Cheukting/mathqa huggingface dataset:
Question (gain): ravi and sunil are partners in a business . ravi invests rs . 12,000 for 4 months and sunil invested rs . 10000 for 5 months then after one year ratio of their profits will be
Options: a ) 1 : 3 , b ) 2 : 3 , c ) 24 : 25 , d ) 20 : 22 , e ) 3 : 4
Rationale: = ( 12000 * 4 ) : ( 10000 * 5 ) = 48000 : 50000 = 24 : 25 answer : c
Answer: c
Question (geometry): the value of “ a ” varies in inverse proportion as the square of “ b ” . if the value of “ a ” is equal to 40 when “ b ” is equal to 12 . what would be the value of “ a ” when “ b ” is equal to 24 ?
Options: a ) 10
b ) 88
c ) 26
d ) 27
e ) 28
Rationale: explanation : we have , a α 1 / b 2 a * b 2 = k ( constant ) when b = 12 , a = 40 … . . given k = 40 * ( 12 ) 2 = 5760 now , b = 24 . hence , a = 5760 / 576 = 10 answer : a
Answer: a
Question (geometry): the dimensions of a room are 25 feet * 15 feet * 12 feet . what is the cost of white washing the four walls of the room at rs . 4 per square feet if there is one door of dimensions 6 feet * 3 feet and three windows of dimensions 4 feet * 3 feet each ?
Options: a ) 4000 , b ) 3624 , c ) 5673 , d ) 4530 , e ) 4566
Rationale: "area of the four walls = 2 h ( l + b ) since there are doors and windows , area of the walls = 2 * 12 ( 15 + 25 ) - ( 6 * 3 ) - 3 ( 4 * 3 ) = 906 sq . ft . total cost = 906 * 4 = rs . 3624 answer : option b"
Answer: b
Question (other): of the 65 cars on a car lot , 45 have power steering , 25 have power windows , and 17 have both power steering and power windows . how many of the cars on the lot have neither power steering nor power windows ?
Options: a ) 2 , b ) 8 , c ) 12 , d ) 15 , e ) 18
Rationale: total - neither = all power steering + all power windows - both or 65 - neither = 45 + 25 - 17 = 53 . = > neither = 12 , hence c . answer : c
Answer: c
Question (physics): if two painters can complete two rooms in two hours , how many hours 10 painters would it take to do 20 rooms ?
Options: a ) 4 , b ) 3 , c ) 5 , d ) 8 , e ) 7
Rationale: "explanation : two painters can complete two rooms in two hours . so 20 rooms can be painted in 4 hrs by 10 painters answer : a ) 4 painters"
Answer: a
Question (physics): convert 0.32 in to a vulgar fraction ?
Options: a ) 8 / 25 , b ) 16 / 50 , c ) 17 / 50 , d ) 19 / 50 , e ) none
Rationale: "answer 0.32 = 32 / 100 = 8 / 25 correct option : a"
Answer: a
Question (other): the l . c . m . of two numbers is 60 . the numbers are in the ratio 2 : 3 . then sum of the number is :
Options: a ) 28 , b ) 32 , c ) 40 , d ) 53 , e ) 50
Rationale: "let the numbers be 2 x and 3 x . then , their l . c . m . = 6 x . so , 6 x = 60 or x = 10 . the numbers are 20 and 30 . hence , required sum = ( 20 + 30 ) = 50 . answer : option e"
Answer: e
Question (physics): the sum of three consecutive even numbers is 63 , find the last one ?
Options: a ) 26 , b ) 24 , c ) 21 , d ) 23 , e ) 19
Rationale: "let the first number be n let the second number be n + 2 let the third number be n + 4 n + n + 2 + n + 4 = 63 combine like terms : 3 n + 6 = 63 3 n = 63 - 6 3 n = 57 n = 19 n + 2 = 21 n + 4 = 23 the last number is 23 answer : d"
Answer: d
Question (gain): a cycle is bought for rs . 900 and sold for rs . 1170 , find the gain percent ?
Options: a ) 27 % , b ) 20 % , c ) 80 % , d ) 30 % , e ) 24 %
Rationale: "900 - - - - 270 100 - - - - ? = > 30 % answer : d"
Answer: d
Question (general): rs 378 is divided among the 3 children such that 12 times of anusha is equal to 8 times of babu which is equal to 6 times of esha . how much the rupee anusha get ?
Options: a ) 74 , b ) 84 , c ) 94 , d ) 104 , e ) 114
Rationale: if money with anusha = a , babu = b & esha = e , then a + b + e = 378 - - - ( i ) & 12 a = 8 b = 6 e , so b = 3 a / 2 & e = 2 a substituting these values of b & e in ( i ) , a + ( 3 a / 2 ) + 2 a = 378 , on solving , a = 84 so , b = 126 , e = 168 answer : b
Answer: b
Question (general): the price of 10 chairs is equal to that of 4 tables . the price of 15 chairs and 2 tables together is rs . 4000 . the total price of 12 chairs and 3 tables is ?
Options: a ) rs . 3900 , b ) rs . 4900 , c ) rs . 4980 , d ) rs . 5000 , e ) rs . 5900
Rationale: let the cost of a chair and that of a table be rs . x and rs . y respectively . then , 10 x = 4 y or y = 5 x . 2 15 x + 2 y = 4000 15 x + 2 x 5 x = 4000 2 20 x = 4000 x = 200 . so , y = 5 x 200 = 500 . 2 hence , the cost of 12 chairs and 3 tables = 12 x + 3 y = rs . ( 2400 + 1500 ) = rs . 3900 . a )
Answer: a
Question (physics): a and b are two multiples of 14 , and q is the set of consecutive integers between a and b , inclusive . if q contains 12 multiples of 14 , how many multiples of 7 are there in q ?
Options: a ) 20 , b ) 21 , c ) 22 , d ) 23 , e ) 24
Rationale: "halfway between the multiples of 14 , there will be another multiple of 7 . the total number of multiples of 7 is 12 + 11 = 23 . the answer is d ."
Answer: d
Question (general): the average age of 15 students of a class is 15 years . out of these , the average age of 6 students is 14 years and that of the other 8 students is 16 years . the age of the 15 th student is
Options: a ) 9 years , b ) 13 years , c ) 14 years , d ) 21 years , e ) 25 years
Rationale: "solution age of the 15 th student = [ 15 x 15 - ( 14 x 6 + 16 x 8 ) ] = ( 225 - 212 ) = 13 years . answer b"
Answer: b
Question (physics): a can do a work in 6 days . b can do the same work in 12 days . if both a & b are working together in how many days they will finish the work ?
Options: a ) 3 , b ) 5 , c ) 4 , d ) 2 , e ) 6
Rationale: "a rate = 1 / 6 b rate = 1 / 12 ( a + b ) rate = ( 1 / 6 ) + ( 1 / 12 ) = 1 / 4 a & b finish the work in 4 days correct option is c"
Answer: c
Question (general): in an organisation there are 1000 employees out of which 250 earn below 10 k $ and 500 earn between 10 k $ and 50 k $ . what is the total percentage of employees who earn less than 50 k $ ?
Options: a ) 66 % , b ) 75 % , c ) 70 % , d ) 50 % , e ) 82 %
Rationale: total percentage = ( 250 + 500 ) / 1000 = 0.75 b
Answer: b
Question (general): how many quarters are equal to 6 dollars ?
Options: a ) 1 , b ) 8 , c ) 12 , d ) 9 , e ) 24
Rationale: 6 * 4 = 24 quarters answer : e
Answer: e
Question (general): the difference between the place value and the face value of 9 in the numeral 856973 is
Options: a ) 973 , b ) 891 , c ) 5994 , d ) 6084 , e ) none of these
Rationale: "( place value of 9 ) - ( face value of 9 ) = ( 900 - 9 ) = 891 answer : option b"
Answer: b
Question (general): the price of 2 sarees and 4 shirts is rs . 1600 . with the same money one can buy 1 saree and 6 shirts . if one wants to buy 12 shirts , how much shall he have to pay ?
Options: a ) 2500 , b ) 2700 , c ) 2200 , d ) 2900 , e ) 2400
Rationale: let the price of a saree and a shirt be rs . x and rs . y respectively . then , 2 x + 4 y = 1600 . . . . ( i ) and x + 6 y = 1600 . . . . ( ii ) divide equation ( i ) by 2 , we get the below equation . = > x + 2 y = 800 . - - - ( iii ) now subtract ( iii ) from ( ii ) x + 6 y = 1600 ( - ) x + 2 y = 800 - - - - - - - - - - - - - - - - 4 y = 800 - - - - - - - - - - - - - - - - therefore , y = 200 . now apply value of y in ( iii ) = > x + 2 x 200 = 800 = > x + 400 = 800 therefore x = 400 solving ( i ) and ( ii ) we get x = 400 , y = 200 . cost of 12 shirts = rs . ( 12 x 200 ) = rs . 2400 . answer is e .
Answer: e
Question (general): in a company with 48 employees , some part - time and some full - time , exactly ( 1 / 3 ) of the part - time employees and ( 1 / 4 ) of the full - time employees take the subway to work . what is the greatest possible number y of employees who take the subway to work ?
Options: a ) 12 , b ) 13 , c ) 14 , d ) 15 , e ) 16
Rationale: "p / 3 + f / 4 = p / 3 + ( 48 - p ) / 4 = 12 + p / 2 p / 3 + f / 3 = ( p + f ) / 3 = 48 / 3 = 16 p / 4 + f / 4 = 12 p / 3 + f / 3 > p / 3 + f / 4 > p / 4 + f / 4 - - > 16 > 12 + p / 12 > 12 greatest possible y : 12 + p / 12 = 15 - - > p = 36 ( integer - - > good ) 15 or d is the answer"
Answer: d
Question (general): a garden center sells a certain grass seed in 5 - pound bags at $ 13.80 per bag , 10 - pound bags at $ 20.43 per bag , and 25 - pound bags $ 32.25 per bag . if a customer is to buy at least 65 pounds of the grass seed , but no more than 80 pounds , what is the least possible cost of the grass seed that the customer will buy ?
Options: a ) $ 98.73 , b ) $ 96.75 , c ) $ 98.78 , d ) $ 102.07 , e ) $ 105.3
Rationale: there can be 2 cases 1 ) 25 + 25 + 10 + 5 = $ 98.73 or 2 ) 25 + 25 + 25 = $ 96.75 a
Answer: a
Question (gain): in the manufacture of a certain product , 5 percent of the units produced are defective and 4 percent of the defective units are shipped for sale . what percent of the units produced are defective units that are shipped for sale ?
Options: a ) 0.125 % , b ) 0.2 % , c ) 0.8 % , d ) 1.25 % , e ) 2.0 %
Rationale: "percent of defective produced = 5 % percent of the defective units that are shipped for sale = 4 % percent of units produced are defective units that are shipped for sale = ( 4 / 100 ) * ( 5 / 100 ) * 100 % = ( 20 / 10000 ) * 100 % = ( 20 / 100 ) % = . 2 % answer b"
Answer: b
Question (general): a student appeared in the mock cat . the test paper contained 3 sections namely qa , di and va . the percentage marks in all va was equal to the average of percentage marks in all the 3 sections . coincidentally , if we reverse the digit of the percentage marks of qa we get the percentage marks of di . the percentage marks in va scored by student could be :
Options: a ) 81 , b ) 48 , c ) 66 , d ) 69 , e ) none of these
Rationale: solution : let the percentage marks in qa = ( 10 a + b ) % let the percentage marks in di = ( 10 b + a ) % let the percentage marks in va = x % . now , according to the question , we have , [ ( 10 a + b ) + x + ( 10 b + a ) ] / 3 = x → 11 a + 11 b + x = 3 x . or , x = 11 ( a + b ) / 2 . clearly , we can see that the percentage of the va section will be a multiple of 11 . so , required answer will be 66 . answer : option c
Answer: c
Question (physics): a cube of side 5 meter length is cut into small cubes of side 25 cm each . how many such small cubes can be obtained ?
Options: a ) 10781 , b ) 1276 , c ) 1000 , d ) 8000 , e ) 5000
Rationale: "along one edge , the number of small cubes that can be cut = 500 / 25 = 20 along each edge 20 cubes can be cut . ( along length , breadth and height ) . total number of small cubes that can be cut = 20 * 20 * 20 = 8000 answer : d"
Answer: d
Question (general): two trains of equal are running on parallel lines in the same direction at 45 km / hr and 36 km / hr . the faster train passes the slower train in 36 sec . the length of each train is ?
Options: a ) 45 , b ) 88 , c ) 66 , d ) 55 , e ) 22
Rationale: "let the length of each train be x m . then , distance covered = 2 x m . relative speed = 45 - 36 = 9 km / hr . = 9 * 5 / 18 = 5 / 2 m / sec . 2 x / 36 = 5 / 2 = > x = 45 . answer : a"
Answer: a
Question (general): what is the value of ( p + q ) / ( p - q ) if p / q is 6 ?
Options: a ) 4 / 3 , b ) 2 / 3 , c ) 2 / 6 , d ) 7 / 5 , e ) 8 / 7
Rationale: "( p + q ) / ( p - q ) = [ ( p / q ) + 1 ] / [ ( p / q ) - 1 ] = ( 6 + 1 ) / ( 6 - 1 ) = 7 / 5 answer : d"
Answer: d
Question (physics): a boat having a length 3 m and breadth 2 m is floating on a lake . the boat sinks by 2 cm when a man gets on it . the mass of man is
Options: a ) 12 kg , b ) 60 kg , c ) 72 kg , d ) 120 kg , e ) none
Rationale: "solution volume of water displaced = ( 3 x 2 x 0.02 ) m 3 = 0.12 m 3 . mass of man = volume of water displaced × density of water = ( 0.12 × 1000 ) kg = 120 kg . answer d"
Answer: d
Question (other): the ratio of three numbers is 3 : 4 : 5 and the sum of their squares is 1250 . the sum of the numbers is ?
Options: a ) 2 , b ) 3 , c ) 4 , d ) 6 , e ) 5
Rationale: "let the numbers be 3 x , 4 x , 5 x then , 9 x ^ 2 + 16 x ^ 2 + 25 x ^ 2 = 1250 50 x ^ 2 = 1250 x ^ 2 = 25 x = 5 answer is e"
Answer: e
Question (other): in what ratio must a grocer mix two varieties of pulses costing rs . 15 and rs . 20 per kg respectively so as to get a mixture worth rs . 16.50 kg ?
Options: a ) 7 : 3 , b ) 3 : 7 , c ) 4 : 6 , d ) 5 : 7 , e ) 8 : 9
Rationale: "required rate = 3.50 : 1.50 = 7 : 3 . answer a"
Answer: a
Question (gain): if the personal income tax rate is lowered from 46 % to 32 % , what is the differential savings for a tax payer having an annual income before tax to the tune of $ 36000 ?
Options: a ) $ 3500 , b ) $ 5040 , c ) $ 3150 , d ) $ 7000 , e ) $ 10000
Rationale: "saving = ( 46 - 32 ) % of 36000 = 5040 . answer : b"
Answer: b
Question (general): how many unique positive odd integers less than 100 are equal to the product of a positive multiple of 5 and an odd number ?
Options: a ) 4 , b ) 10 , c ) 11 , d ) 12 , e ) 15
Rationale: the question basically asks how many positive odd integers less than 100 are odd multiples of 5 so we have 5,15 , 25,35 , 45,55 , 65,75 , 85,95 = 10 ans b
Answer: b
Question (physics): how long does a train 165 meters long running at the rate of 54 kmph take to cross a bridge 625 meters in length ?
Options: a ) 62 , b ) 72 , c ) 55 , d ) 82 , e ) 52.7
Rationale: "explanation : t = ( 625 + 165 ) / 54 * 18 / 5 t = 52.7 answer : option e"
Answer: e
Question (general): what is 2 2 / 3 - 1 1 / 4 divided by 1 / 2 - 1 / 4 ?
Options: a ) 17 / 36 , b ) 36 / 17 , c ) 17 / 6 , d ) 17 / 3 , e ) 51 / 4
Rationale: "2 2 / 3 - 1 1 / 4 = 8 / 3 - 5 / 4 = ( 32 - 15 ) / 12 = 17 / 12 1 / 2 - 1 / 4 = ( 2 - 1 ) / 4 = 1 / 4 so 17 / 12 / 1 / 4 = 17 / 12 * 4 = 17 / 3 answer - d"
Answer: d
Question (geometry): the length of a rectangle is one fourth of the radius of a circle . the radius of the circle is equal to the side of the square , whose area is 784 sq . units . what is the area ( in sq . units ) of the rectangle if the rectangle if the breadth is 5 units ?
Options: a ) 35 sq . units
b ) 45 sq . units
c ) 55 sq . units
d ) 50 sq . units
e ) 40 sq . units
Rationale: given that the area of the square = 784 sq . units = > side of square = â ˆ š 784 = 28 units the radius of the circle = side of the square = 28 units length of the rectangle = 1 / 4 * 28 = 7 units given that breadth = 5 units area of the rectangle = lb = 7 * 5 = 35 sq . units answer : a
Answer: a
Question (gain): 33 1 / 3 % of 36 ?
Options: a ) 16 , b ) 21 , c ) 18 , d ) 12 number , e ) 18
Rationale: explanation : 33 1 / 3 % = 1 / 3 1 / 3 * 36 = 12 answer : option d
Answer: d
Question (physics): an engine moves at the speed of 30 kmph without any coaches attached to it . speed of the train reduces at the rate that varies directly as the square root of the number of coaches attached . when 9 coaches are attached speed decreases to 18 kmph . what will be the speed of train when 16 coaches are attached .
Options: a ) 14 , b ) 16 , c ) 18 , d ) 20 , e ) 22
Rationale: "1 . no . of coaches = 9 sqr root = 3 speed decreases by 12 12 = k * 3 k = 4 no . of coaches = 16 swr root = 4 decrease = 4 * 4 = 16 new speed = 30 - 16 = 14 a"
Answer: a
Question (physics): if 20 typists can type 50 letters in 30 minutes , then how many letters will 40 typists working at the same rate complete in 1 hour ?
Options: a ) 400 , b ) 500 , c ) 350 , d ) 250 , e ) 200
Rationale: "no . of letters typing by 20 typists in 30 minutes = 50 no . of letters typing by 20 typists in 60 minutes = 50 * 2 = 100 no . of letters typing by 40 typists in 60 minutes = 100 / 10 * 40 = 400 answer : a"
Answer: a
Question (general): a man whose speed is 3 kmph in still water rows to a certain upstream point and back to the starting point in a river which flows at 1.5 kmph , find his average speed for the total journey ?
Options: a ) 7 , b ) 4 , c ) 3 , d ) 9 , e ) 3.6
Rationale: "m = 3 s = 1.5 ds = 4.5 us = 3 as = ( 2 * 4.5 * 3 ) / 7.5 = 3.6 answer : e"
Answer: e
Question (general): at joes steakhouse the hourly wage for a chef is 20 % greater than that of a dishwasher , and the hourly wage of a dishwasher is half as much as the hourly wage of a manager . if a managers wage is $ 10.50 per hour , how much less than a manager does a chef earn each hour ?
Options: a ) $ 1.40 , b ) $ 2.40 , c ) $ 3.40 , d ) $ 4.40 , e ) $ 4.30
Rationale: "manager wages per hour = $ 10.50 dishwasher wages per hour = half of manager ' s wages . = 1 / 2 ( $ 10.50 ) = = > $ 5.25 chef wages per hour = 20 % greater than dishwasher wages - - > 20 % of $ 5.25 = ( 20 * ( $ 5.25 ) ) / 100 - - > ( $ 95 ) / 100 - - > $ 0.95 therefore , chef wages per hour = $ 5.25 + $ 0.95 = = > $ 6.20 difference of wages between manager and chef = $ 10.50 - $ 6.20 = = > $ 4.30 answer : e"
Answer: e
Question (geometry): if the height of a cone is increased by 140 % then its volume is increased by ?
Options: a ) 100
b ) 140
c ) 998
d ) 729
e ) 2879
Rationale: 140 % answer : b
Answer: b
Question (general): 1345 - ( 1002 / 20.04 ) = ?
Options: a ) 2984 , b ) 2983 , c ) 2982 , d ) 1295 , e ) none of these
Rationale: "1345 - 50 = 1295 answer : d"
Answer: d
Question (general): the guests at a football banquet consumed a total of 325 pounds of food . if no individual guest consumed more than 2 pounds of food , what is the minimum number of guests that could have attended the banquet ?
Options: a ) 160 , b ) 161 , c ) 162 , d ) 163 , e ) 164
Rationale: "to minimize one quantity maximize other . 162 * 2 ( max possible amount of food a guest could consume ) = 324 pounds , so there must be more than 162 guests , next integer is 163 . answer : d ."
Answer: d
Question (general): if money is invested at r percent interest , compounded annually , the amount of the investment will double in approximately 24 / r years . if pat ' s parents invested $ 6,000 in a long - term bond that pays 8 percent interest , compounded annually , what will be the approximate total amount of the investment 18 years later , when pat is ready for college ?
Options: a ) $ 20000 , b ) $ 15000 , c ) $ 12000 , d ) $ 10000 , e ) $ 30000
Rationale: "since investment doubles in 24 / r years , then for r = 8 it ' ll double in 24 / 8 = ~ 3 years ( we are not asked about the exact amount so such an approximation will do ) . thus after 18 years investment will become $ 5,000 * 6 = $ 30,000 . answer : e ."
Answer: e
Question (general): how many 3 - digit numbers abc , in which a , b , and c are each digits , satisfy the equation 2 b = a + c ?
Options: a ) 33 , b ) 36 , c ) 41 , d ) 45 , e ) 50
Rationale: possible solutions are diff of 0 - - 111222 , . . . . . . . . , 999 = 9 diff of 1 - - 123 , 234 , . . . . . , 789 = 7 x 2 = 14 diff of 2 - - 135 , 246 . . . . . . . 579 = 5 x 2 = 10 diff of 3 - - 147 , 258369 = 3 x 2 = 6 diff of 4 - - 159 = 1 x 2 = 2 last 210 , 420 , 630840 = 4 so total is 9 + 14 + 10 + 6 + 2 + 4 = 45 . answer : d
Answer: d
Question (general): in cliff ’ s impressive rock collection , there are half as many igneous rocks as sedimentary rocks . of the igneous rocks , 2 / 3 are shiny and the rest are matte , while 1 / 5 of the sedimentary rocks are shiny . if there are 40 shiny igneous rocks , how many total rocks does cliff have ?
Options: a ) 180 , b ) 45 , c ) 60 , d ) 90 , e ) 135
Rationale: we can start with the known quantity and then go on to find the others . shiny igneous ricks are 40 . these are ( 2 / 3 ) of total igneous rocks . ( 2 / 3 ) * total igneous rocks = 40 total igneous rocks = 40 * ( 3 / 2 ) = 60 total sedimentary rocks = 2 * total igneous rocks = 2 * 60 = 120 total number of rocks = 60 + 120 = 180 answer ( a )
Answer: a
Question (general): 3 sets of 40 , 50 and 60 students appeared for an examination and the pass percentage was 100 , 90 and 80 respectively . the pass percentage of the whole set is
Options: a ) 88.33 , b ) 84.33 , c ) 88.66 , d ) 84.66 , e ) none of these
Rationale: total passed student = 40 + 45 + 48 = 133 133 is 88.66 % of 150 answer : c
Answer: c
Question (general): a bag of potatoes weighs 60 lbs divided by half of its weight . how much does the bag of potatoes weight ?
Options: a ) 20 lb , b ) 11 lb , c ) 10 lb , d ) 15 lb , e ) 5 lb
Rationale: "sol . 66 ÷ 6 = 11 . answer : b"
Answer: b
Question (physics): ake can dig a well in 16 days . paul can dig the same well in 24 days . jake , paul and hari together dig the well in 8 days . hari alone can dig the well in
Options: a ) 48 , b ) 39 , c ) 37 , d ) 27 , e ) 29
Rationale: simple one . let the total work to be done is 48 meters . now jake can dig 3 mts , paul can dig 2 mts a day . now all of them combined dug in 8 days so per day they dug 48 / 8 = 6 mts . so of these 8 mts , hari capacity is 1 mt . so he takes 48 / 1 = 48 days to complete the digging job . answer : a
Answer: a
Question (physics): a man takes twice as long to row a distance against the stream as to row the same distance in favour of the stream . the ratio of the speed of the boat ( in still water ) and the stream is
Options: a ) 1 : 2 , b ) 1 : 3 , c ) 2 : 1 , d ) 3 : 1 , e ) none
Rationale: "sol . let man ’ s rate upstream be x kmph . then , his rate downstream = 2 x kmph . ∴ ( speed in still water ) : ( speed of stream ) = [ 2 x + x / 2 ] : [ 2 x - x / 2 ] 3 x / 2 : x / 2 = 3 : 1 . answer d"
Answer: d
Question (physics): a can complete the job in 6 hours and b can complete the same job in 3 hours . a works for 1 hour and then b joins and both complete the job . what fraction of the job did b complete
Options: a ) 1 / 9 , b ) 3 / 10 , c ) 1 / 2 , d ) 5 / 6 , e ) 8 / 9
Rationale: a = 1 / 9
Answer: a
Question (general): list r contains 5 numbers that have an average value of 60 . if the median of the numbers in the list is equal to the mean and the largest number is equal to 20 more than two times the smallest number , what is the smallest possible value in the list ?
Options: a ) 25 , b ) 28 , c ) 31 , d ) 34 , e ) 37
Rationale: the middle number is 60 . let the smallest number be x . then the largest number is 2 x + 20 . to make x as small as possible , let ' s make the remaining numbers as large as possible . so the second largest = the largest = 2 x + 20 . the second smallest should be equal to the median . the numbers are x , 60 , 60 , 2 x + 20 , 2 x + 20 . x + 60 + 60 + 2 x + 20 + 2 x + 20 = 5 * 60 = 300 5 x = 140 x = 28 the answer is b .
Answer: b
Question (general): evaluate : 98612 / 22 * 11 * 70 = ?
Options: a ) 700.4 , b ) 704.4 , c ) 740.4 , d ) 744.4 , e ) 700.0
Rationale: "according to order of operations , 22 ? 11 ? 70 ( division and multiplication ) is done first from left to right 22 / 11 = 2 * 70 = 140 hence 98612 / 24 * 11 * 70 = 98612 / 140 = 704.4 correct answer b"
Answer: b
Question (general): if a - b = 6 and a 2 + b 2 = 50 , find the value of ab .
Options: a ) a ) 7 , b ) b ) 12 , c ) c ) 15 , d ) d ) 18 , e ) e ) 20
Rationale: "explanation : 2 ab = ( a 2 + b 2 ) - ( a - b ) 2 = 50 - 36 = 14 ab = 7 . answer : a"
Answer: a
Question (physics): in 5 football games thus far this season , barry has run for 98 , 107 , 85 , 89 , and 91 yards . at a minimum , how many yards m will he need to gain this sunday if he wants to keep his season average above 100 yards ?
Options: a ) 101 , b ) 116 , c ) m = 130 , d ) m = 131 , e ) m = 141
Rationale: sorry the answer m = 141 is d .
Answer: d
Question (general): the price of 3 pants and 6 t - shirts is rs . 750 . with the same money one can buy 1 pant and 12 t - shirts . if one wants to buy 8 t - shirts , how much shall she have to pay ?
Options: a ) 150 , b ) 250 , c ) 400 , d ) 450 , e ) 550
Rationale: "let the price of a pant and a t - shirt be rs . x and rs . y respectively . then , 3 x + 6 y = 750 . . . . ( i ) and x + 12 y = 750 . . . . ( ii ) divide equation ( i ) by 3 , we get the below equation . = x + 2 y = 250 . - - - ( iii ) now subtract ( iii ) from ( ii ) x + 12 y = 750 ( - ) x + 2 y = 250 - - - - - - - - - - - - - - - - 10 y = 500 - - - - - - - - - - - - - - - - y = 50 cost of 8 t - shirts = 8 * 50 = 400 answer : c"
Answer: c