Cheukting/mathqa huggingface dataset:
Question (physics): two trains are moving in the same direction at 54 kmph and 36 kmph . the faster train crosses a man in the slower train in 27 seconds . find the length of the faster train ?
Options: a ) 135 , b ) 277 , c ) 187 , d ) 257 , e ) 271
Rationale: "relative speed = ( 54 - 36 ) * 5 / 18 = 5 mps . distance covered in 27 sec = 27 * 5 = 135 m . the length of the faster train = 135 m . answer : a"
Answer: a
Question (general): drum x is 1 / 2 full of oil and drum y , which has twice the capacity of drum x , is 1 / 4 full of oil . if all of the oil in drum x is poured into drum y , then drum y will be filled to what capacity ?
Options: a ) 1 / 2 , b ) 2 / 3 , c ) 3 / 4 , d ) 5 / 6 , e ) 7 / 8
Rationale: ( 1 / 2 ) x = ( 1 / 4 ) y ( 1 / 4 ) y + ( 1 / 4 ) y = ( 1 / 2 ) y the answer is a .
Answer: a
Question (other): the ratio of three numbers is 1 : 2 : 3 and the sum of their squares is 2744 . the sum of the numbers is ?
Options: a ) 10 , b ) 12 , c ) 15 , d ) 14 , e ) 9
Rationale: "let the numbers be x , 2 x , 3 x then , x ^ 2 + 4 x ^ 2 + 9 x ^ 2 = 2744 14 x ^ 2 = 2744 x ^ 2 = 196 x = 14 answer is d"
Answer: d
Question (other): 0.6 of a number is equal to 0.08 of another number . the ratio of the numbers will be
Options: a ) 3 : 4 , b ) 4 : 3 , c ) 2 : 15 , d ) 2 : 9 , e ) 3 : 8
Rationale: let the numbers be x and y 0.6 x = 0.08 y = > x / y = 0.08 / 0.6 = 2 : 15 answer c .
Answer: c
Question (probability): if a coin is flipped , the probability that the coin will land heads is 1 / 2 . if the coin is flipped 6 times , what is the probability that it will land heads up on all 6 flips ?
Options: a ) 1 / 6 , b ) 1 / 8 , c ) 1 / 32 , d ) 1 / 2 , e ) 1 / 64
Rationale: ( 1 / 2 ) * ( 1 / 2 ) * ( 1 / 2 ) * ( 1 / 2 ) * ( 1 / 2 ) * ( 1 / 2 ) = 1 / 64 answer : e
Answer: e
Question (geometry): the perimeter of one face a of cube is 20 cm . its volume must be
Options: a ) 125 cm 3
b ) 400 cm 3
c ) 1000 cm 3
d ) 8000 cm 3
e ) none
Rationale: solution edge of the cube = ( 20 / 4 ) cm ‹ = › 5 cm . volume = ( 5 × 5 × 5 ) cm 3 ‹ = › 125 cm 3 . answer a
Answer: a
Question (physics): a train 660 m long is running at a speed of 78 km / hr . if it crosses a tunnel in 1 min , then the length of the tunnel is ?
Options: a ) 640 , b ) 277 , c ) 500 , d ) 297 , e ) 435
Rationale: "speed = 78 * 5 / 18 = 65 / 3 m / sec . time = 1 min = 60 sec . let the length of the train be x meters . then , ( 660 + x ) / 60 = 65 / 3 x = 640 m . answer : a"
Answer: a
Question (physics): two goods trains each 850 m long are running in opposite directions on parallel tracks . their speeds are 45 km / hr and 30 km / hr respectively . find the time taken by the slower train to pass the driver of the faster one ?
Options: a ) 22 sec , b ) 81.6 sec , c ) 48 sec , d ) 18.3 sec , e ) 9.32 sec
Rationale: "relative speed = 45 + 30 = 75 km / hr . 75 * 5 / 18 = 125 / 6 m / sec . distance covered = 850 + 850 = 1700 m . required time = 1700 * 6 / 125 = 81.6 sec . answer : b"
Answer: b
Question (gain): the owner of a furniture shop charges his customer 20 % more than the cost price . if a customer paid rs . 8400 for a computer table , then what was the cost price of the computer table ?
Options: a ) rs . 6725 , b ) rs . 6727 , c ) rs . 6908 , d ) rs . 6725 , e ) rs . 7000
Rationale: "cp = sp * ( 100 / ( 100 + profit % ) ) = 8400 ( 100 / 120 ) = rs . 7000 . answer : e"
Answer: e
Question (gain): what is 92 % of 3 / 4 ?
Options: a ) 6.9 , b ) 69.0 , c ) 0.6845 , d ) 0.6859 , e ) 0.69
Rationale: "soln : - 120 % = 12 / 10 5 / 8 * 12 / 10 = 60 / 80 = 6 / 8 = 3 / 4 = 0.69 answer : e ."
Answer: e
Question (gain): the profit earned by selling an article for $ 832 is equal to the loss incurred when the same article is sold for $ 448 . what should be the sale price for making 30 % profit ?
Options: a ) $ 480 , b ) $ 450 , c ) $ 960 , d ) $ 832 , e ) $ 660
Rationale: "let c . p . = $ x . then , 832 - x = x - 448 2 x = 1280 = > x = 640 required s . p . = 130 % of $ 640 = $ 832 . d"
Answer: d
Question (physics): a 140 meter long train crosses a man standing on the platform in 6 sec . what is the speed of the train ?
Options: a ) 228 , b ) 108 , c ) 84 , d ) 188 , e ) 211
Rationale: "s = 140 / 6 * 18 / 5 = 84 kmph answer : c"
Answer: c
Question (other): a certain manufacturer of cake , muffin , and bread mixes has 100 buyers , of whom 50 purchases cake mix , 40 purchase muffin mix , and 18 purchase both cake mix and muffin mix . if a buyer is to be selected at random from the 100 buyers , what is the probability that the buyer selected will be one who purchases neither cake mix nor muffin mix ?
Options: a ) 1 / 10 , b ) 3 / 10 , c ) 1 / 2 , d ) 7 / 25 , e ) 9 / 10
Rationale: "c + m + b - cm - mb - cb - 2 cmb = 100 c - cake buyers , m - muffin and b - bread buyers . cm , mb , cb and cmb are intersecting regions . the question asks for people who have bought only bread mixes = b - cb - mb - 2 cmb has to be found out . 50 + 40 + b - cb - mb - 18 - 2 cmb = 100 b - cb - mb - 2 cmb = 28 hence the probability = 28 / 100 = 7 / 25 . d"
Answer: d
Question (physics): if 11.25 m of a uniform steel rod weighs 42.75 kg . what will be the weight of 5 m of the same rod ?
Options: a ) 22.8 kg , b ) 25.6 kg , c ) 19 kg , d ) 26.5 kg , e ) none of these
Rationale: "explanation : let the required weight be x kg . then , less length , less weight ( direct proportion ) = > 11.25 : 5 : : 42.75 : x = > 11.25 x x = 5 x 42.75 = > x = ( 5 x 42.75 ) / 11.25 = > x = 19 answer : c"
Answer: c
Question (geometry): the area of a rectangle is 460 square metres . if the length is 15 % more than the breadth , what is the breadth of the rectangular field ?
Options: a ) 20
b ) 27
c ) 26
d ) 188
e ) 11
Rationale: explanation : let breadth = x meters . then , length = meters given that , = > x = 20 breadth = 20 answer : a ) 20 m
Answer: a
Question (general): find the product of the local value and absolute value of 6 in 564823
Options: a ) 8000 , b ) 16000 , c ) 12000 , d ) 18000 , e ) 360000
Rationale: "explanation : place value = local value face value = absolute value the place value of 6 in 564823 is 6 x 10000 = 60000 the face value of 6 in 564823 is nothing but 6 . = > 60000 x 6 = 360,000 answer : option e"
Answer: e
Question (gain): find the compound interest on $ 100000 in 2 years at 4 % per annum , the interest being compounded half - yearly ?
Options: a ) $ 645.56 , b ) $ 824.32 , c ) $ 954.26 , d ) $ 745.69 , e ) $ 8243.21
Rationale: "principle = $ 10000 rate = 2 % half yearly = 4 half years amount = 100000 * ( 1 + 2 / 100 ) ^ 4 = 100000 * 51 / 50 * 51 / 50 * 51 / 50 * 51 / 50 = $ 108243.21 c . i . = 108243.21 - 100000 = $ 8243.21 answer is e"
Answer: e
Question (gain): rs . 2500 is divided into two parts such that if one part be put out at 5 % simple interest and the other at 6 % , the yearly annual income may be rs . 135 . how much was lent at 5 % ?
Options: a ) 2333 , b ) 2777 , c ) 2688 , d ) 1500 , e ) 2871
Rationale: "( x * 5 * 1 ) / 100 + [ ( 2500 - x ) * 6 * 1 ] / 100 = 135 x = 1500 answer : d"
Answer: d
Question (general): ( 0.66 ) ( power 3 ) - ( 0.1 ) ( power 3 ) / ( 0.66 ) ( power 2 ) + 0.066 + ( 0.1 ) ( power 2 ) is :
Options: a ) 0.86 , b ) 0.56 , c ) 0.96 , d ) 0.69 , e ) 0.76
Rationale: "given expression = ( 0.66 ) ( power 3 ) - ( 0.1 ) ( power 3 ) / ( 0.66 ) ( power 2 ) + ( 0.66 x 0.1 ) + ( 0.1 ) ( power 2 ) = a ( power 3 ) - b ( power 3 ) / a ( power 2 ) + ab + b ( power 2 ) = ( a - b ) = ( 0.66 - 0.1 ) = 0.56 answer is b"
Answer: b
Question (gain): a trader cheats both his supplier and customer by using faulty weights . when he buys from the supplier , he takes 10 % more than the indicated weight . when he sells to his customer , he gives the customer a weight such that 50 % of that is added to the weight , the weight claimed by the trader is obtained . if he charges the cost price of the weight that he claims , find his profit percentage .
Options: a ) 80 % , b ) 65 % , c ) 28.33 % , d ) 19.109 % , e ) 50 %
Rationale: "anyways , one can infer that he ' steals ' 10 % from suppliers and then charges 50 % extra to customers so basically 1.1 * 1.5 = 1.65 given that 1 is start point , we get 65 % more hence answer is b"
Answer: b
Question (general): when the no . 7 y 86038 is exactly divisible by 11 , then the smallest whole no . in place of y ?
Options: a ) 1 , b ) 3 , c ) 5 , d ) 7 , e ) 9
Rationale: the given number = 7 y 86038 sum of the odd places = 8 + 0 + 8 + 7 = 23 sum of the even places = 3 + 6 + y ( sum of the odd places ) - ( sum of even places ) = number ( exactly divisible by 11 ) 23 - ( 9 + y ) = divisible by 11 14 � y = divisible by 11 . y must be 3 , to make given number divisible by 11 . b
Answer: b
Question (general): set i consists of integers { 3 , - 8 , y , 19 , - 6 } and set b consists of integers { k , - 3 , 0 , 16 , - 5 , 9 } . number l represents the median of set i , number m represents mode of set b and number z = l ^ m . if y is an integer greater than 21 , for what value of k will z be a divisor of 26 ?
Options: a ) - 2 , b ) - 1 , c ) 0 , d ) 1 , e ) 2
Rationale: i = { 3 , - 8 , y , 19 , - 6 } b = { k , - 3 , 0,16 , - 5,9 } y > 21 so l = median of i = 3 m = mode of set b z = ( 3 ) ^ m if z is a divisor of 26 , ( 3 ) ^ m = 1 because 26 does not have 3 as a factor = > m = 0 hence k = 0 , as m is mode and 0 will be the most frequently occuring number in set b . answer - c
Answer: c
Question (geometry): carol and jordan draw rectangles of equal area . if carol ' s rectangle measures 5 inches by 24 inches and jordan ' s rectangle is 12 inches long , how wide is jordan ' s rectangle , in inches ?
Options: a ) 25 , b ) 23 , c ) 22 , d ) 20 , e ) 10
Rationale: "area of carol ' s rectangle = 24 * 5 = 120 let width of jordan ' s rectangle = w since , the areas are equal 12 w = 120 = > w = 10 answer e"
Answer: e
Question (geometry): a rectangular field has to be fenced on three sides leaving a side of 20 feet uncovered . if the area of the field is 680 sq . feet , how many feet of fencing will be required ?
Options: a ) 80 feet
b ) 85 feet
c ) 83 feet
d ) 88 feet
e ) 90 feet
Rationale: given that area of the field = 680 sq . feet = > lb = 680 sq . feet length ( l ) = 20 feet = > 20 × b = 680 = > b = 680 / 20 = 34 feet required length of the fencing = l + 2 b = 20 + ( 2 × 34 ) = 88 feet answer is d .
Answer: d
Question (gain): simple interest on a certain sum of money for 2 years at 12 % per annum is half the compound interest on rs . 6000 for 2 years at 15 % per annum . the sum placed on simple interest is
Options: a ) rs . 6000 , b ) rs . 7935 , c ) rs . 8265.63 , d ) rs . 3967.5 , e ) none
Rationale: "solution c . i . = rs [ 6000 x ( 1 + 15 / 100 ) â ² - 4000 ] rs . ( 4000 x 115 / 100 x 115 / 100 - 6000 ) = rs . 7935 . sum = rs . [ 3967.5 x 100 / 4 x 12 ] = rs . 8265.63 . answer c"
Answer: c
Question (physics): 10 men working 12 hours daily finish a work in 24 days . in how many days will they finish 1 / 4 th of the work working 8 hours daily ?
Options: a ) 9 days , b ) 10 days , c ) 11 days , d ) 12 days , e ) 18 days
Rationale: the number of days needed to finish 1 / 4 of the work = 1 / 4 * 12 / 8 * 24 = 9 days . answer : a
Answer: a
Question (general): 65 % of x = 20 % of 747.50 . find the value of x ?
Options: a ) 100 , b ) 230 , c ) 150 , d ) 180 , e ) 199
Rationale: "65 % of x = 20 % of 747.50 then , 65 / 100 * x = 20 / 100 * 7475 / 10 x = 230 answer is b"
Answer: b
Question (general): what is the remainder wen 2 ^ 35 is divided by 5 ?
Options: a ) 1 , b ) 2 , c ) 3 , d ) 4 , e ) 5
Rationale: "2 ^ 35 / 5 = > ( 2 ^ 4 ) ^ 8 * 2 ^ 3 / 5 = > ( 5 * 3 + 1 ) ^ 8 * ( 5 + 3 ) / 5 = > ( 1 * 3 ) / 5 = > 3 / 5 = > remainder = 3 answer : c"
Answer: c
Question (physics): a certain car can travel 40 kilometers on a liter of fuel . if the fuel tank ’ s contents decrease by 3.9 gallons over a period of 5.7 hours as the car moves at a constant speed , how fast is the car moving , in miles per hour ? ( 1 gallon = 3.8 liters ; 1 mile = 1.6 kilometers )
Options: a ) 52 , b ) 65 , c ) 78 , d ) 91 , e ) 104
Rationale: "fuel used 3.9 gallons ; convert to liters - - > 3.9 x 3.8 liters time = 5.7 hours 1 mile = 1.6 kilometers ; convert to miles - - > 1 km = 1 / 1.6 mile speed ( km / hour ) = d / t = 40 ( km * ) x 3.9 x 3.8 / 5.7 replace ( km * ) to miles ; multiply by 1 / 1.6 mile speed ( miles / hour ) = 40 x 3.9 x 3.8 / 5.7 x 1.6 = 78 miles / hour ans : c ps : i felt the factors were easy to cancel out , so did n ' t require much rounding off = 40 x 3.9 x 3.8 / 5.7 x 1.6 = 65 b"
Answer: b
Question (geometry): each side of a rectangle is increased by 100 % . by what percentage does the area increase ?
Options: a ) 300 % , b ) 400 % , c ) 500 % , d ) 200 % , e ) 600 %
Rationale: original area = a * b where a and b are sides after increase in side increase in area will be = ( ( ( 2 a * 2 b ) - ( a * b ) ) * 100 ) / ( a * b ) = 300 % answer : a
Answer: a
Question (general): the average monthly salary of 20 employees in an organisation is rs . 1300 . if the manager ' s salary is added , then the average salary increases by rs . 100 . what is the manager ' s monthly salary ?
Options: a ) 3600 , b ) 3890 , c ) 88798 , d ) 3400 , e ) 2891
Rationale: "explanation : manager ' s monthly salary rs . ( 1400 * 21 - 1300 * 20 ) = rs . 3400 . answer : d"
Answer: d
Question (physics): convert 2.0 hectares in ares
Options: a ) 130 ares . , b ) 160 ares . , c ) 180 ares . , d ) 200 ares . , e ) 250 ares .
Rationale: "2.0 hectares in ares 1 hectare = 100 ares therefore , 2.0 hectares = 2.0 × 100 ares = 200 ares . answer - d"
Answer: d
Question (general): seller selling an apple for rs . 19 , a seller loses 1 / 6 th of what it costs him . the cp of the apple is ?
Options: a ) 10 , b ) 12 , c ) 20 , d ) 18 , e ) 21
Rationale: sp = 19 loss = cp 20 loss = cp − sp = cp − 19 ⇒ cp 20 = cp − 19 ⇒ 19 cp 20 = 19 ⇒ cp 20 = 1 ⇒ cp = 20 c
Answer: c
Question (general): what is the difference between the largest and the smallest number written with 7 , 7 , 0 , 7 ?
Options: a ) 6893 , b ) 6993 , c ) 6093 , d ) 693 , e ) none
Rationale: "7770 7077 - - - - - - - - - - - - - 693 answer : d"
Answer: d
Question (general): if a certain toy store ' s revenue in november was 2 / 5 of its revenue in december and its revenue in january was 1 / 3 of its revenue in november , then the store ' s revenue in december was how many times the average ( arithmetic mean ) of its revenues in november and january ?
Options: a ) 5 / 3 , b ) 5 / 4 , c ) 10 / 3 , d ) 15 / 4 , e ) 15 / 2
Rationale: "n = 2 d / 5 j = n / 3 = 2 d / 15 the average of november and january is ( n + j ) / 2 = 8 d / 15 / 2 = 4 d / 15 d is 15 / 4 times the average of november and january . the answer is d ."
Answer: d
Question (physics): a man bring 2 cats to his home to eliminate all the mice . they do a half of the work in 5 days , then the man brings 3 more cats . if they hunt at the same rate , how many days will take to hunt all the mice , since the first day ?
Options: a ) 7 days , b ) 8 days , c ) 9 days , d ) 10 days , e ) 11 days
Rationale: we have that : 2 cats - - - - - 5 days , ( 2 + 3 ) c - - - - - x d , that is : ( x d / 2 c ) = ( 5 d / 5 p ) , then : x d = ( 5 d / 5 c ) 2 c = 2 d . is to say , the 5 cats hunt the same quantity in 2 days ; as it is only 1 / 2 of the work , all the mice would be hunt in : m = 5 d + 2 d = 7 days . answer a .
Answer: a
Question (general): a sum of money lent out at s . i . amounts to rs . 720 after 2 years and to rs . 1020 after a further period of 5 years . the sum is ?
Options: a ) 600 , b ) 288 , c ) 2768 , d ) 287 , e ) 191
Rationale: "s . i for 5 years = ( 1020 - 720 ) = rs . 300 . s . i . for 2 years = 300 / 5 * 2 = rs . 120 . principal = ( 720 - 120 ) = rs . 600 . answer : a"
Answer: a
Question (physics): there are 15 members in a family . it takes 180 days for a women to complete the work , however man completes in 120 days . they take 17 days to complete the work if men work on alternate days and women work every third day . if all of them started together on the 1 st day , then how many women are there in the family
Options: a ) 1 , b ) 2 , c ) 3 , d ) 4 , e ) 5
Rationale: let the number of men be m and so the number of women = 15 - m out of 17 days , men and women work together on 1,4 , 7,10 , 13,16 th days ( total of 6 days ) from the start . men work on alternate days , that is 1 , 3,5 , 7,9 , 11,13 , 15,17 th days ( total of 9 days ) . let the total work be 360 units ( lcm of 180 and 120 ) . 1 man does 360 / 120 = 3 units per day 1 woman does 360 / 180 = 2 units per day based on above facts , total work by men + women in these 17 days = 360 units m * 9 * 3 + ( 15 - m ) * 6 * 2 = 360 , 27 m + 180 - 12 m = 360 , solving m = 12 . num of men = 12 and number of women = 15 - 12 = 3 answer : c
Answer: c
Question (general): how many integers between 1000 and 10000 have no digits other than 4 , 5 or 6 ?
Options: a ) 91 , b ) 51 , c ) 81 , d ) 71 , e ) 61
Rationale: any number between 1000 and 10000 is of 4 digits . the unit ’ s place can be filled up by 45 or 6 , that is , in 3 ways . similarly , the ten ’ s place can be filled up by 4 or 5 or 6 , that is in 3 ways . the hundred ’ s place can be filled up by 4 , 5 or 6 , that is in 3 ways and the thousand ’ s place can . be filled up by 4 or 5 or 6 , that is , in 3 ways . hence the required numbers = 3 x 3 x 3 x 3 = 81 answer : c
Answer: c
Question (physics): john completes a piece of work in 8 days , rose completes the same work in 16 days . if both of them work together , then the number of days required to complete the work is ?
Options: a ) 6 days , b ) 5.33 days , c ) 10 days , d ) 12 days , e ) 14 days
Rationale: if a can complete a work in x days and b can complete the same work in y days , then , both of them together can complete the work in x y / x + y days . that is , the required no . of days = 8 × 16 / 24 = 5.33 days answer : b
Answer: b
Question (geometry): what is the area of a triangle with the following vertices l ( 2 , 3 ) , m ( 5 , 1 ) , and n ( 3 , 5 ) ?
Options: a ) 3
b ) 4
c ) 5
d ) 6
e ) 7
Rationale: there is a direct formula to calculate the are of a triangle based on coordinates of its vertices and one could use it to solve this problem . though if you make a diagram minimum simple calculations will be needed : answer : b .
Answer: b
Question (physics): a can complete a project in 20 days and b can complete the same project in 30 days . if a and b start working on the project together and b quits 5 days before the project is completed , in how many days total will the project be completed ?
Options: a ) 10 , b ) 12 , c ) 14 , d ) 16 , e ) 18
Rationale: "a ' s rate is 1 / 20 of the project per day . b ' s rate is 1 / 30 of the project per day . the combined rate is 1 / 12 of the project per day . in the last 5 days , a can do 1 / 4 of the project . thus a and b must complete 3 / 4 of the project , which takes 9 days . the total number of days is 9 + 5 = 14 . the answer is c ."
Answer: c
Question (physics): how long does a train 140 m long running at the speed of 72 km / hr takes to cross a bridge 132 m length ?
Options: a ) 13.6 sec , b ) 12.1 sec , c ) 17.9 sec , d ) 16.8 sec , e ) 14.9 sec
Rationale: "speed = 72 * 5 / 18 = 20 m / sec total distance covered = 140 + 132 = 272 m . required time = 272 / 20 = 13.6 sec . answer : a"
Answer: a
Question (general): in kaya ' s teacher ' s desk there are 10 pink highlighters , 15 yellow highlighters , and 8 blue highlighters . how many highlighters are there in all ?
Options: a ) 11 , b ) 22 , c ) 77 , d ) 33 , e ) 88
Rationale: "add the numbers of highlighters . 10 + 15 + 8 = 33 . answer is d ."
Answer: d
Question (other): income and expenditure of a person are in the ratio 9 : 8 . if the income of the person is rs . 18000 , then find his savings ?
Options: a ) rs . 3600 , b ) rs . 3603 , c ) rs . 2000 , d ) rs . 3632 , e ) rs . 3602
Rationale: "let the income and the expenditure of the person be rs . 9 x and rs . 8 x respectively . income , 9 x = 18000 = > x = 2000 savings = income - expenditure = 9 x - 8 x = x so , savings = rs . 2000 answer : c"
Answer: c
Question (gain): a gambler has won 40 % of his 40 poker games for the week so far . if , all of a sudden , his luck changes and he begins winning 80 % of the time , how many more games must he play to end up winning 60 % of all his games for the week ?
Options: a ) 20 , b ) 25 , c ) 30 , d ) 35 , e ) 40
Rationale: "let x be the number of additional games the gambler needs to play . 0.4 ( 40 ) + 0.8 x = 0.6 ( x + 40 ) 0.2 x = 8 x = 40 the answer is e ."
Answer: e
Question (general): x , y , and z are consecutive numbers and x > y > z . also , 2 x + 3 y + 3 z = 5 y + 8 . what is the value of z ?
Options: a ) 2 , b ) 3 , c ) 4 , d ) 5 , e ) 6
Rationale: if x , y , and z are consecutive numbers and x > y > z , then y = z + 1 and x = z + 2 . 2 x + 3 y + 3 z = 5 y + 8 2 z + 4 + 3 z + 3 + 3 z = 5 z + 5 + 8 3 z = 6 z = 2 the answer is a .
Answer: a
Question (general): in the coordinate plane , points ( x , 6 ) and ( 10 , y ) are on line k . if line k passes through the origin and has slope 1 / 2 , then x * y =
Options: a ) 52 , b ) 46 , c ) 60 , d ) 50 , e ) 35
Rationale: "line k passes through the origin and has slope 1 / 2 means that its equation is y = 1 / 2 * x . thus : ( x , 6 ) = ( 12 , 6 ) and ( 10 , y ) = ( 10,5 ) - - > x * y = 12 * 5 = 60 . answer : c"
Answer: c
Question (general): a vessel of capacity 3 litre has 25 % of alcohol and another vessel of capacity 5 litre had 40 % alcohol . the total liquid of 8 litre was poured out in a vessel of capacity 10 litre and thus the rest part of the vessel was filled with the water . what is the new concentration of mixture ?
Options: a ) 31 % . , b ) 71 % . , c ) 27.5 % . , d ) 29 % . , e ) 51 % .
Rationale: "25 % of 3 litres = 0.75 litres 40 % of 5 litres = 2 litres therefore , total quantity of alcohol is 2.75 litres . this mixture is in a 10 litre vessel . hence , the concentration of alcohol in this 10 litre vessel is 27.5 % c"
Answer: c
Question (probability): a jar contains 18 balls . 3 blue balls are removed from the jar and not replaced . now the probability of getting a blue ball is 1 / 5 then how many blue balls jar contains initially ?
Options: a ) 2 , b ) 3 , c ) 4 , d ) 5 , e ) 6
Rationale: x / 15 = 1 / 5 x = 3 3 + 3 ( removed 3 blue balls ) = 6 answer : e
Answer: e
Question (physics): a rectangular grassy plot 110 m by 65 cm has a gravel path . 5 cm wide all round it on the inside . find the cost of gravelling the path at 80 paise per sq . mt ?
Options: a ) 680 rs , b ) 540 rs , c ) 480 rs , d ) 640 rs , e ) 280 rs
Rationale: area of theplot = 110 * 65 = 7150 sq m area of the plot excluding the path = ( 110 - 5 ) * ( 65 - 5 ) = 6300 sq m area of the path = 7150 - 6300 = 850 sq m cost of gravelling the path = 850 * 80 / 100 = 680 rs answer : a
Answer: a
Question (physics): a motorcyclist goes from nagpur to delhi , a distance of 600 kms at an average of 60 kmph speed . another man starts from nagpur by car 5 â ½ hours after the first , and reaches delhi â ½ hour earlier . what is the ratio of the speed of the motorcycle and the car ?
Options: a ) 1 : 2 , b ) 1 : 7 , c ) 1 : 9 , d ) 1 : 5 , e ) 2 : 5
Rationale: t = 600 / 60 = 10 h t = 10 - 6 = 4 time ratio = 10 : 4 = 5 : 2 speed ratio = 2 : 5 answer : e
Answer: e