Cheukting/mathqa huggingface dataset:
Question (general): joan took out a mortgage from hel local bank . each monthly mortgage payment she makes must be triple the amount of the previous month ' s payment . if her first payment is $ 100 , and the total amount she must pay back is $ 36400 , how many months will it take joan to pay back her mortgage ?
Options: a ) 6 , b ) 8 , c ) 10 , d ) 11 , e ) 13
Rationale: "joan starts off with 100 $ . . which is to be tripled every month her monthly payments look like this : 100 , 300 , 900 , 2700 . . . . . . . . . upto 36400 this can be re written as : 100 x 1 , 100 x 3 , 100 x 9 , 100 x 27 . . . . . . 100 x 364 so we have 1 , 3 , 9 , 27 . . . . . 36400 in gp we know that a = 1 , and r = 3 ( its easy to figure it out by looking at the question , but regardless of it being mentioned in the question we can still compute the value of r using the formula tn = a 3 ^ n - 1 . . . ) therefore to find the sum of n terms of a gp we use this formula : sn = a ( 1 - r ^ n ) / 1 - r using this and plugging in the information we get . . . 364 = 1 - 3 ^ n / 1 - 3 ; 1 - 3 ^ n / - 2 cross multiplying we get 364 x - 2 = 1 - 3 ^ n - 728 = 1 - 3 ^ n - 729 = - 3 ^ n 729 = 3 ^ n ( negatives cancel out ) 729 can also be re written as 3 ^ 6 therefore ; 3 ^ 6 = 3 ^ n thus n = 6 ( a )"
Answer: a
Question (general): the average of first five multiples of 6 is
Options: a ) 3 , b ) 18 , c ) 9 , d ) 12 , e ) 15
Rationale: "solution average = 6 ( 1 + 2 + 3 + 4 + 5 ) / 5 = 90 / 5 . = 18 answer b"
Answer: b
Question (general): a big container is 35 % full with water . if 16 liters of water is added , the container becomes 3 / 4 full . what is the capacity of the big container in liters ?
Options: a ) 32 , b ) 40 , c ) 48 , d ) 54 , e ) 60
Rationale: "16 liters is 40 % of the capacity c . 16 = 0.4 c c = 16 / 0.4 = 40 liters . the answer is b ."
Answer: b
Question (general): in objective test a correct ans score 4 marks and on a wrong ans 2 marks are - - - . a student score 480 marks from 150 question . how many ans were correct ?
Options: a ) 120 , b ) 130 , c ) 110 , d ) 150 , e ) 180
Rationale: let x be the correct answer and y be the wrong answer so the total number of questions is ( x + y ) = 150 = > 4 x - 2 y = 480 = > 6 x = 780 hence x = 130 answer : b
Answer: b
Question (general): a number when divided by a certain divisor left remainder 251 , when twice the number was divided by the same divisor , the remainder was 112 . find the divisor ?
Options: a ) 370 , b ) 365 , c ) 390 , d ) 456 , e ) 460
Rationale: "easy solution : n = dq 1 + 251 2 n = 2 dq 1 + 502 - ( 1 ) 2 n = dq 2 + 112 - ( 2 ) as ( 1 ) = ( 2 ) = 2 n d * ( q 2 - 2 q 1 ) = 390 d * some integer = 390 checking all options only ( c ) syncs with it . answer c"
Answer: c
Question (general): excluding stoppages , the average speed of a bus is 120 km / hr and including stoppages , the average speed of the bus is 40 km / hr . for how many minutes does the bus stop per hour ?
Options: a ) 15 min , b ) 18 min , c ) 16 min , d ) 20 min , e ) 40 min
Rationale: "in 1 hr , the bus covers 120 km without stoppages and 40 km with stoppages . stoppage time = time take to travel ( 120 - 40 ) km i . e 80 km at 120 km / hr . stoppage time = 80 / 120 hrs = 40 min answer : e"
Answer: e
Question (general): the units digit of ( 10 ) ^ ( 87 ) + ( 93 ) ^ ( 46 ) is :
Options: a ) 9 , b ) 4 , c ) 6 , d ) 8 , e ) 0
Rationale: "first part will be zero always 2 nd part with power of three therefore , the second term has a units digit of 9 . of course 0 + 9 = 9 , a"
Answer: a
Question (gain): consider a lady took a loan from a bank at the rate of 12 % p . a . simple interest . after 3 years she had to pay rs . 9900 interest only for the period . the principal amount borrowed by her was
Options: a ) rs . 2000 , b ) rs . 27500 , c ) rs . 15000 , d ) rs . 20000 , e ) none of these
Rationale: "explanation : principal = rs . ( 100 × 9900 / 12 × 3 ) = > rs . 27500 . answer : b"
Answer: b
Question (gain): if the cost price is 96 % of the selling price , then what is the profit percent ?
Options: a ) 4.17 % , b ) 5 % , c ) 6.12 % , d ) 3.25 % , e ) 5.75 %
Rationale: "let s . p . = $ 100 c . p . = $ 96 profit = $ 4 profit % = 4 / 96 * 100 = 25 / 6 = 4.17 % answer is a"
Answer: a
Question (general): how many multiples of 5 are there between 70 and 358 ?
Options: a ) 54 , b ) 55 , c ) 56 , d ) 57 , e ) 58
Rationale: "5 * 14 = 70 5 * 71 = 355 total no of multiples = ( 71 - 14 ) + 1 = 57 + 1 = 58 answer is e ."
Answer: e
Question (gain): a , b and c invests rs . 6000 , rs . 5000 and rs . 3000 in a business . after one year c removed his money ; a and b continued the business for two more year . if the net profit after 3 years be rs . 4206 , then c ' s share in the profit is ?
Options: a ) 276 , b ) 289 , c ) 400 , d ) 350.5 , e ) 300
Rationale: "6 * 36 : 5 * 36 : 3 * 12 6 : 5 : 1 1 / 12 * 4206 = 350.50 answer : d"
Answer: d
Question (gain): a sum of money deposited at c . i . amounts to rs . 5000 in 5 years and to rs . 5750 in 6 years . find the rate percent ?
Options: a ) 1 % , b ) 5 % , c ) 10 % , d ) 15 % , e ) 20 %
Rationale: 5000 - - - 750 100 - - - ? = > 15 % answer : d
Answer: d
Question (physics): renu can do a piece of work in 6 days , but with the help of her friend suma , she can do it in 5 days . in what time suma can do it alone ?
Options: a ) 10 , b ) 12 , c ) 14 , d ) 15 , e ) 30
Rationale: renu â € ™ s one day â € ™ s work = 1 / 6 suma â € ™ s one day â € ™ s work = 1 / 5 - 1 / 6 = 1 / 30 suma can do it alone in 30 days . answer : e
Answer: e
Question (physics): if 5 machines can produce 20 units in 10 hours , how long would it take 20 machines to produce 160 units ?
Options: a ) 50 hours , b ) 40 hours , c ) 20 hours , d ) 12 hours , e ) 8 hours
Rationale: "here , we ' re told that 5 machines can produce 20 units in 10 hours . . . . that means that each machine works for 10 hours apiece . since there are 5 machines ( and we ' re meant to assume that each machine does the same amount of work ) , then the 5 machines equally created the 20 units . 20 units / 5 machines = 4 units are made by each machine every 10 hours now that we know how long it takes each machine to make 4 units , we can break this down further if we choose to . . . 10 hours / 4 units = 2.5 hours per unit when 1 machine is working . the prompt asks us how long would it take 20 machines to produce 160 units . if 20 machines each work for 2.5 hours , then we ' ll have 20 units . since 160 units is ' 8 times ' 20 , we need ' 8 times ' more time . ( 2.5 hours ) ( 8 times ) = 20 hours final answer : [ reveal ] spoiler : c"
Answer: c
Question (physics): a policeman noticed a criminal from a distance of 200 km . the criminal starts running and the policeman chases him . the criminal and the policeman run at the rate of 8 km and 9 km per hour respectively . what is the distance between them after 3 minutes ?
Options: a ) 100 m , b ) 120 m , c ) 130 m , d ) 150 m , e ) none of these
Rationale: "explanation : solution : relative speed = ( 9 - 8 ) = 1 km / hr . distance covered in 3 minutes = ( 1 * 3 / 60 ) km = 1 / 20 km = 50 m . . ' . distance between the criminal and policeman = ( 200 - 50 ) m = 150 m . answer : d"
Answer: d
Question (general): the average of 6 no . ' s is 3.95 . the average of 2 of them is 4 , while the average of theother 2 is 3.85 . what is the average of the remaining 2 no ' s ?
Options: a ) 4.2 , b ) 4.4 , c ) 4.6 , d ) 5.6 , e ) 4
Rationale: "sum of the remaining two numbers = ( 3.95 * 6 ) - [ ( 4 * 2 ) + ( 3.85 * 2 ) ] = 8 required average = ( 8 / 2 ) = 4 e"
Answer: e
Question (general): the population of a town increased from 50000 to 80000 in a decade . the average percent increase of population per year is :
Options: a ) 4.37 % , b ) 5 % , c ) 6 % , d ) 8.75 % , e ) none of these
Rationale: solution increase in 10 year = ( 80000 - 50000 ) = 30000 . increase % = ( 30000 / 50000 x 100 ) % = 60 % â ˆ ´ required average = ( 60 / 10 ) % = 6 % answer c
Answer: c
Question (physics): calculate the speed of a boat in still water ( in km / hr ) if in one hour , the boat goes 13 km / hr downstream and 10 km / hr upstream .
Options: a ) 3 kmph , b ) 9 kmph , c ) 4 kmph , d ) 8 kmph , e ) 6 kmph
Rationale: "speed in still water = ( 13 + 5 ) 1 / 2 kmph = 9 kmph . answer : b"
Answer: b
Question (probability): in a single throw of a die , what is the probability of getting a number greater than 2 ?
Options: a ) 1 / 2 , b ) 2 / 5 , c ) 1 / 3 , d ) 2 / 7 , e ) 2 / 3
Rationale: "s = { 1,2 , 3,4 , 5,6 } e = { 3,4 , 5,6 } probability = 4 / 6 = 2 / 3 answer is e"
Answer: e
Question (probability): what is the probability that when a hand o f 6 cards is drawn from a well shuffled deck of 52 cards , it contains 2 queen ?
Options: a ) 1 / 23445 , b ) 113 / 22434 , c ) 29187 by 1017926 , d ) 1017926 / 29187 , e ) none of these
Rationale: ncr = n ! / ( n - r ) ! r ! total number of possible hands = 52 c 6 52 c 6 = ( 52 ! ) / ( ( 52 - 6 ) ! × 6 ! ) 52 c 6 = 61075560 . number of hands with 2 queen and 4 non - queen cards = 4 c 2 × 48 c 4 4 c 2 = ( 4 ! ) / ( 2 ! × 2 ! ) = 6 . 48 c 4 = ( 48 ! ) / ( 44 ! × 4 ! ) = 3 × 47 × 46 × 45 = 291870 ( other 2 cards must be chosen from the rest 48 cards ) p ( 2 queen ) = ( 4 c 2 × 48 c 4 ) / 52 c 6 = 29187 / 1017926 c
Answer: c
Question (general): carina has 130 ounces of coffee divided into 5 - and 10 - ounce packages . if she has 2 more 5 - ounce packages than 10 - ounce packages , how many 10 - ounce packages does she have ?
Options: a ) 5 , b ) 6 , c ) 7 , d ) 8 , e ) 9
Rationale: "lets say 5 and 10 ounce packages be x and y respectively . given that , 5 x + 10 y = 130 and x = y + 2 . what is the value of y . substituting the x in first equation , 5 y + 10 + 10 y = 130 - > y = 120 / 15 . = 8 d"
Answer: d
Question (general): if x = 1 / q and y = ( 2 / q ) - 6 , then for what value of q , x is equal to y ?
Options: a ) 1 / 3 , b ) 1 / 6 , c ) 6 , d ) 3 , e ) 2
Rationale: explanation : x = y < = > 1 / q = ( 2 / q ) - 6 < = > 1 / q = 6 < = > q = 1 / 6 . answer : b
Answer: b
Question (gain): a watch was sold at a loss of 10 % . if it was sold for rs . 140 more , there would have been a gain of 4 % . what is the cost price ?
Options: a ) rs . 1000 , b ) rs . 1100 , c ) rs . 1200 , d ) rs . 1250 , e ) rs . 1500
Rationale: "explanation : 90 % 104 % - - - - - - - - 14 % - - - - 140 100 % - - - - ? = > rs . 1000 a )"
Answer: a
Question (physics): arun and tarun can do a work in 10 days . after 4 days tarun went to his village . how many days are required to complete the remaining work by arun alone . arun can do the work alone in 50 days .
Options: a ) 16 days . , b ) 17 days . , c ) 18 days . , d ) 30 days . , e ) 20 days .
Rationale: they together completed 4 / 10 work in 4 days . balance 6 / 10 work will be completed by arun alone in 50 * 6 / 10 = 30 days . answer : d
Answer: d
Question (general): a certain telescope increases the visual range at a particular location from 70 kilometers to 150 kilometers . by what percent is the visual range increased by using the telescope ?
Options: a ) 30 % , b ) 33 1 / 2 % , c ) 40 % , d ) 60 % , e ) 114.28 %
Rationale: "original visual range = 70 km new visual range = 150 km percent increase in the visual range by using the telescope = ( 150 - 70 ) / 70 * 100 % = 8 / 7 * 100 % = 114.28 % answer e"
Answer: e
Question (physics): circular gears l and r start to rotate at the same time at the same rate . gear l makes 10 complete revolutions per minute and gear r makes 40 revolutions per minute . how many seconds after the gears start to rotate will gear r have made exactly 9 more revolutions than gear l ?
Options: a ) a ) 6 , b ) b ) 8 , c ) c ) 10 , d ) d ) 18 , e ) e ) 15
Rationale: "gear l - - 10 rotations per 60 seconds - - 1 rotation per 6 seconds . gear r - - 40 rotations per 60 seconds - - 4 rotations per 6 seconds . first 6 seconds - - gear l makes 1 rotation . - - gear r makes 4 rotations - - net difference - - 3 rotations hence every 6 seconds the difference between the number of rotations of r and l gear is 3 units . required net difference should be 9 rotations = > 3 ( 6 seconds later ) = = > 18 seconds . answer : d ) ."
Answer: d
Question (gain): find the simple interest on rs . 68,000 at 16 2 / 3 % per annum for 9 months .
Options: a ) rs . 8500 , b ) rs . 8000 , c ) rs . 7500 , d ) rs . 7000 , e ) rs . 6500
Rationale: "p = rs . 68000 , r = 50 / 3 % p . a and t = 9 / 12 years = 3 / 4 years . s . i . = ( p * r * t ) / 100 = rs . ( 68,000 * ( 50 / 3 ) * ( 3 / 4 ) * ( 1 / 100 ) ) = rs . 8500 answer is a ."
Answer: a
Question (physics): three cubes of iron whose edges are 6 cm , 8 cm and 10 cm respectively are melted and formed into a single cube . the edge of the new cube formed is
Options: a ) 10 cm
b ) 12 cm
c ) 16 cm
d ) 18 cm
e ) none
Rationale: sol . volume of the new cube = ( 63 + 83 + 103 ) cm 3 = 1728 cm 3 . let the edge of the new cube be a cm . ∴ a 3 = 1728 ⇒ a = 12 . answer b
Answer: b
Question (physics): two trains are moving in the same direction at 126 kmph and 54 kmph . the faster train crosses a man in the slower train in 14 seconds . find the length of the faster train ?
Options: a ) 280 , b ) 290 , c ) 300 , d ) 310 , e ) 320
Rationale: "relative speed = ( 126 - 54 ) * 5 / 18 = 4 * 5 = 20 mps . distance covered in 27 sec = 14 * 20 = 280 m . the length of the faster train = 280 m . answer : a"
Answer: a
Question (general): if n is a prime number greater than 17 , what is the remainder when n ^ 2 is divided by 12 ?
Options: a ) 0 , b ) 1 , c ) 2 , d ) 3 , e ) 5
Rationale: "there are several algebraic ways to solve this question , but the easiest way is as follows : since we can not have two correct answers just pick a prime greater than 17 , square it and see what would be the remainder upon division of it by 12 . n = 19 - - > n ^ 2 = 361 - - > remainder upon division 361 by 12 is 1 . answer : b ."
Answer: b
Question (general): what is the remainder when 17 ^ 200 is divided by 18 ?
Options: a ) 3 , b ) 1 , c ) 2 , d ) 4 , e ) 7
Rationale: "( 17 ^ 200 - 1 ^ 200 ) is completely divisible by ( 17 + 1 ) as 200 is even . = > ( 17 ^ 200 - 1 ) is completely divisible by 18 . hence , when 17 ^ 200 is divided by 18 , we will get 1 as remainder . answer is b"
Answer: b
Question (geometry): a block of wood has dimensions 10 cm x 10 cm x 90 cm . the block is painted red and then cut evenly at the 45 cm mark , parallel to the sides , to form two rectangular solids of equal volume . what percentage of the surface area of each of the new solids is not painted red ?
Options: a ) 5 % , b ) 10 % , c ) 15 % , d ) 20 % , e ) 25 %
Rationale: "the area of each half is 100 + 4 ( 450 ) + 100 = 2000 the area that is not painted is 100 . the fraction that is not painted is 100 / 2000 = 1 / 20 = 5 % the answer is a ."
Answer: a
Question (general): after 6 games , team b had an average of 75 points per game . if it got only 47 points in game 7 , how many more points does it need to score to get its total above 500 ?
Options: a ) 5 , b ) 4 , c ) 7 , d ) 3 , e ) 8
Rationale: "( 6 * 75 ) + 47 + x > 500 450 + 47 + x > 500 497 + x > 500 = > x > 3 option d"
Answer: d
Question (other): if both 5 ^ 2 and 3 ^ 3 are factors of n x ( 2 ^ 5 ) x ( 6 ) x ( 7 ^ 3 ) , what is the smallest possible positive value of n ?
Options: a ) 75 , b ) 125 , c ) 145 , d ) 175 , e ) 225
Rationale: ( 2 ^ 5 ) x ( 6 ) x ( 7 ^ 3 ) has one appearance of 3 ( in the 6 ) and no appearances of 5 . thus n must include at least 3 ^ 2 * 5 ^ 2 = 9 * 25 = 225 the answer is e .
Answer: e
Question (physics): a can finish a work in 36 days , b in 9 days and c in 2 days , b and c start the work but are forced to leave after 3 days . the remaining work was done by a in ?
Options: a ) 15 days , b ) 12 days , c ) 6 days , d ) 7 days , e ) 8 days
Rationale: "b + c 1 day work = 1 / 9 + 1 / 12 = 7 / 36 work done by b and c in 3 days = 7 / 36 * 3 = 7 / 12 remaining work = 1 - 7 / 12 = 5 / 12 1 / 36 work is done by a in 1 day 5 / 12 work is done by a in 36 * 5 / 12 = 15 days answer is a"
Answer: a
Question (physics): there are 20 poles with a constant distance between each pole . a car takes 26 second to reach the 12 th pole . how much will it take to reach the last pole .
Options: a ) 44.4543 , b ) 44.9091 , c ) 44.95128 , d ) 44.91288 , e ) 44.91222
Rationale: "assuming the car starts at the first pole . to reach the 12 th pole , the car need to travel 11 poles ( the first pole does n ' t count , as the car is already there ) . 11 poles 26 seconds 1 pole ( 26 / 11 ) seconds to reach the last ( 20 th ) pole , the car needs to travel 19 poles . 19 pole 19 x ( 26 / 11 ) seconds = 44.9091 seconds answer : b"
Answer: b
Question (general): p has $ 21 more than what q and r together would have had if both b and c had 1 / 5 of what p has . how much does p have ?
Options: a ) $ 35 , b ) $ 36 , c ) $ 37 , d ) $ 38 , e ) $ 39
Rationale: "p = ( 2 / 5 ) * p + 21 ( 3 / 5 ) * p = 21 p = 35 the answer is a ."
Answer: a
Question (general): a large box contains 18 small boxes and each small box contains 25 chocolate bars . how many chocolate bars are in the large box ?
Options: a ) 350 , b ) 250 , c ) 450 , d ) 550 , e ) 650
Rationale: "the number of chocolate bars is equal to 18 ? 25 = 450 correct answer c"
Answer: c
Question (gain): because he ’ s taxed by his home planet , mork pays a tax rate of 40 % on his income , while mindy pays a rate of only 30 % on hers . if mindy earned 5 times as much as mork did , what was their combined tax rate ?
Options: a ) 32.5 % , b ) 34 % , c ) 35 % , d ) 31.67 % , e ) 37.5 %
Rationale: "say morks income is - 100 so tax paid will be 40 say mindys income is 5 * 100 = 500 so tax paid is 30 % * 500 = 150 total tax paid = 40 + 150 = 190 . combined tax % will be 190 / 100 + 500 = 31.67 %"
Answer: d
Question (general): if p ( a ) = 0.4 , p ( b ) = 0.6 and p ( a ∪ b ) = 0.8 . what is the value of p ( a ∩ b ' ) = ?
Options: a ) 0.1 , b ) 0.2 , c ) 0.3 , d ) 0.4 , e ) none
Rationale: "solution : p ( a ∪ b ) = p ( a ) + p ( b ) - p ( a ∩ b ' ) = > 0.8 = 0.4 - p ( a ∩ b ) = > p ( a ∩ b ) = 0.2 p ( a ∩ b ' ) = p ( a ) - p ( a ∩ b ) = 0.4 - 0.2 = 0.2 answer b"
Answer: b
Question (gain): a started a business with an investment of rs . 70000 and after 6 months b joined him investing rs . 120000 . if the profit at the end of a year is rs . 26000 , then the share of b is ?
Options: a ) s . 12028 , b ) s . 12000 , c ) s . 12003 , d ) s . 12029 , e ) s . 24029
Rationale: "ratio of investments of a and b is ( 70000 * 12 ) : ( 120000 * 6 ) = 7 : 6 total profit = rs . 26000 share of b = 6 / 13 ( 26000 ) = rs . 12000 answer : b"
Answer: b
Question (general): find the number which is nearest to 3105 and is exactly divisible by 21 .
Options: a ) 1208 , b ) 3108 , c ) 241 , d ) 217 , e ) 3147
Rationale: "sol . on dividing 3105 by 21 , we get 18 as remainder . number to be added to 3105 = ( 21 - 18 ) - 3 . hence , required number = 3105 + 3 = 3108 . option b"
Answer: b
Question (general): evaluate : 980 x 436 + 980 x 764
Options: a ) 1176000 , b ) 968000 , c ) 978000 , d ) 117000 , e ) none of them
Rationale: "980 x 436 + 980 x 764 = 986 x ( 436 + 664 ) = 986 x 1200 = 117600 . answer is a ."
Answer: a
Question (other): how many terminating zeroes r does 200 ! have ?
Options: a ) 40 , b ) 48 , c ) 49 , d ) 55 , e ) 64
Rationale: you have 40 multiples of 5 , 8 of 25 and 1 of 125 . this will give 49 zeros . c
Answer: c
Question (geometry): a girl walking at the rate of 9 km per hour crosses a square field diagonally in 12 seconds . the area of the field is :
Options: a ) 430 sq . m
b ) 425 sq . m
c ) 450 sq . m
d ) 475 sq . m
e ) 350 sq . m
Rationale: distance covered in ( 9 × 1000 ) / ( 3600 ) × 12 = 30 m diagonal of squarre field = 30 m . area of square field = 30 ( power ) 2 / 2 = 900 / 2 = 450 sq . m answer is c .
Answer: c
Question (probability): x , y , and z are all unique numbers . if x is chosen randomly from the set { 6 , 7 , 8 , 9 , 10 , 11 } and y and z are chosen randomly from the set { 20 , 21 , 22 , 23 } , what is the probability that x and y are prime and z is not ?
Options: a ) 1 / 5 , b ) 3 / 20 , c ) 2 / 15 , d ) 1 / 12 , e ) 1 / 10
Rationale: "p ( x is prime ) = 1 / 3 p ( y is prime ) = 1 / 4 if y is prime , then z is not prime since y and z are unique . then the probability is 1 / 3 * 1 / 4 = 1 / 12 the answer is d ."
Answer: d
Question (general): what is the total number of integers between 20 and 100 that are divisible by 9 ?
Options: a ) 5 , b ) 15 , c ) 12 , d ) 7 , e ) 9
Rationale: "27 , 36 , 45 , . . . , 90,99 this is an equally spaced list ; you can use the formula : n = ( largest - smallest ) / ( ' space ' ) + 1 = ( 99 - 27 ) / ( 9 ) + 1 = 8 + 1 = 9 answer is e"
Answer: e
Question (geometry): the perimeter of a triangle is 40 cm and the inradius of the triangle is 2.5 cm . what is the area of the triangle
Options: a ) a ) 72 , b ) b ) 828 , c ) c ) 50 , d ) d ) 34 , e ) e ) 35
Rationale: "explanation : area of a triangle = r * s where r is the inradius and s is the semi perimeter of the triangle . area of triangle = 2.5 * 40 / 2 = 50 cm 2 answer : option c"
Answer: c
Question (gain): the price of an article is cut by 10 % . to restore it to the former value . the new price must be increased by ?
Options: a ) 10 % , b ) 9 1 / 11 , c ) 11 1 / 9 , d ) 11 % , e ) none of these
Rationale: answer let original price = rs . 100 . then , new price = rs . 90 . ∴ increased on rs . 90 = rs . 10 required increase % = ( 10 x 100 ) / 90 % = 111 / 9 % correct option : c
Answer: c
Question (other): the probability that event b occurs is 0.6 , and the probability that events a and b both occur is 0.25 . if the probability that either event a or event b occurs is 0.4 , what is the probability that event a will occur ?
Options: a ) 0.05 , b ) 0.15 , c ) 0.45 , d ) 0.5 , e ) 0.55
Rationale: p ( a or b ) = p ( a ) + p ( b ) - p ( a n b ) 0.4 = 0.6 + p ( a ) - 0.25 p ( a ) = 0.05 ans : a
Answer: a
Question (other): if x and y are both odd prime numbers and x < y , how many distinct positive integer e factors does 2 xy have ?
Options: a ) 3 , b ) 4 , c ) 6 , d ) 8 , e ) 12
Rationale: since 2 xy prime e factors are x ^ 1 * y ^ 1 * 2 ^ 1 , its total number or factors must be ( 1 + 1 ) ( 1 + 1 ) ( 1 + 1 ) = 2 ^ 3 = 8 . thus , i think d would be the correct answer .
Answer: d
Question (other): in a certain group of 10 developers , 4 developers code only in python and the rest program in either ruby on rails or php - but not both . if a developer organization is to choose a 3 - member team , which must have at least 1 developer who codes in python , how many different programming teams can be chosen ?
Options: a ) 100 , b ) 40 , c ) 66 , d ) 80 , e ) 75
Rationale: two ways . . . 1 ) total ways = 10 c 3 = 10 ! / 7 ! 3 ! = 120 . . ways without python developer = 6 c 3 = 6 ! / 3 ! 3 ! = 20 . . ways of at least one python developer = 120 - 20 = 100 . . 2 ) ways of selecting only one = 4 * 6 c 2 = 4 * 15 = 60 . . ways of selecting only two = 4 c 2 * 6 c 1 = 6 * 6 = 36 . . ways of selecting all three = 4 c 3 = 4 = 4 . . total = 60 + 36 + 4 = 100 . . . answer : a
Answer: a
Question (gain): a dishonest shopkeeper professes to sell pulses at the cost price , but he uses a false weight of 920 gm . for a kg . his gain is … % .
Options: a ) 5.26 % , b ) 5.36 % , c ) 4.26 % , d ) 6.26 % , e ) 8.69 %
Rationale: "his percentage gain is 100 * 80 / 920 as he is gaining 80 units for his purchase of 920 units . so 8.69 % . answer : e"
Answer: e
Question (general): 5.40 can be expressed in terms of percentage as
Options: a ) 5.04 % , b ) 50.4 % , c ) 209 % , d ) 540 % , e ) none of these
Rationale: "explanation : while calculation in terms of percentage we need to multiply by 100 , so 5.40 * 100 = 540 answer : option d"
Answer: d