Cheukting/mathqa huggingface dataset:
Question (gain): a company has two types of machines , type r and type s . operating at a constant rate a machine of r does a certain job in 36 hours and a machine of type s does the job in 9 hours . if the company used the same number of each type of machine to do job in 12 hours , how many machine r were used ?
Options: a ) 3 , b ) 4 , c ) 18 / 5 , d ) 9 , e ) 12
Rationale: "yes there is a typo in the question , i got the same ques on my gmat prep last week , and the questions goes as : a company has two types of machines , type r and type s . operating at a constant rate a machine of r does a certain job in 36 hours and a machine of type s does the job in 9 hours . if the company used the same number of each type of machine to do job in 2 hours , how many machine r were used ? so for a job to be done in 2 hours r = 1 / 2 r _ a ( rate of machine r ) = 1 / 36 r _ s ( rate of machine s ) = 1 / 9 lets say x machines are used to attain the desired rate , thus x / 36 + x / 9 = 1 / 2 ( desired r = 1 / 2 i . e . to complete the job in 2 hours ) ( x + 4 x ) / 36 = 1 / 2 5 x / 36 = 1 / 2 x = 18 / 5 . qa = 18 / 5 ( answer c )"
Answer: c
Question (general): a batsman makes a score of 110 runs in the 11 th inning and thus increases his average by 5 . find his average after 11 th inning .
Options: a ) 40 , b ) 50 , c ) 60 , d ) 45 , e ) 56
Rationale: "let the average after 11 th inning = x then , average after 10 th inning = x - 5 10 ( x - 5 ) + 110 = 11 x x = 110 - 50 = 60 answer is c"
Answer: c
Question (physics): if the population of a certain country increases at the rate of one person every 15 seconds , by how many persons does the population increase in 1 hour ?
Options: a ) 100 , b ) 120 , c ) 150 , d ) 180 , e ) 240
Rationale: "answer = 4 * 60 = 240 answer is e"
Answer: e
Question (general): the difference of two numbers is 8 and one - fourth of their sum is 6 . find the numbers .
Options: a ) 16,8 , b ) 10,2 , c ) 17,6 , d ) 14,10 , e ) 12,4
Rationale: "let numbers be x and y . equation ( i ) : x - y = 8 equation ( ii ) : ( x + y ) / 4 = 6 solve system of equations : x = 16 , y = 8 a is the correct answer ."
Answer: a
Question (general): a retailer bought a shirt at wholesale and marked it up 80 % to its initial price of $ 45 . by how many more dollars does he need to increase the price to achieve a 100 % markup ?
Options: a ) 1 , b ) 2 , c ) 3 , d ) 4 , e ) 5
Rationale: "x is the buy price . x + 80 % x = 1,8 x is the sale price = 45 so x , the buy price becomes 45 / 1,8 = 25 % 100 mark up means x + 100 % x = 2 x so 50 . 50 - 45 = 5 answer : e"
Answer: e
Question (gain): indu gave bindu rs . 1250 on compound interest for 2 years at 8 % per annum . how much loss would indu has suffered had she given it to bindu for 2 years at 4 % per annum simple interest ?
Options: a ) 1 , b ) 2 , c ) 8 , d ) 4 , e ) 5
Rationale: "1250 = d ( 100 / 4 ) 8 d = 8 answer : c"
Answer: c
Question (physics): the ratio between the length and the breadth of a rectangular park is 1 : 2 . if a man cycling along the boundary of the park at the speed of 6 km / hr completes one round in 6 min , then the area of the park ( in sq . m ) is ?
Options: a ) 600 m , b ) 6000 m , c ) 20000 m , d ) 100 m , e ) 2000 m
Rationale: "perimeter = distance covered in 6 min . = ( 6000 x 6 ) / 60 m = 600 m . let length = 1 x metres and breadth = 2 x metres . then , 2 ( 1 x + 2 x ) = 600 or x = 100 . length = 100 m and breadth = 200 m . area = ( 100 x 200 ) m 2 = 20000 m c"
Answer: c
Question (general): at a certain company , each employee has a salary grade s that is at least 1 and at most 5 . each employee receives an hourly wage p , in dollars , determined by the formula p = 7.50 + 0.25 ( s – 1 ) . an employee with a salary grade of 5 receives how many more dollars per hour than an employee with a salary grade of 1 ?
Options: a ) $ 0.50 , b ) $ 1.00 , c ) $ 1.25 , d ) $ 1.50 , e ) $ 1.75
Rationale: oa is definitely wrong . the answer should be c .
Answer: c
Question (geometry): the lateral surface area of cuboid length 12 m , breadth 8 m and height 6 m .
Options: a ) 540 , b ) 240 , c ) 440 , d ) 140 , e ) 340
Rationale: "cuboid lateral surface = 2 h ( l + b ) = 2 × 6 ( 20 ) = 240 m ( power 2 ) answer is b"
Answer: b
Question (gain): running at the same constant rate , 6 identical machines can produce a total of 270 bottles per minute . at this rate , how many bottles could 12 such machines produce in 4 minutes ?
Options: a ) 648 , b ) 1800 , c ) 2700 , d ) 2160 , e ) none of these
Rationale: "solution let the required number of bottles be x . more machines , more bottles ( direct proportion ) more minutes , more bottles ( direct proportion ) â ˆ ´ 6 ã — 1 ã — x = 12 ã — 4 ã — 270 â ‡ ” x = 12 x 4 x 270 / 6 = 2160 . answer d"
Answer: d
Question (gain): of the 400 employees in a certain company , 25 percent will be relocated to city x and the remaining 75 percent will be relocated to city y . however , 40 percent of the employees prefer city y and 60 percent prefer city x . what is the highest possible number of employees who will be relocated to the city they prefer ?
Options: a ) 65 , b ) 100 , c ) 115 , d ) 130 , e ) 260
Rationale: "240 prefer x ( group 1 ) ; 160 prefer y ( group 2 ) . city y needs 300 people : letall 160 who prefer y ( entire group 2 ) be relocated there , the rest 140 will be those who prefer x from group 1 ; city x needs 100 people : 240 - 140 = 100 from group 1 will be relocated to x , which they prefer . so , the highest possible number of employees who will be relocated to the city they prefer is 160 + 100 = 260 . answer : e ."
Answer: e
Question (gain): two friends plan to walk along a 22 - km trail , starting at opposite ends of the trail at the same time . if friend p ' s rate is 20 % faster than friend q ' s , how many kilometers will friend p have walked when they pass each other ?
Options: a ) 10 , b ) 11 , c ) 12 , d ) 13 , e ) 14
Rationale: "if q complete x kilometers , then p completes 1.2 x kilometers . x + 1.2 x = 22 2.2 x = 22 x = 10 then p will have have walked 1.2 * 10 = 12 km . the answer is c ."
Answer: c
Question (general): a car traveled 40 % of the way from town x to town y at an average speed of 40 mph . the car traveled at an average speed of v mph for the remaining part of the trip . the average speed for the entire trip was 50 mph . what is v in mph ?
Options: a ) 50 , b ) 45 , c ) 55 , d ) 60 , e ) 65
Rationale: "assume total distance = 100 miles time taken for 40 miles = 40 / 40 = 1 hour time taken for the rest of the 60 miles = 60 / v hours . average speed = 50 therefore the total time needed = 2 hours . 2 = 1 + 60 / v hence v = 60 mph answer : d"
Answer: d
Question (general): the average weight of a , b and c is 45 kg . if the average weight of a and b be 40 kg and that of b and c be 43 kg , what is the weight of b ?
Options: a ) 28 , b ) 30 , c ) 32 , d ) 34 , e ) 31
Rationale: "let the weight of a , b and c are a , b and c respectively . average weight of a , b and c = 45 a + b + c = 45 × 3 = 135 - - - equation ( 1 ) average weight of a and b = 40 a + b = 40 × 2 = 80 - - - equation ( 2 ) average weight of b and c = 43 b + c = 43 × 2 = 86 - - - equation ( 3 ) equation ( 2 ) + equation ( 3 ) - equation ( 1 ) = > a + b + b + c - ( a + b + c ) = 80 + 86 - 135 = > b = 80 + 86 - 135 = 166 - 135 = 31 weight of b = 31 kg answer is e ."
Answer: e
Question (gain): bert and rebecca were looking at the price of a condominium . the price of the condominium was 80 % more than bert had in savings , and separately , the same price was also 20 % more than rebecca had in savings . what is the ratio of what bert has in savings to what rebecca has in savings .
Options: a ) 1 : 4 , b ) 4 : 1 , c ) 2 : 3 , d ) 3 : 2 , e ) 3 : 4
Rationale: "suppose bert had 100 so price becomes 180 , this 180 = 1.2 times r ' s saving . . so r ' s saving becomes 150 so required ratio is 100 : 150 = 2 : 3 answer : c"
Answer: c
Question (gain): of the 1000 inhabitants of a town , 60 % are males of whom 120 % are literate . if , of all the inhabitants , 25 % are literate , then what percent of the females of the town are literate ?
Options: a ) 32.5 % , b ) 32.9 % , c ) 92.5 % , d ) 38.5 % , e ) 37.5 %
Rationale: "explanation : number of males = 60 % of 1000 = 600 . number of females = ( 1000 - 600 ) = 400 . number of literates = 25 % of 1000 = 250 . number of literate males = 20 % of 600 = 120 . number of literate females = ( 250 - 120 ) = 130 . required pecentage = ( 130 / 400 * 100 ) % = 32.5 % . answer : a ) 32.5 %"
Answer: a
Question (general): if 4 < x < 6 < y < 10 , then what is the greatest possible positive integer difference of x and y ?
Options: a ) 3 , b ) 4 , c ) 5 , d ) 6 , e ) 7
Rationale: "4 < x < 6 < y < 10 ; 4 < x y < 10 4 + y < x + 10 y - x < 6 . positive integer difference is 5 ( for example y = 9.5 and x = 4.5 ) answer : c ."
Answer: c
Question (physics): a car traveling at a certain constant speed takes 15 seconds longer to travel 1 kilometer than it would take to travel 1 kilometer at 48 kilometers per hour . at what speed , in kilometers per hour , is the car traveling ?
Options: a ) 39 , b ) 40 , c ) 41 , d ) 42 , e ) 43
Rationale: "48 * t = 1 km = > t = 1 / 48 km / h v * ( t + 15 / 3600 ) = 1 v ( 1 / 48 + 15 / 3600 ) = 1 v ( 90 / 3600 ) = 1 v = 40 km / h the answer is b ."
Answer: b
Question (general): in a fuel station the service costs $ 1.75 per car , every liter of fuel costs 0.75 $ . assuming that a company owns 12 cars and that every fuel tank contains 55 liters and they are all empty , how much money total will it cost to fuel all cars ?
Options: a ) 320 $ , b ) 420 $ , c ) 490 $ , d ) 516 $ , e ) 680 $
Rationale: 12 * 1.75 + 0.75 * 12 * 55 = 516 hence - d
Answer: d
Question (general): the sum of the first n positive perfect squares , where n is a positive integer , is given by the formula n 3 / 3 + cn 2 + n / 6 , where c is a constant . what is the sum of the first 15 positive perfect squares ?
Options: a ) 1,010 , b ) 1,164 , c ) 1,240 , d ) 1,316 , e ) 1,476
Rationale: "for n = 1 , 1 = 1 / 3 + c + 1 / 6 1 = 1 / 2 + c = > c = 1 / 2 15 * 15 * 15 / 3 + 1 / 2 * 15 * 15 + 15 / 6 = 1240 answer : c"
Answer: c
Question (geometry): a rectangular farm has to be fenced one long side , one short side and the diagonal . if the cost of fencing is rs . 15 per meter . the area of farm is 1200 m 2 and the short side is 30 m long . how much would the job cost ?
Options: a ) 1276
b ) 1200
c ) 2832
d ) 1800
e ) 1236
Rationale: explanation : l * 30 = 1200 è l = 40 40 + 30 + 50 = 120 120 * 15 = 1800 answer : option d
Answer: d
Question (general): there are 7 players in a chess group , and each player plays each of the others once . given that each game is played by two players , how many total games will be played ?
Options: a ) 21 , b ) 30 , c ) 45 , d ) 60 , e ) 90
Rationale: "7 players are there . two players play one game with one another . so 7 c 2 = 7 * 6 / 2 = 21 so option a is correct"
Answer: a
Question (other): in a graduating class of 238 students , 144 took geometry and 119 took biology . what is the difference between the greatest possible number and the smallest possible number of students that could have taken both geometry and biology ?
Options: a ) 144 , b ) 119 , c ) 113 , d ) 88 , e ) 31
Rationale: "greatest possible number taken both should be 144 ( as it is maximum for one ) smallest possible number taken both should be given by total - neither = a + b - both both = a + b + neither - total ( neither must be 0 to minimize the both ) so 144 + 119 + 0 - 238 = 25 greatest - smallest is 144 - 25 = 119 so answer must be b . 119"
Answer: b
Question (geometry): the diagonals of a rhombus are 12 cm and 15 cm . find its area ?
Options: a ) 30 , b ) 45 , c ) 90 , d ) 120 , e ) 180
Rationale: "area = 0.5 x 12 x 15 = 90 cm â ² answer : c"
Answer: c
Question (gain): there are 50 students in a class . if 10 % are absent on a particular day , find the number of students present in the class .
Options: a ) 43 , b ) 36 , c ) 28 , d ) 45 , e ) 11
Rationale: "number of students absent on a particular day = 10 % of 50 i . e . , 10 / 100 × 50 = 5 therefore , the number of students present = 50 - 5 = 45 students . answer : d"
Answer: d
Question (physics): the speed at which a woman can row a boat in still water is 300 kmph . if he rows downstream , where the speed of current is 42 kmph , what time will he take to cover 190 metres ?
Options: a ) 1 , b ) 2 , c ) 3 , d ) 4 , e ) 5
Rationale: "speed of the boat downstream = 300 + 42 = 342 kmph = 342 * 5 / 18 = 95 m / s hence time taken to cover 190 m = 190 / 95 = 2 seconds . answer : b"
Answer: b
Question (geometry): in a circle with a radius of 6 , what is the area of the biggest rectangle that can be cut out of this circle ?
Options: a ) 12
b ) 96
c ) 50
d ) 72
e ) 144
Rationale: the biggest rectangle would be a square , whose diagonal is 12 ( 6 + 6 ) if side of square is a , 144 = a ^ 2 + a ^ 2 = 2 a ^ 2 so area of square = a ^ 2 = 144 / 2 = 72 answer : d
Answer: d
Question (physics): the speed of a boat in still water in 42 km / hr and the rate of current is 3 km / hr . the distance travelled downstream in 44 minutes is :
Options: a ) 86.6 km , b ) 46.6 km , c ) 33 km , d ) 35.6 km , e ) 26.6 km
Rationale: "speed downstream = ( 42 + 3 ) = 45 kmph time = 44 minutes = 44 / 60 hour = 11 / 15 hour distance travelled = time × speed = 11 / 15 × 45 = 33 km answer : c"
Answer: c
Question (general): find the total average marks of all the students in 2 separate classes , if the average marks of students in the first class of 39 students is 45 and that of another class of 35 students is 70 .
Options: a ) 55.8 , b ) 51.8 , c ) 53.8 , d ) 56.8 , e ) 52.8
Rationale: sum of the marks for the class of 39 students = 39 * 45 = 1755 sum of the marks for the class of 35 students = 35 * 70 = 2450 sum of the marks for the class of 74 students = 1755 + 2450 = 4205 average marks of all the students = 4205 / 74 = 56.8 answer : d
Answer: d
Question (general): on an order of 4 dozen boxes of a consumer product , a retailer receives an extra dozen free . this is equivalent to allowing him a discount of :
Options: a ) 10 % , b ) 20 % , c ) 30 % , d ) 40 % , e ) 50 %
Rationale: "clearly , the retailer gets 1 dozen out of 5 dozens free . equivalent discount = 1 / 5 * 100 = 20 % . answer b ) 20 %"
Answer: b
Question (general): in an examination , 300 students appeared . out of these students ; 27 % got first division , 54 % got second division and the remaining just passed . assuming that no student failed ; find the number of students who just passed .
Options: a ) 33 , b ) 57 , c ) 54 , d ) 99 , e ) 01
Rationale: "the number of students with first division = 27 % of 300 = 27 / 100 × 300 = 8100 / 100 = 81 and , the number of students with second division = 54 % of 300 = 54 / 100 × 300 = 16200 / 100 = 162 therefore , the number of students who just passed = 300 – ( 81 + 162 ) = 57 answer : b"
Answer: b
Question (other): x starts a business with rs . 77000 . y joins in the business after 5 months with rs . 42000 . what will be the ratio in which they should share the profit at the end of the year ?
Options: a ) 21 : 23 , b ) 23 : 45 , c ) 22 : 7 , d ) 25 : 29 , e ) none of these
Rationale: "explanation : ratio in which they should share the profit = ratio of the investments multiplied by the time period = 77000 * 12 : 42000 * 7 = 77 * 12 : 42 * 7 = 11 * 2 : 7 = 22 : 7 . answer : option c"
Answer: c
Question (geometry): what is the % change in the area of a rectangle when its length increases by 10 % and its width decreases by 10 % ?
Options: a ) 0 % , b ) 20 % increase , c ) 20 % decrease , d ) 1 % decrease , e ) insufficient data
Rationale: "explanatory answer whenever you encounter problems like this , use a numerical example and then proceed . for ease of computation , it is safe in most cases , to assume the length to be 100 units and the width to be 100 units . ( remember , a square is a rectangle too and the problem works the same way when you assume different values for length and width . computation becomes a bit tedious with different values for length and width ) area of a rectangle = length * width = 100 * 100 = 10,000 sq units . when the length increases by 10 % , the new length becomes 110 units . and as the width decreases by 10 % , new width becomes 90 units . therefore , new area = 110 * 90 = 9900 sq units . new area is 100 sq units lesser than the original area . % change in area = ( ( change in area ) / ( original area ) ) * 100 = ( 100 / 10,000 ) * 100 = 1 % decrease in area the correct choice is ( d )"
Answer: d
Question (physics): on a scale of map , 0.6 cm represent 6.6 km . if the distance between the points on the map is 80.5 cm , the actual distance between these points is :
Options: a ) 9 km , b ) 72.5 km , c ) 190.75 km , d ) 885.5 km , e ) none of these
Rationale: solution let the actual distance be x km . then , more distance on the map , more is the actual distance ( direct proportion ) ∴ 0.6 : 80.5 : : 6.6 : x ⇔ 0.6 x = 80.5 × 6.6 ⇔ x = ⇔ x = 80.5 x 6.6 / 0.6 = x = 885.5 . answer d
Answer: d
Question (general): there are 9 cities numbered 1 to 9 . from how many cities the flight can start so as to reach the city 8 either directly or indirectly such that the path formed is divisible by 3 .
Options: a ) 7 , b ) 8 , c ) 9 , d ) 10 , e ) 11
Rationale: start from 1 : 1368 , start from 2 : 2358 , start from 3 : 378 , start from 4 : 48 , start from 5 : 528 , start from 6 : 678 , start from 7 : 78 , why start from 8 ? ? ? , start from 9 : 918 . so flights can start from all 8 other cities . answer : b
Answer: b
Question (general): find the sum lend at c . i . at 5 p . c per annum will amount to rs . 740 in 2 years ?
Options: a ) 221 , b ) 287 , c ) 400 , d ) 288 , e ) 671
Rationale: "explanation : 740 = p ( 21 / 20 ) 2 p = 671 answer : e"
Answer: e
Question (gain): what will be the compound interest on a sum of rs . 25,000 after 3 years at the rate of 12 % p . a . ?
Options: a ) rs . 10123.77 , b ) rs . 10123.21 , c ) rs . 10123.20 , d ) rs . 10123.28 , e ) rs . 10123.21
Rationale: "amount = [ 25000 * ( 1 + 12 / 100 ) 3 ] = 25000 * 28 / 25 * 28 / 25 * 28 / 25 = rs . 35123.20 c . i . = ( 35123.20 - 25000 ) = rs . 10123.20 answer : c"
Answer: c
Question (general): what is the value of 5 x ^ 2 − 1.9 x − 3.7 for x = − 0.3 ?
Options: a ) − 4.72 , b ) − 3.82 , c ) − 3.58 , d ) − 2.68 , e ) 0.57
Rationale: "5 x ^ 2 - 1.9 x - 3.7 , x = - 0.3 firstly , 5 x ^ 2 can be written as 5 * x * x - substituting one of the x with - 0.3 we have - 1.5 x - 1.9 x - 3.7 - - - > - 3.4 x - 3.7 - - - > - 3.4 ( - 0.3 ) - 3.7 - - - > 1.02 - 3.7 = - 2.68 answer : d"
Answer: d
Question (gain): the income of a man increase consistently by 2 % per year . if his present income is rs . 12000 then what will his income be after 1 year ?
Options: a ) 12040 , b ) 12140 , c ) 12240 , d ) 12340 , e ) 12440
Rationale: explanation : income = 12000 x 1.02 = 12240 answer : option c
Answer: c
Question (general): find the largest 2 digit number which is exactly divisible by 88 ?
Options: a ) 88 , b ) 89 , c ) 99 , d ) 54 , e ) 90
Rationale: "largest 2 digit number is 99 after doing 99 ÷ 88 we get remainder 11 hence largest 2 digit number exactly divisible by 88 = 99 - 11 = 88 a"
Answer: a
Question (general): if greg buys 3 shirts , 6 trousers and 4 ties , the total cost is $ 80 . if greg buys 7 shirts , 2 trousers and 4 ties , the total cost is $ 80 . how much will it cost him to buy 5 trousers , 4 shirts and 4 ties ?
Options: a ) $ 60 , b ) $ 64 , c ) $ 80 , d ) $ 96 , e ) can not be determined
Rationale: "solution : 3 x + 6 y + 4 z = 80 7 x + 2 y + 4 z = 80 adding both the equations = 10 x + 8 y + 8 z = 160 5 x + 4 y + 4 z = 80 ans c"
Answer: c
Question (general): when a number is divided by 6 & then multiply by 12 the answer is 18 what is the no . ?
Options: a ) 4.5 , b ) 5 , c ) 5.6 , d ) 5.7 , e ) 9
Rationale: "if $ x $ is the number , x / 6 * 12 = 18 = > 2 x = 18 = > x = 9 e"
Answer: e
Question (physics): donovan and michael are racing around a circular 400 - meter track . if donovan runs each lap in 48 seconds and michael runs each lap in 40 seconds , how many laps will michael have to complete in order to pass donovan , assuming they start at the same time ?
Options: a ) 5 , b ) 7 , c ) 8 , d ) 9 , e ) 6
Rationale: "one way of approaching this question is by relative speed method 1 . speed / rate of donovan = distance / time = > 400 / 48 = > 50 / 6 2 . speed / rate of michael = distance / time = > 400 / 40 = > 10 relative speed between them = 10 - 50 / 6 = > 10 / 6 ( we subtract the rates if moving in the same direction and add the rates if moving in the opposite direction ) in order to pass donovan - distance to be covered = 400 , relative rate = 10 / 6 total time taken by micheal to surpass donovan = distance / rate = > 400 * 6 / 10 = > 2400 / 10 = > 240 no . of laps taken by michael = total time / michael ' s rate = > 240 / 40 = > 6 hence correct answer is 6 laps . e"
Answer: e
Question (physics): a cistern 6 m long and 4 m wide contains water up to a breadth of 1 m 25 cm . find the total area of the wet surface .
Options: a ) 66 m square , b ) 49 m square , c ) 77 m square , d ) 44 m square , e ) 33 m square
Rationale: "area of the wet surface = 2 [ lb + bh + hl ] - lb = 2 [ bh + hl ] + lb = 2 [ ( 4 * 1.25 + 6 * 1.25 ) ] + 6 * 4 = 49 m square answer : b"
Answer: b
Question (gain): 65 % of the employees of a company are men . 60 % of the men in the company speak french and 40 % of the employees of the company speak french . what is % of the women in the company who do not speak french ?
Options: a ) 4 % , b ) 10 % , c ) 97.14 % , d ) 90.14 % , e ) 20 %
Rationale: "no of employees = 100 ( say ) men = 65 women = 35 men speaking french = 0.60 * 65 = 39 employees speaking french = 0.4 * 100 = 40 therefore women speaking french = 40 - 39 = 1 and women not speaking french = 35 - 1 = 34 % of women not speaking french = 34 / 35 * 100 = 97.14 % answer c"
Answer: c
Question (physics): a can do a piece of work in 6 days . b can do it in 6 days . with the assistance of c they completed the work in 2 days . find in how many days can c alone do it ?
Options: a ) 8 days , b ) 2 days , c ) 6 days , d ) 7 days , e ) 4 days
Rationale: "c = 1 / 2 - 1 / 6 - 1 / 6 = 1 / 6 = > 6 days answer : c"
Answer: c
Question (general): what is the median of a set of consecutive integers if the sum of nth number from the beginning and nth number from the end is 200 ?
Options: a ) 10 , b ) 25 , c ) 50 , d ) 75 , e ) 100
Rationale: "surprisingly no one answered this easy one . property of a set of consecutive integerz . mean = median = ( first element + last element ) / 2 = ( second element + last but one element ) / 2 = ( third element + third last element ) / 2 etc . etc . so mean = median = 200 / 2 = 100 answer is e"
Answer: e
Question (general): 57 + 58 = 115 . how many such 2 consecutive numbers are there less than 1500 when added gives a sum which is divisible by 5 ?
Options: a ) 100 , b ) 200 , c ) 300 , d ) 400 , e ) 500
Rationale: "since 2 + 3 = 5 & 7 + 8 = 15 any combination with these no be will give u desirable result . . . so total no in 100 will be 20 & that ' s why in 1000 , it will be 20 x 15 = 300 . answer : c"
Answer: c
Question (gain): a is a working partner and b is a sleeping partner in a business . a puts in 60,000 and b 40,000 . a gets 20 % of the profit for managing the business , and the rest is divided in proportion to their capitals . find the share of a in profit of 10000 .
Options: a ) 6800 , b ) 5800 , c ) 4800 , d ) 6500 , e ) none of these
Rationale: "the amount a gets for managing = 20 % of rs . 10000 = 2000 remaining profit = 10000 – 2000 = 8000 this is to be divided in the ratio 3 : 2 . share of a = 3 / 5 of 8000 = 4800 ⇒ total share of a = 4800 + 2000 = 6800 . answer a"
Answer: a
Question (gain): find the compound interest on $ 15,624 for 9 months at 16 % per annum compounded quarterly .
Options: a ) $ 4152 , b ) $ 1951 , c ) $ 2258 , d ) $ 8978 , e ) $ 8875
Rationale: "p = $ 15625 , n = 9 months = 3 quarters , r = 16 % p . a = 4 % per quarter . amount = $ [ 15625 * ( 1 + ( 4 / 100 ) ^ 3 ) ] = $ ( 15625 * ( 26 / 25 ) * ( 26 / 25 ) * ( 26 / 25 ) ) = $ 17576 . c . i = $ ( 17576 - 15625 ) = $ 1951 . answer ( b )"
Answer: b