 * 21 / 20 ) = rs . 6615.00 answer : e
Answer: e
Question (physics): 30 men can do a work in 40 days . when should 20 men leave the work so that the entire work is completed in 40 days after they leave the work ?
Options: a ) 22 days , b ) 10 days , c ) 77 days , d ) 88 days , e ) 55 days
Rationale: "total work to be done = 30 * 40 = 1200 let 20 men leave the work after ' p ' days , so that the remaining work is completed in 40 days after they leave the work . 40 p + ( 20 * 40 ) = 1200 40 p = 400 = > p = 10 days answer : b"
Answer: b
Question (geometry): find the area of the quadrilateral of one of its diagonals is 50 cm and its off sets 10 cm and 8 cm ?
Options: a ) 189 cm 2 , b ) 150 cm 2 , c ) 127 cm 2 , d ) 450 cm 2 , e ) 187 cm 2
Rationale: "1 / 2 * 50 ( 10 + 8 ) = 450 cm 2 answer : d"
Answer: d
Question (general): for any real number x , the operatoris defined as : ( x ) = x ( 2 − x ) if p + 1 = ( p + 1 ) , then p =
Options: a ) - 2 , b ) 0 , c ) 1 , d ) 2 , e ) 3
Rationale: ( x ) = x ( 2 − x ) ( p + 1 ) = ( p + 1 ) ( 2 - p - 1 ) = ( 1 - p ) ( p + 1 ) we are given that p + 1 = ( p + 1 ) therefore ( 1 - p ) ( p + 1 ) = ( p + 1 ) or ( p + 1 ) + ( p - 1 ) ( p + 1 ) = 0 ( p + 1 ) ( p - 1 ) = 0 p = - 1 , p = 1 option c
Answer: c
Question (gain): sachin borrows rs . 5000 for 2 years at 4 % p . a . simple interest . he immediately lends money to rahul at 25 / 4 % p . a . for 2 years . find the gain of one year by sachin .
Options: a ) 110.5 , b ) 111.5 , c ) 112.5 , d ) 113.5 , e ) none of these
Rationale: explanation : two things need to give attention in this question , first we need to calculate gain for 1 year only . gain in 2 year = [ ( 5000 × 254 × 2100 ) − ( 5000 × 4 × 2100 ) ] = ( 625 − 400 ) = 225 so gain for 1 year = 2252 = 112.50 answer : c
Answer: c
Question (general): this year , mbb consulting fired 8 % of its employees and left remaining employee salaries unchanged . sally , a first - year post - mba consultant , noticed that that the average ( arithmetic mean ) of employee salaries at mbb was 10 % more after the employee headcount reduction than before . the total salary pool allocated to employees after headcount reduction is what percent of that before the headcount reduction ?
Options: a ) 98.5 % , b ) 101.2 % , c ) 102.8 % , d ) 104.5 % , e ) 105.0 %
Rationale: "100 employees getting 1000 $ avg , so total salary for 100 ppl = 100000 8 % reduction in employees lead to 92 employees and a salary increase of 10 % of previous avg salary thus the new avg salary is = 10 % ( 1000 ) + 1000 = 1100 so total salary of 92 employees is 92 * 1100 = 101200 now the new salary is more than previous salary by x % . x = ( 101200 / 100000 ) * 100 = 101.2 % so the answer is b"
Answer: b
Question (general): on average , the bottle - nosed dolphin comes up for air once every 3 minutes ; the beluga whale , a close relative , comes up for air on average once every 6 minutes . the number of times a bottle - nosed dolphin would come up for air in a 24 hour period is approximately what percent greater than the number of times a beluga whale would come up for air in that same period ?
Options: a ) 25 % , b ) 50 % , c ) 75 % , d ) 100 % , e ) 150 %
Rationale: dolphin once in 3 min ; beluga once in 6 min ; so , dolphin comes up 2 times frequently than beluga , which is 150 % ( 6 - 3 ) / 2 * 100 . answer : e .
Answer: e
Question (geometry): the circumference of a circle is equal to 72 pi . find the radius of this circle .
Options: a ) 35
b ) 36
c ) 37
d ) 38
e ) 39
Rationale: the circumference of a circle is given by c = 2 pi r , where r is the radius of the circle . substitute c by 72 pi to obtain the equation 72 pi = 2 pi r simplify and solve for r to obtain r = 36 answer b
Answer: b
Question (general): the average of 25 results is 50 . the average of first 12 of those is 14 and the average of last 12 is 17 . what is the 13 th result ?
Options: a ) 741 , b ) 752 , c ) 878 , d ) 785 , e ) 458
Rationale: "solution : sum of 1 st 12 results = 12 * 14 sum of last 12 results = 12 * 17 13 th result = x ( let ) now , 12 * 14 + 12 * 17 + x = 25 * 50 or , x = 878 . answer : option c"
Answer: c
Question (physics): two trains each 475 m long are running in opposite directions on parallel tracks . their speeds are 55 km / hr and 40 km / hr respectively . find the time taken by the slower train to pass the driver of the faster one ?
Options: a ) 77 sec , b ) 66 sec , c ) 48 sec , d ) 36 sec , e ) 45 sec
Rationale: relative speed = 55 + 40 = 95 km / hr . 95 * 5 / 18 = 475 / 18 m / sec . distance covered = 475 + 475 = 950 m . required time = 950 * 18 / 475 = 36 sec . answer : d
Answer: d
Question (geometry): mr . loyd wants to fence his square shaped land of 150 sqft each side . if a pole is laid every 10 ft how many poles do he need ?
Options: a ) 20 , b ) 30 , c ) 40 , d ) 60 , e ) 65
Rationale: "if each side is 120 feet . . then total perimeter is 150 * 4 = 600 poles every 10 feet hence no of poles = 600 / 10 = 60 answer : d"
Answer: d
Question (physics): in a city where all streets run east - to - west , all avenues run north - to - south , and all intersections are right angles as shown below , jenn needs to walk from the corner of 1 st street and 1 st avenue to the corner of 6 th street and 3 rd avenue . if her friend amanda is sitting on a bench on 4 th street halfway between 1 st and 2 nd avenues , and jenn chooses her path randomly from any route that will allow her to walk exactly 7 blocks to her destination , what is the probability that jenn will walk down 4 th st . past amanda ?
Options: a ) 1 / 42 , b ) 1 / 21 , c ) 1 / 7 , d ) 1 / 3 , e ) 1 / 2
Rationale: all routes between ( 1,1 ) to ( 3,6 ) = 7 ! / ( 2 ! * 5 ! ) = 21 routes which pass 4 th st . between 1 st and 2 nd avenue = routs between ( 1,1 ) to ( 1,4 ) * routs between ( 2,4 ) to ( 3,6 ) = 1 * ( 3 ! / ( 2 ! * 1 ! ) ) = 3 the probability that jenn will walk down 4 th st . past amanda = 3 / 21 = 1 / 7 c is correct .
Answer: c
Question (physics): length of a rectangular plot is 50 mtr more than its breadth . if the cost of fencin g the plot at 26.50 per meter is rs . 5300 , what is the length of the plot in mtr ?
Options: a ) 46 m , b ) 60 m , c ) 58 m , d ) 75 m , e ) 80 m
Rationale: "let breadth = x metres . then , length = ( x + 50 ) metres . perimeter = 5300 / 26.5 m = 200 m . 2 [ ( x + 50 ) + x ] = 200 2 x + 50 = 100 2 x = 50 x = 25 . hence , length = x + 50 = 75 m d"
Answer: d
Question (general): 10 camels cost as much as 24 horses , 16 horses cost as much as 4 oxen and 6 oxen as much as 4 elephants . if the cost of 10 elephants is rs . 110000 , find the cost of a camel ?
Options: a ) s . 9800 , b ) s . 3800 , c ) s . 9800 , d ) s . 4400 , e ) s . 6880
Rationale: "cost of the camel = p 10 camels = 24 horses 16 horses = 4 oxen 6 oxen = 4 elephants 10 elephants = rs . 110000 p = rs . [ ( 24 * 4 * 4 * 110000 ) / ( 10 * 16 * 6 * 10 ) ] p = rs . ( 42240000 / 9600 ) = > p = rs . 4400 answer : d"
Answer: d
Question (general): kyle , david , and catherine each try independently to solve a problem . if their individual probabilities for success are 1 / 3 , 2 / 7 and 5 / 9 , respectively , what is the probability that kyle and catherine , but not david will solve the problem ?
Options: a ) 35 / 189 , b ) 33 / 129 , c ) 25 / 189 , d ) 24 / 113 , e ) 20 / 189
Rationale: p ( kyle will solve ) = 1 / 3 p ( david will not solve ) = 1 - 2 / 7 = 5 / 7 p ( catherine will solve ) = 5 / 9 p = ( 1 / 3 ) * ( 5 / 7 ) * ( 5 / 9 ) = 25 / 189 answer : c
Answer: c
Question (general): a car travels uphill at 30 km / hr and downhill at 60 km / hr . it goes 100 km uphill and 50 km downhill . find the average speed of the car ?
Options: a ) 32 kmph , b ) 33 kmph , c ) 34 kmph , d ) 35 kmph , e ) 36 kmph
Rationale: "avg speed = total distance / total time . total distance traveled = 100 + 50 = 150 km ; time taken for uphill journey = 100 / 30 = 10 / 3 ; time taken for down hill journey = 50 / 60 = 5 / 6 ; avg speed = 150 / ( 10 / 3 + 5 / 6 ) = 36 kmph answer : e"
Answer: e
Question (physics): a work which could be finished in 11 days was finished 3 days earlier after 10 more men joined . the number of men employed was ?
Options: a ) 22 , b ) 20 , c ) 88 , d ) 71 , e ) 12
Rationale: "x - - - - - - - 11 ( x + 10 ) - - - - 6 x * 11 = ( x + 10 ) 6 x = 12 \ answer : e"
Answer: e
Question (other): the ratio of numbers is 3 : 4 and their h . c . f is 5 . their l . c . m is :
Options: a ) 12 , b ) 16 , c ) 24 , d ) 60 , e ) 98
Rationale: "let the numbers be 3 x and 4 x . then their h . c . f = x . so , x = 5 . so , the numbers are 15 and 20 . l . c . m of 15 and 20 = 60 . answer : d"
Answer: d
Question (general): if the average ( arithmetic mean ) of a and b is 50 and the average of b and c is 70 , what is the value of c − a ?
Options: a ) 40 , b ) 50 , c ) 90 , d ) 140 , e ) it can not be determined from the information given .
Rationale: "- ( a + b = 100 ) b + c = 140 c - a = 40 a . 40"
Answer: a
Question (gain): a invested $ 15000 in a business after 6 months b invested $ 18000 in the business . end of the year if they got $ 16000 as profit . find b shares ?
Options: a ) $ 10000 , b ) $ 12000 , c ) $ 5000 , d ) $ 6000 , e ) $ 7500
Rationale: "a : b = 15000 * 12 : 18000 * 6 a : b = 5 : 3 a ' s share = 16000 * 5 / 8 = 10000 b ' s share = 16000 * 3 / 8 = 6000 answer is d"
Answer: d
Question (other): if 85 percent of the test takers taking an old paper and pencil gmat exam answered the first question on a given math section correctly , and 70 percent of the test takers answered the second question correctly , and 5 percent of the test takers answered neither question correctly , what percent answered both correctly ?
Options: a ) 60 % , b ) 65 % , c ) 70 % , d ) 75 % , e ) 80 %
Rationale: "{ total } = { first correctly } + { second correctly } - { both correctly } + { neither correctly } 100 = 85 + 70 - { both correctly } + 5 { both correctly } = 60 . answer : a ."
Answer: a
Question (general): a number when divided by 44 , gives 400 as quotient and 0 as remainder . what will be the remainder when dividing the same number by 35
Options: a ) a ) 30 , b ) b ) 3 , c ) c ) 4 , d ) d ) 6 , e ) e ) 7
Rationale: "explanation : p ÷ 44 = 400 = > p = 400 * 44 = 17600 p / 35 = 17600 / 35 = 502 , remainder = 30 answer : option a"
Answer: a
Question (geometry): what is the area of a square field whose diagonal of length 22 m ?
Options: a ) 300 sq m , b ) 220 sq m , c ) 200 sq m , d ) 400 sq m , e ) 800 sq m
Rationale: "d 2 / 2 = ( 22 * 22 ) / 2 = 220 answer : b"
Answer: b
Question (general): if p ( a ) = 0.18 , p ( b ) = 0.5 and p ( b | a ) = 0.2 , find p ( a n b ) ?
Options: a ) 0.28 , b ) 0.36 , c ) 0.45 , d ) 0.56 , e ) 0.7
Rationale: p ( b | a ) = p ( a n b ) / p ( a ) p ( a n b ) = p ( b | a ) × p ( a ) p ( a n b ) = 0.2 × 0.18 p ( a n b ) = 0.36 b )
Answer: b