Cheukting/mathqa huggingface dataset:
Question (general): how many numbers between 100 and 600 are divisible by 2 , 3 , and 7 together ?
Options: a ) 11 , b ) 12 , c ) 14 , d ) 16 , e ) 18
Rationale: "explanation : as the division is by 2 , 3 , 7 together , the numbers are to be divisible by : 2 * 3 * 7 = 42 the limits are 100 and 600 the first number divisible is 42 * 3 = 126 to find out the last number divisible by 42 within 600 : 600 / 42 = 14.28 hence , 42 * 14 = 588 is the last number divisible by 42 within 600 hence , total numbers divisible by 2 , 3 , 7 together are ( 14 – 2 ) = 12 answer : b"
Answer: b
Question (physics): a pump can fill a tank with water in 2 hours . because of a leak , it took 2 1 / 5 hours to fill the tank . the leak can drain all the water of the tank in ?
Options: a ) 17 hr , b ) 19 hr , c ) 22 hr , d ) 24 hr , e ) 26 hr
Rationale: work done by the tank in 1 hour = ( 1 / 2 - 2 1 / 5 ) = 1 / 22 leak will empty the tank in 22 hrs . answer : c
Answer: c
Question (gain): the salary of a labourer increase consistently by 40 % per year . if his present salary is rs . 3000 then what will his salary be after 3 years ?
Options: a ) 8232 , b ) 3282 , c ) 4282 , d ) 8242 , e ) 2382
Rationale: explanation : salary = 3000 x 1.4 x 1.4 x 1.4 = 8232 answer : option a
Answer: a
Question (gain): in country z , 10 % of the people do not have a university diploma but have the job of their choice , and 30 % of the people who do not have the job of their choice have a university diploma . if 40 % of the people have the job of their choice , what percent of the people have a university diploma ?
Options: a ) 35 % , b ) 48 % , c ) 55 % , d ) 65 % , e ) 75 %
Rationale: setting up a matrix is how i solve this one . diploma no diploma totals job of choice w / diploma job of choice w / o diploma = 10 % job of choice total = 40 % not job of choice with diploma = . 3 x not job of choice w / o diploma = . 7 x total not job of choice = x total with diploma total without diploma total citizen = 100 if 40 % of people have their job of choice , then 60 % of people do not have their job of choice . 30 % of 60 % = 18 % . we can also see that 30 % of the people have their job of choice and a diploma ( 40 % - 10 % = 30 % ) . 30 % + 18 % = 48 % . therefore 48 % of the people in country z have a diploma . ans b
Answer: b
Question (general): in a house a hall is 20 m long , 15 m wide and 5 m high . its interior has to be covered with mat . what will be the total expenditure if it costs rs . 50 per square m ?
Options: a ) s . 43000 , b ) s . 50000 , c ) s . 57000 , d ) s . 60000 , e ) s . 47500
Rationale: "length ( l ) = 20 m , breadth ( b ) = 15 m and height ( h ) = 5 m total area of the hall to be covered with mat = 2 ( lb + bh + hl ) = 2 ( 20 * 15 + 15 * 5 + 5 * 20 ) = 2 ( 300 + 75 + 100 ) = 2 * 475 = 950 sq . m total expenditure = 50 * 950 = rs . 47500 e"
Answer: e
Question (physics): there is a 55 cm line marked at each centimeter and an insect is placed at every centimeter . 9 frogs are trained to jump a constant distance . the first one jumps 2 cm in every leap , the second one jumps 3 cm and so on until the 9 th one jumps 10 cm in every leap and they eat any insect that is available at that spot . if all of them start from start line and finish the entire 55 cm , how many insects were still left after the race was over ?
Options: a ) 0 , b ) 3 , c ) 6 , d ) 9 , e ) 12
Rationale: only the prime numbers greater than 10 and less than 55 were left . that is 11 , 13 , 17 , 19 , 23 , 29 , 31 , 37 , 41 , 43 , 47 , and 53 . the total is 12 . the answer is e .
Answer: e
Question (gain): jayant opened a shop investing rs . 30,000 . madhu joined him 2 months later , investing rs . 45,000 . they earned a profit of rs . 58,000 after completion of one year . what will be madhu ' s share of profit ?
Options: a ) rs . 27,000 , b ) rs . 24,000 , c ) rs . 30,000 , d ) rs . 29,000 , e ) none of these
Rationale: 30,000 * 12 = 45,000 * 8 1 : 1 madhu ' s share = 1 / 2 * 58,000 i . e . rs . 29,000 answer : d
Answer: d
Question (physics): there is enough provisions for 600 men in an army camp for 35 days . if there were 300 men less , how long will the provision last ?
Options: a ) 40 days , b ) 50 days , c ) 60 days , d ) 70 days , e ) 80 days
Rationale: "exp : we have , m 1 d 1 = m 2 d 2 600 * 35 = 300 * d 2 d 2 = 600 * 35 / 300 = 70 days . answer : d"
Answer: d
Question (physics): if 8 parallel lines in a plane is intersected by a family of another 8 parallel lines , how many parallelograms are there in the network thus formed ?
Options: a ) 784 , b ) 763 , c ) 120 , d ) 160 , e ) 1260
Rationale: "parallelogram can formed by 2 horizontal and 2 vertical lines for horizontal 8 c 2 for vertical 8 c 2 total parallelogram is 10 c 2 * 8 c 2 = 28 * 28 = 784 answer : a"
Answer: a
Question (other): there are 100 lights which are functional and each is controlled by a separate on / off switch . two children a and b start playing with the switches . a starts by pressing every third switch till he reaches the end . b , thereafter , presses every fifth switch till he too reaches the end . if all switches were in off position at the beggining , how many lights are switched on by the end of this operation ?
Options: a ) 13 , b ) 41 , c ) 47 , d ) 48 , e ) 53
Rationale: "number of switches = 100 number of switches turned on by a : 3 , 6 , . . . 99 = 33 number of switches turned on by b : 5 , 10 , . . . . 100 = 20 few switches are turned on by a and later turned off by b : lcm ( 3,5 ) = 15 x = 15 , 30 , . . . . 90 = 6 . subtract the above 6 switches from both a and b as they are turned off . number of switches that are turned on = ( 33 - 6 ) + ( 20 - 6 ) = 41 answer : b"
Answer: b
Question (general): at a certain committee meeting only associate professors and assistant professors are present . each associate professor has brought 2 pencils and 1 chart to the meeting , while each assistant professor has brought 1 pencil and 2 charts . if a total of 10 pencils and 14 charts have been brought to the meeting , how many people are present ?
Options: a ) 6 , b ) 7 , c ) 8 , d ) 9 , e ) 10
Rationale: say there are ' a ' associate professors . so we have 2 a pencils and a charts . say there are ' b ' assistant professors . so we have b pencils and 2 b charts . total pencils are 10 so 2 a + b = 10 total charts are 11 so a + 2 b = 14 add both : 3 a + 3 b = 24 so a + b = 8 total number of people = 8 c
Answer: c
Question (general): 30 % people of a village in sri lanka died by bombardment , 25 % of the remainder left the village on account of fear . if now the population is reduced to 6695 , how much was it in the beginning ?
Options: a ) 7000 , b ) 6700 , c ) 6695 , d ) 7645 , e ) 6575
Rationale: "x * ( 70 / 100 ) * ( 75 / 100 ) = 3515 x = 6695 answer : c"
Answer: c
Question (gain): i gain 70 paise on rs . 70 . my gain percent is
Options: a ) 0.1 % , b ) 1 % , c ) 7 % , d ) 10 % , e ) none
Rationale: "solution gain % = ( 0.70 / 70 × 100 ) % = 1 % . answer b"
Answer: b
Question (physics): 50 men took a dip in a water tank 40 m long and 20 m broad on a religious day . if the average displacement of water by a man is 4 , then the rise in the water level in the tank will be :
Options: a ) 22 , b ) 25 , c ) 32 , d ) 99 , e ) 88
Rationale: explanation : total volume of water displaced = ( 4 x 50 ) = 200 rise in water level = = 0.25 m = 25 cm answer : b ) 25 cm
Answer: b
Question (gain): the price of a t . v . set worth rs . 10000 is to be paid in 20 installments of rs . 1000 each . if the rate of interest be 6 % per annum , and the first installment be paid at the time of purchase , then the value of the last installment covering the interest as well will be ?
Options: a ) 9000 , b ) 26699 , c ) 96000 , d ) 19000 , e ) 26711
Rationale: "money paid in cash = rs . 1000 balance payment = ( 10000 - 1000 ) = rs . 9000 answer : a"
Answer: a
Question (gain): find the principle on a certain sum of money at 5 % per annum for 3 years if the amount being rs . 1120 ?
Options: a ) 974 , b ) 1067 , c ) 1977 , d ) 1056 , e ) 1097
Rationale: "1120 = p [ 1 + ( 5 * 3 ) / 100 ] p = 974 answer : a"
Answer: a
Question (physics): a water tank is two - fifth full . pipe a can fill a tank in 10 minutes and pipe b can empty it in 6 minutes . if both the pipes are open , how long will it take to empty or fill the tank completely ?
Options: a ) 6 min , b ) 4 min , c ) 2 min , d ) 5 min , e ) 8 min
Rationale: "clearly , pipe b is faster than pipe a and so , the tank will be emptied . part to be emptied = 2 / 5 part emptied by ( a + b ) in 1 minute = ( 1 / 6 - 1 / 10 ) = 1 / 15 1 / 15 : 2 / 5 : : 1 : x x = ( 2 / 5 * 1 * 15 ) = 6 min . so , the tank will be emptied in 6 min . answer : a"
Answer: a
Question (other): how many two digit prime numbers are there in which both digits are prime numbers ? ( for example , 23 is one of these numbers but 31 is not , since 1 is not a prime number . )
Options: a ) 3 , b ) 4 , c ) 5 , d ) 8 , e ) 15
Rationale: the second digit can only be 3 or 7 , so the choice quickly narrows down to 23 , 27 , 33 , 37 , 53 , 57 , 73 , and 77 . of these , 27 , 33 , and 57 are divisible by 3 , and 77 by 7 , leaving 23 , 37 , 53 , and 73 . it is easy to see that none of these is divisible by 2 , 3 , 5 , or 7 , and there is no need to look at greater prime divisors since root 77 < 11 . correct answer b
Answer: b
Question (gain): a candidate got 35 % of the votes polled and he lost to his rival by 2460 votes . how many votes were cast ?
Options: a ) 7500 , b ) 3388 , c ) 2665 , d ) 8200 , e ) 2661
Rationale: "35 % - - - - - - - - - - - l 65 % - - - - - - - - - - - w - - - - - - - - - - - - - - - - - - 30 % - - - - - - - - - - 2460 100 % - - - - - - - - - ? = > 8200 answer : d"
Answer: d
Question (general): { 8 , 46 , 53 , 127 } what number should be inserted in the set of 7 values to get a median of 9 ?
Options: a ) 20 , b ) 14 , c ) 16 , d ) 5 , e ) 8
Rationale: median is the middle number of a sorted distribution . in case of even number of items , median will be the average of middle two values . the question asks fora new number that will cause the median of new set at 9 . mentionable that given set is already sorted and number of items of new set will be 7 + 1 = 8 . to get median 9 , the sum of 4 th 5 th term should be 18 and it ' s 5 + 14 . so to keep the median 9 , the new item should be > = 14 . the answer is b
Answer: b
Question (general): the ratio 2 : 3 expressed as a percent equals
Options: a ) 12.5 % , b ) 40 % , c ) 67 % , d ) 125 % , e ) none
Rationale: "solution 2 : 3 = 2 / 3 = ( 2 / 3 x 100 ) % . = 66.6 % . answer c"
Answer: c
Question (general): two brother x and y appeared for an exam . the probability of selection of x is 1 / 7 and that of b is 2 / 5 . find the probability that both of them are selected .
Options: a ) 2 / 69 , b ) 2 / 60 , c ) 2 / 63 , d ) 2 / 35 , e ) 2 / 38
Rationale: "explanation : let a be the event that x is selected and b is the event that y is selected . p ( a ) = 1 / 7 , p ( b ) = 2 / 5 . let c be the event that both are selected . p ( c ) = p ( a ) ã — p ( b ) as a and b are independent events : = ( 1 / 7 ) ã — ( 2 / 5 ) = 2 / 35 answer : d ) 2 / 35"
Answer: d
Question (general): 3 consecutive odd integers are in increasing order such that the sum of the last two integers is 17 more than the first integer . find the 3 integers ?
Options: a ) 11 , 1315 , b ) 7 , 2 , 10 , c ) 7 , 9 , 10 , d ) 7 , 9 , 11 , e ) 7 , 9 , 29
Rationale: explanation : let the three consecutive odd integers be x , x + 2 and x + 4 respectively . x + 4 + x + 2 = x + 17 = > x = 11 hence three consecutive odd integers are 11 , 13 and 15 answer : a
Answer: a
Question (physics): p is able to do a piece of work in 5 days and q can do the same work in 10 days . if they can work together for 3 days , what is the fraction of work completed ?
Options: a ) 13 / 10 , b ) 4 / 5 , c ) 11 / 10 , d ) 7 / 10 , e ) 9 / 10
Rationale: "explanation : amount of work p can do in 1 day = 1 / 5 amount of work q can do in 1 day = 1 / 10 amount of work p and q can do in 1 day = 1 / 5 + 1 / 10 = 3 / 10 amount of work p and q can together do in 3 days = 3 × ( 3 / 10 ) = 9 / 10 answer : option e"
Answer: e
Question (general): the sum of three consecutive multiples of 3 is 81 . what is the largest number ?
Options: a ) 24 , b ) 28 , c ) 30 , d ) 32 , e ) 35
Rationale: "let the numbers be 3 x , 3 x + 3 and 3 x + 6 . then , 3 x + ( 3 x + 3 ) + ( 3 x + 6 ) = 81 9 x = 72 x = 8 largest number = 3 x + 6 = 30 . answer : c"
Answer: c
Question (geometry): what is the area of square field whose side of length 15 m ?
Options: a ) 225 sq m
b ) 186 sq m
c ) 586 sq m
d ) 287 sq m
e ) 296 sq m
Rationale: 15 * 15 = 225 sq m answer : a
Answer: a
Question (gain): how many liters of water must be evaporated from 50 liters of a 4 percent sugar solution to get a 10 percent sugar solution ?
Options: a ) 15 , b ) 20 , c ) 25 , d ) 28 , e ) 30
Rationale: "let x be the amount that needs to be evaporated . 0.04 ( 50 ) = 0.1 ( 50 - x ) 0.1 x = 5 - 2 x = 3 / 0.1 = 30 liters the answer is e ."
Answer: e
Question (gain): at what rate percent per annum will a sum of money double in 16 years ?
Options: a ) 10.6 % , b ) 3.65 % , c ) 6.25 % , d ) 8.32 % , e ) 11 %
Rationale: "let principle = p s . i . = p t = 16 yrs rate = 100 * p / p * 16 = 25 / 4 % = 6.25 % answer is c"
Answer: c
Question (general): a hat company ships its hats , individually wrapped , in 8 - inch by 10 - inch by 12 - inch boxes . each hat is valued at $ 7.50 . if the company ’ s latest order required a truck with at least 240,000 cubic inches of storage space in which to ship the hats in their boxes , what was the minimum value of the order ?
Options: a ) $ 960 , b ) $ 1,875 , c ) $ 1,725 , d ) $ 2,050 , e ) $ 2,250
Rationale: "number of boxes = total volume / volume of one box = 240,000 / ( 8 * 10 * 12 ) = 250 one box costs 7.50 , so 250 box will cost = 250 * 7.5 = 1875 b is the answer"
Answer: b
Question (geometry): 10 business executives and 7 chairmen meet at a conference . if each business executive shakes the hand of every other business executive and every chairman once , and each chairman shakes the hand of each of the business executives but not the other chairmen , how many handshakes would take place ?
Options: a ) 144 , b ) 131 , c ) 115 , d ) 90 , e ) 45
Rationale: "there are 10 business exec and in each handshake 2 business execs are involved . hence 10 c 2 = 45 also , each of 10 exec will shake hand with every 7 other chairmen for total of 70 handshake . total = 45 + 70 = 115 ans : c"
Answer: c
Question (gain): in what ratio must water be mixed with milk to gain 16 ( 2 / 3 ) % on selling the mixture at cost price ?
Options: a ) 1 : 6 , b ) 6 : 1 , c ) 2 : 3 , d ) 4 : 3 , e ) 3 : 2
Rationale: "explanation : let c . p . of 1 litre milk be re . 1 . s . p . of 1 litre of mixture = re . 1 , gain = 50 / 3 % c . p . of 1 litre of mixture = ( 100 x 3 / 350 x 1 ) = 6 / 7 by the rule of alligation , we have : ratio of water and milk = 1 / 7 : 6 / 7 = 1 : 6 . answer is a"
Answer: a
Question (physics): two pipes a and b can fill a tank in 2 and 6 minutes respectively . if both the pipes are used together , then how long will it take to fill the tank ?
Options: a ) 2.5 min , b ) 1.8 min , c ) 1.5 min , d ) 3.5 min , e ) 2 min
Rationale: "part filled by the first pipe in 1 minute = 1 / 2 part filled by the second pipe in 1 minute = 1 / 6 net part filled by pipe a and pipe b in 1 minute = ( 1 / 2 ) + ( 1 / 6 ) = 2 / 3 i . e , pipe a and b together can fill the tank in 3 / 2 minutes = 1.5 minutes answer is c"
Answer: c
Question (physics): a train requires 8 seconds to pass a pole while it requires 18 seconds to cross a stationary train which is 400 mtrs long . find the speed of the train .
Options: a ) 144 kmph , b ) 124 kmph , c ) 134 kmph , d ) 150 kmph , e ) 160 kmph
Rationale: in 8 s the train crosses the pole and in 18 sec the train crosses one more stationary train in 10 sec the train travels a distance of 400 mtrs speed = 400 / 10 = 40 m / s = 40 ( 3600 / 1000 ) = 40 * 18 / 5 = 144 kmph answer : a
Answer: a
Question (general): there are 6 people in the elevator . their average weight is 154 lbs . another person enters the elevator , and increases the average weight to 151 lbs . what is the weight of the 7 th person .
Options: a ) 133 , b ) 168 , c ) 189 , d ) 190 , e ) 200
Rationale: "solution average of 7 people after the last one enters = 151 . â ˆ ´ required weight = ( 7 x 151 ) - ( 6 x 154 ) = 1057 - 924 = 133 . answer a"
Answer: a
Question (general): for any number z , z * is defined as the greatest positive even integer less than or equal to y . what is the value of 6.25 – 6.25 * ?
Options: a ) 1.5 , b ) 0.5 , c ) 6.25 , d ) 0.25 , e ) 6.0
Rationale: "since z * is defined as the greatest positive even integer less than or equal to z , then 6.25 * = 6 ( the greatest positive even integer less than or equal to 6.25 is 6 ) . hence , 6.25 – 6.25 * = 6.25 - 6 = 0.25 answer : d ."
Answer: d
Question (physics): a river boat leaves silver town and travels upstream to gold town at an average speed of 3 kilometers per hour . it returns by the same route at an average speed of 7 kilometers per hour . what is the average speed for the round - trip in kilometers per hour ?
Options: a ) 4.2 , b ) 7.1 , c ) 7.2 , d ) 7.5 , e ) 8.0
Rationale: pick a number which is lcm of 7 and 3 = 21 . upstream time = 21 / 3 = 7 hrs downstream time = 21 / 7 = 3 hrs total time = 10 hrs total distance = 42 average speed = 42 / 10 = 4.2 km / hr
Answer: a
Question (general): 6 friends visited a book stall and brought 6 books , and everyone decided to contribute equally to the total bill of $ 400 . if one of the friends had a coupon for 5 % off the total bill , and if each friend still contributed equally after the coupon was applied to the bill , how much did each friend pay ?
Options: a ) 62.12 , b ) 63 , c ) 63.33 , d ) 64 , e ) 65
Rationale: at the non - discounted price , each friend would pay $ 66.66 , as $ 400 divided by 6 friends is $ 66.66 per friend . but if the bill is 5 % off , then each friend would pay 5 % less . 5 % of $ 66.66 is $ 3.33 , so each friend saves $ 3.33 and pays the remaining $ 63.33 correct option : option c
Answer: c
Question (general): the ages of two persons differ by 32 years . if 5 years ago , the elder one be 5 times as old as the younger one , their present ages ( in years ) are respectively
Options: a ) 20,20 , b ) 46,14 , c ) 25,15 , d ) 30,10 , e ) none of these
Rationale: "explanation : let their ages be x and ( x + 32 ) years . 5 ( x - 5 ) = ( x + 32 - 5 ) or 4 x = 52 or x = 14 . their present ages are 46 years and 14 years option b"
Answer: b
Question (general): let f ( x ) = x ^ 2 + bx + c . if f ( 5 ) = 0 and f ( - 3 ) = 0 , then b + c =
Options: a ) 18 , b ) - 17 , c ) - 15 , d ) - 21 , e ) - 24
Rationale: "f ( x ) = x ^ 2 + bx + c . if f ( 5 ) = 0 and f ( - 3 ) = 0 , then b + c = f ( 5 ) = 0 = 25 + 5 b + c - - - taking 25 to the other side - > 5 b + c = - 25 f ( - 3 ) = 0 = 9 - 3 b + c - - - taking - 3 b + c to the other side - > 3 b - c = 9 when we add these 2 equations , we get 8 b = - 16 - - - > b = - 2 and while substituting b = - 2 we get c = - 15 . b + c = - 17 - - - answer b"
Answer: b
Question (general): the average weight of 8 person ' s increases by 5 kg when a new person comes in place of one of them weighing 35 kg . what might be the weight of the new person ?
Options: a ) 80 kg , b ) 85 kg , c ) 75 kg , d ) 100 kg , e ) 110 kg
Rationale: "total weight increased = ( 8 x 5 ) kg = 40 kg . weight of new person = ( 35 + 40 ) kg = 75 kg . answer : c"
Answer: c
Question (general): the average marks of a class of 22 students is 40 and that of another class of 28 students is 60 . find the average marks of all the students ?
Options: a ) 51.2 , b ) 59.5 , c ) 52.8 , d ) 52.5 , e ) 52.1
Rationale: "sum of the marks for the class of 22 students = 22 * 40 = 880 sum of the marks for the class of 28 students = 28 * 60 = 1680 sum of the marks for the class of 50 students = 880 + 1680 = 2560 average marks of all the students = 2560 / 50 = 51.2 answer : a"
Answer: a
Question (general): y = x ^ 2 + bx + 512 cuts the x axis at ( h , 0 ) and ( k , 0 ) . if h and k are integers , what is the least value of b ?
Options: a ) - 512 , b ) - 257 , c ) - 256 , d ) - 513 , e ) 128
Rationale: as the curve cuts the x - axis at ( h , 0 ) and ( k , 0 ) . therefore h , k are the roots of the quadratic equation . for the quadratic equation is in the form of ax ^ 2 + bx + c = 0 , the product of the roots = c / a = 512 / 1 = 256 and the sum of the roots = - b / a = - b 512 can be expressed as product of two numbers in the following ways : 1 * 512 2 * 256 4 * 128 8 * 64 16 * 32 the sum of the roots is maximum when the roots are 1 and 256 and the maximum sum is 1 + 512 = 513 . the least value possible for b is therefore - 513 . d
Answer: d
Question (geometry): the slant height of a cone is 10 cm and radius of the base is 5 cm , find the curved surface of the cone .
Options: a ) 250 , b ) 170 , c ) 148 , d ) 157 , e ) 150
Rationale: "π * 5 * 10 = 157 answer : d"
Answer: d
Question (geometry): find the area of a parallelogram with base 30 cm and height 12 cm ?
Options: a ) 290 cm 2 , b ) 360 cm 2 , c ) 270 cm 2 , d ) 280 cm 2 , e ) 260 cm 2
Rationale: "area of a parallelogram = base * height = 30 * 12 = 360 cm 2 answer : b"
Answer: b
Question (general): if 45 - [ 28 - { 37 - ( 15 - * ) } ] = 57 , then * is equal to :
Options: a ) - 29 , b ) - 19 , c ) 18 , d ) 29 , e ) 39
Rationale: "45 - [ 28 - { 37 - ( 15 - * ) } ] = 57 = > 45 - [ 28 - { 37 - 15 + * } ] = 57 45 - [ 28 - 37 + 15 - * ] = 57 = > 45 [ 43 - 37 - * ] = 57 45 - [ 6 - * ] = 57 = > 45 - 6 + * = 57 39 + * = 57 = > * = 57 - 39 = 18 answer : c"
Answer: c
Question (physics): in a kilometer race , a beats b by 51 meters or 11 seconds . what time does a take to complete the race ?
Options: a ) 22 , b ) 190 , c ) 277 , d ) 204 , e ) 208
Rationale: "time taken by b run 1000 meters = ( 1000 * 11 ) / 51 = 215 sec . time taken by a = 215 - 11 = 204 sec . answer : d"
Answer: d
Question (general): how many three - digit numbers that do not contain the digits 2 or 5 are there ?
Options: a ) 488 , b ) 996 , c ) 228 , d ) 456 , e ) 1986
Rationale: "we can have 7 digits ( 1 , 3,4 , 6,7 , 8,9 ) for the first place ( hundred ' s place ) . and similarly 8 digits for tenth ' s and unit digit . ( 0,1 , 3,4 , 6,7 , 8,9 ) so in total 7 * 8 * 8 = 488 hence b"
Answer: b
Question (gain): a person borrows rs . 5000 for 2 years at 4 % p . a . simple interest . he immediately lends it to another person at 6 % p . a for 2 years . find his gain in the transaction per year .
Options: a ) 100 , b ) 150 , c ) 225 , d ) 112.5 , e ) 212.5
Rationale: "explanation : the person borrows rs . 5000 for 2 years at 4 % p . a . simple interest simple interest that he needs to pay = prt / 100 = 5000 × 4 × 2 / 100 = 400 he also lends it at 6 % p . a for 2 years simple interest that he gets = prt / 100 = 5000 × 6 × 2 / 100 = 600 his overall gain in 2 years = rs . 600 - rs . 400 = rs . 200 his overall gain in 1 year = 200 / 2 = rs . 100 answer : option a"
Answer: a
Question (gain): shop offered 25 % offer for every shirt , smith bought a shirt at rs . 560 . and what was the shop ' s original selling price ?
Options: a ) 500 , b ) 550 , c ) 746 , d ) 700 , e ) 750
Rationale: sp * ( 75 / 100 ) = 560 sp = 7.46 * 100 = > cp = 746 answer : c
Answer: c
Question (physics): what is the least number of square tiles required to pave the floor of a room 10 m 17 cm long and 9 m 9 cm broad ?
Options: a ) 724 , b ) 804 , c ) 11413 , d ) 844 , e ) none
Rationale: "solution length of largest tile = h . c . f . of 1017 cm & 909 cm = 9 cm . area of each tile = ( 9 x 9 ) cm 2 ∴ required number of tiles = [ 1017 x 909 / 9 x 9 ] = 11413 . answer c"
Answer: c
Question (general): if a person walks at 15 km / hr instead of 9 km / hr , he would have walked 20 km more . the time traveled by him is ?
Options: a ) 8 hours , b ) 9 / 5 hours , c ) 10 / 3 hours , d ) 6 hours , e ) 11 / 3 hours
Rationale: "let the actual distance traveled be x km . then , x / 9 = ( x + 20 ) / 15 5 x - 3 x = 60 = > x = 30 km . travel time is = 30 / 9 hours = 10 / 3 hours answer : c"
Answer: c