Cheukting/mathqa huggingface dataset:
Question (general): a local elementary school has 1049 students and 9 teachers , how many students would have to be added to the school to make sure each teacher has the same amount of students in their classroom ?
Options: a ) 4 , b ) 6 , c ) 5 , d ) 1 , e ) 2
Rationale: using the rule on the divisibility of nine , we add the digits of 1049 together to get 14 . since we are doing addition , the next number that is divisible by nine would be 18 . therefore , our answer 4 ( option a )
Answer: a
Question (general): the average marks of 30 students in a class is 100 . but a student mark is wrongly noted as 70 instead of 10 then find the correct average marks ?
Options: a ) a ) 78 , b ) b ) 82 , c ) c ) 98 , d ) d ) 91 , e ) e ) 85
Rationale: "correct avg marks = 100 + ( 10 - 70 ) / 30 avg = 100 - 2 = 98 answer is c"
Answer: c
Question (general): if a and b are positive real numbers , and a ^ 3 + b ^ 3 = 25 , then the greatest possible value of a is between :
Options: a ) 0 and 3 , b ) 3 and 4 , c ) 4 and 5 , d ) 5 and 7 , e ) 7 and 9
Rationale: if a > 3 , then a ^ 3 + b ^ 3 > 25 . the answer is a .
Answer: a
Question (gain): a 440 - liter solution of kola is made from 88 % water , 8 % concentrated kola and the rest is made from sugar . if 3.2 liters of sugar , 10 liter of water and 6.8 liters of concentrated kola were added to the solution , what percent of the solution is made from sugar ?
Options: a ) 4.52 % . , b ) 7.5 % . , c ) 9.2 % . , d ) 10.5 % . , e ) 11 % .
Rationale: "denominator : 440 + 10 + 3.2 + 6.8 = 460 numerator : 440 ( 1 - . 88 - . 08 ) + 3.2 440 ( 0.04 ) + 3.2 17.6 + 3.2 20.8 ratio : 20.8 / 460 = 0.045 answer : a"
Answer: a
Question (geometry): a wire in the form of a circle of radius 3.5 m is bent in the form of a rectangule , whose length and breadth are in the ratio of 6 : 5 . what is the area of the rectangle ?
Options: a ) 65 cm 2
b ) 30 cm 2
c ) 76 cm 2
d ) 68 cm 2
e ) 46 cm 2
Rationale: the circumference of the circle is equal to the permeter of the rectangle . let l = 6 x and b = 5 x 2 ( 6 x + 5 x ) = 2 * 22 / 7 * 3.5 = > x = 1 therefore l = 6 cm and b = 5 cm area of the rectangle = 6 * 5 = 30 cm 2 answer : b
Answer: b
Question (general): sandy gets 3 marks for each correct sum and loses 2 marks for each incorrect sum . sandy attempts 30 sums and obtains 50 marks . how many sums did sandy get correct ?
Options: a ) 20 , b ) 22 , c ) 24 , d ) 26 , e ) 28
Rationale: "let x be the correct sums and ( 30 - x ) be the incorrect sums . 3 x - 2 ( 30 - x ) = 50 5 x = 110 x = 22 the answer is b ."
Answer: b
Question (general): if a is a positive integer , and if the units digit of a ^ 2 is 9 and the units digit of ( a + 1 ) ^ 2 is 6 , what is the units digit of ( a + 2 ) ^ 2 ?
Options: a ) 1 , b ) 3 , c ) 5 , d ) 6 , e ) 8
Rationale: "if the units digit of a ^ 2 is 9 , then the units digit of a is either 3 or 7 . if the units digit of ( a + 1 ) ^ 2 is 6 , then the units digit of a + 1 is either 4 or 6 . to satisfy both conditions , the units digit of a must be 3 . then a + 2 has the units digit of 5 , thus the units digit of ( a + 2 ) ^ 2 will be 5 . the answer is c ."
Answer: c
Question (gain): a person borrows 20000 for 6 years at 8 % p . a . simple interest . he immediately lends it to another person at 9 % p . a . for 6 years . find his gain in the transaction per year .
Options: a ) 200 , b ) 250 , c ) 210 , d ) 190 , e ) 180
Rationale: gain in 6 years = [ ( 20000 ã — 9 ã — 6 / 100 ) â ˆ ’ ( 20000 ã — 6 ã — 8 / 100 ) ] = ( 10800 â € “ 9600 ) = 1200 â ˆ ´ gain in 6 year = ( 1200 / 6 ) = 200 answer a
Answer: a
Question (physics): a solid yellow stripe is to be painted in the middle of a certain highway . if 1 gallon of paint covers an area of w square feet of highway , how many gallons of paint will be needed to paint a stripe of t inches wide on a stretch of highway m miles long ? ( 1 mile = 5,280 feet and 1 foot = 12 inches )
Options: a ) ( 5,280 mt ) / 12 w
b ) ( 5,280 pt ) / 12 m
c ) ( 5,280 pmt ) / 12
d ) ( 5,280 ) ( 12 m ) / pt
e ) ( 5,280 ) ( 12 p ) / mt
Rationale: given that : 1 gallon of paint covers an area ofwsquare feet . question : how many gallonsof paint will be needed . . . in any case you will have : ( total area in square feet ) / ( gallons per feet ) = ( total area in square feet ) / w , so w must be in the denominator : eliminate all but a and d . now , lets see where should be t : ( area in square feet ) = ( width in feet ) * ( length in feet ) - - > width = tinchesas 1 feet = 12 inchesthent inches = t / 12 feet , so ( area in square feet ) = ( t / 12 ) * ( length in feet ) , so t must be in the nominator : only a is left . answer : a .
Answer: a
Question (general): what is the units digit of 23 ^ 2 * 17 ^ 2 * 39 ^ 2 ?
Options: a ) 1 , b ) 3 , c ) 5 , d ) 7 , e ) 9
Rationale: "the units digit of 23 ^ 2 is the units digit of 3 * 3 = 9 which is 9 . the units digit of 17 ^ 2 is the units digit of 7 * 7 = 49 which is 9 . the units digit of 39 ^ 2 is the units digit of 9 * 9 = 81 which is 1 . the units digit of 9 * 9 * 1 = 81 is 1 . the answer is a ."
Answer: a
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 8 , inclusive ?
Options: a ) 1 / 32 , b ) 2 / 25 , c ) 5 / 16 , d ) 8 / 25 , e ) 3 / 4
Rationale: "from july 4 to july 8 , we have total of 5 days . prob of raining on exactly 3 days = 5 c 3 ∗ ( 1 / 2 ) 3 ∗ ( 1 / 2 ) 25 c 3 ∗ ( 1 / 2 ) 3 ∗ ( 1 / 2 ) 2 = 5 / 16 ans : c"
Answer: c
Question (general): if m is a positive integer and m ^ 2 is divisible by 24 , then the largest positive integer that must divide m is ?
Options: a ) 3 , b ) 6 , c ) 8 , d ) 12 , e ) 16
Rationale: "m ^ 2 is divisible by 48 so m ^ 2 must be multiple of 48 . if the value of m is multiples of 8 then it will satisfy the condition . if we if m is 12 or 24 or 36 then it ans is c but if m = 48 then answer should be 16 . is the question right ? or am i missing some thing ? c"
Answer: c
Question (physics): a flagstaff 17.5 m high casts a shadow of length 40.25 m . the height of the building , which casts a shadow of length 28.75 m under similar conditions will be ?
Options: a ) 10 m , b ) 12.5 m , c ) 12 m , d ) 13 m , e ) 14 m
Rationale: "let the height of the building x metres . less lengthy shadow , less in the height ( direct proportion ) 40.25 : 28.75 : : 17.5 : x 40.25 x x = 28.75 x 17.5 x = 28.75 x 17.5 / 40.25 x = 12.5 answer : b"
Answer: b
Question (general): average monthly income of a family of 4 earning members was rs . 840 . one of the earning members died and therefore , the average income came down to rs 650 . the income of the deceased was ?
Options: a ) rs . 692.80 , b ) rs . 820 , c ) rs . 990 , d ) rs . 1410 , e ) none
Rationale: answer income of the deceased = total income of 4 members - total income of remaining 3 members . = 840 x 4 - 650 x 3 rs . = 1410 rs . correct option : d
Answer: d
Question (general): x and y are two towns . ganesh covers the distance from x to y at an average speed of 43 km / hr . however , he covers the distance from y to x at an average speed of 34 km / hr . his average speed during the whole journey in km / hr . is :
Options: a ) 34 , b ) 43 , c ) 40 , d ) 38 , e ) 29
Rationale: "solution : average speed = 2 xy / x + y = 2 * 43 * 34 / 43 + 34 = 2924 / 77 = 37.974 . . . = 38 answer : d"
Answer: d
Question (geometry): what is the measure of the angle q made by the diagonals of the any adjacent sides of a cube .
Options: a ) 30 , b ) 45 , c ) 60 , d ) 75 , e ) 90
Rationale: "c . . 60 degrees all the diagonals are equal . if we take 3 touching sides and connect their diagonals , we form an equilateral triangle . therefore , each angle would be q = 60 . c"
Answer: c
Question (general): visitors to show were charged rs . 15 each on the first day . rs . 7.50 on the second day , rs . 2.50 on the third day and total attendance on the 3 days were in ratio 2 : 5 : 13 respectively . the average charge per person for the whole show is ?
Options: a ) 1 , b ) 4 , c ) 5 , d ) 6 , e ) 8
Rationale: 2 : 5 : 13 2 x 5 x 13 x 15 7.5 2.5 30 x + 37.5 x + 32.5 x = 100 x / 20 x average = 5 answer : c
Answer: c
Question (general): hillary and eddy are climbing to the summit of mt . everest from a base camp 4,900 ft from the summit . when they depart for the summit at 06 : 00 , hillary climbs at a rate of 800 ft / hr with eddy lagging behind at a slower rate of 500 ft / hr . if hillary stops 900 ft short of the summit and then descends at a rate of 1,000 ft / hr , at what time do hillary and eddy pass each other on her return trip ?
Options: a ) 10.0 , b ) 11.0 , c ) 13.0 , d ) 12.0 , e ) 14.0
Rationale: "solution : h stopped 900 ft before reaching the final point , time taken to reach 4000 ft = 4000 / 800 = 5 hrs . this means she reached there at 11 : 00 . speed difference between them is 800 - 500 = 300 ft / hr so by the time h stops they have 1500 ft of distance so now here we use relative speed formula they both are travelling toward each other with speed of 1000 and 500 total 1500 ft / hr and distance bwn them is 1500 ft so time taken to meet = 1 hr from 11 : 00 means 12 : 00 is the answer . d"
Answer: d
Question (gain): a dishonest person wants to make a profit on the selling of milk . he would like to mix water ( costing nothing ) with milk costing 33 $ per litre so as to make a profit of 70 % on cost when he sells the resulting milk and water mixture for 36 $ . in what ratio should he mix the water and milk ?
Options: a ) 1 : 120 , b ) 67 : 120 , c ) 67 : 8 , d ) 8 : 120 , e ) 1 : 2
Rationale: "first of all , let ' s consider 1 liter of the stuff he is going to sell - - - naive customers think it ' s pure milk , but we know it ' s some milk - water mixture . he is going to sell this liter of milk - water for $ 36 . this $ 36 should be a 20 % increase over cost . here , we need to think about percentage increases as multipliers . using multipliers ( cost ) * 1.70 = $ 36 cost = 36 / 1.7 = 360 / 12 = $ 30 if he wants a 70 % increase over cost on the sale of one liter of his milk - water , the cost has to be $ 21.17 well , a liter of milk costs $ 33 , so if he is going to use just $ 30 of milk in his mixture , that ' s 21.17 / 33 = 120 / 187 of a liter . if milk is 120 / 87 of the liter , then water is 67 / 187 of the liter , and the ratio of water to milk is 67 : 120 . answer choice ( b )"
Answer: b
Question (gain): the price of a book is increased from $ 300 to $ 390 . what is the % of increase in its price ?
Options: a ) 10 % , b ) 20 % , c ) 30 % , d ) 35 % , e ) 45 %
Rationale: "explanation : change in the price = rs 390 – rs 300 = rs 90 percentage of increase = change in the price initial price * 100 . percentage increase in price = ( 90 / 300 ) * 100 = 30 % c"
Answer: c
Question (physics): a , b and c , each working alone can complete a job in 6 , 8 and 12 days respectively . if all three of them work together to complete a job and earn $ 1170 , what will be b ' s share of the earnings ?
Options: a ) $ 390 , b ) $ 520 , c ) $ 1080 , d ) $ 1170 , e ) $ 630
Rationale: "explanatory answer a , b and c will share the amount of $ 1170 in the ratio of the amounts of work done by them . as a takes 6 days to complete the job , if a works alone , a will be able to complete 1 / 6 th of the work in a day . similarly , b will complete 1 / 8 th and c will complete 1 / 12 th of the work . so , the ratio of the work done by a : b : c when they work together will be equal to 1 / 6 : 1 / 8 : 1 / 12 multiplying the numerator of all 3 fractions by 24 , the lcm of 6 , 8 and 12 will not change the relative values of the three values . we get 24 / 6 : 24 / 8 : 24 / 12 = 4 : 3 : 2 . i . e . , the ratio in which a : b : c will share $ 1170 will be 4 : 3 : 2 . hence , b ' s share will be 3 * 1170 / 9 = 390 . correct choice is ( a )"
Answer: a
Question (physics): 12 spheres of the same size are made from melting a solid cylinder of 8 cm diameter and 27 cm height . what is the diameter of each sphere ?
Options: a ) 2 cm , b ) 4 cm , c ) 6 cm , d ) 8 cm , e ) 10 cm
Rationale: "volume of cylinder = pi * r ^ 2 * h volume of a sphere = 4 * pi * r ^ 3 / 3 12 * 4 * pi * r ^ 3 / 3 = pi * r ^ 2 * h r ^ 3 = r ^ 2 * h / 16 = 27 cm ^ 3 r = 3 cm d = 6 cm the answer is c ."
Answer: c
Question (other): what is the units digit of 32 ! + 50 ! + 4 ! + 4 ! ?
Options: a ) 0 , b ) 2 , c ) 4 , d ) 6 , e ) 8
Rationale: "for all n greater than 4 , the units digit of n ! is 0 . the sum of the four units digits is 0 + 0 + 4 + 4 = 8 the units digit is 8 . the answer is e ."
Answer: e
Question (physics): if jack walked 8 miles in 1 hour and 15 minutes , what was his rate of walking in miles per hour ?
Options: a ) 4 , b ) 4.5 , c ) 6 , d ) 6.4 , e ) 15
Rationale: "distance walked in 1 hour and 15 mins = 8 miles speed per hour = distance / time = 8 / ( 5 / 4 ) = 6.4 miles per hour answer d"
Answer: d
Question (gain): a particular library has 75 books in a special collection , all of which were in the library at the beginning of the month . these book are occasionally loaned out through an inter - library program . if , by the end of the month , 80 percent of books that were loaned out are returned and there are 67 books in the special collection at that time , how many books of the special collection were loaned out during that month ?
Options: a ) 20 , b ) 30 , c ) 35 , d ) 40 , e ) 55
Rationale: "there are 8 books less ( 75 - 68 ) which represents 20 % of the loaned books ( 100 - 80 ) so total loaned out books = 40 answer d"
Answer: d
Question (physics): if a farmer wants to plough a farm field on time , he must plough 120 hectares a day . for technical reasons he ploughed only 85 hectares a day , hence he had to plough 2 more days than he planned and he still has 40 hectares left . what is the area of the farm field and how many days the farmer planned to work initially ?
Options: a ) 600 , b ) 490 , c ) 720 , d ) 435 , e ) 679
Rationale: let x be the number of days in the initial plan . therefore , the whole field is 120 ⋅ x hectares . the farmer had to work for x + 2 days , and he ploughed 85 ( x + 2 ) hectares , leaving 40 hectares unploughed . then we have the equation : 120 x = 85 ( x + 2 ) + 40 35 x = 210 x = 6 so the farmer planned to have the work done in 6 days , and the area of the farm field is 120 ⋅ 6 = 720 hectares correct answer c
Answer: c
Question (general): for each color copy , print shop x charges $ 1.20 and print shop y charges $ 1.70 . how much greater is the charge for 40 color copies at print shop y than at print shop x ?
Options: a ) $ 14 , b ) $ 16 , c ) $ 18 , d ) $ 20 , e ) $ 22
Rationale: "the difference in the two prices is $ 1.70 - $ 1.20 = $ 0.50 for each color copy . each color copy will cost an extra $ 0.50 at print shop y . 40 * $ 0.50 = $ 20 the answer is d ."
Answer: d
Question (gain): in a school of 300 boys , 44 % of muslims , 28 % hindus , 10 % sikhs and the remaining of other communities . how many belonged to the other communities ?
Options: a ) 54 , b ) 63 , c ) 70 , d ) 42 , e ) 31
Rationale: "44 + 28 + 10 = 82 % 100 – 82 = 18 % 300 * 18 / 100 = 54 answer : a"
Answer: a
Question (general): a number x is 12 times another number y . the percentage that y is less than x is
Options: a ) 91.6 % , b ) 87.5 % , c ) 80 % , d ) 11 % , e ) 1 %
Rationale: "say y = 1 and x = 12 . then y = 1 is less than x = 12 by ( 12 - 1 ) / 12 * 100 = 11 / 12 * 100 = 91.6 % . answer : a ."
Answer: a
Question (physics): a train 90 m long is running with a speed of 60 km / hr . in what time will it pass a man who is running at 6 km / hr in the direction opposite to that in which the train is going ?
Options: a ) 7 , b ) 6 , c ) 8 , d ) 5 , e ) 4
Rationale: "speed of train relative to man = 60 + 6 = 66 km / hr . = 66 * 5 / 18 = 55 / 3 m / sec . time taken to pass the men = 90 * 3 / 55 = 5 sec . answer d"
Answer: d
Question (general): the average age of a family of 5 members is 20 years . if the age of the youngest member be 10 years then what was the average age of the family at the time of the birth of the youngest member ?
Options: a ) 13.5 , b ) 14 , c ) 15 , d ) 12.5 , e ) none
Rationale: solution : at present the total age of the family = 5 * 20 = 100 . the total age of the family at the time of the birth of the youngest member , = [ 100 − 10 − ( 10 * 4 ) ] = 50 . therefore , average age of the family at the time of birth of the youngest member , = 50 / 4 = 12.5 . answer : option d
Answer: d
Question (general): on a certain day , orangeade was made by mixing a certain amount of orange juice with an equal amount of water . on the next day , orangeade was made by mixing the same amount of orange juice with five times the amount of water . on both days , all the orangeade that was made was sold . if the revenue from selling the orangeade was the same for both days and if the orangeade was sold at $ 0.80 per glass on the first day , what was the price per glass on the second day ?
Options: a ) $ 015 , b ) $ 0.27 , c ) $ 0.30 , d ) $ 0.40 , e ) $ 0.45
Rationale: "on the first day 1 unit of orange juice and 1 unit of water was used to make 2 units of orangeade ; on the second day 1 unit of orange juice and 5 units of water was used to make 6 units of orangeade ; so , the ratio of the amount of orangeade made on the first day to the amount of orangeade made on the second day is 2 to 6 . naturally the ratio of the # of glasses of orangeade made on the first day to the # of glasses of orangeade made on the second day is 2 to 6 . we are told thatthe revenue from selling the orangeade was the same for both daysso the revenue from 2 glasses on the first day equals to the revenue from 6 glasses on the second day . say the price of the glass of the orangeade on the second day was $ x then 2 * 0.8 = 6 * x - - > x = $ 0.27 . answer : b ."
Answer: b
Question (general): how many unique positive odd integers less than 90 are equal to the product of a positive multiple of 5 and an odd number ?
Options: a ) 4 , b ) 9 , c ) 11 , d ) 12 , e ) 15
Rationale: "the question basically asks how many positive odd integers less than 90 are odd multiples of 5 so we have 5 , 15,25 , 35,45 , 55,65 , 75,85 = 9 ans b"
Answer: b
Question (general): if # is an operation which results in adding the digits of integer until a single digit is left , what is the probability that a number picked up in first 90 positive integers will have the result of # as an odd digit ? ( example 99 = 9 + 9 = 18 = 1 + 8 = 9 , so # = 9 )
Options: a ) 4 / 10 , b ) 4 / 9 , c ) 1 / 2 , d ) 6 / 10 , e ) 5 / 9
Rationale: first of all let us find out what is the maximum sum we will get by adding digits of numbers from 1 to 90 . that will be 17 ( 8 + 9 + 17 ) why did i calculate this ? i will come to that in a moment . so to get an odd digit by carrying out the operation # , the sum of the digits of the integer should be 1 , 3 , 5 , 7 , 9 , 10 , 12 , 14 , and 16 ( why not 18 ? because we know the maximum sum can be 17 ) number of integers , whose digits add to 1 : 1 and 10 = 2 number of integers , whose digits add to 3 : 3 , 12 , 21 , 30 = 4 number of integers , whose digits add to 5 : 5 , 14 , 23 , 32 , 41 , 50 = 6 number of integers , whose digits add to 7 : 7 , 16 , 25 , 34 , 43 , 52 , 61 , 70 = 8 number of integers , whose digits add to 9 : 10 multiples of 9 up to 90 = 10 number of integers , whose digits add to 10 : 19 , 28 , 37 , 46 , 55 , 64 , 73 , 82 = 8 number of integers , whose digits add to 12 : 39 , 48 , 57 , 66 , 75 , 84 = 6 number of integers , whose digits add to 14 : 59 , 68 , 77 , 86 = 4 number of integers , whose digits add to 16 : 79 , 88 = 2 so in total there are 2 + 4 + 6 + 8 + 10 + 8 + 6 + 4 + 2 = 50 such numbers probability = 50 / 90 = 5 / 9 correct answer e
Answer: e
Question (general): operation # is defined as : a # b = 4 a ^ 2 + 4 b ^ 2 + 8 ab for all non - negative integers . what is the value of ( a + b ) + 6 , when a # b = 100 ?
Options: a ) 5 , b ) 8 , c ) 10 , d ) 11 , e ) 17
Rationale: "official solution : ( b ) we know that a # b = 100 and a # b = 4 a ² + 4 b ² + 8 ab . so 4 a ² + 4 b ² + 8 ab = 100 we can see that 4 a ² + 4 b ² + 8 ab is a well - known formula for ( 2 a + 2 b ) ² . therefore ( 2 a + 2 b ) ² = 100 . ( 2 a + 2 b ) is non - negative number , since both a and b are non - negative numbers . so we can conclude that 2 ( a + b ) = 10 . ( a + b ) + 6 = 10 / 2 + 6 = 11 . the correct answer is d ."
Answer: d
Question (general): jerry and michelle play a card game . in the beginning of the game they have an equal number of cards . each player , at her turn , gives the other a third of her cards . michelle plays first , giving jerry a third of her cards . jerry plays next , and michelle follows . then the game ends . jerry ended up with 14 more cards than michelle . how many cards did each player have originally ?
Options: a ) 27 , b ) 30 , c ) 34 , d ) 36 , e ) 38
Rationale: game michelle jerry michelle initially 2727 assume after game 1 1836 after game 2 3024 after game 3 2034 now jerry has 14 cards more than michelle . so the answer is a
Answer: a
Question (general): in a fuel station the service costs $ 1.75 per car , every liter of fuel costs 0.65 $ . assuming that a company owns 12 cars and that every fuel tank contains 50 liters and they are all empty , how much money total will it cost to fuel all cars ?
Options: a ) 320 $ , b ) 380 $ , c ) 420 $ , d ) 450 $ , e ) 411 $
Rationale: "total cost = ( 1.75 * 12 ) + ( 0.65 * 12 * 50 ) = 21 + 390 = > 411 hence answer will be ( e )"
Answer: e
Question (geometry): a circular swimming pool is surrounded by a concrete wall 4 feet wide . if the area of the wall is 11 / 25 of the area of the pool , then the radius of the pool in feet is ?
Options: a ) 22
b ) 20
c ) 9
d ) 8
e ) 1
Rationale: let the radius of the pool be r . then area of the wall and pool = π ( r + 4 ) 2 π ( r + 4 ) 2 area of the pool = π ( r ) 2 π ( r ) 2 area of the wall = π ( r + 4 ) 2 − π ( r ) 2 π ( r + 4 ) 2 − π ( r ) 2 given π ( r + 4 ) 2 − π ( r ) 2 π ( r + 4 ) 2 − π ( r ) 2 = 1125 ( π r 2 ) 1125 ( π r 2 ) r 2 + 8 r + 16 − r 2 = 1125 r 2 r 2 + 8 r + 16 − r 2 = 1125 r 2 11 r 2 − 200 r − 400 = 011 r 2 − 200 r − 400 = 0 solving r = 20 answer : b
Answer: b
Question (gain): the population of a town increases 25 % and 40 % respectively in two consecutive years . after the growth the present population of the town is 1750 . then what is the population of the town 2 years ago ?
Options: a ) a ) 750 , b ) b ) 800 , c ) c ) 850 , d ) d ) 900 , e ) e ) 950
Rationale: "explanation : formula : ( after = 100 denominator ago = 100 numerator ) 1750 * 100 / 125 * 100 / 140 = 1000 answer : option b"
Answer: b
Question (physics): a truck travels 20 miles due north , 30 miles due east , and then 20 miles due north . how many miles is the truck from the starting point ?
Options: a ) 20.3 , b ) 44.7 , c ) 50 , d ) 70 , e ) 120
Rationale: we have two right angle triangles with sides 20 and 15 the distance between starting and end point = sum of the hypotenuse of both the triangles . hypotenuse = [ 400 + 225 ] ^ ( 1 / 2 ) = 25 hence the total distance between end point and starting point = 25 + 25 = 50 correct option : c
Answer: c
Question (geometry): find the area of a parallelogram with base 22 cm and height 14 cm ?
Options: a ) 298 cm 2 , b ) 384 cm 2 , c ) 308 cm 2 , d ) 286 cm 2 , e ) 276 cm 2
Rationale: "area of a parallelogram = base * height = 22 * 14 = 308 cm 2 answer : c"
Answer: c
Question (gain): the salary of a typist was at first raised by 10 % and then the same was reduced by 5 % . if he presently draws rs . 4180 . what was his original salary ?
Options: a ) 2277 , b ) 2999 , c ) 4000 , d ) 2651 , e ) 1971
Rationale: "x * ( 110 / 100 ) * ( 95 / 100 ) = 4180 x * ( 11 / 10 ) * ( 1 / 100 ) = 44 x = 4000 answer : c"
Answer: c