Cheukting/mathqa huggingface dataset:
Question (general): whats the reminder when 445876 , 985420 , 215546 , 656452 is divided by 8
Options: a ) 1 , b ) 7 . , c ) 4 , d ) 3 , e ) 9
Rationale: a number ending in a 0 is divisible by 2 . a number ending in 2 zeroes is divisible by 4 . a number ending in 3 zeroes is divisible by 8 . given the obscene number , you should immediately be convinced that you will need to focus on a very small part of it . 445876 , 985420 , 215546 , 656452 = 445876 , 985420 , 215546 , 656000 + 452 the first number is divisible by 8 . you just have to find the remainder when you divide 452 by 8 . that will be the remainder when you divide the original number by 8 . 452 / 8 gives remainder 4 . answer ( c )
Answer: c
Question (physics): each day a man meets his wife at the train station after work , and then she drives him home . she always arrives exactly on time to pick him up . one day he catches an earlier train and arrives at the station an hour early . he immediately begins walking home along the same route the wife drives . eventually his wife sees him on her way to the station and drives him the rest of the way home . when they arrive home the man notices that they arrived 10 minutes earlier than usual . how much time did the man spend walking ?
Options: a ) 45 minutes , b ) 50 minutes , c ) 55 minutes , d ) 52 minutes , e ) 35 minutes
Rationale: as they arrived 10 minutes earlier than usual , they saved 10 minutes on round trip from home to station ( home - station - home ) - - > 5 minutes in each direction ( home - station ) - - > wife meets husband 5 minutes earlier the usual meeting time - - > husband arrived an hour earlier the usual meeting time , so he must have spent waking the rest of the time before their meeting , which is hour - 5 minutes = 55 minutes . answer : c
Answer: c
Question (physics): in what time will a railway train 75 m long moving at the rate of 50 kmph pass a telegraph post on its way ?
Options: a ) 3 , b ) 5.4 , c ) 4.3 , d ) 6.5 , e ) 7
Rationale: "t = 75 / 50 * 18 / 5 = 5.4 sec answer : b"
Answer: b
Question (general): in a division sum , the remainder is 6 and the divisor is 5 times the quotient and is obtained by adding 27 to the thrice of the remainder . the dividend is
Options: a ) 74 , b ) 78 , c ) 186 , d ) 92 , e ) 98
Rationale: "divisor = ( 6 * 3 ) + 27 = 45 5 * quotient = 45 quotient = 9 . dividend = ( divisor * quotient ) + remainder dividend = ( 20 * 9 ) + 6 = 186 . c )"
Answer: c
Question (general): the sum of two numbers is 64 , and one of them is 12 more than the other . what are the two numbers ?
Options: a ) 26 - 38 , b ) 50 - 34 , c ) 60 - 24 , d ) 42 - 42 , e ) 21 - 63
Rationale: "in this problem , we are asked to find two numbers . therefore , we must let x be one of them . let x , then , be the first number . we are told that the other number is 12 more , x + 12 . the problem states that their sum is 64 : word problem = 64 the line over x + 12 is a grouping symbol called a vinculum . it saves us writing parentheses . we have : 2 x = 64 â ˆ ’ 12 = 52 . x = 52 / 2 = 26 . this is the first number . therefore the other number is x + 12 = 26 + 12 = 38 . the sum of 26 + 38 is 64 . a"
Answer: a
Question (other): two whole numbers whose sum is 36 can not be in the ratio
Options: a ) 2 : 4 , b ) 3 : 4 , c ) 3 : 6 , d ) 1 : 3 , e ) 3 : 36
Rationale: b ) 3 : 4
Answer: b
Question (general): if x ⁄ 2 + 3 ⁄ 4 = 9 ⁄ 4 , what is the value of x ?
Options: a ) – 2 , b ) – 1 , c ) 1 , d ) 3 , e ) 5
Rationale: "x ⁄ 2 + 3 ⁄ 4 = 9 ⁄ 4 let ' s multiply both sides by 4 . 2 x + 3 = 9 2 x = 6 x = 3 the answer is d ."
Answer: d
Question (general): a man is 24 years older than his son . in two years , his age will be twice the age of his son . the present age of the son is
Options: a ) 14 years , b ) 18 years , c ) 20 years , d ) 22 years , e ) none
Rationale: "solution let the son ' s present age be x years . then , man ' s present age = ( x + 24 ) years . then ‹ = › ( x + 24 ) + 2 = 2 ( x + 2 ) ‹ = › x + 26 = 2 x + 4 x = 22 . answer d"
Answer: d
Question (physics): two mechanics were working on your car . one can complete the given job in 4 hours , but the new guy takes eight hours . they worked together for the first two hours , but then the first guy left to help another mechanic on a different job . how long will it take the new guy to finish your car ?
Options: a ) 2 , b ) 4 / 3 , c ) 15 / 4 , d ) 10 / 3 , e ) 17 / 5
Rationale: "rate ( 1 ) = 1 / 4 rate ( 2 ) = 1 / 8 combined = 3 / 8 work done in 2 days = 3 / 4 work left = 1 / 4 rate * time = work left 1 / 8 * time = 1 / 4 time = 2 a"
Answer: a
Question (general): yearly subscription to professional magazines cost a company $ 940.00 . to make a 30 % cut in the magazine budget , how much less must be spent ?
Options: a ) 654 , b ) 655 , c ) 656 , d ) 657 , e ) 658
Rationale: "total cost 940 940 * 30 / 100 = 282 so the cut in amount is 282 the less amount to be spend is 940 - 282 = 658 answer : e"
Answer: e
Question (physics): water is leaking out from a cylinder container at the rate of 0.31 m ^ 3 per minute . after 10 minutes , the water level decreases 9 meters . what is value of the radius in meters ?
Options: a ) 1 / 2 , b ) 1 / 3 , c ) 1.5 , d ) 3 , e ) 6
Rationale: 10 * 0.31 = 3.1 = pi * r ^ 2 * h r ^ 2 = 3.1 / ( pi * 9 ) which is about 1 / 9 r = 1 / 3 the answer is b .
Answer: b
Question (general): what is 10 - 8 + 6 - 4 + . . . + ( - 16 ) ?
Options: a ) 8 , b ) 10 , c ) 12 , d ) 14 , e ) 16
Rationale: "the expression considers all even numbers between 10 and - 16 with alternate addition and subtraction of the numbers . the numbers to be used are : 10 , 8 , 6 , 4 , 2 , 0 , - 2 , - 4 , - 6 , - 8 , - 10 , - 12 , - 14 , and - 16 . now , the first term is positive and the next term is subtracted . so , the required expression becomes , 10 - 8 + 6 - 4 + 2 - 0 + ( - 2 ) - ( - 4 ) + ( - 6 ) - ( - 8 ) + ( - 10 ) - ( - 12 ) + ( - 14 ) - ( - 16 ) = 10 - 8 + 6 - 4 + 2 - 0 - 2 + 4 - 6 + 8 - 10 + 12 - 14 + 16 = 58 - 44 = 14 hence the correct answer choice is d ."
Answer: d
Question (general): how many 7 in between 1 to 90 ?
Options: a ) 19 , b ) 20 , c ) 22 , d ) 23 , e ) 24
Rationale: "7 , 17,27 , 37,47 , 57,67 , 70,71 , 72,73 , 74,75 , 76,77 ( two 7 ' s ) , 78 , 79,87 , 19 7 ' s between 1 to 90 answer : a"
Answer: a
Question (physics): for a race a distance of 224 meters can be covered by p in 16 seconds and q in 32 seconds . by what distance does p defeat q eventually ?
Options: a ) 232 m , b ) 238 m , c ) 224 m , d ) 331 m , e ) 236 m
Rationale: "explanation : this is a simple speed time problem . given conditions : = > speed of p = 224 / 16 = 14 m / s = > speed of q = 224 / 32 = 7 m / s = > difference in time taken = 16 seconds therefore , distance covered by p in that time = 14 m / s x 16 seconds = 224 metres answer : c"
Answer: c
Question (general): a merchant has selected two items to be placed on sale , one of which currently sells for 25 percent less than the other . if he wishes to raise the price of the cheaper item so that the two items are equally priced , by what percentage must he raise the price of the less expensive item ?
Options: a ) 52 % , b ) 40 % , c ) 30 % , d ) 20 % , e ) 10 %
Rationale: "expensive item = $ 100 ; cheap item = $ 75 ; we must increase $ 75 to $ 100 , so by $ 25 , which is approximately 30 % increase : ( 100 - 75 ) / 75 = 1 / 3 = ~ 0.33 answer : c ."
Answer: c
Question (physics): if the wheel is 15 cm then the number of revolutions to cover a distance of 1540 cm is ?
Options: a ) 11 , b ) 14 , c ) 18 , d ) 12 , e ) 16
Rationale: "2 * 22 / 7 * 15 * x = 1540 = > x = 16 answer : e"
Answer: e
Question (gain): you enter a weight loss challenge game and manage to lose 14 % of your body weight . for the final weigh in you are forced to wear clothes that add 2 % to your weight . what percentage of weight loss is measured at the final weigh in ?
Options: a ) 13 % , b ) 9.22 % , c ) 9 % , d ) 14 % , e ) 12.28 %
Rationale: "( 100 % - 14 % ) * ( 100 % + 2 % ) = 0.86 * 1.02 = 12.28 % the weigh in records your weight loss at 12.28 % ! the answer is e"
Answer: e
Question (general): in what proportion must flour at $ 0.8 per pound be mixed with flour at $ 0.9 per pound so that the mixture costs $ 0.865 per pound ?
Options: a ) 1 : 3 , b ) 1 : 2 , c ) 1 : 1 , d ) 2 : 1 , e ) 3 : 1
Rationale: using weighted average method : let x be the proportion in which the $ 0.8 per pound flour is mixed with $ 0.9 per pound flour . thus 0.8 * x + 0.9 * ( 1 - x ) = 0.865 0.9 – 0.1 x = 0.865 x = 0.35 thus ratio of both flours is 1 : 2 b
Answer: b
Question (geometry): a rectangular block 12 cm by 20 cm by 36 cm is cut into an exact number of equal cubes . find the least possible number of cubes ?
Options: a ) 135 , b ) 10 , c ) 15 , d ) 40 , e ) 22
Rationale: "volume of the block = 12 * 20 * 36 = 8640 cm ^ 3 side of the largest cube = h . c . f of 12 , 20,36 = 4 cm volume of the cube = 4 * 4 * 4 = 64 cm ^ 3 number of cubes = 8640 / 64 = 135 answer is a"
Answer: a
Question (general): the average of 45 results is 10 . the average of first 22 of them is 16 and that of last 22 is 20 . find the 23 result ?
Options: a ) 600 , b ) 480 , c ) 538 , d ) 650 , e ) 560
Rationale: "23 th result = sum of 45 results - sum of 44 results 10 * 45 - 16 * 22 + 20 * 22 = 450 - 352 + 440 = 538 answer is c"
Answer: c
Question (gain): an escalator moves towards the top level at the rate of 15 ft . sec and its length is 200 feet . if a person walks on the moving escalator at the rate of 5 feet per second towards the top level , how much time does he take to cover the entire length .
Options: a ) 5 sec , b ) 10 sec , c ) 20 sec , d ) 15 sec , e ) 25 sec
Rationale: "explanation : time taken to cover the entire length = tot . dist / resultant speed = 200 / ( 15 + 5 ) = 10 sec answer : b"
Answer: b
Question (general): 4 barrels of water have an average capacity of 8 gallons . what is the maximum possible capacity of the smallest barrel e if the median is 10 gallons ?
Options: a ) 1 , b ) 2 , c ) 3 , d ) 4 , e ) 5
Rationale: suppose 4 barrels are b 1 , b 2 , b 3 , b 4 in ascending capacity . ( b 1 + b 2 + b 3 + b 4 ) / 4 = 8 b 1 + b 2 + b 3 + b 4 = 32 median is 10 . . . . . . . as the no . of terms are even i . e 4 , median = ( b 2 + b 3 ) / 2 = = > b 2 + b 3 = 20 now we have b 1 + b 4 = 32 - 20 = 12 only the following possible cases can be there : 19 , 1111 110 , 1011 210 , 1010 max value of smallest barrel e = 2 = b
Answer: b
Question (other): the ratio of incomes of two person p 1 and p 2 is 5 : 4 and the ratio of their expenditures is 3 : 2 . if at the end of the year , each saves rs . 1200 , then what is the income of p 1 ?
Options: a ) s . 800 , b ) s . 2400 , c ) s . 3000 , d ) s . 3200 , e ) s . 4200
Rationale: "let the income of p 1 and p 2 be rs . 5 x and rs . 4 x respectively and let their expenditures be rs . 3 y and 2 y respectively . then , 5 x – 3 y = 1200 … ( i ) and 4 x – 2 y = 1200 … … . . ( ii ) on multiplying ( i ) by 2 , ( ii ) by 3 and subtracting , we get : 2 x = 1200 - > x = 600 p 1 ’ s income = rs 5 * 600 = rs . 3000 answer : c"
Answer: c
Question (general): in a two - digit number , if it is known that its unit ' s digit exceeds its 10 ' s digit by 2 and that the product of the given number and the sum of its digits is equal to 144 , then the number is :
Options: a ) 24 , b ) 26 , c ) 42 , d ) 46 , e ) 48
Rationale: let the ten ' s digit be x . then , unit ' s digit = x + 2 . number = 10 x + ( x + 2 ) = 11 x + 2 sum of digits = x + ( x + 2 ) = 2 x + 2 ( 11 x + 2 ) ( 2 x + 2 ) = 144 2 x 2 + 26 x - 140 = 0 ( x - 2 ) ( 11 x + 35 ) = 0 x = 2 hence , required number = 11 x + 2 = 24 . answer : a
Answer: a
Question (general): what is the greatest value of positive integer x such that 2 ^ x is a factor of 100 ^ 70 ?
Options: a ) 120 , b ) 140 , c ) 130 , d ) 150 , e ) 160
Rationale: "put in simple words , we need to find the highest power of 2 in 100 ^ 70 100 = 2 ^ 2 * 5 ^ 2 therefore 100 ^ 70 = ( 2 ^ 2 * 5 ^ 2 ) ^ 70 = 2 ^ 140 * 5 ^ 140 answer : b"
Answer: b
Question (general): a certain box has 12 cards and each card has one of the integers from 1 to 12 inclusive . each card has a different number . if 2 different cards are selected at random , what is the probability that the sum of the numbers written on the 2 cards is less than the average ( arithmetic mean ) of all the numbers written on the 12 cards ?
Options: a ) 1 / 11 , b ) 2 / 23 , c ) 3 / 34 , d ) 4 / 45 , e ) 5 / 56
Rationale: "the average of the numbers is 6.5 the total number of ways to choose 2 cards from 12 cards is 12 c 2 = 66 . the ways to choose 2 cards with a sum less than the average are : { 1,2 } , { 1,3 } , { 1,4 } , { 1,5 } , { 2,3 } , { 2,4 } the probability is 6 / 66 = 1 / 11 the answer is a ."
Answer: a
Question (general): the average of first five multiples of 4 is ?
Options: a ) 6 , b ) 8 , c ) 9 , d ) 5 , e ) 12
Rationale: "average = 4 ( 1 + 2 + 3 + 4 + 5 ) / 5 = 60 / 5 = 12 . answer : e"
Answer: e
Question (physics): priya takes a trip and drives 5 hours from town x to town z at a rate of 50 miles per hour . on her way back , priya drives 60 miles per hour and stops in town y which is midway between town x and town z . how many hours does it take scott to drive from town z to town y ?
Options: a ) 3.0 , b ) 2.25 , c ) 2.08 , d ) 1.75 , e ) 2.0
Rationale: distance from x to z = 5 hr * 50 mph = 250 miles hence distance from y to z = 1 / 2 * 250 = 125 time = 125 / 60 = 2.08 hrs imo : c
Answer: c
Question (other): in a ratio which is equal to 4 : 6 , if the antecedent is 50 , then the consequent is ?
Options: a ) 75 , b ) 85 , c ) 64 , d ) 51 , e ) 45
Rationale: we have 4 / 6 = 50 / x 4 x = 50 * 6 x = 75 consequent = 75 answer is a
Answer: a
Question (general): shekar scored 76 , 65 , 82 , 67 and 85 marks in mathematics , science , social studies , english and biology respectively . what are his average marks ?
Options: a ) 65 , b ) 69 , c ) 75 , d ) 85 , e ) 90
Rationale: "explanation : average = ( 76 + 65 + 82 + 67 + 85 ) / 5 = 375 / 5 = 75 hence average = 75 answer : c"
Answer: c
Question (gain): an escalator moves towards the top level at the rate of 12 ft . sec and its length is 210 feet . if a person walks on the moving escalator at the rate of 2 feet per second towards the top level , how much time does he take to cover the entire length .
Options: a ) 15 sec , b ) 10 sec , c ) 12 sec , d ) 8 sec , e ) 9 sec
Rationale: "time taken to cover the entire length = tot . dist / resultant speed = 210 / ( 12 + 2 ) = 15 sec answer : a"
Answer: a
Question (general): two employees x and y are paid a total of rs . 800 per week by their employer . if x is paid 120 percent of the sum paid to y , how much is y paid per week ?
Options: a ) s . 200.63 , b ) s . 250.63 , c ) s . 290.63 , d ) s . 300.63 , e ) s . 363.63
Rationale: "let the amount paid to x per week = x and the amount paid to y per week = y then x + y = 800 but x = 120 % of y = 120 y / 100 = 12 y / 10 ∴ 12 y / 10 + y = 800 ⇒ y [ 12 / 10 + 1 ] = 800 ⇒ 22 y / 10 = 800 ⇒ 22 y = 8000 ⇒ y = 8000 / 22 = rs . 363.63 e )"
Answer: e
Question (general): elena ’ s bread recipe calls for 5 ounces of butter for each 7 cups of flour used . she needs to make 4 times the original recipe . if 12 ounces of butter is used , then how many cups of flour are needed ?
Options: a ) 1 , b ) 4 , c ) 9 , d ) 13 , e ) 28
Rationale: solving through algebra route : 5 b + 7 f = x amount if we multiply this equation with 4 we get : 20 b + 28 f = 4 x therefore , we got 20 ounces of butter and 4 x amount of quantity when we use 28 ounces of floor . ans : e
Answer: e
Question (general): tom left a job paying $ 75000 per year to accept a sales job paying $ 45000 per year plus 15 percent commission . if each of his sales is for $ 750 , what is the least number of sales he must make per year if he is not to lose money because of the change ?
Options: a ) 40 , b ) 200 , c ) 266 , d ) 267 , e ) 600
Rationale: in order not to lose money because of the change tom ' s total commission must beat least $ 75000 - $ 45000 = $ 30000 , so total sales must beat least $ 30000 / 0.15 = $ 200000 . which means that he must makeat least $ 200000 / 750 = 800 / 3 = 266.6 sales , so 267 sales . answer : d .
Answer: d
Question (other): there are 192 items that are members of set u . of these items , 49 are members of set b , 59 are not members of either of set a or set b , and 23 are members of both sets a and b . how many of the members of set u are members of set a ?
Options: a ) 72 , b ) 85 , c ) 107 , d ) 98 , e ) 108
Rationale: "you had the answer almost right . the x = 84 refers to only set a . however what ' s being asked is how many members are part of set a . this will include : 1 . only set a 2 . set a and set b so the answer is set a = 84 + set ab = 84 + 23 = 17 c"
Answer: c
Question (physics): a family travelled for 12 hours . they covered the first half of the distance at 35 kmph and remaining half of the distance at 40 kmph . find the distance travelled by the family ?
Options: a ) 270 km , b ) 890 km , c ) 684 km , d ) 320 km , e ) 560 km
Rationale: let the distance travelled be x km . total time = ( x / 2 ) / 35 + ( x / 2 ) / 40 = 12 = > x / 70 + x / 80 = 12 = > ( 8 x + 7 x ) / 560 = 12 = > x = 560 km answer : e
Answer: e
Question (general): of the 250 employees at company x , 80 are full - time , and 100 have worked at company x for at least a year . there are 20 employees at company x who aren ’ t full - time and haven ’ t worked at company x for at least a year . how many full - time employees of company x have worked at the company for at least a year ?
Options: a ) 20 , b ) 30 , c ) 50 , d ) 80 , e ) 100
Rationale: "full time employee who have not worked for at least one year = a full time employee who have worked for at least one year = b non full time employee who have worked for at least one year = c non full time employee who have not worked for at least one year = d a + b + c + d = 150 a + b = 80 i . e . c + d = 70 b + c = 100 i . e . a + d = 50 d = 20 i . e . c = 70 - 20 = 50 i . e . b = 100 - 50 = 50 i . e . a = 80 - 50 = 30 b = 100 answer : option e"
Answer: e
Question (gain): the difference between the compound interest compounded annually and simple interest for 2 years at 20 % per annum is rs . 360 . find the principal ?
Options: a ) 2277 , b ) 2667 , c ) 9000 , d ) 2766 , e ) 1811
Rationale: "p = 360 ( 100 / 5 ) ^ 2 = > p = 9000 answer : c"
Answer: c
Question (general): the average of 6 integers is 63 , and none of these integers is greater than 100 . if the average of 3 of the integers is 65 , what is the least possible value of one of the other two integers ?
Options: a ) 45 , b ) 62 , c ) 75 , d ) 83 , e ) 90
Rationale: when it comes to averages , we know thataverage value = ( sum of n values ) / n we can rewrite this into a useful formula : sum of n values = ( average value ) ( n ) the average of five integers is 63 so , the sum of all 5 integers = ( 63 ) ( 6 ) = 378 the average of three of the integers is 65 so , the sum of the 3 integers = ( 65 ) ( 3 ) = 195 so , the sum of the 2 remaining integers = 378 - 195 = 183 if the sum of the 2 remaining integers = 183 , and we want to minimize one value , we must maximize the other value . 100 is the maximum value so let 1 integer = 100 , which means the other must equal 83 answer : d
Answer: d
Question (general): in a flight of 600 km , an aircraft was slowed down due to bad weather . its average speed for the trip was reduced by 200 km / hr and the time of flight increased by 30 minutes . what is the duration of the flight ?
Options: a ) 3 hours , b ) 2.4 hours , c ) 1.4 hours , d ) 1 hour , e ) none of these
Rationale: "explanation : let the duration of the flight be x hours . then 600 / x − 600 / x + 1 / 2 = 200 600 / x − 1200 / 2 x + 1 = 200 x ( 2 x + 1 ) = 3 2 x 2 + x − 3 = 0 = > ( 2 x + 3 ) ( x − 1 ) = 0 neglecting the negative value for x we get x = 1 option d"
Answer: d
Question (general): what is the tens digit of 7 ^ 1415 ?
Options: a ) 0 , b ) 1 , c ) 2 , d ) 3 , e ) 4
Rationale: "7 ^ 1 = 7 7 ^ 2 = 49 7 ^ 3 = 343 7 ^ 4 = 2401 7 ^ 5 = 16807 7 ^ 6 = 117649 we should see this as pattern recognition . we have a cycle of 4 . ( we can multiply the last 2 digits only as we care about ten ' s digit ) 0 , 4 , 4 , 0 . 1415 = 4 * 353 + 3 the ten ' s digit will be 4 . answer e"
Answer: e
Question (other): the ratio of 2 numbers is 3 : 4 and their h . c . f . is 4 . their l . c . m . is ?
Options: a ) 20 , b ) 24 , c ) 48 , d ) 36 , e ) 60
Rationale: "let the numbers be 3 x and 4 x their h . c . f . = 4 so the numbers are 3 * 4 , 4 * 4 = 12,16 l . c . m . = 48 answer is c"
Answer: c
Question (physics): a 140 cm long wire is to be cut into two pieces so that one piece will be 2 / 5 th of the other , how many centimeters will the shorter piece be ?
Options: a ) 35 , b ) 20 , c ) 47 , d ) 36 , e ) 40
Rationale: "1 : 2 / 5 = 5 : 2 2 / 7 * 140 = 40 answer : e"
Answer: e
Question (physics): the sum of 3 consecutive numbers is definitely :
Options: a ) positive , b ) divisible by 2 . , c ) divisible by 3 , d ) divisible by 4 . , e ) divisible by 5
Rationale: "if 1 st term is x : x + ( x + 1 ) + ( x + 2 ) = 3 x + 3 - - - > always divisible by 3 if 2 nd term is x : ( x - 1 ) + x + ( x + 1 ) = 3 x - - - > always divisible by 3 if 3 rd term is x : ( x - 2 ) + ( x - 1 ) + x = 3 x - 3 - - - > always divisible by 3 answer : c"
Answer: c
Question (physics): a tree is 12 m tall and casts an an 8 m long shadow . at the same time , a flag pole caste a 100 m long shadow . how long is the flag pole ?
Options: a ) 150 m , b ) 200 m , c ) 125 m , d ) 115 m , e ) none
Rationale: answer ∵ 8 m shadow means original height = 12 m ∴ 1 m shadow means original height = 12 / 8 m ∴ 100 m shadow means original height = ( 12 / 8 ) x 100 m = ( 6 / 4 ) x 100 = 6 x 25 = 150 m correct option : a
Answer: a
Question (general): in a division sum , the remainder is 4 and the divisor is 3 times the quotient and is obtained by adding 2 to the thrice of the remainder . the dividend is :
Options: a ) 53 , b ) 58 , c ) 51 , d ) 60 , e ) 62
Rationale: "diver = ( 4 * 3 ) + 2 = 14 4 * quotient = 14 quotient = 3.5 dividend = ( divisor * quotient ) + remainder dividend = ( 14 * 3.5 ) + 4 = 53 a"
Answer: a
Question (general): if x is equal to the sum of the integers from 20 to 30 , inclusive , and y is the number of even integers from 20 to 30 , inclusive , what is the value of x + y ?
Options: a ) 171 , b ) 281 , c ) 361 , d ) 461 , e ) 561
Rationale: "sum s = n / 2 { 2 a + ( n - 1 ) d } = 11 / 2 { 2 * 20 + ( 11 - 1 ) * 1 } = 11 * 25 = 275 = x number of even number = ( 30 - 20 ) / 2 + 1 = 6 = y x + y = 275 + 6 = 281 b"
Answer: b
Question (gain): the difference between c . i . and s . i . on an amount of $ 10,000 for 2 years is $ 36 . what is the rate of interest per annum ?
Options: a ) 5 % , b ) 6 % , c ) 7 % , d ) 8 % , e ) 9 %
Rationale: "$ 36 is the interest on the first year of interest . let x be the interest rate . the interest after the first year is 10000 * x . the interest on the first year ' s interest is 10000 * x * x 10000 * x ^ 2 = 36 x = 0.06 the answer is b ."
Answer: b
Question (geometry): there are 60 slots around a circle , numbered 1 to 60 . a man starts fromthe first slot and jumps to the 5 th slot . from there he jumps to the 9 th slot andso on . in which slot will he land in his 2200 th jump ?
Options: a ) 1
b ) 5
c ) 41
d ) 45
e ) 46
Rationale: every 15 th jump , he comes back to 1 st position so , 2200 / 15 = remainder 10 hence 10 th position is 41 st slot answer : c
Answer: c
Question (physics): a cistern can be filled by a tap in 3 hours while it can be emptied by another tap in 6 hours . if both the taps are opened simultaneously , then after how much time will the cistern get filled ?
Options: a ) 5.2 hrs , b ) 2.9 hrs , c ) 1.9 hrs , d ) 6 hrs , e ) 5 hrs
Rationale: "net part filled in 1 hour = ( 1 / 3 - 1 / 6 ) = 1 / 6 the cistern will be filled in 6 / 1 hrs i . e . , 6 hrs . answer : d"
Answer: d