Cheukting/mathqa huggingface dataset:
Question (general): the average of 15 numbers is calculated as 20 . it is discovered later on that while calculating the average , one number namely 36 was wrongly read as 26 . the correct average is ?
Options: a ) 30 , b ) 26 , c ) 16 , d ) 97 , e ) 12
Rationale: "15 * 20 + 36 – 26 = 300 / 10 = 30 answer : a"
Answer: a
Question (geometry): what is the area of a square field whose diagonal of length 16 m ?
Options: a ) 128 , b ) 289 , c ) 200 , d ) 112 , e ) 178
Rationale: "d 2 / 2 = ( 16 * 16 ) / 2 = 128 answer : a"
Answer: a
Question (general): the avg age of an adult class is 40 years . 12 new students with an avg age of 32 years join the class . therefore decreasingthe avg by 4 year . find what was the original strength of class ?
Options: a ) 8 , b ) 12 , c ) 15 , d ) 16 , e ) 19
Rationale: let original strength = y then , 40 y + 12 x 32 = ( y + 12 ) x 36 ⇒ 40 y + 384 = 36 y + 432 ⇒ 4 y = 48 ∴ y = 12 b
Answer: b
Question (physics): what distance will be covered by a bus moving at 108 kmph in 30 seconds ?
Options: a ) 287 , b ) 600 , c ) 289 , d ) 276 , e ) 900
Rationale: "108 kmph = 108 * 5 / 18 = 30 mps d = speed * time = 30 * 30 = 900 m . answer : e"
Answer: e
Question (gain): vijay sells a cupboard at 12 % below cost price . had he got rs . 1500 more , he would have made a profit of 12 % . what is the cost price of the cupboard ?
Options: a ) 7450 , b ) 14900 , c ) 6250 , d ) 6000 , e ) none of these
Rationale: "explanation : cost price = 1500 / ( 0.12 + 0.12 ) = 1500 / 0.24 = rs . 6250 answer c"
Answer: c
Question (physics): if 20 men can build a wall 112 metres long in 6 days , what length of a similar wall can be built by 30 men in 3 days ?
Options: a ) 65 mtr . , b ) 84 mtr , c ) 70 mtr . , d ) 78 mtr . , e ) 17 mtr .
Rationale: 20 men is 6 days can build 112 metres 30 men in 3 days can build = 112 * ( 30 / 20 ) x ( 3 / 6 ) = 84 meters answer : b .
Answer: b
Question (physics): if the speed of a man is 57 km per hour , then what is the distance traveled by him in 30 seconds ?
Options: a ) 275 m , b ) 360 m , c ) 475 m , d ) 420 m , e ) 440 m
Rationale: "the distance traveled in 30 sec = 57 * ( 5 / 18 ) * 30 = 475 m answer : c"
Answer: c
Question (gain): victor gets 90 % marks in examinations . if these are 405 marks , find the maximum marks .
Options: a ) 334 , b ) 500 , c ) 376 , d ) 450 , e ) 271
Rationale: "let the maximum marks be m then 90 % of m = 405 ⇒ 90 / 100 × m = 405 ⇒ m = ( 405 × 100 ) / 90 ⇒ m = 40500 / 90 ⇒ m = 450 therefore , maximum marks in the examinations are 450 answer : d"
Answer: d
Question (general): there are 3 fictions and 6 non - fictions . how many cases are there such that 2 fictions and 2 non - fictions are selected from them ?
Options: a ) 90 , b ) 120 , c ) 45 , d ) 180 , e ) 200
Rationale: "number of ways of selecting 2 fiction books = 3 c 2 number of ways of selecting 2 non fiction books = 6 c 2 3 c 2 * 6 c 2 = 3 * 15 = 45 answer : c"
Answer: c
Question (general): when positive integer n is divided by positive integer j , the remainder is 16 . if n / j = 134.08 , what is value of j ?
Options: a ) 22 , b ) 56 , c ) 78 , d ) 112 , e ) 200
Rationale: "when a number is divided by another number , we can represent it as : dividend = quotient * divisor + remainder so , dividend / divisor = quotient + remainder / divisor given that n / j = 134.08 here 134 is the quotient . given that remainder = 16 so , 134.08 = 134 + 16 / j so , j = 200 ans e"
Answer: e
Question (geometry): find the circumference and area of radius 13 cm .
Options: a ) 124 cm ² , b ) 531 cm ² , c ) 354 cm ² , d ) 584 cm ² , e ) 594 cm ²
Rationale: "area of circle = π r ² = 22 / 7 × 13 × 13 cm ² = 531 cm ² answer : b"
Answer: b
Question (general): ( 0.0048 ) ( 3.5 ) / ( 0.05 ) ( 0.1 ) ( 0.004 ) =
Options: a ) 8.4 , b ) 840 , c ) 84.0 , d ) 0.84 , e ) 0.084
Rationale: ( 0.0048 ) ( 3.5 ) / ( 0.05 ) ( 0.1 ) ( 0.004 ) = 0.0048 * 350 / 5 ( 0.1 ) ( 0.004 ) = 0.048 * 70 / 1 ( 0.004 ) = 48 * 70 / 4 = 12 * 70 = 840 answer : b
Answer: b
Question (general): a batsman in his 17 th innings makes a score of 85 , and thereby increases his average by 3 . what is his average after the 17 th innings ? he had never been ’ not out ’ .
Options: a ) 47 , b ) 37 , c ) 39 , d ) 43 , e ) 42
Rationale: average score before 17 th innings = 85 - 3 × 17 = 34 average score after 17 th innings = > 34 + 3 = 37 answer : b
Answer: b
Question (geometry): a snooker tournament charges $ 40.00 for vip seats and $ 15.00 for general admission ( “ regular ” seats ) . on a certain night , a total of 300 tickets were sold , for a total cost of $ 7,500 . how many fewer tickets were sold that night for vip seats than for general admission seats ?
Options: a ) 190 , b ) 180 , c ) 150 , d ) 200 , e ) 300
Rationale: "let no of sits in vip enclosure is x then x * 40 + 15 ( 300 - x ) = 7500 or 25 x = 7500 - 4500 , x = 3000 / 25 = 120 vip = 120 general 200 d"
Answer: d
Question (physics): a hiker walked for 3 days . she walked 18 miles on the first day , walking 3 miles per hour . on the second day she walked for one less hour but she walked one mile per hour , faster than on the first day . on the third day she walked the same number of hours as on the first day , but at the same speed as on the second day . how many miles in total did she walk ?
Options: a ) 24 , b ) 44 , c ) 58 , d ) 60 , e ) 62
Rationale: first day - 18 miles with 3 miles per hours then total - 6 hours for that day second day - 4 miles per hour and 5 hours - 20 miles third day - 4 miles per hour and 6 hours - 24 miles total 18 + 20 + 24 - 62 answer : option e .
Answer: e
Question (general): sum of two numbers is 30 . two times of the first exceeds by 10 from the three times of the other . then the numbers will be ?
Options: a ) 14 , 16 , b ) 16 , 14 , c ) 18 , 12 , d ) 12 , 18 , e ) 17 , 13
Rationale: "explanation : x + y = 30 2 x ã ¢ â ‚ ¬ â € œ 3 y = 10 x = 16 y = 14 answer : b"
Answer: b
Question (physics): a runner runs the 40 miles from marathon to athens at a constant speed . halfway through the run she injures her foot , and continues to run at half her previous speed . if the second half takes her 4 hours longer than the first half , how many hours did it take the runner to run the second half ?
Options: a ) 6 , b ) 7 , c ) 8 , d ) 9 , e ) 10
Rationale: "the runner runs the first 20 miles at speed v and the second 20 miles at speed v / 2 . the time t 2 to run the second half must be twice the time t 1 to run the first half . t 2 = 2 * t 1 = t 1 + 4 t 1 = 4 and so t 2 = 8 . the answer is c ."
Answer: c
Question (physics): a man can do a job in 15 days . his father takes 20 days and his son finishes it in 25 days . how long will they take to complete the job if they all work together ?
Options: a ) 6.4 days , b ) 4.4 days , c ) 5.4 days , d ) 8.4 days , e ) 2.4 days
Rationale: a 6.4 days 1 day work of the three persons = ( 1 / 15 + 1 / 20 + 1 / 25 ) = 47 / 300 so , all three together will complete the work in 300 / 47 = 6.4 days . -
Answer: a
Question (gain): cricket match is conducted in us . the run rate of a cricket game was only 3.2 in first 10 over . what should be the run rate in the remaining 40 overs to reach the target of 272 runs ?
Options: a ) 6 , b ) 6.25 , c ) 7.25 , d ) 7.5 , e ) 8
Rationale: required run rate = 272 - ( 3.2 x 10 ) = 240 = 6 40 40 a
Answer: a
Question (gain): two numbers are less than third number by 34 % and 37 % respectively . how much percent is the second number less than by the first
Options: a ) 8 % , b ) 10 % , c ) 9 % , d ) 11 % , e ) 22 %
Rationale: "let the third number is x . then first number = ( 100 - 34 ) % of x = 66 % of x = 66 x / 100 second number is ( 63 x / 100 ) difference = 66 x / 100 - 63 x / 100 = 3 x / 100 so required percentage is , difference is what percent of first number ( 3 x / 100 * 100 / 63 x * 100 ) % = 22 % answer : e"
Answer: e
Question (gain): how many liters of a 40 % iodine solution need to be mixed with 35 liters of a 20 % iodine solution to create a 30 % iodine solution ?
Options: a ) 30.5 , b ) 49 , c ) 100 , d ) 105 , e ) 140
Rationale: "solution 1 : assume the iodine solution to be mixed = x lts . iodine = 0.4 x lts , water = 0.6 x lts . solution 2 : 35 liters of a 20 % iodine solution iodine = 7 lts , water = 28 lts . total iodine = 0.4 x + 7 total water = 0.6 x + 28 the resultant is a 35 % idoine solution . hence ( 0.4 x + 7 ) / ( x + 35 ) = 30 / 100 40 x + 700 = 30 x + 1050 10 x = 305 x = 30.5 lts correct option : a"
Answer: a
Question (general): of the total amount that jill spent on a shopping trip , excluding taxes , she spent 50 percent on clothing , 20 percent on food , and 30 percent on other items . if jill paid a 5 percent tax on the clothing , no tax on the food , and an 10 percent tax on all other items , then the total tax that she paid was what percent of the total amount that she spent , excluding taxes ?
Options: a ) 5.5 % , b ) 3.6 % , c ) 4.4 % , d ) 5.2 % , e ) 6.0 %
Rationale: "let amount spent by jill = 100 clothing = 50 , food = 20 , others = 30 tax on clothing = 2.5 tax on others = 3 percentage = 5.5 / 100 = 5.5 % answer : a"
Answer: a
Question (general): in a certain warehouse , 70 percent of the packages weigh less than 75 pounds , and a total of 48 packages weigh less than 25 pounds . if 80 percent of the packages weigh at least 25 pounds , how many of the packages weigh at least 25 pounds but less than 75 pounds ?
Options: a ) 8 , b ) 64 , c ) 120 , d ) 102 , e ) 144
Rationale: if 80 % of the packages weigh at least 25 pounds this means that 20 % of the packages weigh less than 25 pounds let t = total number of packages so , 20 % of t = # of packages that weigh less than 25 pounds 48 packages weigh less than 25 pounds great . so , 20 % of t = 48 rewrite to get : 0.2 t = 48 solve : t = 240 70 % of the packages weigh less than 75 pounds so , 70 % oft = number of packages that weigh less than 75 pounds 70 % of 240 = 168 , so 168 packages weigh less than 75 pounds of those 168 packages that weigh less than 75 pounds , 48 packages weigh less than 25 pounds . so , the number of packages that weight between 25 and 75 pounds = 168 - 48 = 120 = c
Answer: c
Question (other): in the standard formulation of a flavored drink the ratio by volume of flavoring to corn syrup to water is 1 : 12 : 30 . in the sport formulation , the ratio of flavoring to corn syrup is 3 times as great as in the standard formulation , and the ratio of flavoring to water is half that of the standard formulation . if a large bottle of the sport formulation contains 2 ounces of corn syrup , how many ounces of water does it contain ?
Options: a ) 15 , b ) 30 , c ) 45 , d ) 60 , e ) 90
Rationale: standard : fl : corn s : water = 1 : 12 : 30 sport : fl : corn s : water = 3 : 12 : 180 this simplifies to 1 : 4 : 60 if the large bottle has a capacity of x ounces , then 4 x / 65 = 2 . so , x = 32.5 ounces . water = ( 60 / 65 ) * ( 65 / 2 ) = = 30 ounces . ans b
Answer: b
Question (physics): a machine , working at a constant rate , manufactures 18 pens in 30 minutes . how many pens does it make in 1 hr 45 min ?
Options: a ) 63 , b ) 65 , c ) 62 , d ) 60 , e ) 45
Rationale: change 1 hr 45 min to 105 min . for this , we need to set up a simple proportion of pens per time 18 / 30 = s / 105 the absolutely worst thing you could do at this point in the problem is to cross - multiply . that would be a supremely unstrategic move . instead , cancel before you multiply . for what we can see this post . we can cancel 18 / 30 as 6 / 10 6 / 10 = s / 105 we can cross - multiply . 10 * s = 6 * 105 = 630 if we divide both sides by 10 , s = 63 the machine would be 63 pens in 1 hr 45 min . answer : a
Answer: a
Question (physics): a car traveling at a certain constant speed takes 2 seconds longer to travel 1 kilometer than it would take to travel 1 kilometer at 225 kilometers per hour . at what speed , in kilometers per hour , is the car traveling ?
Options: a ) 220 , b ) 200 , c ) 210 , d ) 225 , e ) 230
Rationale: "b 225 * t = 1 km = > t = 1 / 225 km / h v * ( t + 2 / 3600 ) = 1 v ( 1 / 225 + 2 / 3600 ) = 1 = > v = 200 km / h"
Answer: b
Question (general): if ( - 7 ) ^ ( 8 x ) = 7 ^ ( 12 - 5 x ) and x is an integer , what is the value of x ?
Options: a ) 5 , b ) - 4 , c ) 1 , d ) 2 , e ) 3
Rationale: "since x is an integer , ( - 7 ) ^ ( 8 x ) is always positive . so , 7 ^ 8 x = 7 ^ ( 13 - 5 x ) 8 x = 12 - 5 x 12 x = 12 x = 1 answer : c"
Answer: c
Question (gain): a library branch originally contained 18360 volumes , 30 % of which were fiction novels . 1 / 4 of the volumes were transferred to another location and 1 / 3 of the volumes transferred were fiction novels . what percent of the remaining collection was fiction novels ?
Options: a ) 2.5 % , b ) 17.67 % , c ) 28.8 % , d ) 45.2 % , e ) 73.6 %
Rationale: "fiction novels = 5,508 transferred to another location = 4590 transferred fiction novels = 1530 non transferred fiction novels = 3,978 percent of the remaining collection was fiction novels = 3978 / ( 18360 - 4590 ) * 100 = > 28.888 . . . % hence answer will be ( c )"
Answer: c
Question (general): ( 51 + 52 + 53 + … … … + 100 ) is equal to :
Options: a ) 2525 , b ) 2975 , c ) 3225 , d ) 3775 , e ) 3885
Rationale: "( 51 + 52 + 53 + … … … + 100 ) = ( 1 + 2 + 3 + … … . + 100 ) - ( 1 + 2 + 3 + 4 + … … + 50 ) = ( 100 * 101 ) / 2 - ( 50 * 51 ) / 2 = ( 5050 - 1275 ) = 3775 . answer : d"
Answer: d
Question (general): the mean of 50 observations was 30 . it was found later that an observation 48 was wrongly taken as 23 . the corrected new mean is
Options: a ) 35.2 , b ) 36.1 , c ) 30.5 , d ) 39.1 , e ) none
Rationale: "sol . therefore correct sum = ( 30 × 50 + 48 – 23 ) = 1525 . therefore correct mean = 1525 / 50 = 30.5 . answer c"
Answer: c
Question (physics): a train running at the speed of 60 km / hr crosses a pole in 42 seconds . what is the length of the train ?
Options: a ) 120 metres , b ) 700 metres , c ) 324 metres , d ) 828 metres , e ) 600 metres
Rationale: "speed = 60 x 5 / 18 m / sec = 50 / 3 m / sec . length of the train = ( speed x time ) . length of the train = 50 / 3 x 42 m = 150 m . option b"
Answer: b
Question (general): the average weight of 6 person ' s increases by 3.5 kg when a new person comes in place of one of them weighing 47 kg . what might be the weight of the new person ?
Options: a ) 60 kg , b ) 75 kg , c ) 68 kg , d ) 85 kg , e ) 90 kg
Rationale: "total weight increased = ( 6 x 3.5 ) kg = 21 kg . weight of new person = ( 47 + 21 ) kg = 68 kg option c"
Answer: c
Question (physics): ajay can walk 6 km in 1 hour . in how many hours he can walk 70 km ?
Options: a ) 5 hrs , b ) 11.6 hrs , c ) 15.6 hrs , d ) 20.1 hrs , e ) 30 hrs
Rationale: "1 hour he walk 6 km he walk 70 km in = 70 / 6 * 1 = 11.6 hours answer is b"
Answer: b
Question (physics): the speed of a boat in still water in 18 km / hr and the rate of current is 6 km / hr . the distance travelled downstream in 14 minutes is :
Options: a ) 11.4 km , b ) 10.9 km , c ) 10.4 km , d ) 6.06 km , e ) 12.56 km
Rationale: "explanation : speed downstream = ( 18 + 6 ) = 24 kmph time = 14 minutes = 14 / 60 hour = 7 / 30 hour distance travelled = time × speed = ( 7 / 30 ) × 26 = 6.06 km answer : option d"
Answer: d
Question (other): tea worth rs . 126 per kg are mixed with a third variety in the ratio 1 : 1 : 2 . if the mixture is worth rs . 133 per kg , the price of the third variety per kg will be
Options: a ) rs . 169.50 , b ) rs . 1700 , c ) rs . 175.50 , d ) rs . 155.50 , e ) none
Rationale: "solution since first second varieties are mixed in equal proportions , so their average price = rs . ( 126 + 135 / 2 ) = rs . 130.50 so , the mixture is formed by mixing two varieties , one at rs . 130.50 per kg and the other at say , rs . x per kg in the ratio 2 : 2 , i . e . , 1 : 1 . we have to find x . x - 133 / 22.50 = 1 = â € º x - 133 = 22.50 = â € º x = 155.50 . hence , price of the third variety = rs . 155.50 per kg . answer d"
Answer: d
Question (gain): find the simple interest on rs . 71,000 at 16 2 / 3 % per year for 9 months .
Options: a ) 7500 , b ) 6500 , c ) 8875 , d ) 9500 , e ) none of them
Rationale: "p = rs . 71000 , r = 50 / 3 % p . a and t = 9 / 12 years = 3 / 4 years . simple interest = ( p * r * t ) / 100 = rs . ( 71,000 * ( 50 / 3 ) * ( 3 / 4 ) * ( 1 / 100 ) ) = rs . 8875 answer is c ."
Answer: c
Question (gain): john makes $ 65 a week from his job . he earns a raise andnow makes $ 72 a week . what is the % increase ?
Options: a ) 16 % , b ) 10.76 % , c ) 10.69 % , d ) 10.98 % , e ) 10 %
Rationale: "increase = ( 7 / 65 ) * 100 = ( 7 / 65 ) * 100 = 10.76 % . b"
Answer: b
Question (physics): if 20 men take 15 days to to complete a job , in how many days can 20 men finish that work ?
Options: a ) 15 , b ) 16 , c ) 17 , d ) 18 , e ) 19
Rationale: ans . 15 days
Answer: a
Question (physics): a can do a piece of work 40 days . b can do work in 60 days . in how many days they will complete the work together ?
Options: a ) 15 days , b ) 16 days , c ) 19 days , d ) 17 days , e ) 24 days
Rationale: "lcm = 120 , ratio = 40 : 60 = 2 : 3 no of days = 120 / ( 2 + 3 ) = 90 / 5 = 24 days answer : e"
Answer: e
Question (general): a profit of rs . 800 is divided between x and y in the ratio of 1 / 2 : 1 / 3 . what is the difference between their profit shares ?
Options: a ) s . 260 , b ) s . 160 , c ) s . 360 , d ) s . 50 , e ) s . 90
Rationale: "a profit of rs . 800 is divided between x and y in the ratio of 1 / 2 : 1 / 3 or 3 : 2 . so profits are 480 and 320 . difference in profit share = 480 - 320 = 160 answer : b"
Answer: b
Question (physics): two trains are moving in opposite directions at 60 km / hr and 90 km / hr . their lengths are 1.50 km and 1.0 km respectively . the time taken by the slower train to cross the faster train in seconds is ?
Options: a ) 48 , b ) 9 , c ) 7 , d ) 60 , e ) 15
Rationale: ": relative speed = 60 + 90 = 150 km / hr . = 150 * 5 / 18 = 125 / 3 m / sec . distance covered = 1.50 + 1.0 = 2.5 km = 2500 m . required time = 2500 * 3 / 125 = 60 sec . answer : d"
Answer: d
Question (general): what is the smallest integer that is multiple of 3 , 5,9
Options: a ) a ) 70 , b ) b ) 45 , c ) c ) 200 , d ) d ) 280 , e ) e ) 140
Rationale: "it is the lcm of 3 , 5 and 9 which is 45 . the answer is b ."
Answer: b
Question (gain): a book is bought for $ 60 and sold for $ 78 . what is the profit in percentage ?
Options: a ) 10 , b ) 20 , c ) 30 , d ) 40 , e ) 50
Rationale: "78 / 60 = 1.3 the answer is c ."
Answer: c
Question (general): a is a positive integer and multiple of 2 ; p = 4 ^ a , what is the remainder when p is divided by 10 ?
Options: a ) 10 , b ) 6 , c ) 4 , d ) 0 , e ) it can not be determined
Rationale: it is essential to recognize that the remainder when an integer is divided by 10 is simply the units digit of that integer . to help see this , consider the following examples : 4 / 10 is 0 with a remainder of 4 14 / 10 is 1 with a remainder of 4 5 / 10 is 0 with a remainder of 5 105 / 10 is 10 with a remainder of 5 it is also essential to remember that the a is a positive integer and multiple of 2 . any integer that is a multiple of 2 is an even number . so , a must be a positive even integer . with these two observations , the question can be simplified to : what is the units digit of 4 raised to an even positive integer ? the units digit of 4 raised to an integer follows a specific repeating pattern : 4 ^ 1 = 4 4 ^ 2 = 16 4 ^ 3 = 64 4 ^ 4 = 256 4 ^ ( odd number ) - - > units digit of 4 4 ^ ( even number ) - - > units digit of 6 there is a clear pattern regarding the units digit . 4 raised to any odd integer has a units digit of 4 while 4 raised to any even integer has a units digit of 6 . since a must be an even integer , the units digit of p = 4 ^ a will always be 6 . consequently , the remainder when p = 4 ^ a is divided by 10 will always be 6 . in case this is too theoretical , consider the following examples : a = 2 - - > p = 4 ^ a = 16 - - > p / 10 = 1 with a remainder of 6 a = 4 - - > p = 4 ^ a = 256 - - > p / 10 = 25 with a remainder of 6 a = 6 - - > p = 4 ^ a = 4096 - - > p / 10 = 409 with a remainder of 6 a = 8 - - > p = 4 ^ a = 65536 - - > p / 10 = 6553 with a remainder of 6 answer : b .
Answer: b
Question (general): product of two natural numbers is 7 . then , the sum of reciprocals of their squares is
Options: a ) 50 / 49 , b ) 1 / 289 , c ) 290 / 90 , d ) 290 / 19 , e ) none of these
Rationale: "explanation : if the numbers are a , b , then ab = 7 , as 17 is a prime number , so a = 1 , b = 7 . 1 / a 2 + 1 / b 2 = 1 / 1 ( 2 ) + 1 / 7 ( 2 ) = 50 / 49 option a"
Answer: a
Question (general): in a fuel station the service costs $ 1.15 per car , every liter of fuel costs 0.4 $ . assuming that you own 2 sports cars and 2 executive cars and all fuel tanks are empty . how much will it cost to fuel all cars together if a sports car tank is 32 liters and an executive car tank is 75 % bigger ?
Options: a ) 37.5 $ , b ) 75 $ , c ) 87.5 $ , d ) 94.5 $ , e ) 98.4 $
Rationale: "total cars = 4 1.15 * 4 = 4.6 - > service cost fuel cost in sports car = 2 * 32 * 0.4 = 25.6 fuel cost in executive car = 25.6 * 7 / 4 = 44.8 total fuel cost = 25.6 + 44.8 = 70.4 cost to fuel car = 70.4 + 4.6 = 75 answer : b"
Answer: b
Question (physics): a , band c can do a piece of work in 11 days , 20 days and 67 days respectively , working alone . how soon can the work be done if a is assisted by band c on alternate days ?
Options: a ) 7.1 days , b ) 8.1 days , c ) 9.1 days , d ) 10 days , e ) 11 days
Rationale: "( a + b ) ' s 1 day ' s work = 1 / 11 + 1 / 20 = 31 / 220 ( a + c ) ' s 1 day ' s work = 1 / 11 + 1 / 67 = 78 / 737 work done in 2 day ' s = 31 / 220 + 78 / 737 = 19 / 77 19 / 77 th work done in 2 days work done = 77 / 19 * 2 = 8.1 days answer : b"
Answer: b
Question (general): a telephone company needs to create a set of 3 - digit area codes . the company is entitled to use only digits 6 , 4 and 3 , which can be repeated . if the product of the digits in the area code must be even , how many different codes can be created ?
Options: a ) 20 , b ) 22 , c ) 26 , d ) 24 , e ) 30
Rationale: "total # of codes possible is 3 * 3 * 3 = 27 . oit of those 27 codes only the product of 333 and will be odd , the remaining 26 will have either 2 or 4 in them , which ensures that their product will be even . therefore the number of codes where the product of the digits is even = ( total ) - ( restriction ) = 27 - 1 = 26 . answer : c"
Answer: c
Question (geometry): in a rectangular axis system , what is the area of a parallelogram with the coordinates : ( 3,5 ) , ( 9,5 ) , ( 2,7 ) , ( 8,7 ) ?
Options: a ) 21 . , b ) 28 . , c ) 35 . , d ) 12 . , e ) 52 .
Rationale: "delta x will give us the dimension of one side of the parallelogram = 9 - 3 = 6 unit delta y will give us the dimension of the other side of parallelogram = 7 - 5 = 2 unit area of parallelogram = 6 * 2 = 12 answer is d"
Answer: d
Question (gain): find the c . i . on a sum of rs . 10000 for 6 months at 25 % per annum , interest being compounded quarterly ?
Options: a ) 10290 , b ) 5290 , c ) 1289 , d ) 1290 , e ) 2290
Rationale: c . i . = 2000 ( 21 / 20 ) ^ 2 - 1800 = 1289 answer : c
Answer: c
Question (general): you collect pens . suppose you start out with 5 . mike gives you another 20 pens . since her father makes pens , cindy decides to double your pens . since you ' re nice , you give sharon 10 pens . how many pens do you have at the end ?
Options: a ) 39 , b ) 40 , c ) 41 , d ) 42 , e ) 43
Rationale: "solution start with 5 pens . mike gives you 20 pens : 5 + 20 = 25 pens . cindy doubles the number of pens you have : 25 ã — 2 = 50 pens . sharon takes 10 pens from you : 50 - 10 = 40 pens . so you have 40 at the end . correct answer : b"
Answer: b
Question (gain): a sum of money at simple interest amounts to rs . 1560 in 4 years and to rs . 1590 in 6 years . the sum is :
Options: a ) rs . 1400 , b ) rs . 1450 , c ) rs . 1500 , d ) rs . 1550 , e ) rs . 1525
Rationale: "s . i . for 2 years = rs . ( 1590 - 1560 ) = rs . 30 . s . i . for 4 years = rs . ( 30 x 2 ) = rs . 60 . principal = rs . ( 1560 - 60 ) = rs . 1500 . answer : option c"
Answer: c