Cheukting/mathqa huggingface dataset:
Question (physics): a 1200 m long train crosses a tree in 120 sec , how much time will i take to pass a platform 1100 m long ?
Options: a ) 200 sec , b ) 230 sec , c ) 167 sec , d ) 197 sec , e ) 179 sec
Rationale: "l = s * t s = 1200 / 120 s = 10 m / sec . total length ( d ) = 2300 m t = d / s t = 2300 / 10 t = 230 sec answer : b"
Answer: b
Question (general): a , b and c rents a pasture for rs . 841 . a put in 12 horses for 8 months , b 16 horses for 9 months and 18 horses for 6 months . how much should b pay ?
Options: a ) 270 , b ) 279 , c ) 348 , d ) 371 , e ) 372
Rationale: "12 * 8 : 16 * 9 = 18 * 6 8 : 12 : 9 12 / 29 * 841 = 348 answer : c"
Answer: c
Question (general): a one - foot stick is marked in 1 / 4 and 1 / 6 portion . how many total markings will there be , including the end points ?
Options: a ) 8 , b ) 10 , c ) 12 , d ) 14 , e ) 16
Rationale: "lcm of 24 = 12 1 / 4 marking are ( table of 3 ) 0 . . . . . . 3 . . . . . . . . . . . 6 . . . . . . . . . . 9 . . . . . . . . . . 12 ( total = 5 ) 1 / 6 marking are ( table of 2 ) 0 . . . . . . . 2 . . . . . . 4 . . . . . . 6 . . . . . . . . 8 . . . . . . . . . 12 ( ( total = 6 ) overlapping markings are 0 . . . . . . . . 6 . . . . . . . . . 12 ( total = 3 ) total markings = 5 + 6 - 3 = 8 answer = a"
Answer: a
Question (geometry): the curved surface area of a cylindrical pillar is 264 sq . m and its volume is 924 cub . m . find the ratio of its diameter to its height
Options: a ) 7 : 9
b ) 7 : 3
c ) 7 : 7
d ) 7 : 6
e ) 7 : 1
Rationale: explanation : { \ color { black } \ frac { \ prod r ^ { 2 } h } { 2 \ prod rh } = \ frac { 924 } { 264 } } { \ color { black } \ rightarrow r = \ frac { 924 } { 264 } \ times 2 = 7 m } { \ color { black } and \ ; \ ; 2 \ prod rh = 264 \ rightarrow h = ( 264 \ times \ frac { 7 } { 22 } \ times \ frac { 1 } { 2 } \ times \ frac { 1 } { 7 } ) = 6 m } { \ color { black } \ therefore } required rato = { \ color { black } \ frac { 2 r } { h } } = { \ color { black } \ frac { 14 } { 6 } = 7 : 3 } answer : b ) 7 : 3
Answer: b
Question (physics): a can run 128 metre in 28 seconds and b in 32 seconds . by what distance a beat b ?
Options: a ) 38 metre , b ) 28 metre , c ) 23 metre , d ) 16 metre , e ) 28 metre
Rationale: clearly , a beats b by 4 seconds now find out how much b will run in these 4 seconds speed of b = distance / time taken by b = 128 / 32 = 4 m / s distance covered by b in 4 seconds = speed ã — time = 4 ã — 4 = 16 metre i . e . , a beat b by 16 metre answer is d
Answer: d
Question (general): jacob is now 13 years younger than michael . if 9 years from now michael will be twice as old as jacob , how old will jacob be in 4 years ?
Options: a ) 8 , b ) 7 , c ) 15 , d ) 21 , e ) 25
Rationale: "jacob = x years , michael = x + 13 years 9 years from now , 2 ( x + 9 ) = x + 22 2 x + 18 = x + 22 x = 4 x + 4 = 8 years answer a"
Answer: a
Question (general): a group of students decided to collect as many paise from each member of group as is the number of members . if the total collection amounts to rs . 86.49 , the number of the member is the group is :
Options: a ) 93 , b ) 67 , c ) 77 , d ) 87 , e ) 97
Rationale: "money collected = ( 86.49 x 100 ) paise = 8649 paise numbers of members = 8649 squareroot = 93 answer a"
Answer: a
Question (general): lagaan is levied on the 60 percent of the cultivated land . the revenue department collected total rs . 3 , 84,000 through the lagaan from the village of mettur . mettur , a very rich farmer , paid only rs . 480 as lagaan . the percentage of total land of mettur over the total taxable land of the village is :
Options: a ) 0.20833 , b ) 0.35424 , c ) 0.10982 , d ) 0.20933 , e ) 0.10984
Rationale: "total land of sukhiya = \ inline \ frac { 480 x } { 0.6 } = 800 x \ therefore cultivated land of village = 384000 x \ therefore required percentage = \ inline \ frac { 800 x } { 384000 } \ times 100 = 0.20833 a"
Answer: a
Question (general): in a certain lottery , the probability that a number between 12 and 20 , inclusive , is drawn is 1 / 4 . if the probability that a number 12 or larger is drawn is 2 / 3 , what is the probability that a number less than or equal to 20 is drawn ?
Options: a ) 1 / 18 , b ) 1 / 6 , c ) 1 / 3 , d ) 1 / 2 , e ) 7 / 12
Rationale: "you can simply use sets concept in this question . the formula total = n ( a ) + n ( b ) - n ( a and b ) is applicable here too . set 1 : number 12 or larger set 2 : number 20 or smaller 1 = p ( set 1 ) + p ( set 2 ) - p ( set 1 and set 2 ) ( combined probability is 1 because every number will be either 12 or moreor 20 or lessor both ) 2 / 3 + p ( set 2 ) - 1 / 4 = 1 p ( set 2 ) = 7 / 12 answer ( e )"
Answer: e
Question (gain): if $ 5,000 is invested in an account at a simple annual rate of r percent , the interest is $ 250 . when $ 15,000 is invested at the same interest rate , what is the interest from the investment ?
Options: a ) $ 700 , b ) $ 850 , c ) $ 800 , d ) $ 750 , e ) $ 900
Rationale: "- > 250 / 5,000 = 5 % and 15,000 * 5 % = 750 . thus , d is the answer ."
Answer: d
Question (general): the average of 65 numbers is 40 . if two numbers , 83 and 30 are discarded , then the average of the remaining numbers is nearly
Options: a ) 28.32 , b ) 39 , c ) 38.78 , d ) 29 , e ) 39.47
Rationale: explanation : total sum of 63 numbers = ( 65 * 40 ) - ( 83 + 30 ) = 2600 - 113 = 2487 average = 2487 / 63 = 39.47 answer : e
Answer: e
Question (general): a + b + c + d = d + e + f + g = g + h + i = 17 given a = 4 . find value of g and h ?
Options: a ) 29 , b ) 39 , c ) 19 , d ) 49 , e ) 59
Rationale: a + b + c + d = 17 4 + 2 + 6 + 5 = 17 d = 5 d + e + f + g = 17 5 + 3 + 8 + 1 = 17 g = 1 g + h + i = 17 1 + 9 + 7 = 17 g = 1 , h = 9 . answer : c
Answer: c
Question (general): when a merchant imported a certain item , she paid a 7 percent import tax on the portion of the total value of the item in excess of $ 1,000 . if the amount of the import tax that the merchant paid was $ 111.30 , what was the total value of the item ?
Options: a ) $ 2380 , b ) $ 2590 , c ) $ 2760 , d ) $ 2940 , e ) $ 3150
Rationale: "let x be the value of the item . 0.07 * ( x - 1000 ) = 111.30 x = 2590 the answer is b ."
Answer: b
Question (geometry): find the smallest number which should be multiplied with 13225 to make it a perfect square .
Options: a ) 25 , b ) 5 , c ) 1 , d ) 23 , e ) 6
Rationale: "13225 = 5 * 5 * 23 * 23 required smallest number = 1 1 is the smallest number which should be multiplied with 13225 to make it a perfect square . answer : c"
Answer: c
Question (gain): 3 candidates in an election and received 2500 , 5000 and 20000 votes respectively . what % of the total votes did the winningcandidate got in that election ?
Options: a ) 72.72 % , b ) 50 % , c ) 57.57 % , d ) 60 % , e ) 65 %
Rationale: "total number of votes polled = ( 2500 + 5000 + 20000 ) = 27500 so , required percentage = 20000 / 27500 * 100 = 72.72 % a"
Answer: a
Question (physics): in a lake , there is a patch of lily pads . every day , the patch doubles in size . it takes 25 days for the patch to cover the entire lake , how many days would it take the patch to cover half of the lake ?
Options: a ) 36 , b ) 2 ^ 4 * 3 , c ) 24 , d ) 38 , e ) 47
Rationale: "so 24 days answer c = 24"
Answer: c
Question (general): a 30 % alcohol mixture is added to a 50 % alcohol mixture to form a 10 litre mixture of 45 % alcohol . how much of the 30 % mixture was used ?
Options: a ) 1.5 liters , b ) 2.5 liters , c ) 3.5 liters , d ) 4.5 liters , e ) 5.5 liters
Rationale: solution a = 50 % solution solution b = 30 % solution 30 % - 45 % = 15 % solution b 50 % - 45 % = 5 % solution a so the ratio is 3 : 1 for 30 % : 50 % solutions 3 / 4 * 10 liter = 7.5 for 30 % solution and 2.5 for 50 % solution . . answer : b
Answer: b
Question (general): if the charge of staying in a student youth hostel $ 18.00 / day for the first week , and $ 11.00 / day for each additional week , how much does it cost to stay for 23 days ?
Options: a ) $ 160 , b ) $ 176 , c ) $ 282 , d ) $ 302 , e ) $ 286
Rationale: "total number of days of stay = 23 charge of staying in first week = 18 * 7 = 126 $ charge of staying for additional days = ( 23 - 7 ) * 11 = 16 * 11 = 176 $ total charge = 126 + 176 = 302 $ answer d"
Answer: d
Question (general): nails and screws are manufactured at a uniform weight per nail and a uniform weight per screw . if the total weight of one screw and one nail is half that of 6 screws and one nail , then the total weight of 3 screws , and 3 nails is how many times that of 1 screws and 5 nails ?
Options: a ) a . 4 , b ) b . 5 / 2 , c ) c . 2 , d ) d . 3 / 2 , e ) e . 5 / 4
Rationale: "let the weight of nail be n and that of screw be s . . so s + w = 1 / 2 * ( 6 s + 1 n ) . . . or 1 n = 4 s . . lets see the weight of 3 s and 3 n = 3 s + 3 * 4 s = 15 s . . and weight of 1 s and 5 n = 1 s + 5 * 1 s = 6 s . . ratio = 15 s / 6 s = 15 / 6 = 5 / 2 b"
Answer: b
Question (general): a number x is multiplied with itself and then added to the product of 4 and x . if the result of these two operations is - 3 , what is the value of x ?
Options: a ) - 4 , b ) - 1 and - 3 , c ) 2 , d ) 4 , e ) can not be determined .
Rationale: a number x is multiplied with itself - - > x ^ 2 added to the product of 4 and x - - > x ^ 2 + 4 x if the result of these two operations is - 3 - - > x ^ 2 + 4 x = - 3 i . e x ^ 2 + 4 x + 3 = 0 is the quadratic equation which needs to be solved . ( x + 1 ) ( x + 3 ) = 0 hence x = - 1 . x = - 3 imo b
Answer: b
Question (general): each week , harry is paid x dollars per hour for the first 30 hours and 1.5 x dollars for each additional hour worked that week . each week , james is paid x dollars per hour for the first 40 hours and 2 x dollars for each additional hour worked that week . last week james worked a total of 44 hours . if harry and james were paid the same amount last week , how many hours did harry work last week ?
Options: a ) 35 , b ) 36 , c ) 37 , d ) 38 , e ) 42
Rationale: "amount earned by james = 40 * x + 4 * 2 x = 48 x therefore , amount earned by james = 48 x but we know the amount harry earned assuming working y hours ( y > 30 ) is 30 * x + ( y - 30 ) * 1.5 x [ [ we know y > 30 because in 30 h the most harry could earn is 30 x , but he has earned 48 x ] ] so x * ( 1.5 y - 45 + 30 ) = 48 x or x * ( 1.5 y - 15 ) = 48 x so 1.5 y - 15 = 48 so 1.5 y = 63 so y = 42 answer is e"
Answer: e
Question (physics): sides of a rectangular park are in the ratio 3 : 2 and its area is 5766 sq m , the cost of fencing it at 50 ps per meter is ?
Options: a ) 287 , b ) 1287 , c ) 125 , d ) 155 , e ) 271
Rationale: "3 x * 2 x = 5766 = > x = 31 2 ( 93 + 62 ) = 310 m 310 * 1 / 2 = rs . 155 answer : d"
Answer: d
Question (general): find the smallest number of 6 digits which is exactly divisible by 111
Options: a ) 100011 , b ) 111111 , c ) 101111 , d ) 1011111 , e ) 211111
Rationale: "smallest number of 6 digits is 100000 . on dividing 100000 by 111 , we get 100 as remainder . number to be added = ( 111 - 100 ) - 11 . hence , required number = 100011 answer a 100011"
Answer: a
Question (general): when the positive integer k is divided by the positive integer n , the remainder is 13 . if k / n = 81.2 , what is the value of n ?
Options: a ) 9 , b ) 20 , c ) 55 , d ) 70 , e ) 81
Rationale: "here ' s an approach that ' s based on number properties and a bit ofbrute forcemath : we ' re told that k and n are both integers . since k / n = 81.2 , we can say that k = 81.2 ( n ) n has tomultiply outthe . 2 so that k becomes an integer . with the answers that we have to work with , n has to be a multiple of 5 . eliminate a and e . with the remaining answers , we can test the answers and find the one that fits the rest of the info ( k / n = 81.2 and k / n has a remainder of 11 ) answer b : if n = 20 , then k = 1624 ; 1624 / 20 has a remainder of 4 not a match answer c : if n = 55 , then k = 4466 ; 4466 / 55 has a remainder of 11 match . final answer : b"
Answer: b
Question (general): kareem is 3 times as old as his son . after 10 years , the sum of their ages will be 76 years . find their present ages .
Options: a ) 13 , b ) 14 , c ) 15 , d ) 16 , e ) 17
Rationale: sol . let the present age of kareem ’ s son be x years . then , kareem ’ s age = 3 x years after 10 years , kareem ’ s age = 3 x + 10 years and kareem ’ s son ’ s age = x + 10 years ∴ ( 3 x + 10 ) + ( x + 10 ) = 76 = > 4 x = 56 = > x = 14 ∴ kareem ’ s present age = 3 x = 3 × 14 = 42 years kareem ’ s son ’ s age = x = 14 years . answer b
Answer: b
Question (other): what is the greatest value of x such that 4 ^ x is a factor of 21 ! ?
Options: a ) 5 , b ) 6 , c ) 3 , d ) 2 , e ) 4
Rationale: pretty simple , really . if m = 6 , then 4 m = 24 , which is 12 x 2 , both of which are included in 21 ! since 6 is the largest number here , its the answer . answer is b
Answer: b
Question (physics): if 8 spiders make 8 webs in 8 days , then 1 spider will make 1 web in how many days ?
Options: a ) 7 , b ) 6 , c ) 5 , d ) 8 , e ) 3
Rationale: "let the required number days be x . less spiders , more days ( indirect proportion ) less webs , less days ( direct proportion ) spiders 1 : 8 webs 8 : 1 1 x 8 x x = 8 x 1 x 8 = > x = 8 answer is d"
Answer: d
Question (general): what is the sum of the integers from - 160 to 162 , inclusive ?
Options: a ) 325 , b ) 327 , c ) 323 , d ) 330 , e ) 350
Rationale: "in an arithmetic progression , the nth term is given by tn = a + ( n - 1 ) d here tn = 162 , a = - 160 , d = 1 hence , 162 = - 160 + ( n - 1 ) or n = 323 sum of n terms can be calculated by sn = n / 2 ( a + l ) a = first term , l = last term , n = no . of terms sn = 323 * ( - 160 + 162 ) / 2 sn = 323 * 2 / 2 = 323 answer : c"
Answer: c
Question (geometry): chloe has $ 27 dollars to go to the fair . she is bringing 2 other friends along . admission to the fair is $ 3 . each ride costs $ 1.70 . how many rides can she and her friends go on and how much money will be left over ?
Options: a ) they can go on 15 rides and $ 1.50 will be left over .
b ) they can go on 3 rides and $ 2.70 will be left over .
c ) they can go on 7 rides and $ 0 will be left over .
d ) they can go on 6 rides and $ 0 will be left over .
e ) they can go on 5 rides and $ 1.50 will be left over .
Rationale: admission to the fair is $ 3 per person . if she wants her and her friends to go , the cost will be $ 9 . 27 - 9 is 18 . to go on a ride is $ 5.10 . 5.10 x 3 is 15.30 . 18 - 15.30 is 2.70 . they can go on 3 rides and $ 2.70 will be left over . the correct answer is b .
Answer: b
Question (gain): if the selling price of 50 articles is equal to the cost price of 30 articles , then the loss or gain percent is :
Options: a ) 10 % , b ) 40 % , c ) 30 % , d ) 25 % , e ) 35 %
Rationale: "let c . p . of each article be re . 1 . then , c . p . of 50 articles = rs . 50 ; s . p . of 50 articles = rs . 30 . loss % = 20 / 50 * 100 = 40 % answer : b"
Answer: b
Question (general): solution x is 10 percent alcohol by volume , and solution y is 30 percent alcohol by volume . how many milliliters of solution y must be added to 200 milliliters of solution x to create a solution that is 25 percent alcohol by volume ?
Options: a ) 250 / 3 , b ) 500 / 3 , c ) 400 , d ) 480 , e ) 600
Rationale: we know that x is 10 % , y is 30 % and w . avg = 25 % . what does this mean with respect to w . avg technique ? w . avg is 1 portion away from y and 3 portion away from x so for every 1 portion of x we will have to add 3 portions of y . if x = 200 then y = 600 answer : e
Answer: e
Question (gain): what will be the compound interest on a sum of rs . 26,000 after 3 years at the rate of 12 % p . a . ?
Options: a ) s . 10123.77 , b ) s . 10123.21 , c ) s . 10123.20 , d ) s . 10123.28 , e ) s . 10528.12
Rationale: "amount = [ 26000 * ( 1 + 12 / 100 ) 3 ] = 26000 * 28 / 25 * 28 / 25 * 28 / 25 = rs . 36528.12 c . i . = ( 36528.12 - 26000 ) = rs . 10528.12 answer : e"
Answer: e
Question (general): the star running back on our football team got most of his total yardage running . the rest was catching passes . he caught passes for 60 yards . his total yardage was 150 yards . the running back for the other team got 200 yards . how many yards did the star running back on our football team get running ?
Options: a ) 50 yards , b ) 60 yards , c ) 70 yards , d ) 80 yards , e ) 90 yards
Rationale: . the other team is extra information . 150 – 60 = 90 he got 90 yards running . correct answer e
Answer: e
Question (other): in what ratio must rice of rs . 30 per kg be mixed with rice of rs . 56 per kg so that cost of mixture is rs . 35 per kg ?
Options: a ) 28 : 15 , b ) 6 : 7 , c ) 7 : 6 , d ) 5 : 21 , e ) 21 : 5
Rationale: "( 35 - 56 ) / ( 30 - 35 ) = 6 / 2 = 21 : 5 answer : e"
Answer: e
Question (general): an automobile parts supplier charges $ 25 per package of gaskets . when a customer orders more than 10 packages of gaskets , the supplier charges 4 / 5 the price for each package in excess of 10 . during a certain week , the supplier sold 60 packages of gaskets . if 30 percent of the gaskets went to company x , 15 percent to company y , and the rest to company z , what was the total amount , in dollars , that the parts supplier received in payment for the gaskets ?
Options: a ) 1305 , b ) 1375 , c ) 1345 , d ) 1415 , e ) 1455
Rationale: "$ 25 per packet of gasket in case a customer orders less than 10 in case a customer orders > 10 price per gasket = 25 * 4 / 5 = 20 a certain week the supplier sold 60 gasket 1 . he sold 30 % of the gaskets to x = 18 gaskets = 25 * 10 + 20 * 8 = 250 + 160 = 410 2 . he sold 15 % of the gaskets to y = 9 gaskets = 25 * 9 = 225 3 . he sold remaining 55 % to z = 33 gaskets = 25 * 10 = 250 + 20 * 23 = 710 thus , total money earned 410 + 225 + 710 = 1345 answer is c"
Answer: c
Question (physics): two cars start from the opposite places of a main road , 113 km apart . first car runs for 25 km and takes a right turn and then runs 15 km . it then turns left and then runs for another 25 km and then takes the direction back to reach the main road . in the mean time , due to minor break down the other car has run only 35 km along the main road . what would be the distance between two cars at this point ?
Options: a ) 65 , b ) 38 , c ) 20 , d ) 28 , e ) 21
Rationale: answer : d ) 28 km
Answer: d
Question (general): a straight line in the xy - plane has a slope of 4 and a y - intercept of 4 . on this line , what is the x - coordinate of the point whose y - coordinate is 800 ?
Options: a ) 233 , b ) 299 , c ) 333 , d ) 199 , e ) 339
Rationale: eq of line = y = mx + c m = 4 , c = 4 y = 4 x + 4 , substitute y by 800 as given in question . 800 = 4 x + 4 , x = 199 . correct option is d
Answer: d
Question (gain): a shop owner sells 25 mtr of cloth and gains sp of 10 mtrs . find the gain % ?
Options: a ) 30 % , b ) 40 % , c ) 50 % , d ) 66.67 % , e ) 70 %
Rationale: "here , selling price of 10 m cloth is obtained as profit . profit of 10 m cloth = ( s . p . of 25 m cloth ) – ( c . p . of 25 m cloth ) selling price of 15 m cloth = selling price of 25 m of cloth let cost of each metre be rs . 100 . therefore , cost price of 15 m cloth = rs . 1500 and s . p . of 15 m cloth = rs . rs . 2500 profit % = 10 / 15 × 100 = 66.67 % profit of 66.67 % was made by the merchant . d"
Answer: d
Question (other): what number has a 150 : 1 ratio to the number 2 ?
Options: a ) 130 , b ) 300 , c ) 200 , d ) 30 , e ) 75
Rationale: "150 : 1 = x : 2 x = 150 * 2 x = 300 answer : b"
Answer: b
Question (gain): on a saturday night , each of the rooms at a certain motel was rented for either $ 40 or $ 60 . if 10 of the rooms that were rented for $ 60 had instead been rented for $ 40 , then the total rent the motel charged for that night would have been reduced by 50 percent . what was the total rent the motel actually charged for that night ?
Options: a ) $ 400 , b ) $ 800 , c ) $ 1,000 , d ) $ 1,600 , e ) $ 2,400
Rationale: "let total rent the motel charge for all rooms = x if 10 rooms that were rented for 60 $ had instead been rented for 40 $ , then total difference in prices = 20 $ * 10 = 200 $ total rent the motel charged would have been reduced by 50 % . 5 x = 200 = > x = 400 answer a"
Answer: a
Question (gain): a sum fetched a total simple interest of rs . 6016.75 at the rate of 8 p . c . p . a . in 5 years . what is the sum ?
Options: a ) rs . 16241.875 , b ) rs . 15041.85 , c ) rs . 15401.875 , d ) rs . 15041.875 , e ) none of these
Rationale: "explanation : principal = rs 100 x 6016.75 / 8 x 5 = rs . 601675 / 40 = rs . 15041.875 answer : option d"
Answer: d
Question (other): x starts a business with rs . 45000 . y joins in the business after 2 months with rs . 30000 . what will be the ratio in which they should share the profit at the end of the year ?
Options: a ) 1 : 2 , b ) 9 : 5 , c ) 1 : 5 , d ) 3 : 1 , e ) 1 : 1
Rationale: "explanation : ratio in which they should share the profit = ratio of the investments multiplied by the time period = 45000 ã — 12 : 30000 ã — 10 = 45 ã — 12 : 30 ã — 10 = 3 ã — 12 : 2 ã — 10 = 9 : 5 answer : option b"
Answer: b
Question (physics): a train 360 m long is running at a speed of 45 km / hr . in what time will it pass a bridge 165 m long ?
Options: a ) 40 , b ) 99 , c ) 88 , d ) 77 , e ) 42
Rationale: ": speed = 45 * 5 / 18 = 25 / 2 m / sec total distance covered = 360 + 165 = 525 m required time = 525 * 2 / 25 = 42 sec answer : e"
Answer: e
Question (physics): two pipes can fill a tank in 8 minutes and 5 minutes . an outlet pipe can empty the tank in 12 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 ) 10 minutes , e ) 14 minutes
Rationale: "part of the filled by all the three pipes in one minute = 1 / 8 + 1 / 5 - 1 / 12 = ( 15 + 24 - 10 ) / 120 = 29 / 120 so , the tank becomes full in 14 minutes . answer : e"
Answer: e
Question (gain): the owner of a furniture shop charges his customer 15 % more than the cost price . if a customer paid rs . 8325 for a computer table , then what was the cost price of the computer table ?
Options: a ) rs . 6725 , b ) rs . 7239.13 , c ) rs . 6908 , d ) rs . 6725 , e ) rs . 6728
Rationale: "cp = sp * ( 100 / ( 100 + profit % ) ) = 8325 ( 100 / 115 ) = rs . 7239.13 . answer : b"
Answer: b
Question (physics): a boat takes 19 hours for travelling downstream from point a to point b and coming back to a point c midway between a and b . if the velocity of the stream is 4 km / h and the speed of the boat in still water is 14 km / h , what is the distance between a and b ?
Options: a ) 200 km , b ) 180 km , c ) 160 km , d ) 220 km , e ) none of these
Rationale: "speed of boat for downstream = 14 + 4 = 18 km / hr speed of boat for upstream = 14 – 4 = 10 km / hr distance = x x / 18 + ( x / 2 ) / 10 = 19 x = 180 km answer : b"
Answer: b
Question (other): if 73 ! has 16 zeroes at the end , how many zeroes will 80 ! have at the end ?
Options: a ) 16 , b ) 17 , c ) 18 , d ) 19 , e ) 20
Rationale: prime factoring : you need a 2 and a 5 to make a 10 ( a ` ` zero ' ' ) , and there are tons of 2 ' s so let ' s skip these and focus on the ( rarer ) 5 s : 80 ! = 1 * 2 * 3 * 4 * 5 * 6 . . . * 78 * 79 * 80 since there are 80 consecutive numbers , there are 16 multiples of 5 in there , but if we ' re prime factoring , we need to remember that some multiples of 5 actually contain more than just one 5 . which ? 25 comes to mind - - it ' s got two of them ! so all the multiples of 25 actually contain two 5 ' s ( ie : 50 and 75 ) so , to recap , we have 16 of them , plus 3 more ( the additional 5 ' s in 25 , 50 , and 75 ) , so that makes 19 , and since we have more than enough 2 ' s , we know our number will have exactly 19 zeros at the end . answer : d
Answer: d
Question (general): in 1990 the budgets for projects q and v were $ 700,000 and $ 780,000 , respectively . in each of the next 10 years , the budget for q was increased by $ 30,000 and the budget for v was decreased by $ 10,000 . in which year was the budget for q equal to the budget for v ?
Options: a ) 1992 , b ) 1993 , c ) 1994 , d ) 1995 , e ) 1996
Rationale: "let the no of years it takes is x . 700 + 30 x = 780 - 10 x - - > 40 x = 80 and x = 2 . thus , it happens in 1992 . a ."
Answer: a