Cheukting/mathqa huggingface dataset:
Question (physics): a large tanker can be filled by two pipes a and b in 60 and 40 minutes respectively . how many minutes will it take to fill the tanker from empty state if b is used for half the time and a and b fill it together for the other half ?
Options: a ) 30 , b ) 15 , c ) 20 , d ) 25 , e ) 50
Rationale: suppose the tank is filled in x minutes . then , x / 2 ( 1 / 24 + 1 / 40 ) = 1 x / 2 * 1 / 15 = 1 = > x = 30 min answer a
Answer: a
Question (general): the captain of a cricket team of 11 members is 27 years old and the wicket keeper is 1 year older . if the ages of these two are excluded , the average age of the remaining players is one year less than the average age of the whole team . what is the average age of the team ?
Options: a ) 20 , b ) 21 , c ) 22 , d ) 23 , e ) 24
Rationale: "let the average age of the whole team be x years . 11 x - ( 27 + 28 ) = 9 ( x - 1 ) 11 x - 9 x = 46 2 x = 46 x = 23 . the average age of the team is 23 years . the answer is d ."
Answer: d
Question (other): if log 1087.5 = 6.9421 , then the number of digits in ( 875 ) 10 is ?
Options: a ) 30 , b ) 28 , c ) 80 , d ) 26 , e ) 25
Rationale: "x = ( 875 ) 10 = ( 87.5 x 10 ) 10 therefore , log 10 x = 10 ( log 1087.5 + 1 ) = 10 ( 6.9421 + 1 ) = 10 ( 7.9421 ) = 79.421 x = antilog ( 79.421 ) therefore , number of digits in x = 80 . answer : c"
Answer: c
Question (general): two heavily loaded sixteen - wheeler transport trucks are 787 kilometers apart , sitting at two rest stops on opposite sides of the same highway . driver a begins heading down the highway driving at an average speed of 90 kilometers per hour . exactly one hour later , driver b starts down the highway toward driver a , maintaining an average speed of 80 kilometers per hour . how many kilometers farther than driver b , will driver a have driven when they meet and pass each other on the highway ?
Options: a ) 90 , b ) 131 , c ) 150 , d ) 320 , e ) 450
Rationale: i ' ve been reading the website for a while and i ' m always keen to see different approaches so i would like to share one that works for me : short version : truck a travels for an hour . distance remaining = 787 - 90 = 697 k ratio of speeds 9 : 8 - > 697 / 17 = 41 truck a = 90 + 41 * 9 = 459 truck b = 41 * 8 = 328 delta = 131 km answer b
Answer: b
Question (general): in a group of 800 people , 1 / 5 play at least one instrument , 64 play two or more . what is the probability that one student play exactly one instrument ?
Options: a ) 3 / 25 , b ) 3 / 125 , c ) c ) 2 / 25 , d ) 3 / 25 , e ) 1 / 5
Rationale: "p ( playing 2 or more instruments ) = 64 / 800 = 2 / 25 . then , the probability of playing exactly one instrument is given by : p ( playing 1 or more instruments ) - p ( playing 2 or more instruments ) = 1 / 5 - 2 / 25 = 3 / 25 . answer a ."
Answer: a
Question (geometry): what is the angle between the hands of a clock when time is 8 : 30 ?
Options: a ) 65 deg , b ) 75 deg , c ) 45 deg , d ) 15 deg , e ) 30 deg
Rationale: "angle between two hands = 30 h - 11 / 2 m = 30 * 8 - 30 * 11 / 2 = 240 - 165 = 75 deg answer : b"
Answer: b
Question (gain): if the difference between compound interest ( interest compounded yearly ) and simple interest on a certain sum at the rate 20 % p . a . after 3 years is rs . 1280 then what is the principal ?
Options: a ) 7900 , b ) 8,000 , c ) 10,000 , d ) 8,300 , e ) 9,300
Rationale: "let p is the principal , so p ( [ 120 / 100 ] ^ 3 - 1 ) - p * 20 / 100 * 3 = 1280 p [ 728 / 1000 - 3 / 5 ] = 1280 p = 1280 * 5 * 1000 / 728 * 5 - 3000 = 10000 answer : c"
Answer: c
Question (general): in the xy - coordinate system , if ( m , n ) and ( m + 4 , n + k ) are two points on the line with the equation x = 2 y + 5 , then k =
Options: a ) 1 / 2 , b ) 1 , c ) 2 , d ) 5 / 2 , e ) 4
Rationale: "since ( m , n ) and ( m + 2 , n + k ) are two points on the line with the equation x = 2 y + 5 they should satisfy m = 2 n + 5 and m + 4 = 2 * ( n + k ) + 5 . by 1 st equation we have m - 2 n = 5 and by 2 nd equation m - 2 n = 2 k + 1 - - - > 5 = 2 k + 1 - - - > k = 2 . the answer is , therefore , ( c ) ."
Answer: c
Question (general): during the first week of performances of a certain play , 5400 tickets were sold , all at reduced price . during the remaining weeks of performances , 5 times as many tickets were sold at full price as were sold at reduced price . if the total number of tickets r sold was 25200 , how many of them were sold at full price ?
Options: a ) 21000 , b ) 19800 , c ) 16500 , d ) 15800 , e ) 8700
Rationale: given : the question tells us about the number of tickets sold in the first week at reduced price = 5400 . it also tells us that during the remaining weeks , the number of tickets sold at full price was 5 times the no . of tickets sold at reduced price . the total tickets sold was 25200 , and we are asked to find the number of tickets that where sold at full price . approach : the question asks us to find the number of ticket sold at full price . we know that the number of tickets sold at full price was 5 times the no . of tickets sold at reduced price in remaining weeks . hence , assuming tickets sold at reduced price in remaining weeks to be x would give us the no . of tickets sold at full price to be 5 x . tickets sold in first week + tickets sold in remaining weeks = total no . of tickets soldi . e . tickets sold in first week + tickets sold at full price in remaining weeks + tickets sold at reduced price in remaining weeks = total no . of tickets sold we know the no . of tickets sold during first week and the total no . of tickets sold . we will use this relation to get to our answer . working out : tickets sold in first week + tickets sold at full price in remaining weeks + tickets sold at reduced price in remaining weeks = total no . of tickets sold substituting values in the equation , we get 5400 + 5 x + x = 25200 x = 3300 tickets sold at full price = 5 x = 16500 answer : option c
Answer: c
Question (other): income and expenditure of a person are in the ratio 10 : 4 . if the income of the person is rs . 19000 , then find his savings ?
Options: a ) 79754 , b ) 87689 , c ) 59875 , d ) 11400 , e ) 87648
Rationale: "let the income and the expenditure of the person be rs . 10 x and rs . 4 x respectively . income , 10 x = 19000 = > x = 1900 savings = income - expenditure = 10 x - 4 x = 6 x = 6 ( 1900 ) so , savings = rs . 11400 . answer : d"
Answer: d
Question (gain): a , b and c started a business with capitals of rs . 8000 , rs . 10000 and rs . 12000 respectively . at the end of the year , the profit share of b is rs . 2000 . the difference between the profit shares of a and c is ?
Options: a ) 621 , b ) 276 , c ) 236 , d ) 800 , e ) 211
Rationale: "explanation : ratio of investments of a , b and c is 8000 : 10000 : 12000 = 4 : 5 : 6 and also given that , profit share of b is rs . 2000 = > 5 parts out of 15 parts is rs . 2000 now , required difference is 6 - 4 = 2 parts required difference = 2 / 5 ( 2000 ) = rs . 800 answer : d"
Answer: d
Question (probability): if a card is drawn from a well shuffled deck of cards , what is the probability of drawing a black card or a face card ?
Options: a ) 7 / 13 , b ) 15 / 26 , c ) 9 / 12 , d ) 8 / 13 , e ) 29 / 52
Rationale: "p ( b á ´ œ f ) = p ( b ) + p ( f ) - p ( b â ˆ © f ) , where b denotes black cards and f denotes face cards . p ( b á ´ œ f ) = 26 / 52 + 12 / 52 - 6 / 52 = 8 / 13 answer : d"
Answer: d
Question (physics): a cistern 4 m long and 2 m wide contains water up to a depth of 1 m 25 cm . the total area of the wet surface is :
Options: a ) 23 m 2 , b ) 20 m 2 , c ) 52 m 2 , d ) 24 m 2 , e ) 55 m 2
Rationale: "area of the wet surface = [ 2 ( lb + bh + lh ) - lb ] = 2 ( bh + lh ) + lb = [ 2 ( 2 x 1.25 + 4 x 1.25 ) + 4 x 2 ] m 2 = 23 m 2 . answer : a"
Answer: a
Question (physics): jane makes toy bears . when she works with an assistant , she makes 62 percent more bears per week and works 10 percent fewer hours each week . having an assistant increases jane ’ s output of toy bears per hour by what percent ?
Options: a ) 20 % , b ) 80 % , c ) 100 % , d ) 180 % , e ) 200 %
Rationale: "let ' s assume just jane 40 bears per 40 / hrs a week , so that is 1 bear / hr . with an assistant she makes 64.8 bears per 36 hours a week or 1.8 bears / hr ( [ 40 bears * 1.62 ] / [ 40 hrs * . 90 ] ) . [ ( 1.8 - 1 ) / 1 ] * 100 % = 80 % answer : b"
Answer: b
Question (general): find the average of all numbers between 5 and 37 which are divisible by 4
Options: a ) 25 , b ) 20 , c ) 45 , d ) 30 , e ) 35
Rationale: "explanation : average = ( 4 + 8 + 12 + 16 + 20 + 24 + 28 + 32 + 36 ) / 4 ) = 180 / 4 = 45 option c"
Answer: c
Question (gain): uncle bruce is baking chocolate chip cookies . he has 36 ounces of dough ( with no chocolate ) and 18 ounces of chocolate . how many ounces of chocolate are left over if he uses all the dough but only wants the cookies to consist of 20 % chocolate ?
Options: a ) 3 , b ) 6 , c ) 7.2 , d ) 7.8 , e ) 9
Rationale: "answer is e . x / x + 36 = 1 / 5 x = 9 18 - 9 = 9"
Answer: e
Question (gain): a broker invested her own money in the stock market . during the first year , she increased her stock market wealth by 50 percent . in the second year , largely as a result of a slump in the stock market , she suffered a 30 percent decrease in the value of her stock investments . what was the net increase or decrease on her overall stock investment wealth by the end of the second year ?
Options: a ) − 5 % , b ) 5 % , c ) 15 % , d ) 20 % , e ) 80 %
Rationale: "assume the broker invested $ 100 . after year 1 ( 50 % increase in wealth ) : $ 100 * 0.5 = $ 50 increase + $ 100 = $ 150 after year 2 ( 30 % decrease in wealth ) : $ 150 * 0.3 = $ 45 ; $ 150 - $ 45 decrease = $ 105 net increase = $ 105 / $ 100 - 1 = 5 % answer is b ."
Answer: b
Question (general): the sum of the squares of three numbers is 225 , while the sum of their products taken two at a time is 200 . their sum is :
Options: a ) 10 , b ) 30 , c ) 40 , d ) 25 , e ) none of these
Rationale: "x ^ + y ^ 2 + z ^ 2 = 225 xy + yz + zx = 200 as we know . . ( x + y + z ) ^ 2 = x ^ 2 + y ^ 2 + z ^ 2 + 2 ( xy + yz + zx ) so ( x + y + z ) ^ 2 = 225 + ( 2 * 200 ) ( x + y + z ) ^ 2 = 625 so x + y + z = 25 answer : d"
Answer: d
Question (physics): a train travels from new york to chicago , a distance of approximately 480 miles , at an average rate of 40 miles per hour and arrives in chicago at 6 : 00 in evening , chicago time . at what hour in the morning , new york time , did the train depart for chicago ? ( note : chicago time is one hour earlier than new york time )
Options: a ) 3 : 00 , b ) 4 : 00 , c ) 5 : 00 , d ) 6 : 00 , e ) 7 : 00
Rationale: "6 : 00 in evening in chicago = 7 : 00 in evening in new york . so , the train was in chicago 7 : 00 in the evening , new york time . the trip took t = d / r = 480 / 40 = 12 hours . therefore , the train depart from new york at 7 : 00 - 12 hours = 7 : 00 in the morning , new york time . answer : e ."
Answer: e
Question (physics): if m is the set of all consecutive multiples of 9 between 100 and 500 , what is the median of m ?
Options: a ) 300 , b ) 301 , c ) 301.5 , d ) 302.5 , e ) 306
Rationale: since 100 / 9 = 11.11 , 500 / 9 = 55.55 , m can be written as { 9 * 12 , 9 * 13 , . . . . , 9 * 54 , 9 * 55 } . the number of elements of m is , therefore , 44 ( = 55 - 12 + 1 ) . since the number of elements is even number the median is the average of the 22 nd element ( = 9 * 33 ) and 23 rd element ( = 9 * 34 ) . so the median is ( 9 * 33 + 9 * 34 ) / 2 = 301.5 . the answer is c .
Answer: c
Question (physics): a 300 meter long train crosses a platform in 42 seconds while it crosses a signal pole in 18 seconds . what is the length of the platform ?
Options: a ) 99 , b ) 289 , c ) 350 , d ) 882 , e ) 400
Rationale: "speed = [ 300 / 18 ] m / sec = 50 / 3 m / sec . let the length of the platform be x meters . then , x + 300 / 42 = 50 / 3 3 ( x + 300 ) = 2100 è x = 400 m . answer : e"
Answer: e
Question (gain): shop offered 20 % offer for every shirt , smith bought a shirt at rs . 780 . and what was the shop ' s original selling price ?
Options: a ) 500 , b ) 550 , c ) 600 , d ) 700 , e ) 975
Rationale: "sp * ( 80 / 100 ) = 780 sp = 9.75 * 100 = > cp = 975 answer : e"
Answer: e
Question (general): two positive integers differ by 4 , and sum of their reciprocals is 1 . then one of the numbers is
Options: a ) 2 , b ) b ) 1 , c ) c ) 5 , d ) d ) 21 , e ) e ) 28
Rationale: algebraic approach : let n be the smaller integer = > 1 / n + 1 / ( n + 4 ) = 1 or ( ( n + 4 ) + n ) / n ( n + 4 ) = 1 or n ^ 2 + 4 n = 2 n + 4 or n = 2 as n can not be - negative solve for n = > n = 2 . hence , a
Answer: a
Question (physics): john has rs 360 for his expenses . if he exceeds his days by 4 days he must cut down daily expenses by rs 3 . the number of days of john ' s tour program is
Options: a ) 10 , b ) 15 , c ) 20 , d ) 24 , e ) 27
Rationale: let john under takes a tour of x days . then , expenses for each day = 360 x 360 x + 4 = 360 x − 3 x = 20 and − 24 hence , x = 20 days . c
Answer: c
Question (other): three numbers are in the ratio 3 : 4 : 5 and their l . c . m . is 1200 . their h . c . f is ?
Options: a ) 20 , b ) 30 , c ) 40 , d ) 50 , e ) 60
Rationale: "let the numbers be 3 x , 4 x and 5 x their l . c . m . = 60 x 60 x = 1200 x = 20 the numbers are 3 * 20 , 4 * 20 , 5 * 20 hence required h . c . f . = 20 answer is a"
Answer: a
Question (general): the price of food in the area where the sims family lives is scheduled to increase by 50 % next year . since the sims family can not afford an increase in their food bill , how much will they have to reduce consumption to keep their cost the same ?
Options: a ) 17 % , b ) 25.6 % , c ) none % , d ) 33.3 % , e ) 50 %
Rationale: solution : let the current food expense be represented by rs . 100 . the cost of food rises 50 % . so , to buy same amount of food , they need to increase their expense , = ( 100 + 50 % of 100 ) = rs . 150 . but , they want to keep food expense the same , so they have to cut rs . by 50 to keep it to rs . = 100 . the % decrease in consumption is , ( 50 / 150 ) * 100 = 33.3 % . mental calculation method ; 100 - - - - - 50 % ↑ - - - → 150 - - - - - - x % ↓ - - - → 100 . here , x = ( 50 / 125 ) * 100 = 33.3 % . answer : option d
Answer: d
Question (gain): find the simple interest on $ 10000 at 5 % per annum for 12 months ?
Options: a ) $ 410 , b ) $ 500 , c ) $ 650 , d ) $ 710 , e ) $ 1000
Rationale: "p = $ 10000 r = 5 % t = 12 / 12 years = 1 year s . i . = p * r * t / 100 = 10000 * 5 * 1 / 100 = $ 500 answer is b"
Answer: b
Question (gain): if the given two numbers are respectively 8 % and 16 % of a third number , then what percentage is the first of the second ?
Options: a ) 20 % , b ) 25 % , c ) 18 % , d ) 50 % , e ) none of these
Rationale: "here , l = 8 and m = 16 therefore , first number = l / m x 100 % of second number = 8 / 16 x 100 % of second number = 50 % of second number answer : d"
Answer: d
Question (probability): if you keep rolling a pair of dice together till a sum of 5 or 7 is obtained , then what is the probability that a sum of 5 comes before a sum of 7 ?
Options: a ) 5 / 5 , b ) 4 / 5 , c ) 3 / 5 , d ) 2 / 5 , e ) 1 / 5
Rationale: this can be solved in a generic and complex way but let us not go into all that . there can be four ways through which the pair of dice results in a sum of 5 . there can be six ways through which the pair of dice can result in a sum of 7 . now , we want the probability of the pair of dice resulting in a sum of 5 before a sum of 7 . thus probability = 4 / ( 4 + 6 ) = 4 / 10 or 2 / 5 . correct answer is d ) 2 / 5
Answer: d
Question (general): a pupil ' s marks were wrongly entered as 73 instead of 63 . due to the average marks for the class got increased by half . the number of pupils in the class is ?
Options: a ) 18 , b ) 82 , c ) 20 , d ) 27 , e ) 29
Rationale: "let there be x pupils in the class . total increase in marks = ( x * 1 / 2 ) = x / 2 x / 2 = ( 73 - 63 ) = > x / 2 = 10 = > x = 20 . answer : c"
Answer: c
Question (geometry): in the coordinate plane , one of the vertices of a square is the point ( - 3 , - 4 ) . if the diagonals of that square intersect at point ( 4 , 2 ) , what is the area of that square ?
Options: a ) 196 , b ) 125 , c ) 140 , d ) 128 , e ) 134
Rationale: "one point ( - 3 - 4 ) , intersection ( 4,2 ) so the distance from the first point - 3 - 4 = - 7 is the midpoint of the square - - > whole side 14 , 14 * 14 = 196 a"
Answer: a
Question (general): a sports equipment store sold ping pong rackets for a total of $ 588 . if the average ( arithmetic mean ) price of a pair of rackets is $ 9.8 , how many pairs were sold ?
Options: a ) 50 , b ) 60 , c ) 490 , d ) 500 , e ) 980
Rationale: "average price for a pair of rackets = $ 9.8 total cost = $ 9.8 * x = $ 588 x = 60 pairs were sold . answer : b"
Answer: b
Question (general): if a is a positive integer , and if the units digit of a ^ 2 is 1 and the units digit of ( a + 1 ) ^ 2 is 4 , what is the units digit of ( a + 2 ) ^ 2 ?
Options: a ) 1 , b ) 3 , c ) 5 , d ) 7 , e ) 9
Rationale: "if the units digit of a ^ 2 is 1 , then the units digit of a is either 1 or 9 . if the units digit of ( a + 1 ) ^ 2 is 4 , then the units digit of a + 1 is either 2 or 8 . to satisfy both conditions , the units digit of a must be 1 . then a + 2 has the units digit of 3 , thus the units digit of ( a + 2 ) ^ 2 will be 9 . the answer is e ."
Answer: e
Question (gain): the difference between simple interest and compound interest on $ 1200 for one year at 10 % per annum reckoned half - yearly is :
Options: a ) $ 5 , b ) $ 8 , c ) $ 9 , d ) $ 3 , e ) $ 7
Rationale: "s . i = $ [ ( 1200 * 10 * 1 ) / 100 ] = $ 120 . c . i = $ [ 1200 * ( 1 + ( 5 / 100 ) ^ 2 ) - 1200 ] = $ 123 . difference = $ ( 123 - 120 ) = $ 3 . answer ( d )"
Answer: d
Question (physics): a train 110 meters long takes 6 seconds to cross a man walking at 5 kmph in the direction opposite to that of the train . find the speed of the train .
Options: a ) 45 kmph , b ) 50 kmph , c ) 55 kmph , d ) 61 kmph , e ) 70 kmph
Rationale: explanation : let the speed of the train be x kmph . speed of the train relative to man = ( x + 5 ) kmph = ( x + 5 ) × 5 / 18 m / sec . therefore 110 / ( ( x + 5 ) × 5 / 18 ) = 6 < = > 30 ( x + 5 ) = 1980 < = > x = 61 speed of the train is 61 kmph . answer : option d
Answer: d
Question (gain): the price of a bushel of corn is currently $ 3.20 , and the price of a peck of wheat is $ 5.80 . the price of corn is increasing at a constant rate of 5 x 5 x cents per day while the price of wheat is decreasing at a constant rate of 2 √ ∗ x − x 2 ∗ x − x cents per day . what is the approximate price when a bushel of corn costs the same amount as a peck of wheat ?
Options: a ) $ 4.50 , b ) $ 5.10 , c ) $ 5.30 , d ) $ 5.50 , e ) $ 5.60
Rationale: "let yy be the # of days when these two bushels will have the same price . first let ' s simplify the formula given for the rate of decrease of the price of wheat : 2 √ ∗ x − x = 1.41 x − x = 0.41 x 2 ∗ x − x = 1.41 x − x = 0.41 x , this means that the price of wheat decreases by 0.41 x 0.41 x cents per day , in yy days it ' ll decrease by 0.41 xy 0.41 xy cents ; as price of corn increases 5 x 5 x cents per day , in yy days it ' ll will increase by 5 xy 5 xy cents ; set the equation : 320 + 5 xy = 580 − 0.41 xy 320 + 5 xy = 580 − 0.41 xy , solve for xyxy - - > xy = 48 xy = 48 ; the cost of a bushel of corn in yy days ( the # of days when these two bushels will have the same price ) will be 320 + 5 xy = 320 + 5 ∗ 48 = 560320 + 5 xy = 320 + 5 ∗ 48 = 560 or $ 5.6 . answer : e ."
Answer: e
Question (general): find a positive number which when increased by 17 is equal to 60 times the reciprocal of the number
Options: a ) 17 , b ) 15 , c ) 12 , d ) 8 , e ) 3
Rationale: "f the number is x , then , x + 17 = 60 / x x 2 + 17 x - 60 = 0 ( x + 20 ) ( x - 3 ) = 0 x = 3 , - 20 , so x = 3 ( as 3 is positive ) answer : e"
Answer: e
Question (geometry): the length of a rectangular garden is three times its width . if the area of the rectangular garden is 588 square meters , then what is the width of the rectangular garden ?
Options: a ) 12 , b ) 13 , c ) 14 , d ) 15 , e ) 16
Rationale: "let x be the width of the garden . 3 x ^ 2 = 588 x ^ 2 = 196 x = 14 the answer is c ."
Answer: c
Question (physics): a train 360 m long is running at a speed of 72 km / hr . in what time will it pass a bridge 140 m long ?
Options: a ) 40 sec , b ) 29 sec , c ) 25 sec , d ) 27 sec , e ) 34 sec
Rationale: "speed = 72 * 5 / 18 = 20 m / sec total distance covered = 360 + 140 = 500 m required time = 500 * 1 / 20 = 25 sec answer : c"
Answer: c
Question (physics): if 20 typists can type 48 letters in 20 minutes , then how many letters will 30 typists working at the same rate complete in 1 hour ?
Options: a ) 63 , b ) 72 , c ) 144 , d ) 216 , e ) 400
Rationale: "20 typists can type 48 letters , so 30 typists can type = 48 * 30 / 20 48 * 30 / 20 letters can be typed in 20 mins . in 60 mins typist can type = 48 * 30 * 60 / 20 * 20 = 216 d is the answer"
Answer: d
Question (physics): a car traveling at a certain constant speed takes 15 seconds longer to travel 1 kilometer than it would take to travel 1 kilometer at 60 kilometers per hour . at what speed , in kilometers per hour , is the car traveling ?
Options: a ) 48 , b ) 50 , c ) 52 , d ) 54 , e ) 56
Rationale: "60 * t = 1 km = > t = 1 / 60 km / h v * ( t + 15 / 3600 ) = 1 v ( 1 / 60 + 15 / 3600 ) = 1 v ( 75 / 3600 ) = 1 v = 48 km / h the answer is a ."
Answer: a
Question (gain): p and q started a business investing rs . 96,000 and rs . 28,000 respectively . in what ratio the profit earned after 2 years be divided between p and q respectively ?
Options: a ) 17 : 6 , b ) 24 : 7 , c ) 25 : 6 , d ) 21 : 3 , e ) 17 : 4
Rationale: "p : q = 96000 : 28000 = 24 : 7 answer : b"
Answer: b
Question (physics): a train 90 m long running at 56 kmph crosses a platform in 18 sec . what is the length of the platform ?
Options: a ) 190 , b ) 200 , c ) 180 , d ) 881 , e ) 271
Rationale: "d = 56 * 5 / 18 = 25 = 280 – 90 = 190 answer : a"
Answer: a
Question (probability): a card is drawn from a pack of 52 cards . the probability of ge ƫ ng a queen of club or a king of heart is
Options: a ) 1 / 13 , b ) 2 / 13 , c ) 1 / 26 , d ) 1 / 52 , e ) none of these
Rationale: "explanation : total number of cases = 52 favourable cases = 2 probability = 2 / 56 = 1 / 26 answer : c"
Answer: c
Question (physics): this topic is locked . if you want to discuss this question please re - post it in the respective forum . matt and peter can do together a piece of work in 20 days . after they have worked together for 12 days matt stops and peter completes the remaining work in 14 days . in how many days peter complete the work separately .
Options: a ) 26 days , b ) 27 days , c ) 23 days , d ) 35 days , e ) 24 days
Rationale: together they complete the job in 20 days means they complete 12 / 20 of the job after 12 days . peter completes the remaining ( 8 / 20 ) of the job in 14 days which means that the whole job ( 1 ) can be completed in x days . < = > 8 / 20 - > 14 < = > x = 14 / ( 8 / 20 ) = 35 thus the answer is d .
Answer: d
Question (general): we bought a total of 80 books at the store . math books cost $ 4 and history books cost $ 5 . the total price was $ 373 . how many math books did we buy ?
Options: a ) 23 , b ) 27 , c ) 31 , d ) 35 , e ) 39
Rationale: "m + h = 80 h = 80 - m 4 m + 5 h = 373 4 m + 5 * ( 80 - m ) = 373 m = 27 the answer is b ."
Answer: b
Question (general): if a , b , c , d , e and f are integers and ( ab + cdef ) < 0 , then what is the maximum number s of integers that can be negative ?
Options: a ) 2 , b ) 3 , c ) 4 , d ) 5 , e ) 6
Rationale: "minimuum should be 1 maximum should be 4 : 1 out of a or b to make the multiplication negative 3 out of c , d , e or f to make the multiplication negative . negative + negative < 0 answer : c maximum will be 5 . . you dont require both the multiplicatin to be negative for entire equation to be negative . . . any one a or b can be negative to make ab negative and it can still be more ( away from 0 ) than the multiplication of 4 other - ve numbers . . . actually by writing minimum required as 1 out of 6 , you are actually meaning s = 5 out of 6 also possible as you will see 5 or 1 will give you same equation . . ans d"
Answer: d