Cheukting/mathqa huggingface dataset:
Question (general): a is two years older than b who is twice as old as c . the total of the ages of a , b and c is 27 . how old is b ?
Options: a ) 25 , b ) 20 , c ) 15 , d ) 10 , e ) 5
Rationale: "let age of c = x . then , age of b = 2 x age of a = 2 + 2 x total age of a , b and c = 27 ⇒ ( 2 + 2 x ) + 2 x + x = 27 ⇒ 5 x = 25 ⇒ x = 255 = 5 b ' s age = 2 x = 2 × 5 = 10 answer is d ."
Answer: d
Question (general): find the value of x : x ² + 6 x + 9 .
Options: a ) 9 , b ) - 1 , c ) - 3 , d ) 3 , e ) - 9
Rationale: that quadratic is factored as follows : x ² + 6 x + 9 = ( x + 3 ) ( x + 3 ) . lesson 17 . now , it is easy to see that that both factors will be 0 when x = - 3 . the solution is : x = - 3 c
Answer: c
Question (physics): joe needs to paint all the airplane hangars at the airport , so he buys 360 gallons of paint to do the job . during the first week , he uses 1 / 6 of all the paint . during the second week , he uses 1 / 5 of the remaining paint . how many gallons of paint has joe used ?
Options: a ) 18 , b ) 120 , c ) 175 , d ) 216 , e ) 250
Rationale: "total paint initially = 360 gallons paint used in the first week = ( 1 / 6 ) * 360 = 60 gallons . remaning paint = 300 gallons paint used in the second week = ( 1 / 5 ) * 300 = 60 gallons total paint used = 120 gallons . option b"
Answer: b
Question (physics): the e train leaves station a moving at a constant speed , and passes by stations b and c , in this order . it takes the e train 7 hours to reach station b , and 5 additional hours to reach station c . the distance between stations a and b is m kilometers longer than the distance between stations b and c . what is the distance between stations a and c in terms of m ?
Options: a ) 1.8 m , b ) 6 m , c ) 7 m , d ) 9 m , e ) 12 m
Rationale: the reason it is failing for you is that you chose incorrect numbers . if the question says e it took 7 hrs to reach from a to b and 5 hrs to reach from b to c at a constant speed . it shows that distance ab and bc should be in ratio of 7 / 5 . if you take such numbers you can solve problem . ab = 7 , bc = 5 therefore ab - bc = 2 but from question , ab - bc = m = > m = 2 now total distance = ab + bc = 12 substitute 12 to get answer in terms of m total distance = 12 = 6 m ans b
Answer: b
Question (gain): dana borrows 5000 pounds annually for her college education . if dana gives her parents 4 % of that amount back each month , how much will she still owe her parents after 4 years of college ?
Options: a ) 9800 , b ) 10000 , c ) 10200 , d ) 10400 , e ) 10600
Rationale: dana borrows 5000 and returns 4 % per month . so returns 200 per month . and 2400 per year . so dana owes 5000 - 2400 = 2600 per year . after 4 years she will owe 10400 . ans ( c )
Answer: c
Question (general): a student scored an average of 75 marks in 3 subjects : physics , chemistry and mathematics . if the average marks in physics and mathematics is 90 and that in physics and chemistry is 70 , what are the marks in physics ?
Options: a ) 86 , b ) 16 , c ) 76 , d ) 95 , e ) 26
Rationale: "given m + p + c = 75 * 3 = 225 - - - ( 1 ) m + p = 90 * 2 = 180 - - - ( 2 ) p + c = 70 * 2 = 140 - - - ( 3 ) where m , p and c are marks obtained by the student in mathematics , physics and chemistry . p = ( 2 ) + ( 3 ) - ( 1 ) = 180 + 140 - 225 = 95 answer : d"
Answer: d
Question (general): a positive number x is multiplied by 8 , and this product is then divided by 3 . if the positive square root of the result of these two operations equals x , what is the value of x ?
Options: a ) 9 / 4 , b ) 3 / 2 , c ) 8 / 3 , d ) 2 / 3 , e ) 1 / 2
Rationale: "sq rt ( 8 x / 3 ) = x = > 8 x / 3 = x ^ 2 = > x = 8 / 3 ans - c"
Answer: c
Question (physics): a and b working together could mow a field in 28 days and with the help of c they could have mowed it in 21 days . how long would c take by himself ?
Options: a ) 68 days , b ) 84 days , c ) 90 days , d ) 72 days , e ) 50 days
Rationale: required answer = 28 * 21 / 28 - 21 = 84 days answer is b
Answer: b
Question (general): two employees x and y are paid a total of rs . 590 per week by their employer . if x is paid 120 percent of the sum paid to y , how much is y paid per week ?
Options: a ) s . 268 , b ) s . 288 , c ) s . 298 , d ) s . 300 , e ) s . 388
Rationale: "let the amount paid to x per week = x and the amount paid to y per week = y then x + y = 590 but x = 120 % of y = 120 y / 100 = 12 y / 10 ∴ 12 y / 10 + y = 590 ⇒ y [ 12 / 10 + 1 ] = 590 ⇒ 22 y / 10 = 590 ⇒ 22 y = 5900 ⇒ y = 5900 / 22 = 500 / 2 = rs . 268 a )"
Answer: a
Question (gain): tom opened a shop investing rs . 30000 . jose joined him 2 months later , investing rs . 45000 . they earned a profit of rs . 36000 after completion of one year . what will be jose ' s share of profit ?
Options: a ) 20000 , b ) 10000 , c ) 25000 , d ) 34000 , e ) 30000
Rationale: "sol = ~ s - so anju ’ s share = [ 5 / 9 ] x 36000 = 20000 a"
Answer: a
Question (general): if 10 % of x = 20 % of y , then x : y is equal to ?
Options: a ) 2 : 6 , b ) 2 : 1 , c ) 7 : 1 , d ) 2 : 8 , e ) 2 : 2
Rationale: 10 % of x = 20 % of y 10 x / 100 = 20 y / 100 = > x / 10 = y / 5 x / y = 10 / 5 = 2 / 1 x : y = 2 : 1 . answer : b
Answer: b
Question (gain): in a certain math department , students are required to enroll in either calculus or trigonometry , each of which is offered in beginner and advanced courses . the number of students enrolled in trigonometry is 50 % greater than the number of students enrolled in calculus , and 70 % of calculus students are enrolled in the beginner course . if 4 / 5 of students are in the beginner courses , and one student is selected at random , what is the probability that a beginner trigonometry student is selected ?
Options: a ) 40 % , b ) 44 % , c ) 48 % , d ) 52 % , e ) 56 %
Rationale: "let x be the number of students in calculus . then the number of students in trigonometry is 1.5 x the number of students on beginner calculus is 0.7 x the number of students in beginner trigonometry is 4 / 5 * ( 2.5 x ) - 0.7 x = 1.3 x the percentage in beginner trigonometry is 1.3 x / 2.5 x = 52 % the answer is d ."
Answer: d
Question (physics): a and b can do a work in 12 days , b and c in 30 days and c and a in 36 days . in how many days will the work be completed , if all three of them work together ?
Options: a ) 180 / 15 , b ) 180 / 10 , c ) 180 / 13 , d ) 180 / 15 , e ) 180 / 11
Rationale: "one day work of a and b = 1 / 12 one day work of b and c = 1 / 30 one day work of c and a = 1 / 36 2 ( a + b + c ) = 1 / 12 + 1 / 30 + 1 / 36 2 ( a + b + c ) = 13 / 90 ( a + b + c ) = 13 / 180 number of days required = 180 / 13 days . answer : c"
Answer: c
Question (general): if the median of a list of numbers is m , the first quartile of the list is the median of the numbers in the list that are less than m . what is the first quartile of the list of numbers 42 , 24 , 30 , 22 , 28 , 19 , 33 and 35 ?
Options: a ) 33 , b ) 25 , c ) 27 , d ) 24 , e ) 23
Rationale: "it is given that a quartile is the middle number of all numbers less than median . . so lets arrange the number in ascending order - 42 , 24 , 30 , 22 , 28 , 19 , 33 and 35 19 , 22 , 24 , 28 , 30 , 33 , 35 , 42 . . . numbers less than median are 19 , 22 , 24 , 28 . . the median of these numbers = center of 22 and 24 = 23 e"
Answer: e
Question (physics): a and b can do a piece of work in 18 days ; band c can do it in 24 days a and c can do it in 36 days . in how many days will a , band c finish it together ?
Options: a ) 15 days , b ) 12 days , c ) 8 days , d ) 16 days , e ) 9 days
Rationale: sol . ( a + b ) ' s 1 day ' s work = ( 1 / 18 ) ( b + c ) ' s 1 day ' s work = ( 1 / 24 ) and ( a + c ) ' s 1 day ' s work = ( 1 / 36 ) adding , we get : 2 ( a + b + c ) ' s 1 day ' s work = ¬ ( 1 / 18 + 1 / 24 + 1 / 36 ) = 9 / 72 = 1 / 8 ( a + b + c ) ' s 1 day ' s work = 1 / 16 thus , a , band c together can finish the work in 16 days . ans : d
Answer: d
Question (general): what is the sum of all possible solutions to | x - 3 | ^ 2 + | x - 3 | = 30 ?
Options: a ) 4 , b ) 5 , c ) 3 , d ) 2 , e ) 1
Rationale: "denote | x - 3 | as y : y ^ 2 + y = 30 - - > y = - 6 or y = 5 . discard the first solution since y = | x - 3 | , so it ' s an absolute value and thus can not be negative . y = | x - 3 | = 5 - - > x = 8 or x = - 3 . the sum = 5 . answer : b ."
Answer: b
Question (general): let the number which when multiplied by 12 is increased by 198 .
Options: a ) 18 , b ) 20 , c ) 26 , d ) 28 , e ) 30
Rationale: "solution let the number be x . then , 12 x - x = 198 ‹ = › 11 x = 198 x ‹ = › 18 . answer a"
Answer: a
Question (other): 200 college students were asked in a survey if they preferred windows or mac brand computers . 70 students claimed that they preferred mac to windows brand computers . one third as many of the students who preferred mac to windows , equally preferred both brands . 80 of the students had no preference . how many of the students in the survey preferred windows to mac brand computers ?
Options: a ) 25 , b ) 50 , c ) 57 , d ) 60 , e ) 75
Rationale: "200 = 70 ( mac ) + x ( window ) + 80 ( both ) = > x = 50 answer : b"
Answer: b
Question (general): what is the smallest no . that should be added to 27452 to make it exactly divisible by 9 ?
Options: a ) 1 , b ) 3 , c ) 5 , d ) 6 , e ) 9
Rationale: if a number is divisible by 9 , the sum of its digits must be a multiple of 9 . here , 2 + 7 + 4 + 5 + 2 = 20 , the next multiple of 9 is 27 . 7 must be added to 27452 to make it divisible by 9 e
Answer: e
Question (gain): a circle graph shows how the megatech corporation allocates its research and development budget : 14 % microphotonics ; 25 % home electronics ; 15 % food additives ; 29 % genetically modified microorganisms ; 8 % industrial lubricants ; and the remainder for basic astrophysics . if the arc of each sector of the graph is proportional to the percentage of the budget it represents , how many degrees of the circle are used to represent basic astrophysics research ?
Options: a ) 8 ° , b ) 10 ° , c ) 18 ° , d ) 33 ° , e ) 52 °
Rationale: "here all percentage when summed we need to get 100 % . as per data 14 + 25 + 15 + 29 + 8 = 91 % . so remaining 9 % is the balance for the astrophysics . since this is a circle all percentage must be equal to 360 degrees . 100 % - - - - 360 degrees then 9 % will be 33 degrees . . imo option d ."
Answer: d
Question (physics): two trains 140 m and 160 m long run at the speed of 60 km / hr and 40 km / hr respectively in opposite directions on parallel tracks . the time ( in seconds ) which they take to cross each other , is :
Options: a ) 9 , b ) 9.6 , c ) 10 , d ) 10.8 , e ) 7
Rationale: "explanation : relative speed = ( 60 + 40 ) km / hr = [ 100 x ( 5 / 18 ) ] m / sec = ( 250 / 9 ) m / sec . distance covered in crossing each other = ( 140 + 160 ) m = 300 m . required time = [ 300 x ( 9 / 250 ) ] sec = ( 54 / 5 ) sec = 10.8 sec . answer : d"
Answer: d
Question (other): a certain company that sells only cars and trucks reported that revenues from car sales in 1997 were down 11 percent from 1996 and revenues from truck sales were up 7 percent from 1996 . if total revenues from car sales and truck sales in 1997 were up 1 percent from 1996 , what is the ratio t of revenue from car sales in 1996 to revenue from truck sales in 1996 ?
Options: a ) 1 : 2 , b ) 4 : 5 , c ) 1 : 1 , d ) 3 : 2 , e ) 5 : 3
Rationale: a . . i have probably solved this question 3 - 4 times by now . . remember the answer . . 1 : 2
Answer: a
Question (gain): in a recent election , geoff received 0.5 percent of the 6,000 votes cast . to win the election , a candidate needed to receive more than x % of the vote . if geoff needed exactly 3,000 more votes to win the election , what is the value of x ?
Options: a ) 50 , b ) 50.5 , c ) 56 , d ) 60 , e ) 63
Rationale: word problems are tricky in somehow more than other problem because you have the additional step to translate . breaking the problem : geoff how many votes he receives ? ? 30 votes he needs 3571 more votes so : 30 + 3000 = 3030 now what ' s the problem wants ? ? a x % . . . . . . . . 3030 is what % of total votes 6000 . . . . . . . . translating : 3030 = x / 100 * 6000 - - - x = 50.5 % . . . . . . . . . . b
Answer: b
Question (general): if a ^ 3 is divisible by 240 what is the least possible value of integer a ?
Options: a ) 12 , b ) 30 , c ) 60 , d ) 90 , e ) 120
Rationale: 240 can be written as ( 2 ^ 4 ) * 3 * 5 . for a ^ 3 to be divisible by 240 it should contain atleast 2 ^ 4 and 3 and 5 in its factors . we can leave out option a because 12 doesnt have 5 as one of its factor . now if we check for option b , 30 can be written as 2 * 3 * 5 , hence 30 ^ 3 will have 3 as the maximum power of 2 , so we can leave out this option too . option c is the right answer if we follow the same method as we followed for other two previous options . 60 = ( 2 ^ 2 ) * 3 * 5 ; 60 ^ 3 = ( 2 ^ 6 ) * ( 3 ^ 3 ) * ( 5 ^ 3 ) . so it shows that 60 ^ 3 is divisible by 240 and hence the answer . answer : c
Answer: c
Question (physics): a goods train runs at a speed of 72 kmph and crosses a 250 m long platform in 26 seconds . what is the length of the goods train ?
Options: a ) 230 m , b ) 240 m , c ) 260 m , d ) 270 m , e ) 250 m
Rationale: "s = 250 + x / t 72 * 5 / 18 = 250 + x / 26 x = 270 answer : d"
Answer: d
Question (geometry): a metallic sheet is of rectangular shape with dimensions 40 m x 30 m . from each of its corners , a square is cut off so as to make an open box . if the length of the square is 8 m , the volume of the box ( in m cube ) is :
Options: a ) 3220 m cube
b ) 4140 m cube
c ) 2688 m cube
d ) 4000 m cube
e ) none of these
Rationale: explanation : l = ( 40 - 16 ) m = 24 m , [ because 8 + 8 = 16 ] b = ( 30 - 16 ) m = 14 m , h = 8 m . volume of the box = ( 24 x 14 x 8 ) m cube = 2688 m cube . option c
Answer: c
Question (general): the average of temperatures at noontime from monday to friday is 60 ; the lowest one is 50 , what is the possible maximum range of the temperatures ?
Options: a ) 50 , b ) 25 , c ) 40 , d ) 45 , e ) 75
Rationale: "average = 60 , sum of temperatures = 60 * 5 = 300 as the min temperature is 50 , max would be 300 - 4 * 50 = 100 - - > the range = 100 ( max ) - 50 ( min ) = 50 answer : a"
Answer: a
Question (geometry): find the area of a rhombus one side of which measures 20 cm and one diagonal is 26 cm .
Options: a ) 600 cm 2 , b ) 500 cm 2 , c ) 516 cm 2 , d ) 416 cm 2 , e ) 100 cm 2
Rationale: "explanation : let other diagonal = 2 x cm . since diagonals of a rhombus bisect each other at right angles , we have : ( 20 ) 2 = ( 12 ) 2 + ( x ) 2 = > x = √ ( 20 ) 2 – ( 12 ) 2 = √ 256 = 16 cm . _ i so , other diagonal = 32 cm . area of rhombus = ( 1 / 2 ) x ( product of diagonals ) = ( 1 / 2 × 26 x 32 ) cm 2 = 416 cm 2 answer : option d"
Answer: d
Question (general): what are the last two digits of ( 301 * 402 * 503 * 604 * 646 * 547 * 448 * 349 ) ^ 2
Options: a ) 96 , b ) 76 , c ) 56 , d ) 36 , e ) 16
Rationale: "( ( 301 * 402 * 503 * 604 * 646 ) * ( 547 * 448 * 349 ) ) ^ 2 if you observe above digits , last digit are : 1,2 , 3,4 , 6,7 , 8,9 ; 5 is missing ; so i have rearranged them so that multiplication will be easy for me as initial 4 digits have last two digits as 01 , 02,03 , 04,46 and final three as 47 * 48 * 49 . solving for only last two digits and multiplying them we get : ( ( 06 * 04 * 46 ) ( 56 * 49 ) ) ^ 2 = ( 44 * 44 ) ^ 2 = 36 ^ 2 = 76 hence answer is b"
Answer: b
Question (general): if two of the 4 expressions x + y , x + 5 y , x - y , and 5 x - y are chosen at random , what is the probability t that their product will be of the form of x ^ 2 - ( by ) ^ 2 , where b is an integer ?
Options: a ) 1 / 2 , b ) 1 / 3 , c ) 1 / 4 , d ) 1 / 5 , e ) t = 1 / 6
Rationale: only ( x + y ) ( x - y ) pair will give the form x ^ 2 - ( by ) ^ 2 the probability of selecting these two pairs are 1 / 4 * 1 / 3 = 1 / 12 , assuming x + y is picked first , then x - y , but x - y can be picked first followed by x + y . so the probability t = 1 / 12 * 2 = 1 / 6 ans e
Answer: e
Question (general): if n = 2.0767 and n * is the decimal obtained by rounding n to the nearest hundredth , what is the value of n * – n ?
Options: a ) - 0.0053 , b ) - 0.0003 , c ) 0.0007 , d ) 0.0047 , e ) 0.0033
Rationale: "n * = 2.08 n * - n = 2.08 - 2.0767 0.0033 answer : e"
Answer: e
Question (general): list f consists of 12 consecutive integers . if - 4 is the least integer in list f , what is the range of positive integers in list f ?
Options: a ) 5 , b ) 6 , c ) 7 , d ) 11 , e ) 12
Rationale: since - 4 is the least integer in list f , then 7 is the largest integer in that list . thus the range of the positive integers in the list is 7 - 1 = 6 . answer : b .
Answer: b
Question (general): a man is 32 years older than his son . in two years , his age will be twice the age of his son . the present age of the son is ?
Options: a ) 16 , b ) 19 , c ) 15 , d ) 22 , e ) 30
Rationale: "let the son ' s present age be x years . then , man ' s present age = ( x + 24 ) years . ( x + 32 ) + 2 = 2 ( x + 2 ) x + 34 = 2 x + 4 = > x = 30 . answer : e"
Answer: e
Question (physics): a man can row upstream at 8 kmph and downstream at 13 kmph . the speed of the stream is ?
Options: a ) 3 kmph , b ) 2.5 kmph , c ) 3.5 kmph , d ) 4.3 kmph , e ) 5 kmph
Rationale: "speed of stream = 1 / 2 ( 13 - 8 ) = 2.5 kmph answer is b"
Answer: b
Question (physics): a vessel of capacity 30 litres is fully filled with pure milk . nine litres of milk is removed from the vessel and replaced with water . nine litres of the solution thus formed is removed and replaced with water . find the quantity of pure milk in the final milk solution ?
Options: a ) 14.7 , b ) 2.9 , c ) 38.3 , d ) 78.3 , e ) 79.3
Rationale: "explanation : let the initial quantity of milk in vessel be t litres . let us say y litres of the mixture is taken out and replaced by water for n times , alternatively . quantity of milk finally in the vessel is then given by [ ( t - y ) / t ] ^ n * t for the given problem , t = 30 , y = 9 and n = 2 . hence , quantity of milk finally in the vessel = [ ( 30 - 9 ) / 30 ] ^ 2 ( 30 ) = 14.7 litres . answer : option a"
Answer: a
Question (general): the tax on a commodity is diminished by 20 % but its consumption is increased by 5 % . find the decrease percent in the revenue derived from it ?
Options: a ) 12 % , b ) 14 % , c ) 16 % , d ) 20 % , e ) 22 %
Rationale: "explanation : 100 * 100 = 10000 80 * 105 = 8400 10000 - - - - - - - 1600 100 - - - - - - - ? = 16 % c )"
Answer: c
Question (general): if 15 ! / 3 ^ x is an integer , what is the greatest possible value of x ?
Options: a ) 3 , b ) 4 , c ) 5 , d ) 6 , e ) 7
Rationale: "15 - 5 * 3 12 - 4 * 3 9 - 3 * 3 6 - 2 * 3 3 - 1 * 3 hence max of 3 ^ 6 is allowed . imo d ."
Answer: d
Question (physics): how many cubes of 50 cm edge can be put in a cubical box of 1 m edge .
Options: a ) 17 cm , b ) 10 cm , c ) 8 cm , d ) 6 cm , e ) 7 cm
Rationale: "number of cubes = 100 â ˆ — 100 â ˆ — 100 / 50 * 50 * 50 = 8 number of cubes = 100 â ˆ — 100 â ˆ — 10010 â ˆ — 10 â ˆ — 10 = 1000 note : 1 m = 100 cm answer : c"
Answer: c
Question (general): we have boxes colored either red or blue . in each blue box there is a fixed number of blueberries . in each red box there is a fixed number of strawberries . if we dispose of one blue box for one additional red box , the total number of berries would increase by 20 , and the difference between the total number of strawberries and the total number of blueberries would increase by 80 . each blue box contains how many blueberries ?
Options: a ) 25 , b ) 30 , c ) 35 , d ) 40 , e ) 45
Rationale: let x be the number of blueberries in each blue box . then there are x + 20 strawberries in each red box . x + ( x + 20 ) = 80 x = 30 the answer is b .
Answer: b
Question (gain): a portion of the 90 % solution of chemicals was replaced with an equal amount of 20 % solution of chemicals . as a result , 40 % solution of chemicals resulted . what part of the original solution was replaced ?
Options: a ) 5 / 7 , b ) 6 / 7 , c ) 9 / 5 , d ) 13 / 9 , e ) 13 / 6
Rationale: this is a weighted average question . say x % of the solution was replaced - - > equate the amount of chemicals : 0.90 ( 1 - x ) + 0.2 * x = 0.4 - - > x = 5 / 7 . answer : a .
Answer: a
Question (general): in smithtown , the ratio of right - handed people to left - handed people is 3 to 1 and the ratio of men to women is 3 to 2 . if the number of right - handed men is maximized , then what s percent of all the people in smithtown are left - handed women ?
Options: a ) 50 % , b ) 40 % , c ) 25 % , d ) 20 % , e ) 10 %
Rationale: "looking at the ratio we can take total number of people = 20 . . ans 5 / 20 or 25 % c"
Answer: c
Question (general): a man is 24 years older than his son . in two years , his age will be twice the age of his son . the present age of this son is
Options: a ) 21 years , b ) 22 years , c ) 23 years , d ) 24 years , e ) 26 years
Rationale: "explanation : let ' s son age is x , then father age is x + 24 . = > 2 ( x + 2 ) = ( x + 24 + 2 ) = > 2 x + 4 = x + 26 = > x = 22 years option b"
Answer: b
Question (physics): how many cubes of 10 cm edge can be put in a cubical box of 1 m edge
Options: a ) 10 , b ) 100 , c ) 1000 , d ) 10000 , e ) none of these
Rationale: "explanation : number of cubes = ( 100 x 100 x 100 ) / ( 10 x 10 x 10 ) = 1000 answer : c"
Answer: c
Question (general): each of the integers from 1 to 14 is written on the a seperate index card and placed in a box . if the cards are drawn from the box at random without replecement , how many cards must be drawn to ensure that the product of all the integers drawn is even ?
Options: a ) 19 , b ) 12 , c ) 11 , d ) 10 , e ) 8
Rationale: "out of the 14 integers : 7 are odd and 7 are even . if we need to make sure that the product of all the integers withdrawn is even then we need to make sure that we have at least one even number . in the worst case : 1 . we will end up picking odd numbers one by one , so we will pick all 7 odd numbers first 2 . 8 th number will be the first even number so we need to withdraw at least 8 numbers to make sure that we get one even number and the product of all the integers picked is even . so , answer will be 8 . ( e )"
Answer: e
Question (physics): two trains of length 200 m and 300 m are 200 m apart . they start moving towards each other on parallel tracks , at speeds 36 kmph and 72 kmph . in how much time will the trains cross each other ?
Options: a ) 70 / 8 , b ) 70 / 7 , c ) 70 / 5 , d ) 70 / 3 , e ) 70 / 1
Rationale: "relative speed = ( 36 + 72 ) * 5 / 18 = 6 * 5 = 30 mps . the time required = d / s = ( 200 + 200 + 300 ) / 30 = 700 / 30 = 70 / 3 sec . answer : d"
Answer: d
Question (general): a salesman ’ s terms were changed from a flat commission of 5 % on all his sales to a fixed salary of rs . 1200 plus 2.5 % commission on all sales exceeding rs . 4,000 . if his remuneration as per new scheme was rs . 1200 more than that by the previous schema , his sales were worth ?
Options: a ) 12028 , b ) 12000 , c ) 12019 , d ) 16000 , e ) 12012
Rationale: "[ 1200 + ( x - 4000 ) * ( 2.5 / 100 ) ] - x * ( 5 / 100 ) = 600 x = 16000 answer : d"
Answer: d
Question (general): i chose a number and divide it by 6 . then i subtracted 15 from the result and got 5 . what was the number i chose ?
Options: a ) 600 , b ) 700 , c ) 120 , d ) 900 , e ) none
Rationale: "solution : let xx be the number i chose , then x / 6 â ˆ ’ 15 = 5 x / 6 = 20 x = 120 answer c"
Answer: c
Question (other): veena ranks 44 rd from the top in a class of 182 . what is her rank from the bottom if 22 students have failed the examination ?
Options: a ) 88 , b ) 108 , c ) 110 , d ) 90 , e ) 117
Rationale: "total student = 182 failed = 22 paasd student = 182 - 22 = 160 from bottom her rank is = 160 - 44 + 1 = 117 answer : e"
Answer: e