Cheukting/mathqa huggingface dataset:
Question (gain): if $ 5,000 is invested in an account at a simple annual rate of r percent , the interest is $ 250 . when $ 17,000 is invested at the same interest rate , what is the interest from the investment ?
Options: a ) $ 700 , b ) $ 750 , c ) $ 800 , d ) $ 850 , e ) $ 900
Rationale: "5000 * r * t / 100 = 250 rt = 5 17000 * 5 / 100 = 850 answer is d"
Answer: d
Question (physics): 30 binders can bind 1400 books in 21 days . how many binders will be required to bind 1600 books in 20 days ?
Options: a ) 87 , b ) 18 , c ) 17 , d ) 36 , e ) 10
Rationale: binders books days 30 1400 21 x 1600 20 x / 30 = ( 1600 / 1400 ) * ( 21 / 20 ) = > x = 36 answer : d
Answer: d
Question (geometry): if the radius of a circle is decreased 30 % , what happens to the area ?
Options: a ) 51 % decrease , b ) 20 % decrease , c ) 36 % decrease , d ) 40 % decrease , e ) 50 % decrease
Rationale: "area of square = pi * radius ^ 2 new radius = 0.7 * old radius so new area = ( 0.7 ) ^ 2 old area = > 0.49 of old area = > 49 % old area ans : a"
Answer: a
Question (gain): find the amount on rs . 5000 in 2 years , the rate of interest being 4 % per first year and 5 % for the second year ?
Options: a ) 3377 , b ) 2678 , c ) 5460 , d ) 1976 , e ) 1671
Rationale: "5000 * 104 / 100 * 105 / 100 = > 5460 answer : c"
Answer: c
Question (general): the average monthly salary of 8 workers and one supervisor in a factory was 430 . @ sswhen @ ssthe @ sssupervisor @ cc @ sswhose @ sssalary @ sswas @ ss 430 . @ sswhen @ ssthe @ sssupervisor @ cc @ sswhose @ sssalary @ sswas @ ss 430 . whenthesupervisor , whosesalarywas 430 . when the supervisor , whose salary was 870 per month , retired , a new person was appointed and then the average salary of 9 people was $ $ 410 per month . the salary of the new supervisor is :
Options: a ) 233 , b ) 690 , c ) 287 , d ) 771 , e ) 191
Rationale: "explanation : total salary of 8 workers and supervisor together = 9 ã — 430 = 3870 now total salary of 8 workers = 3870 â ˆ ’ 870 = 3000 total salary of 9 workers including the new supervisor = 9 ã — 410 = 3690 salary of the new supervisor = 3690 â ˆ ’ 3000 = 690 answer : b"
Answer: b
Question (general): if there are 4 peanuts in a box and mary puts 6 more peanuts inside , how many peanuts are in the box ?
Options: a ) 8 , b ) 9 , c ) 10 , d ) 11 , e ) 12
Rationale: 6 + 4 = 10 correct answer is c ) 10
Answer: c
Question (general): how many 3 digit positive integers exist that when divided by 7 leave a remainder of 5 ?
Options: a ) 128 , b ) 142 , c ) 143 , d ) 141 , e ) 129
Rationale: "explanatory answer step 1 : find the first and last term of the series the smallest 3 - digit positive integer that leaves a remainder of 5 when divided by 7 is 103 . the largest 3 - digit positive integer that leaves a remainder of 5 when divided by 7 is 999 . the series of numbers that satisfy the condition that the number should leave a remainder of 5 when divided by 7 is an a . p ( arithmetic progression ) with the first term being 103 and the last term being 999 . the common difference of the sequence is 7 . step 2 : compute the number of terms in an a . p , the last term l = a + ( n - 1 ) * d , where ' a ' is the first term , ' n ' is the number of terms of the series and ' d ' is the common difference . therefore , 999 = 103 + ( n - 1 ) * 7 or 999 - 103 = ( n - 1 ) * 7 or 896 = ( n - 1 ) * 7 so , n - 1 = 128 or n = 129 choice e is the correct answer ."
Answer: e
Question (general): if ( 10 ^ 4 * 3.456789 ) ^ 9 is written as a single term , how many digits would be to the right of the decimal place ?
Options: a ) 6 , b ) 12 , c ) 18 , d ) 32 , e ) 48
Rationale: "3.456789 ^ 9 has 6 * 9 = 54 decimal places . 10 ^ 36 moves the decimal place to the right 36 places . ( 10 ^ 4 * 3.456789 ) ^ 9 has 54 - 36 = 18 digits after the decimal point . the answer is c ."
Answer: c
Question (gain): if c is 30 % of a and 25 % of b , what percent of a is b ?
Options: a ) 2.5 % , b ) 15 % , c ) 120 % , d ) 35 % , e ) 250 %
Rationale: "answer = c 30 a / 100 = 25 b / 100 b = 30 a / 25 = 120 a / 100 = 120 %"
Answer: c
Question (gain): find the principal which yields a simple interest of rs . 20 and compound interest of rs . 24 in two years , at the same percent rate per annum ?
Options: a ) s . 50 , b ) s . 48 , c ) s . 42 , d ) s . 20 , e ) s . 60
Rationale: "explanation : si in 2 years = rs . 20 , si in 1 year = rs . 10 ci in 2 years = rs . 24 % rate per annum = [ ( ci – si ) / ( si in 1 year ) ] * 100 = [ ( 24 – 20 ) / 20 ] * 100 = 20 % p . a . let the principal be rs . x time = t = 2 years % rate = 20 % p . a . si = ( prt / 100 ) 20 = ( x * 20 * 2 ) / 100 x = rs . 50 answer : a"
Answer: a
Question (physics): the moon revolves around the earth at a speed of approximately 0.9 kilometers per second . this approximate speed is how many kilometers per hour ?
Options: a ) 60 , b ) 61.2 , c ) 3240 , d ) 3,600 , e ) 3,672
Rationale: "moon revolves around the earth at a speed of 1.02 kilometers per second . one hour equal to 60 minutes . one minute equals to 60 seconds . so one hour equals to 3600 seconds . so one hour , speed = 0.9 * 3600 = 3240 kilometers per hour . option c is correct"
Answer: c
Question (physics): john traveled 80 % of the way from yellow - town to green - fields by train at an average speed of 80 miles per hour . the rest of the way john traveled by car at an average speed of v miles per hour . if the average speed for the entire trip was 60 miles per hour , what is v in miles per hour ?
Options: a ) 30 , b ) 40 , c ) 50 , d ) 55 , e ) 70
Rationale: "let distance be d . we can find the total time & equate it , which comes as : 0.8 d / 80 + 0.2 d / v = d / 60 = > v = 30 answer : a"
Answer: a
Question (other): the ratio of boarders to day students at a school was originally 5 to 12 . however , after a number of new boarders join the initial 150 boarders , the ratio changed to 1 to 2 . if no boarders became day students and vice versa , and no students left the school , how many new boarders joined the school ?
Options: a ) 30 , b ) 50 , c ) 70 , d ) 80 , e ) 90
Rationale: "let x be the number of new boarders . the ratio changed from 5 : 12 up to 1 : 2 = 6 : 12 . 150 / ( 150 + x ) = 5 / 6 x = 30 the answer is a ."
Answer: a
Question (general): divide rs . 1300 among a , b and c so that a receives 1 / 3 as much as b and c together and b receives 2 / 3 as a and c together . a ' s share is ?
Options: a ) 346 , b ) 368 , c ) 375 , d ) 337 , e ) 325
Rationale: "a + b + c = 1300 a = 1 / 3 ( b + c ) ; b = 2 / 3 ( a + c ) a / ( b + c ) = 1 / 3 a = 1 / 4 * 1300 = > 325 answer : e"
Answer: e
Question (physics): a boy is travelling from his home to school at 4 km / hr and reached 7 min late . next day he traveled at 8 km / hr and reached 8 min early . distance between home and school ?
Options: a ) 2 km , b ) 3 km , c ) 4 km , d ) 5 km , e ) 6 km
Rationale: "let the distance be x t 1 = x / 4 hr t 2 = x / 8 hr difference in time = 7 + 8 = 15 = 1 / 4 hr x / 4 - x / 8 = 1 / 4 x / 8 = 1 / 4 x = 2 km answer is a"
Answer: a
Question (physics): a , b and c , each working alone can complete a job in 2 , 4 and 6 days respectively . if all three of them work together to complete a job and earn $ 2500 , what will be c ' s share of the earnings ?
Options: a ) $ 1206.60 , b ) $ 1363.63 , c ) $ 1263.63 , d ) $ 1463.53 , e ) $ 1163.03
Rationale: "the dollars earned will be in the same ratio as amount of work done 1 day work of c is 1 / 6 ( or 2 / 12 ) 1 day work of the combined workforce is ( 1 / 2 + 1 / 4 + 1 / 6 ) = 11 / 12 c ' s contribution is 2 / 9 of the combined effort translating effort to $ = 6 / 11 * 2500 = $ 1363.63 hence : b"
Answer: b
Question (general): according to the direction on a can of frozen orange juice concentrate is to be mixed with 3 cans of water to make orange juice . how many 5 - ounce cans of the concentrate are required to prepare 200 6 - ounce servings of orange juice ?
Options: a ) 25 , b ) 34 , c ) 50 , d ) 60 , e ) 100
Rationale: orange juice concentrate : water : : 1 : 3 total quantity of orange juice = 200 * 6 = 1200 oz so orange juice concentrate : water : : 300 oz : 900 oz no . of 5 oz can = 300 oz / 5 oz = 60 answer d , 60 cans
Answer: d
Question (general): each of the 30 boxes in a certain shipment weighs either 10 pounds or 20 pounds , and the average ( arithmetic mean ) weight of the boxes in the shipment is 18 pounds . if the average weight of the boxes in the shipment is to be reduced to 16 pounds by removing some of the 20 - pound boxes , how many 20 - pound boxes must be removed ?
Options: a ) 9 , b ) 12 , c ) 15 , d ) 18 , e ) 21
Rationale: if the average of 10 - pound and 20 - pound boxes is 18 , the ratio of 10 - pound boxes : 20 - pound boxes is 1 : 4 . so out of 30 boxes , 6 are 10 - pound boxes and 24 are 20 - pound boxes . if the average of 10 and 20 - pound boxes is to be 16 , the ratio of 10 - pound boxes : 20 - pound boxes should be 2 : 3 . the number of 10 pound boxes remain the same so we still have 6 of them . to get a ratio of 2 : 3 , the number of 20 - pound boxes must be 9 . we need to remove 15 of the 20 - pound boxes . the answer is c .
Answer: c
Question (physics): two pipes can fill a tank in 18 minutes and 15 minutes . an outlet pipe can empty the tank in 54 minutes . if all the pipes are opened when the tank is empty , then how many minutes will it take to fill the tank ?
Options: a ) 30 minutes , b ) 17 minutes , c ) 15 minutes , d ) 6 minutes , e ) 12 minutes
Rationale: "part of the filled by all the three pipes in one minute = 1 / 18 + 1 / 15 - 1 / 54 = ( 15 + 18 - 5 ) / 270 = 28 / 270 = 14 / 135 so , the tank becomes full in 6 minutes . answer : d"
Answer: d
Question (physics): how many bricks each measuring 25 cm x 11.25 cm x 6 cm , will be needed to build a wall 8 m x 6 m x 22.5 m
Options: a ) 5600 , b ) 600 , c ) 6400 , d ) 7200 , e ) none of these
Rationale: "explanation : no . of bricks = volume of the wall / volume of 1 brick = ( 800 x 600 x 22.5 ) / ( 25 x 11.25 x 6 ) = 6400 answer : c"
Answer: c
Question (general): a prize of $ 500 is to be distributed among 20 winners , each of whom must be awarded at least $ 20 . if 2 / 5 of the prize will be distributed to 3 / 5 of the winners , what is the greatest possible individual award ?
Options: a ) $ 160 , b ) $ 220 , c ) $ 280 , d ) $ 300 , e ) $ 360
Rationale: total value of the prize = $ 500 number of people = 20 2 / 5 of 500 ( = $ 200 ) should be distributed among 3 / 5 of 20 ( = 12 people ) with each getting $ 20 each . remaining money = 500 - 200 = $ 300 . now in order to ' maximize ' 1 prize , we need to minimise the others and we have been given that each should get $ 20 . thus , minimising the remaining 7 people ( = 20 - 12 - 1 . ' - 1 ' to exclude 1 that needs to be maximised ) = 7 * 20 = 140 . thus the maximum award can be = 300 - 140 = $ 160 , hence a is the correct answer .
Answer: a
Question (physics): two trains , each 100 m long , moving in opposite directions , cross other in 8 sec . if one is moving twice as fast the other , then the speed of the faster train is ? a . 30 km / hr b . 45 km / hr
Options: a ) 11 , b ) 78 , c ) 60 , d ) 28 , e ) 81
Rationale: let the speed of the slower train be x m / sec . then , speed of the train = 2 x m / sec . relative speed = ( x + 2 x ) = 3 x m / sec . ( 100 + 100 ) / 8 = 3 x = > x = 25 / 3 . so , speed of the faster train = 50 / 3 = 50 / 3 * 18 / 5 = 60 km / hr . answer : c
Answer: c
Question (physics): a car going at 40 miles per hour set out on an 90 - mile trip at 9 : 00 a . m . exactly 10 minutes later , a second car left from the same place and followed the same route . how fast , in miles per hour , was the second car going if it caught up with the first car at 10 : 30 a . m . ?
Options: a ) 45 , b ) 50 , c ) 53 , d ) 55 , e ) 90
Rationale: "let car a = car that starts at 9 am car b = car that starts at 9 : 10 am time for which car a travels at speed of 40 m per hour = 1.5 hours distance travelled by car a = 40 * 1.5 = 60 miles since car b catches up car a at 10 : 30 , time = 90 mins = 3 / 2 hour speed of car b = 60 / ( 3 / 2 ) = 90 miles per hour answer e"
Answer: e
Question (physics): how many bricks each measuring 30 cm x 12 cm x 10 cm , will be needed to build a wall 6 m x 4 m x 20.5 m
Options: a ) 5655 , b ) 1366 , c ) 6444 , d ) 7266 , e ) none of these
Rationale: explanation : no . of bricks = volume of the wall / volume of 1 brick = ( 600 x 400 x 20.5 ) / ( 30 x 12 x 10 ) = 1366 answer : b
Answer: b
Question (physics): a , b and c can do a work in 6 , 8 and 12 days respectively doing the work together and get a payment of rs . 1800 . what is b ’ s share ?
Options: a ) 300 , b ) 245 , c ) 600 , d ) 743 , e ) 215
Rationale: c 600 wc = 1 / 6 : 1 / 8 : 1 / 12 = > 4 : 3 : 2 3 / 9 * 1800 = 600
Answer: c
Question (general): how many positive integers less than 50 have a reminder 01 when divided by 4 ?
Options: a ) 13 , b ) 14 , c ) 15 , d ) 16 , e ) 17
Rationale: "1 also gives the remainder of 1 when divided by 4 . so , there are total of 13 numbers . answer : a ."
Answer: a
Question (general): the proportion of water to alcohol in solution a is 2 : 1 and the proportion of water to alcohol in solution b is 2 : 3 . if an equal amount of each solution is mixed together , what is the concentration of alcohol in the new solution ?
Options: a ) 46.7 % , b ) 47.3 % , c ) 48.4 % , d ) 50.6 % , e ) 51.8 %
Rationale: "let v be the total volume of the new solution . then a volume of v / 2 was added from each solution a and b . the amount of alcohol added to the new solution was : ( 1 / 3 ) ( v / 2 ) + ( 3 / 5 ) ( v / 2 ) = v / 6 + 3 v / 10 = 14 v / 30 = 7 v / 15 . the concentration of alcohol is 7 / 15 = 46.7 % the answer is a ."
Answer: a
Question (physics): a worker makes a toy in every 2 h . if he works for 100 h , then how many toys will he make ?
Options: a ) 40 , b ) 54 , c ) 50 , d ) 39 , e ) none
Rationale: "no . of toys = 100 / 2 = 50 answer : c"
Answer: c
Question (gain): a book is bought for $ 32 and sold for $ 56 . what is the profit in percentage ?
Options: a ) 15 , b ) 35 , c ) 75 , d ) 25 , e ) 85
Rationale: 56 / 32 = 1.75 the answer is c .
Answer: c
Question (gain): an alloy weighing 24 ounces is 70 percent gold . how many ounces of pure gold must be added to create an alloy that is 90 percent gold ?
Options: a ) 6 , b ) 9 , c ) 12 , d ) 24 , e ) 48
Rationale: "in 24 ounces , gold is 24 * ( 70 / 100 ) = 16.8 ounces . now we add x ounces of pure gold to make it 90 % gold . so 16.8 + x = ( 24 + x ) * 90 / 100 = > x = 48 . answer is e ."
Answer: e
Question (general): the youngest of 4 children has siblings who are 3 , 5 , and 8 years older than she is . if the average ( arithmetic mean ) age of the 4 siblings is 20 , what is the age of the youngest sibling ?
Options: a ) 14 , b ) 15 , c ) 16 , d ) 17 , e ) 18
Rationale: "x + ( x + 3 ) + ( x + 5 ) + ( x + 8 ) = 80 4 x + 16 = 80 4 x = 64 x = 16 the answer is c ."
Answer: c
Question (physics): on a map the distance between two mountains is 310 inches . the actual distance between the mountains is 136 km . ram is camped at a location that on the map is 34 inch from the base of the mountain . how many km is he from the base of the mountain ?
Options: a ) 14.83 , b ) 14.81 , c ) 14.91 , d ) 14.82 , e ) 14.12
Rationale: "explanation : since 310 inch = 136 km so 1 inch = 136 / 310 km so 34 inch = ( 136 ã — 34 ) / 310 = 14.91 km answer : c"
Answer: c
Question (physics): brenda and sally run in opposite direction on a circular track , starting at diametrically opposite points . they first meet after brenda has run 100 meters . they next meet after sally has run 100 meters past their first meeting point . each girl runs at a constant speed . what is the length of the track in meters ?
Options: a ) 250 , b ) 300 , c ) 350 , d ) 400 , e ) 500
Rationale: "nice problem . + 1 . first timetogetherthey run half of the circumference . second timetogetherthey run full circumference . first time brenda runs 100 meters , thus second time she runs 2 * 100 = 200 meters . since second time ( when they run full circumference ) brenda runs 200 meters and sally runs 100 meters , thus the circumference is 200 + 100 = 300 meters . answer : b ."
Answer: b
Question (general): for the symbol , m ” n = n ^ 2 − m for all values of m and n . what is the value of 3 ” 3 ?
Options: a ) 6 , b ) 3 , c ) 2 , d ) 1 , e ) 0
Rationale: "3 ” 3 = 9 - 3 = 6 answer : a"
Answer: a
Question (physics): a river 3 m deep and 32 m wide is flowing at the rate of 2 kmph the amount of water that runs into the sea per minute is ?
Options: a ) 4500 , b ) 3200 , c ) 3400 , d ) 2761 , e ) 2882
Rationale: "( 2000 * 3 * 32 ) / 60 = 3200 m 3 answer : b"
Answer: b
Question (physics): a factory produces 7500 toys per week . if the workers at this factory work 5 days a week and if these workers make the same number of toys everyday , how many toys are produced each day ?
Options: a ) 4436 toys , b ) 5487 toys , c ) 6113 toys , d ) 1875 toys , e ) 1375 toys
Rationale: "to find the number of toys produced every day , we divide the total number of toys produced in one week ( of 5 days ) by 5 . 7500 / 4 = 1875 toys correct answer d"
Answer: d
Question (geometry): if a 7 cm cube is cut into 1 cm cubes , then what is the percentage increase in the surface area of the resulting cubes ?
Options: a ) 140 %
b ) 350 %
c ) 450 %
d ) 600 %
e ) 700 %
Rationale: the area a of the large cube is 7 * 7 * 6 = 294 square cm . the area of the 343 small cubes is 7 * 7 * 7 * 6 = 7 a , an increase of 600 % . the answer is d .
Answer: d
Question (general): a student chose a number , multiplied it by 4 , then subtracted 142 from the result and got 110 . what was the number he chose ?
Options: a ) 58 , b ) 59 , c ) 60 , d ) 62 , e ) 63
Rationale: "let x be the number he chose , then 4 ⋅ x − 142 = 110 4 x = 252 x = 63 correct answer e"
Answer: e
Question (gain): a merchant purchased a jacket for $ 56 and then determined a selling price that equalled the purchase price of the jacket plus a markup that was 30 percent of the selling price . during a sale , the merchant discounted the selling price by 20 percent and sold the jacket . what was the merchant ’ s gross profit on this sale ?
Options: a ) $ 0 , b ) $ 8 , c ) $ 4 , d ) $ 12 , e ) $ 15
Rationale: "actual cost = $ 56 sp = actual cost + mark up = actual cost + 30 % sp = 56 * 100 / 70 on sale sp = 80 / 100 ( 56 * 100 / 70 ) = 64 gross profit = $ 8 answer is b"
Answer: b
Question (physics): a and b can do a piece of work in 3 days , b and c in 4 days , c and a in 6 days . how long will c take to do it ?
Options: a ) 33 , b ) 77 , c ) 24 , d ) 55 , e ) 71
Rationale: "2 c = ¼ + 1 / 6 – 1 / 3 = 1 / 12 c = 1 / 24 = > 24 days answer : c"
Answer: c
Question (physics): how many seconds will a 500 meter long train take to cross a man walking with a speed of 3 km / hr in the direction of the moving train if the speed of the train is 63 km / hr
Options: a ) 25 seconds , b ) 28 seconds , c ) 30 seconds , d ) 35 seconds , e ) 40 seconds
Rationale: "explanation : relative speed = 63 - 3 = 60 km / hr = 60 * ( 5 / 18 ) = 50 / 3 m / sec time taken to pass the man will be 500 â ˆ — 3 / 50 = 30 seconds answer is c"
Answer: c
Question (physics): the current in a river is 3 mph . a boat can travel 21 mph in still water . how far up the river can the boat travel if the round trip is to take 10 hours ?
Options: a ) 69 miles , b ) 88 miles , c ) 96 miles , d ) 102.8 miles , e ) 112 miles
Rationale: "upstream speed = 21 - 3 = 18 mph downstream speed = 21 + 3 = 24 mph d / 18 + d / 24 = 10 hours solving for d we get d = 102.8 answer : d"
Answer: d
Question (gain): if leo gains 10 pounds , he will weigh 50 % more than his sister kendra . currently their combined weight is 180 pounds . what is leo ' s current weight ?
Options: a ) 80 , b ) 86 , c ) 92 , d ) 98 , e ) 104
Rationale: l + k = 180 and so k = 180 - l l + 10 = 1.5 k = 1.5 ( 180 - l ) 2.5 l = 260 l = 104 the answer is e .
Answer: e
Question (physics): if the perimeter of a rectangular garden is 1200 m , its length when its breadth is 240 m is ?
Options: a ) 338 m , b ) 778 m , c ) 200 m , d ) 276 m , e ) 360 m
Rationale: "2 ( l + 240 ) = 1200 = > l = 360 m answer : e"
Answer: e
Question (geometry): the volumes of two cones are in the ratio 1 : 35 and the radii of the cones are in the ratio of 1 : 2 . what is the length of the wire ?
Options: a ) 7 : 5 , b ) 2 : 9 , c ) 7 : 2 , d ) 2 : 2 , e ) 2 : 8
Rationale: "the volume of the cone = ( 1 / 3 ) π r 2 h only radius ( r ) and height ( h ) are varying . hence , ( 1 / 3 ) π may be ignored . v 1 / v 2 = r 12 h 1 / r 22 h 2 = > 1 / 35 = ( 1 ) 2 h 1 / ( 2 ) 2 h 2 = > h 1 / h 2 = 7 / 5 i . e . h 1 : h 2 = 7 : 5 answer : a"
Answer: a
Question (general): a jar of 144 marbles is divided equally among a group of marble - players today . if 2 people joined the group in the future , each person would receive 1 marble less . how many people are there in the group today ?
Options: a ) 12 , b ) 14 , c ) 16 , d ) 18 , e ) 20
Rationale: "144 = 16 * 9 = 18 * 8 there are 16 people in the group today . the answer is c ."
Answer: c
Question (physics): how many minutes does aditya take to cover a distance of 400 m , if he runs at a speed of 20 km / hr
Options: a ) 115 min , b ) 215 min , c ) 315 min , d ) 415 min , e ) none of these
Rationale: "explana ɵ on : we know that , time = distancespeedspeed = 20 km / hr = 20 ∗ 518 m / sec = 509 m / sec time = ( 400 ∗ 950 ) = 72 sec = 115 min answer : op ɵ on a"
Answer: a
Question (general): a cyclist rides a bicycle 7 km at an average speed of 10 km / hr and again travels 10 km at an average speed of 7 km / hr . what is the average speed for the entire trip ?
Options: a ) 7.59 , b ) 7.79 , c ) 7.99 , d ) 8.19 , e ) 8.39
Rationale: distance = 17 km time = 7 / 10 + 10 / 7 = ( 49 + 100 ) / 70 = 149 / 70 hours average speed = ( 17 * 70 ) / 149 = 7.99 km / h the answer is c .
Answer: c
Question (physics): a train 240 m long passed a pole in 24 sec . how long will it take to pass a platform 650 m long ? a . 65
Options: a ) 28 sec , b ) 89 sec , c ) 85 sec , d ) 16 sec , e ) 15 sec
Rationale: speed = 240 / 24 = 10 m / sec . required time = ( 240 + 650 ) / 10 = 89 sec . answer : b
Answer: b
Question (geometry): if the radius of a circle that centers at the origin is 5 , how many k points on the circle have integer coordinates ?
Options: a ) 4 , b ) 8 , c ) 12 , d ) 15 , e ) 20
Rationale: "i understand this might not be required but i used the equation of a circle . since the origin is at 0 , x ^ 2 + y ^ 2 = 5 ^ 2 . x , y could be + / - ( 0,5 or 5,0 ) - 4 possibilities . x , y could be + / - ( 3,4 or 4,3 ) - 8 possibilities . ans : k = c"
Answer: c
Question (general): 1504 x 1504 = ?
Options: a ) 2262016 , b ) 2250000 , c ) 12000 , d ) 2262000 , e ) 2250016
Rationale: "1504 x 1504 = ( 1504 ) 2 = ( 1500 + 4 ) 2 = ( 1500 ) 2 + ( 4 ) 2 + ( 2 x 1500 x 4 ) = 2250000 + 16 + 12000 = 2250016 + 12000 = 2262016 a"
Answer: a
Question (general): marcella has 23 pairs of shoes . if she loses 9 individual shoes , what is the greatest number of matching pairs she could have left ?
Options: a ) 21 , b ) 20 , c ) 19 , d ) 18 , e ) 15
Rationale: marcella has 23 pairs of shoes and loses 9 shoes . to minimize the loss of identical pairs of shoes we want marcella to lose as many identical pairs as possible . this would yield 4 identical pairs and 1 additional shoe ( destroying 5 pairs of shoes ) . the 23 pairs of shoes minus the 5 ' destroyed ' pairs yields 20 pairs that still fulfill the requirements . answer : d
Answer: d
Question (physics): a room 3 m 21 cm long and 7 m 77 cm broad is to be paved with square tiles . find the least number of square tiles required to cover the floor .
Options: a ) 27636 , b ) 27640 , c ) 27647 , d ) 27713 , e ) 27675
Rationale: "explanation : area of the room = ( 321 x 777 ) cm 2 . size of largest square tile = h . c . f . of 321 cm and 777 cm = 3 cm . area of 1 tile = ( 3 x 3 ) cm 2 . number of tiles required = ( 321 × 777 ) / ( 3 × 3 ) = 27713 answer : option d"
Answer: d
Question (gain): a shopkeeper sold 15 articles at the cost price of 20 articles . then find the profit % or lost %
Options: a ) 30 % , b ) 31 % , c ) 20 % , d ) 33.33 % , e ) 40 %
Rationale: "here 15 articles selling price = 20 articles cost price so the difference = 20 - 15 = 5 % of profit = 5 * 100 / 15 = 33.33 % correct option is d"
Answer: d