Cheukting/mathqa huggingface dataset:
Question (general): a certain debt will be paid in 65 installments from january 1 to december 31 of a certain year . each of the first 20 payments is to be $ 410 ; each of the remaining payments is to be $ 65 more than each of the first 20 payments . what is the average ( arithmetic mean ) payment that will be made on the debt for the year ?
Options: a ) 443 , b ) 455 , c ) 465 , d ) 468 , e ) 475
Rationale: "total number of installments = 65 payment per installment for the first 20 installments = 410 payment per installment for the remaining 45 installments = 410 + 65 = 475 average = ( 20 * 410 + 45 * 475 ) / 65 = 455 answer b"
Answer: b
Question (general): in 7 given numbers , the average of first 4 numbers is 4 and that of last 4 numbers is also 4 . if the average of these 7 numbers is 3 , the fourth number is ?
Options: a ) 3 , b ) 4 , c ) 7 , d ) 11 , e ) 12
Rationale: let 7 numbers are a , b , c , d , e , f , g . given avg of first 4 nums are 4 . . . i . e ( a + b + c + d ) / 4 = 4 a + b + c + d = 16 given avg of last 4 nums are also 4 . . i . e . ( d + e + f + g ) / 4 = 4 d + e + f + g = 16 e + f + g = 16 - d given avg of 7 nums are 3 . . . . i . e ( a + b + c + d + e + f + g ) / 7 = 3 a + b + c + d + e + f + g = 21 16 + 16 - d = 21 d = 32 - 21 d = 11 answer : d
Answer: d
Question (gain): in a certain parking lot , 4 % of the cars are towed for parking illegally . however 80 % of the cars which are parked illegally are not towed . what percentage of cars in the parking lot are parked illegally ?
Options: a ) 20 % , b ) 25 % , c ) 30 % , d ) 35 % , e ) 40 %
Rationale: "let x be the number of cars and let y be the number of cars parked illegally . 4 % * x = 20 % * y y / x = 1 / 5 = 20 % the answer is a ."
Answer: a
Question (general): at the beginning of a year , the owner of a jewel shop raised the price of all the jewels in his shop by x % and lowered them by x % . the price of one jewel after this up and down cycle reduced by rs . 100 . the owner carried out the same procedure after a month . after this second up - down cycle , the price of that jewel was rs . 2304 . find the original price of that jewel ( in rs . )
Options: a ) 2500 , b ) 550 , c ) 2600 , d ) 2650 , e ) none of these
Rationale: solution : let the original price = y , after first change , it becomes , y * ( 1 + ( x / 100 ) ) after second change , it becomes y * ( 1 + ( x / 100 ) ) ( 1 - ( x / 100 ) ) = y ( 1 - ( x / 100 ) ^ 2 ) thus , x 2 * y = 106 - - - - - - - ( 1 ) x 2 = 106 / y now , y ( 1 - ( 106 / 10000 y ) ) 2 = 2304 ( similar to above ) y ( 1 - 100 / y ) 2 = 2304 y = 2500 . answer : option a
Answer: a
Question (general): in goshawk - eurasian nature reserve 30 percent of the birds are hawks , and 40 percent of the non - hawks are paddyfield - warblers . if there are 25 percent as many kingfishers as paddyfield - warblers in the reserve , then what percent of the birds in the nature reserve are not hawks , paddyfield - warblers , or kingfishers ?
Options: a ) 25 % , b ) 35 % , c ) 45 % , d ) 70 % , e ) 80 %
Rationale: "since the problem does n ' t depend on the number of birds in reserve you can suppose that there are 100 birds . from them 100 * 0.3 = 30 are hawks . so , there are 70 non - hawks . there are 0.4 * 70 = 28 paddyfield - warblers . therefore , there are 0.25 * 28 = 7 kingfishers . the total number of birds in the nature reserve that are not hawks , paddyfield - warblers , or kingfishers is 100 - 30 - 28 - 7 = 35 . the answer is b"
Answer: b
Question (probability): a bag contains 6 black and 4 white balls . one ball is drawn at random . what is the probability that the ball drawn is white ?
Options: a ) 3 / 4 , b ) 2 / 5 , c ) 1 / 7 , d ) 1 / 8 , e ) 4 / 3
Rationale: "let number of balls = ( 6 + 4 ) = 10 . number of white balls = 4 . p ( drawing a white ball ) = 4 / 10 = 2 / 5 . option b ."
Answer: b
Question (gain): alfred buys an old scooter for $ 4700 and spends $ 600 on its repairs . if he sells the scooter for $ 5800 , his gain percent is ?
Options: a ) 5.45 % , b ) 6.23 % , c ) 7 % , d ) 9.43 % , e ) 10 %
Rationale: c . p . = 4700 + 600 = $ 5300 s . p . = $ 5800 gain = 5800 - 5300 = $ 500 gain % = 500 / 5300 * 100 = 9.43 % answer is d
Answer: d
Question (general): ( 4300531 ) - ? = 2535618
Options: a ) 1865113 , b ) 1775123 , c ) 1764913 , d ) 1675123 , e ) none of them
Rationale: "let 4300531 - x = 2535618 then x = 4300531 - 2535618 = 1764913 answer is c"
Answer: c
Question (general): a dog is tied to a tree by a long nylon cord . if the dog runs from the due north side of the tree to the due south side of the tree with the cord extended to its full length at all items , and the dog ran approximately 30 feet , what was the approximate length of the nylon cord , in feet ?
Options: a ) 30 , b ) 25 , c ) 15 , d ) 10 , e ) 5
Rationale: "because the cord was extended to its full length at all items , the dog ran along a semi - circular path , from north to south . the circumference of a full circle is 2 * pi * r , but since we only care about the length of half the circle , the semi - circle path is pi * r . pi * r = 30 . round pi = 3 , then r = 10 . chord is about 10 feet long answer : d"
Answer: d
Question (general): the sum of two numbers is 66 . how much should be added to the sum for it to be exactly divisible by 9 leaving 0 as the reminder ?
Options: a ) 6 , b ) 7 , c ) 8 , d ) 9 , e ) 1
Rationale: the sum is 66 . adding 6 to 66 = 66 + 6 = 72 . 72 is exactly divisible by 9 leaving 0 as the reminder = 8 . so the answer is a = 6
Answer: a
Question (general): what is next no . 11 23 47 83 131 191 263 347 443 551 ? ? ?
Options: a ) 171 , b ) 181 , c ) 191 , d ) 201 , e ) 671
Rationale: 11 + 12 * 1 = 23 23 + 12 * 2 = 47 47 + 12 * 3 = 83 83 + 12 * 4 = 131 131 + 12 * 5 = 191 191 + 12 * 6 = 263 263 + 12 * 7 = 347 347 + 12 * 8 = 443 443 + 12 * 9 = 551 551 + 12 * 10 = 671 answer : e
Answer: e
Question (general): zinc and copper are melted together in the ratio 9 : 11 . what is the weight of melted mixture , if 31.5 kg of zinc has been consumed in it ?
Options: a ) 58 kg , b ) 60 kg , c ) 64 kg , d ) 70 kg , e ) none
Rationale: "sol . for 9 kg zinc , mixture melted = ( 9 + 11 ) kg . for 31.5 kg zinc , mixture , melted = [ 20 / 9 x 31.5 ] kg = 70 kg . answer d"
Answer: d
Question (general): a man is 20 years older than his son . in two years , his age will be twice the age of his son . the present age of his son is
Options: a ) 16 , b ) 14 , c ) 15 , d ) 18 , e ) 20
Rationale: "explanation : let the son ' s present age be x years . then , man ' s present age = ( x + 20 ) years = > ( x + 20 ) + 2 = 2 ( x + 2 ) = > x + 22 = 2 x + 4 so , x = 18 . answer : d"
Answer: d
Question (gain): a person buys an article at rs . 400 . at what price should he sell the article so as to make a profit of 40 % ?
Options: a ) 600 , b ) 277 , c ) 560 , d ) 261 , e ) 281
Rationale: "cost price = rs . 400 profit = 40 % of 400 = rs . 160 selling price = cost price + profit = 400 + 160 = 560 answer : c"
Answer: c
Question (general): an order was placed for the supply of a carpet whose breadth was 6 m and length was 1.44 times the breadth . what be the cost of a carpet whose length and breadth are 40 % more and 25 % more respectively than the first carpet . given that the ratio of carpet is rs . 45 per sq m ?
Options: a ) rs . 3642.40 , b ) rs . 3868.80 , c ) rs . 4216.20 , d ) rs . 4082.40 , e ) none of these
Rationale: "length of the first carpet = ( 1.44 ) ( 6 ) = 8.64 cm area of the second carpet = 8.64 ( 1 + 40 / 100 ) 6 ( 1 + 25 / 100 ) = 51.84 ( 1.4 ) ( 5 / 4 ) sq m = ( 12.96 ) ( 7 ) sq m cost of the second carpet = ( 45 ) ( 12.96 * 7 ) = 315 ( 13 - 0.04 ) = 4095 - 12.6 = rs . 4082.40 answer : d"
Answer: d
Question (general): jack , jill , and sandy each have one try to make a basket from half court . if their individual probabilities of making the basket are 1 / 6 , 1 / 7 , and 1 / 8 respectively , what is the probability that jill and sandy will make a basket but jack will miss ?
Options: a ) 3 / 168 , b ) 5 / 168 , c ) 7 / 168 , d ) 5 / 336 , e ) 7 / 336
Rationale: the probability that jill and sandy will make a basket but jack will miss is 5 / 6 * 1 / 7 * 1 / 8 = 5 / 336 . the answer is d .
Answer: d
Question (physics): a man sitting in a train which is travelling at 100 kmph observes that a goods train , travelling in opposite direction , takes 9 seconds to pass him . if the goods train is 280 m long , find its speed ?
Options: a ) 52 kmph . , b ) 62 kmph . , c ) 12 kmph . , d ) 80 kmph . , e ) none
Rationale: "solution relative speed = ( 280 / 9 ) m / sec = ( 280 / 9 x 18 / 5 ) = 112 kmph . speed of the train = ( 112 - 100 ) kmph = 12 kmph . answer c"
Answer: c
Question (gain): a 11 % stock yields 8 % . the market value of the stock is :
Options: a ) rs . 72 , b ) rs . 137.50 , c ) rs . 112.50 , d ) rs . 116.50 , e ) none of these
Rationale: "solution to obtain rs . 8 , investment = rs . 100 . to obtain rs . 11 , investment = rs . ( 100 / 8 x 11 ) = rs . 137.50 ∴ market value of rs . 100 stock = rs . 137.50 answer b"
Answer: b
Question (other): the ratio of the present age of viju to that of aju is 7 : 2 . 4 years from now , the ratio of the ages of viju to aju will be 5 : 2 . what was viju age 5 years ago ? ( rbi assistant 2015 )
Options: a ) 24 , b ) 18 , c ) 12 , d ) 16 , e ) 13
Rationale: let the present age of viju be 7 x years and that of aju be 2 x years . then , 4 years from now 7 x + 4 / 2 x + 4 = 5 / 2 or 4 x = 12 or x = 3 viju present age = 7 * 3 = 21 years viju age 5 years ago = 21 - 5 = 16 years answer : d
Answer: d
Question (physics): yesterday it took robert 3 hours to drive from city a to city b . today it took robert 2.5 hours to drive back from city в to city a along the same route . if he had saved 30 minutes in both trips , the speed for the round trip would be 80 miles per hour . what is the distance between city a and city b ?
Options: a ) 90 , b ) 180 , c ) 150 , d ) 240 , e ) 300
Rationale: "2 d / 80 = 4.5 ( because time = 3 + 2.5 - 1 hrs ) = > d = 180 answer - b"
Answer: b
Question (general): if abc = ab ^ 3 = 180 where a , b and c are positive integers , what is the value of ` c ’ ?
Options: a ) 0 , b ) 1 , c ) 2 , d ) 3 , e ) 4
Rationale: abc = a ( b ^ 3 ) = 180 on solving abc = a ( b ^ 3 ) we get c = b ^ 2 and for a ( b ^ 3 ) = 180 , there is only one possibility a = 180 and b = 1 so c = 1 ^ 2 = 1 answer : b
Answer: b
Question (gain): each of the cucumbers in 100 pounds of cucumbers is composed of 99 % water , by weight . after some of the water evaporates , the cucumbers are now 95 % water by weight . what is the new weight of the cucumbers , in pounds ?
Options: a ) 2 , b ) 20 , c ) 92 , d ) 96 , e ) 98
Rationale: "out of 100 pounds 99 % or 99 pounds is water and 1 pound is non - water . after somewaterevaporates the cucumbers become 95 % water and 5 % of non - water , so now 1 pound of non - water composes 5 % of cucucmbers , which means that the new weight of cucumbers is 1 / 0.05 = 20 pounds . answer : b ."
Answer: b
Question (gain): a customer went to a shop and paid a total of $ 40 , out of which $ 1.28 was for sales tax on taxable purchases . if the tax rate was 8 % , then what was the cost of the tax free items ?
Options: a ) $ 19.54 , b ) $ 2076 , c ) $ 21.36 , d ) $ 22.72 , e ) $ 23.58
Rationale: "the total cost was $ 40 . the tax was $ 1.28 let the original price of the taxable items = x given that tax rate = 8 % 0.08 x = 1.28 x = $ 16 the cost of the tax free items was $ 40 - $ 16 - $ 1.28 = $ 22.72 the answer is d ."
Answer: d
Question (general): what is the sum of all remainders obtained when the first 100 natural numbers are divided by 8 ?
Options: a ) 397 , b ) 401 , c ) 403 , d ) 405 , e ) 399
Rationale: "a positive integer can give only the following 9 remainders when divided by 9 : 1 , 2 , 3 , 4 , 5 , 6 , 7 , 8 , and 0 . 1 divided by 9 gives the remainder of 1 ; 2 divided by 9 gives the remainder of 2 ; . . . 8 divided by 9 gives the remainder of 8 ; 9 divided by 9 gives the remainder of 0 . we ' ll have 11 such blocks , since 99 / 9 = 11 . the last will be : 91 divided by 9 gives the remainder of 1 ; 92 divided by 9 gives the remainder of 2 ; . . . 98 divided by 9 gives the remainder of 8 ; 99 divided by 9 gives the remainder of 0 . the last number , 100 , gives the remainder of 1 when divided by 9 , thus the sum of all remainders will be : 11 ( 1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 0 ) + 1 = 401 . answer : b ."
Answer: b
Question (general): the average of first 12 even numbers is ?
Options: a ) 19 , b ) 18 , c ) 16 , d ) 13 , e ) 17
Rationale: "sum of 12 even numbers = 12 * 13 = 156 average = 156 / 12 = 13 answer : d"
Answer: d
Question (other): if all 6 are replaced by 9 , the algebric sum of all numbers from 1 to 100 ( both inclusive ) varies by ,
Options: a ) 980 , b ) 330 , c ) 660 , d ) 990 , e ) 300
Rationale: 6 , 16,26 , 36,46 , 56,76 , 86,96 replace by 9 then 3 * 9 = 27 60,61 , 62,63 , 64,65 , 66,67 , 68,69 then increase by 30 i . e , 30 * 10 = 300 + 3 99 - 66 = 33 - 30 it will be 330 answer : b
Answer: b
Question (physics): how many seconds will a 1000 meter long train take to cross a man walking with a speed of 3 km / hr in the direction of the moving train if the speed of the train is 63 km / hr ?
Options: a ) 287 , b ) 300 , c ) 500 , d ) 277 , e ) 121
Rationale: "let length of tunnel is x meter distance = 1000 + x meter time = 1 minute = 60 seconds speed = 78 km / hr = 78 * 5 / 18 m / s = 65 / 3 m / s distance = speed * time 1000 + x = ( 65 / 3 ) * 60 1000 + x = 20 * 65 = 1300 x = 1300 - 1000 = 300 meters answer : b"
Answer: b
Question (general): if n = 2.0563 and n * is the decimal obtained by rounding n to the nearest hundredth , what is the value of n * – n ?
Options: a ) - 0.0053 , b ) - 0.0003 , c ) 0.0007 , d ) 0.0037 , e ) 0.0153
Rationale: "n * = 2.06 n * - n = 2.06 - 2.0563 0.0037 answer : d"
Answer: d
Question (general): in a company with 48 employees , some part - time and some full - time , exactly ( 1 / 3 ) of the part - time employees and ( 1 / 4 ) of the full - time employees take the subway to work . what is the greatest possible number h of employees who take the subway to work ?
Options: a ) 12 , b ) 13 , c ) 14 , d ) 15 , e ) 16
Rationale: "p / 3 + f / 4 = p / 3 + ( 48 - p ) / 4 = 12 + p / 2 p / 3 + f / 3 = ( p + f ) / 3 = 48 / 3 = 16 p / 4 + f / 4 = 12 p / 3 + f / 3 > p / 3 + f / 4 > p / 4 + f / 4 - - > 16 > 12 + p / 12 > 12 greatest possible h : 12 + p / 12 = 15 - - > p = 36 ( integer - - > good ) 15 or d is the answer"
Answer: d
Question (general): a family pays $ 700 per year for an insurance plan that pays 70 percent of the first $ 1,000 in expenses and 100 percent of all medical expenses thereafter . in any given year , the total amount paid by the family will equal the amount paid by the plan when the family ' s medical expenses total how much ?
Options: a ) $ 1,100 , b ) $ 1,300 , c ) $ 1,400 , d ) $ 1,800 , e ) $ 2,200
Rationale: "assuming the medical expenses are $ 1000 or more , the family pays $ 700 + $ 300 = $ 1000 . the total amount paid by insurance plan for the first $ 1000 of expenses is $ 700 . the insurance will pay another $ 300 when the medical expenses are $ 1300 . the answer is b ."
Answer: b
Question (general): a batsman in his 12 th innings makes a score of 60 and thereby increases his average by 2 runs . what is his average after the 12 th innings if he had never been ‘ not out ’ ?
Options: a ) 38 , b ) 43 , c ) 44 , d ) 45 , e ) 46
Rationale: "let ‘ x ’ be the average score after 12 th innings ⇒ 12 x = 11 × ( x – 2 ) + 60 ∴ x = 38 answer a"
Answer: a
Question (physics): john can complete a given task in 18 days . jane will take only 12 days to complete the same task . john and jane set out to complete the task by beginning to work together . however , jane was indisposed 6 days before the work got over . in how many days did the work get over from the time john and jane started to work on it together ?
Options: a ) 11 , b ) 34 / 5 , c ) 44 / 5 , d ) 54 / 5 , e ) 12
Rationale: "in such questions , you need to start from the end . last 4 days john works alone and completes 6 * ( 1 / 18 ) = 1 / 3 of the work . so 2 / 3 of the work should have been completed by the two of them together before jane left . their combined rate of work is 1 / 18 + 1 / 12 = 5 / 36 time taken to complete 2 / 3 of the work = ( 2 / 3 ) / ( 5 / 36 ) = 24 / 5 days . so total number of days taken to complete the work = 24 / 5 + 6 = 54 / 5 days . d"
Answer: d
Question (physics): a man walks at a rate of 10 mph . after every ten miles , he rests for 7 minutes . how much time does he take to walk 50 miles ?
Options: a ) 300 , b ) 318 , c ) 322 , d ) 328 , e ) 330
Rationale: "to cover 50 miles the man needs ( time ) = ( distance ) / ( rate ) = 50 / 10 = 5 hours = 300 minutes . he will also rest 4 times ( after 10 , 20 , 30 and 40 miles ) , so total resting time = 4 * 7 = 28 minutes . total time = 300 + 28 = 328 minutes . answer : d ."
Answer: d
Question (gain): by selling an article for $ 225 a person gains $ 75 . what is the gain % ?
Options: a ) 25 % , b ) 30 % , c ) 50 % , d ) 20 % , e ) 10 %
Rationale: "s . p . = $ 225 gain = $ 75 c . p . = 225 - 75 = 150 gain % = 75 / 150 * 100 = 50 % answer is c"
Answer: c
Question (general): a mixture of 150 liters of wine and water contains 15 % water . how much more water should be added so that water becomes 25 % of the new mixture ?
Options: a ) 10 , b ) 30 , c ) 20 , d ) 15 , e ) 17
Rationale: "number of liters of water in 150 liters of the mixture = 15 % of 150 = 15 / 100 * 150 = 22.5 liters . p liters of water added to the mixture to make water 25 % of the new mixture . total amount of water becomes ( 22.5 + p ) and total volume of mixture is ( 150 + p ) . ( 22.5 + p ) = 25 / 100 * ( 150 + p ) 90 + 4 p = 150 + p p = 20 liters . answer : c"
Answer: c
Question (physics): it is only in the second option we find the sentence a in continuation with the opening sentence d . sentence a alone explains , why the fear has such enormous effect on the human beings .
Options: a ) 28 , b ) 99 , c ) 728 , d ) 27 , e ) 271
Rationale: answer : b
Answer: b
Question (gain): on a sum of money , the simple interest for 2 years is rs . 327 , while the compound interest is rs . 340 , the rate of interest being the same in both the cases . the rate of interest is
Options: a ) 15 % , b ) 14.25 % , c ) 7.95 % , d ) 10.5 % , e ) 11.5 %
Rationale: "explanation : the difference between compound interest and simple interest on rs . p for 2 years at r % per annum = ( r ã — si ) / ( 2 ã — 100 ) difference between the compound interest and simple interest = 340 - 327 = 13 ( r ã — si ) / ( 2 ã — 100 ) = 13 ( r ã — 327 ) / ( 2 ã — 100 ) = 13 r = 7.95 % answer : option c"
Answer: c
Question (physics): my grandson is about as many days as my son in weeks , and my grandson is as many months as i am in years . my grandson , my son and i together are 120 years . can you tell me my age in years ?
Options: a ) 65 , b ) 72 , c ) 44 , d ) 73 , e ) 89
Rationale: "b i am 72 years old . let m be my age in years . if s is my son ' s age in years , then my son is 52 s weeks old . if g is my grandson ' s age in years , then my grandson is 365 g days old . thus , 365 g = 52 s . since my grandson is 12 g months old , 12 g = m . since my grandson , my son and i together are 120 years , g + s + m = 120 . the above system of 3 equations in 3 unknowns ( g , s and m ) can be solved as follows . m / 12 + 365 m / ( 52 x 12 ) + m = 120 or 52 m + 365 m + 624 m = 624 x 120 or m = 624 x 120 / 1041 = 72 . so , i am 72 years old ."
Answer: b
Question (other): the simple form of the ratio 4 / 3 : 2 / 5 is ?
Options: a ) 10 : 6 , b ) 10 : 3 , c ) 15 : 3 , d ) 25 : 3 , e ) 30 : 3
Rationale: "4 / 3 : 2 / 5 = 20 : 6 = 10 : 3 answer : b"
Answer: b
Question (general): a fruit - salad mixture consists of apples , peaches , and grapes in the ratio 6 : 5 : 4 , respectively , by weight . if 60 pounds of the mixture is prepared , the mixture includes how many more pounds of apples than grapes ?
Options: a ) 15 , b ) 12 , c ) 8 , d ) 6 , e ) 4
Rationale: "we can first set up our ratio using variable multipliers . we are given that a fruit - salad mixture consists of apples , peaches , and grapes , in the ratio of 6 : 5 : 4 , respectively , by weight . thus , we can say : apples : peaches : grapes = 6 x : 5 x : 4 x we are given that 60 pounds of the mixture is prepared so we can set up the following question and determine a value for x : 6 x + 5 x + 4 x = 60 15 x = 60 x = 4 now we can determine the number of pounds of apples and of grapes . pounds of grapes = ( 4 ) ( 4 ) = 16 pounds of apples = ( 6 ) ( 4 ) = 24 thus we know that there are 24 - 16 = 8 more pounds of apples than grapes . answer is c ."
Answer: c
Question (other): the ratio between speed of the two trains is 7 : 8 . if the 2 nd train runs 400 km in 4 hrs , what is the speed of the 1 st train ?
Options: a ) 87.9 , b ) 87.5 , c ) 87.7 , d ) 87.6 , e ) 43.3
Rationale: answer : b explanation : speed of 2 nd train = 400 / 4 = 100 kmph since the ratios are in 7 : 8 speed of first train = 7 / 8 × 100 = 87.5 kmph answer : b
Answer: b
Question (general): the circulation for magazine p in 1961 was 4 times the average ( arithmetic mean ) yearly circulation for magazine p for the years 1962 - 1970 . what is the ratio of the circulation in 1961 to the total circulation during 1961 - 1970 for magazine p ?
Options: a ) 2 / 7 , b ) 5 / 7 , c ) 3 / 7 , d ) 4 / 7 , e ) 1 / 7
Rationale: "there are 9 years from 1962 - 1970 , inclusive . let ' s say the average circulation every year between 1962 - 1970 inclusive is x . so the total circulation is 9 x from 1962 - 1970 , inclusive . in 1961 , the circulation is 4 x . so total circulation for 1961 - 1970 is 4 x + 9 x = 13 x . ratio of circulation in 1961 to total circulation during 1961 - 1970 is 4 x to 14 x or 4 / 14 = 2 / 7 answer : a"
Answer: a
Question (gain): in how many years rs 100 will produce the same interest at 5 % as rs . 200 produce in 2 years at 10 %
Options: a ) 8 , b ) 10 , c ) 9 , d ) 12 , e ) 11
Rationale: "explanation : clue : firstly we need to calculate the si with prinical 200 , time 2 years and rate 10 % , it will be rs . 40 then we can get the time as time = ( 100 * 40 ) / ( 100 * 5 ) = 8 option a"
Answer: a
Question (gain): the profit obtained by selling an article for rs . 54 is the same as the loss obtained by selling it for rs . 40 . what is the cost price of the article ?
Options: a ) rs . 40 , b ) rs . 50 , c ) rs . 49 , d ) rs . 59 , e ) rs . 47
Rationale: "s . p 1 - c . p = c . p – s . p 2 54 - c . p = c . p - 40 2 c . p = 54 + 40 ; c . p = 94 / 2 = 47 answer : e"
Answer: e
Question (general): mary , peter , and lucy were picking chestnuts . mary picked twice as much chestnuts than peter . lucy picked 2 kg more than peter . together the 3 of them picked 26 kg of chestnuts . how many kilograms did mary pick ?
Options: a ) 12 , b ) 24 , c ) 48 , d ) 52 , e ) 37
Rationale: let x be the amount peter picked . then mary and lucy picked 2 x and x + 2 x , respectively . so x + 2 x + x + 2 = 26 4 x = 24 x = 6 so 2 x = 2 * 6 = 12 correct answer is a ) 12
Answer: a
Question (physics): a train traveling at 72 kmph crosses a platform in 35 seconds and a man standing on the platform in 18 seconds . what is the length of the platform in meters ?
Options: a ) 340 meters , b ) 360 meters , c ) 420 meters , d ) 600 meters , e ) can not be determined
Rationale: "speed of train = 72 * ( 5 / 18 ) = 20 m / s lets consider the man as a stationery point on the platform . crossing the point gives us the length of the train . lt = 20 * 18 = 360 m . crossing the platform gives us the length of trainlength of platform . l ( t + p ) = 20 * 35 = 700 m . so , length of platform = 700 - 360 = 340 m imo , answer a"
Answer: a
Question (general): how many integers between 1 and 10 ^ 16 are such that the sum of their digits is 2 ?
Options: a ) 106 , b ) 116 , c ) 126 , d ) 136 , e ) 146
Rationale: "the integers with a sum of 2 are : 2 , 20 , 200 , . . . , 2 * 10 ^ 15 and there are 16 integers in this list . also , these integers have a sum of 2 : 11 101 , 110 1001 , 1010 , 1100 etc . . . the number of integers in this list is 1 + 2 + . . . + 15 thus , the total number of integers is 1 + 2 + . . . + 15 + 16 = 16 * 17 / 2 = 136 the answer is d ."
Answer: d