Cheukting/mathqa huggingface dataset:
Question (general): john want to buy a $ 100 trouser at the store , but he think it ’ s too expensive . finally , it goes on sale for $ 10 . what is the percent decrease ?
Options: a ) 90 % , b ) 30 % , c ) 40 % , d ) 70 % , e ) 80 %
Rationale: "the is always the difference between our starting and ending points . in this case , it ’ s 100 – 10 = 90 . the “ original ” is our starting point ; in this case , it ’ s 100 . ( 90 / 100 ) * 100 = ( 0.9 ) * 100 = 90 % . a"
Answer: a
Question (physics): a river 2 m deep and 45 m wide is flowing at the rate of 2 kmph the amount of water that runs into the sea per minute is ?
Options: a ) 3000 m 3 , b ) 4580 m 3 , c ) 18500 m 3 , d ) 4900 m 3 , e ) 4700 m 3
Rationale: "explanation : ( 2000 * 2 * 45 ) / 60 = 3000 m 3 answer : option a"
Answer: a
Question (gain): the sale price sarees listed for rs . 400 after successive discount is 20 % and 5 % is ?
Options: a ) 338 , b ) 277 , c ) 342 , d ) 882 , e ) 304
Rationale: "400 * ( 80 / 100 ) * ( 95 / 100 ) = 304 answer : e"
Answer: e
Question (gain): calculate how many seconds it eill take for 4 bells to toll together again , given that they begin to toll together respectively at the intervals of 5 , 8 , 11 and 15 seconds . ?
Options: a ) 1310 , b ) 1320 , c ) 1322 , d ) 1323 , e ) 1312
Rationale: lcm of 5 , 8 , 11 and 15 is 1320 lcm = 1320 answer : b
Answer: b
Question (general): the price of 3 pants and 6 t - shirts is rs . 2250 . with the same money one can buy 1 pant and 12 t - shirts . if one wants to buy 8 t - shirts , how much shall she have to pay ?
Options: a ) 1300 , b ) 1100 , c ) 1000 , d ) 1200 , e ) 800
Rationale: "let the price of a pant and a t - shirt be rs . x and rs . y respectively . then , 3 x + 6 y = 2250 . . . . ( i ) and x + 12 y = 2250 . . . . ( ii ) divide equation ( i ) by 3 , we get the below equation . = x + 2 y = 750 . - - - ( iii ) now subtract ( iii ) from ( ii ) x + 12 y = 2250 ( - ) x + 2 y = 750 - - - - - - - - - - - - - - - - 10 y = 1500 - - - - - - - - - - - - - - - - y = 150 cost of 8 t - shirts = 8 * 150 = 1200 answer : d"
Answer: d
Question (physics): a train running at the speed of 30 km / hr crosses a pole in 24 seconds . what is the length of the train ?
Options: a ) 200 m , b ) 250 m , c ) 300 m , d ) 350 m , e ) 400 m
Rationale: "speed = ( 30 * 5 / 18 ) m / sec = ( 25 / 3 ) m / sec length of the train = ( speed x time ) = ( 25 / 3 * 24 ) m = 200 m . answer : a"
Answer: a
Question (general): - - - - - - - - - - - - - - - - yes - - - - - - - - - no - - - - unsure subject m - - - - 500 - - - - - - - - 200 - - - - - 100 subject r - - - - 400 - - - - - - - - 100 - - - - - 300 a total of 800 students were asked whether they found two subjects , m and r , interesting . each answer was either yes or no or unsure , and the numbers of students who gave these answers are listed in the table above . if 190 students answered yes only for subject m , how many of the students did not answer yes for either subject ?
Options: a ) 100 , b ) 210 , c ) 300 , d ) 400 , e ) 500
Rationale: "since 190 students answered yes only for subject m , then the remaining 310 students who answered yes for subject m , also answered yes for subject r . so , 310 students answered yes for both subjects . if 310 students answered yes for both subjects , then 400 - 310 = 90 students answered yes only for subject r . so , we have that : 200 students answered yes only for subject m ; 90 students answered yes only for subject r ; 300 students answered yes for both subjects ; therefore 800 - ( 200 + 90 + 300 ) = 210 students did not answer yes for either subject . answer : b ."
Answer: b
Question (general): in may mrs lee ' s earnings were 45 percent of the lee family ' s total income . in june mrs lee earned 20 percent more than in may . if the rest of the family ' s income was the same both months , then , in june , mrs lee ' s earnings were approximately what percent of the lee family ' s total income ?
Options: a ) 50 % , b ) 68 % , c ) 72 % , d ) 76 % , e ) 80 %
Rationale: "let in may lee family ' s total income = 100 in may mrs lee ' s income = 45 in may rest of the family ' s income = 55 in june mrs lees income = 45 * 120 / 100 = 54 in june total income = 54 + 55 = 109 % of mrs lee ' s income = 54 / 109 = 49.54 ( a )"
Answer: a
Question (general): 217 * 217 + 183 * 183
Options: a ) 70578 , b ) 82578 , c ) 80578 , d ) 80568 , e ) 89045
Rationale: "explanation : 1 / 2 × 2 ( a 2 + b 2 ) = 1 / 2 × [ ( a + b ) 2 + ( a − b ) 2 ] = 1 / 2 × [ ( 217 + 183 ) 2 + ( 217 − 183 ) 2 ] = 80578 option c"
Answer: c
Question (physics): the length of a bridge in meters , which a train 100 - meters long and traveling at 45 km / hr can cross in 30 seconds is ?
Options: a ) 225 , b ) 245 , c ) 275 , d ) 325 , e ) 375
Rationale: "45 km / h = 45000 m / 3600 s = 12.5 m / s in 30 seconds , the train can go 30 ( 12.5 ) = 375 meters let x be the length of the bridge . x + 100 = 375 meters x = 275 meters the answer is c ."
Answer: c
Question (gain): reema took a loan of rs 800 with simple interest for as many years as the rate of interest . if she paid rs . 632 as interest at the end of the loan period , what was the rate of interest .
Options: a ) 8.62 % , b ) 8.88 % , c ) 8.32 % , d ) 8 % , e ) 9 %
Rationale: "explanation : let rate = r % then time = r years . = > 800 ∗ r ∗ r / 100 = 632 = > r 2 = 79 = > r = 8.88 % option b"
Answer: b
Question (physics): pipe a can fill a tank in 32 minutes . pipe b can fill the same tank 3 times faster than pipe a . if both the pipes are connected to the tank so that they fill the tank simultaneously , how long will it take for the empty tank to overflow ?
Options: a ) 4 minutes , b ) 32 / 7 minutes , c ) 192 / 7 minutes , d ) 224 / 7 minutes , e ) 32 / 5 minutes
Rationale: pipe a can fill a tank in 32 minutes - - > the rate of a = 1 / 32 tank / minute ; pipe b can fill the same tank 3 times fasterthan pipe a - - > the rate of b = 1 / 32 + 3 / 32 = 4 / 32 tank / minute . their combined rate = 1 / 32 + 4 / 32 = 5 / 32 tank / minute ; therefore , a and b can fill the tank in 32 / 5 minutes . answer : e
Answer: e
Question (physics): a train 125 m long passes a man , running at 4 km / hr in the same direction in which the train is going , in 10 seconds . the speed of the train is :
Options: a ) 49 km / hr , b ) 50 km / hr , c ) 45 km / hr , d ) 65 km / hr , e ) 87 km / hr
Rationale: "speed of the train relative to man = ( 125 / 10 ) m / sec = ( 25 / 2 ) m / sec . [ ( 25 / 2 ) * ( 18 / 5 ) ] km / hr = 45 km / hr . let the speed of the train be x km / hr . then , relative speed = ( x - 4 ) km / hr . x - 4 = 45 = = > x = 49 km / hr . answer : a"
Answer: a
Question (other): divide $ 1000 among a , b in the ratio 1 : 4 . how many $ that b get ?
Options: a ) $ 500 , b ) $ 800 , c ) $ 1000 , d ) $ 200 , e ) $ 750
Rationale: "sum of ratio terms = 1 + 4 = 5 a = 1000 * 4 / 5 = $ 800 answer is b"
Answer: b
Question (general): the positive number z is divisible by 4 . what is the remainder of dividing z ( 2 + 4 + z ) + 3 by 2 ?
Options: a ) 0 , b ) 1 , c ) 2 , d ) 3 , e ) 4
Rationale: when we solve any of these equations : 28 + 3 ( z = 4 ) or 56 + 3 ( z = 8 ) we end up with numbers to which we have to subtract 1 to end up with a number that is exactly divisible by 2 . this is why we know that every result we get is going to have 1 as a remainder . hence answer is b .
Answer: b
Question (other): an alloy of zinc and copper contains the metals in the ratio 5 : 3 . the quantity of zinc to be added to 16 kg of the alloy so that the ratio of the metal may be 3 : 1 is :
Options: a ) 2 , b ) 4 , c ) 8 , d ) 3 , e ) 1
Rationale: "5 / 8 * 16 = 10 3 / 8 * 16 = 6 ( 10 + x ) / 6 = 3 / 1 = 8 answer : c"
Answer: c
Question (general): what is the value of ( 2 ) ^ - 6 ?
Options: a ) 1 / 62 , b ) 1 / 64 , c ) 1 / 65 , d ) 1 / 66 , e ) 1 / 67
Rationale: "2 ^ - 6 = 1 / ( 2 ) ^ 6 = 1 / 64 answer : b"
Answer: b
Question (gain): the population of a village is 7800 . it increases annually at the rate of 18 % p . a . what will be its population after 2 years ?
Options: a ) 10000 , b ) 12000 , c ) 13000 , d ) 10860 , e ) 14400
Rationale: "formula : ( after = 100 denominator ago = 100 numerator ) 7800 × 118 / 100 × 118 / 100 = 10860 d"
Answer: d
Question (general): find the numbers which are in the ratio 5 : 2 : 4 such that the sum of the first and the second added to the difference of the third and the second is 18 ?
Options: a ) 4 , 3,22 , b ) 4 , 4,22 , c ) 10 , 4,8 , d ) 9 , 6,12 , e ) 9 , 2,23
Rationale: "let the numbers be a , b and c . a : b : c = 5 : 2 : 4 given , ( a + b ) + ( c - b ) = 21 = > a + c = 21 = > 5 x + 4 x = 18 = > x = 2 a , b , c are 5 x , 2 x , 4 x a , b , c are 10 , 4 , 8 . answer : c"
Answer: c
Question (other): apple costs l rupees per kilogram for first 30 kgs and q rupees per kilogram for each additional kilogram . if the price of 33 kilograms is 168 and for 36 kgs of apples is 186 then the cost of first 20 kgs of apples is
Options: a ) 3.69 , b ) 3.66 , c ) 3.6 , d ) 100 , e ) 3.61
Rationale: "ans : by framing equations we get 30 l + 3 q = 168 30 l + 6 q = 186 eliminate q by multiplying the first equation by 2 and subtracting second equation from the first 30 l = 150 = > l = 5 then we get l = 5 cost of 20 kgs of apples = 20 x 5 = 100 answer : d"
Answer: d
Question (physics): two trains 200 m and 160 m long run at the speed of 68 kmph and 40 kmph in opposite directions in parallel tracks . the time which they take to cross each other is ?
Options: a ) 5.6 sec , b ) 8.9 sec , c ) 10.8 sec , d ) 12 sec , e ) 15 sec
Rationale: "relative speed = 68 + 40 = 108 kmph * 5 / 18 = 30 m / s distance covered in crossing each other = 200 + 160 = 360 m required time = 360 * 1 / 30 = 12 sec answer is d"
Answer: d
Question (general): the total age of a and b is 11 years more than the total age of b and c . c is how many years younger than a . ?
Options: a ) 16 , b ) 12 , c ) 11 , d ) 20 , e ) 10
Rationale: "( a + b ) - ( b - c ) = 11 a - c = 11 answer is c"
Answer: c
Question (general): lagaan is levied on the 60 percent of the cultivated land . the revenue department collected total rs . 3 , 44,000 through the lagaan from the village of mutter . mutter , a very rich farmer , paid only rs . 480 as lagaan . the percentage of total land of mutter over the total taxable land of the village is :
Options: a ) 0.23255 , b ) 0.14544 , c ) 0.25632 , d ) 0.35466 , e ) 0.63435
Rationale: total land of sukhiya = \ inline \ frac { 480 x } { 0.6 } = 800 x \ therefore cultivated land of village = 344000 x \ therefore required percentage = \ inline \ frac { 800 x } { 344000 } \ times 100 = 0.23255 a
Answer: a
Question (general): s = { 2 , 3 , 4 , 5 } b = { 4 , 5 , 6 , 7 , 8 } two integers will be randomly selected from the sets above , one integer from set s and one integer from set b . what is the probability that the sum of the two integers will equal 9 ?
Options: a ) 0.15 , b ) 0.20 , c ) 0.25 , d ) 0.30 , e ) 0.33
Rationale: the total number of pairs s , b possible is 4 * 5 = 20 . out of these 20 pairs only 4 sum up to 9 : ( 2 , 7 ) ; ( 3 , 6 ) , ( 4 , 5 ) and ( 5 , 4 ) . the probability thus is 4 / 20 = 0.2 . answer : b .
Answer: b
Question (general): every student in a room is either a junior or a senior . there is at least one junior and at least one senior in the room . if 1 / 3 of the juniors is equal to 4 / 3 of the seniors , what fraction of the students in the room are juniors ?
Options: a ) 3 / 20 , b ) 1 / 3 , c ) 5 / 2 , d ) 2 / 7 , e ) 4 / 5
Rationale: "let total number of juniors = j total number of seniors = s ( 1 / 3 ) j = ( 4 / 3 ) s = > s = 1 / 4 j total number of students = j + s = ( 5 / 4 ) j fraction of the students in the room are juniors = j / ( j + s ) = j / [ ( 5 / 4 ) j ] = 4 / 5 answer e"
Answer: e
Question (general): how many 7 in between 1 to 130 ?
Options: a ) 18 , b ) 20 , c ) 22 , d ) 23 , e ) 24
Rationale: "7 , 17,27 , 37,47 , 57,67 , 70,71 , 72,73 , 74,75 , 76,77 ( two 7 ' s ) , 78 , 79,87 , 97,107 , 117,127 23 7 ' s between 1 to 130 answer : d"
Answer: d
Question (general): given that 100.48 = x , 100.70 = y and xz = y ² , then the value of z is close to
Options: a ) 1.2 , b ) 1.45 , c ) 2.2 , d ) 2.9 , e ) none
Rationale: sol . xz = y ² ⇔ ( 10 0.48 ) z ( 100.70 ) 2 ( 10 0.48 z ) = 10 ( 2 × 0.70 ) = 101.40 ⇔ 0.48 z = 1.40 ⇔ z = 140 / 48 = 35 / 12 = 2.9 ( approx ) . answer d
Answer: d
Question (other): the number of stamps that p and q had were in the ratio of 7 : 4 respectively . after p gave q 8 stamps , the ratio of the number of p ' s stamps to the number of q ' s stamps was 6 : 5 . as a result of the gift , p had how many more stamps than q ?
Options: a ) 4 , b ) 8 , c ) 12 , d ) 16 , e ) 20
Rationale: p started with 7 k stamps and q started with 4 k stamps . ( 7 k - 8 ) / ( 4 k + 8 ) = 6 / 5 35 k - 24 k = 48 + 40 11 k = 88 k = 8 p has 7 ( 8 ) - 8 = 48 stamps and q has 4 ( 8 ) + 8 = 40 stamps . the answer is b .
Answer: b
Question (geometry): a certain cube floating in a bucket of water has between 80 and 85 percent of its volume below the surface of the water . if between 8 and 15 cubic centimeters of the cube ' s volume is above the surface of the water , then the length of a side of the cube is approximately
Options: a ) 3 , b ) 4 , c ) 7 , d ) 8 , e ) 9
Rationale: "if sides are 7 , vol = 7 ^ 3 = 343 80 % = 274.4 , 85 % = 291.55 so vol above water , between 68.6 and 51.45 - - > too big if side are 4 , vol = 64 80 % = 51.2 , 85 % = 54.4 vol above water between 12.8 and 9.6 so 4 should be the answer . check option c , if sides are 5 , vol = 125 80 % = 100 , . 85 % = 106.25 vol above water between 18.75 - 25 ( sides are 4 cubic centimeters ) b"
Answer: b
Question (geometry): a circular logo is enlarged to fit the lid of a jar . the new diameter is 10 per cent larger than the original . by what percentage has the area of the logo increased ?
Options: a ) 50 , b ) 80 , c ) 100 , d ) 125 , e ) 21
Rationale: "let old diameter be 4 , so radius is 2 old area = 4 π new diameter is 4.4 , so radius is 2.2 new area = 4.84 π increase in area is 0.84 π % increase in area = 0.84 / 4 * 100 so , % increase is 21 % answer will be ( e )"
Answer: e
Question (general): a certain car traveled twice as many miles from town a to town b as it did from town b to town c . from town a to town b , the car averaged 20 miles per gallon , and from town b to town c , the car averaged 25 miles per gallon . what is the average miles per gallon that the car achieved on its trip from town a through town b to town c ?
Options: a ) 20 , b ) 18 , c ) 21.4 , d ) 16 , e ) 10
Rationale: "step 1 ) took lcm of 20 and 25 . . came as 100 . step 2 ) 100 distance between b to c . . . do 100 / 25 hence 4 gallons used step 3 ) twice distance . . hence 100 * 2 = 200 . . . do as above . . 200 / 20 = 10 gallons used step 4 ) total gallons . . 4 + 10 = 14 gallons step ) total miles = 100 + 200 = 300 miles hence . . average of whole journey = 300 / 14 which comes to 21.4 answer : c"
Answer: c
Question (gain): the market value of a certain machine decreased by 20 percent of its purchase price each year . if the machine was purchased in 1982 for its market value of $ 8,000 , what was its market value two years later ?
Options: a ) $ 8,000 , b ) $ 5,600 , c ) $ 3,200 , d ) $ 2,400 , e ) $ 4,800
Rationale: "e . market value in 1982 = $ 8000 market value in 1983 = $ 8000 - ( $ 8000 x 20 / 100 ) = 8000 - 1600 = $ 6400 market value in 1984 = market value in 1983 - ( 20 % of $ 8000 ) = 6400 - 1600 = $ 4800"
Answer: e
Question (general): sum of the squares of 3 no . ' s is 267 and the sum of their products taken two at a time is 131 . find the sum ?
Options: a ) 20 , b ) 24 , c ) 26 , d ) 23 , e ) 30
Rationale: "( a + b + c ) 2 = a 2 + b 2 + c 2 + 2 ( ab + bc + ca ) = 267 + 2 * 131 a + b + c = √ 529 = 23 d"
Answer: d
Question (general): the average age of 10 students in a class is 15 years . if the age of teacher is also included , the average becomes 16 years , find the age of the teacher .
Options: a ) 30 , b ) 26 , c ) 28 , d ) 29 , e ) 45
Rationale: "explanation : if teacher ' s age is 15 years , there is no change in the average . but teacher has contributed 1 year to all the students along with maintaining his age at 16 . age of teacher = average age of all + total increase in age = 16 + ( 1 x 10 ) = 26 years answer : b"
Answer: b
Question (probability): the maitre ' d at an expensive manhattan restaurant has noticed that 60 % of the couples order dessert and coffee . however , 20 % of the couples who order dessert do n ' t order coffee . what is the probability w that the next couple the maitre ' d seats will not order dessert ?
Options: a ) 20 % , b ) 25 % , c ) 40 % , d ) 60 % , e ) 75 %
Rationale: "could you use a venn diagram and just go with the number 100 . 60 people order dessert and coffee . . . which is the union of d and c . w = 2 / 10 of d are n ' t in d u c = so 8 / 10 of d are in duc which means = 60 = 8 / 10 d . so d in total = 75 , and 15 d ' s are n ' t in d union c . which means 25 people are in c only + neither . b 25 %"
Answer: b
Question (physics): two passenger trains start at the same hour in the day from two different stations and move towards each other at the rate of 17 kmph and 21 kmph respectively . when they meet , it is found that one train has traveled 60 km more than the other one . the distance between the two stations is ?
Options: a ) 11 , b ) 444 , c ) 2881 , d ) 287 , e ) 456
Rationale: "1 h - - - - - 5 ? - - - - - - 60 12 h rs = 17 + 21 = 38 t = 12 d = 38 * 12 = 456 answer : e"
Answer: e
Question (gain): in a college , 70 % of total 100 arts students are locals . 50 % of students from 200 science students are locals and 85 % of total 120 commerce students are locals . what is the total percentage of locals from arts , science and commerce .
Options: a ) 56 , b ) 86.7 , c ) 25.7 , d ) 66 , e ) 64.7
Rationale: "locals from arts = 70 % of 100 = 70 locals from science = 50 % of 200 = 100 locals from commerce = 85 % of 120 = 102 total local percentage = ( 70 + 100 + 102 ) / ( 100 + 200 + 120 ) = 272 / 420 = 0.647 e"
Answer: e
Question (general): every letter in the alphabet has a number value that is equal to its place in the alphabet . thus , the letter a has a value of 1 , the letter b has a value of 2 , the letter c has a value of 3 , etc . . . the number value of a word is obtained by adding up the value of the letters in the word and then multiplying that sum by the length of the word . what is the number value of the word ` ` cow ' ' ?
Options: a ) 120 , b ) 123 , c ) 126 , d ) 129 , e ) 132
Rationale: "` ` cow ' ' = ( 3 + 15 + 23 ) * 3 = 123 . the answer is b ."
Answer: b
Question (physics): if the population of a certain country increases at the rate of 1 person every 60 seconds , by how many persons does the population increase in 2 hours ?
Options: a ) 120 , b ) 80 , c ) 100 , d ) 150 , e ) 140
Rationale: "answer = 1 * 120 ( 2 hour = 120 minutes ) = 120 answer = a"
Answer: a
Question (general): a straight line in the xy - plane has y - intercept of 79 and slope of 6 . on this line the y - coordinate of the point is 14 , then what is the x - coordinate of the point ?
Options: a ) 11 , b ) - 10.83 , c ) 71 , d ) 20.83 , e ) - 12
Rationale: "eq of line = y = mx + c c = 79 m = 6 y = 14 substitute given : x = ( y - c ) / m = ( 14 - 79 ) / 6 = - 65 / 6 = - 10.83 correct option is b"
Answer: b
Question (geometry): a rectangular lawn of length 200 m by 120 m has two roads running along its center , one along the length and the other along the width . if the width of the roads is 5 m what is the area t covered by the two roads ?
Options: a ) 400 , b ) 1550 , c ) 1575 , d ) 1600 , e ) 1625
Rationale: "area covered by road along the length = 5 * 200 = 1000 square meter area covered by road along the width = 5 * 120 = 600 square meter common area in both roads ( where the roads intersect ) = square with side 5 meter = 5 * 5 = 25 total area of the roads t = 1000 + 600 - 25 = 1575 answer : option c"
Answer: c
Question (gain): 3 candidates in an election and received 5136 , 7636 and 11628 votes respectively . what % of the total votes did the winningcandidate got in that election ?
Options: a ) 45 % , b ) 48 % , c ) 57 % , d ) 59 % , e ) 61 %
Rationale: "total number of votes polled = ( 5136 + 7636 + 11628 ) = 24400 so , required percentage = 11628 / 24400 * 100 = 48 % b"
Answer: b
Question (general): 3550 - ( 1002 / 20.04 ) = ?
Options: a ) 2984 , b ) 2983 , c ) 3500 , d ) 2981 , e ) none of these
Rationale: "3550 - 50 = 3500 answer : c"
Answer: c
Question (general): two ants , arthur and amy , have discovered a picnic and are bringing crumbs back to the anthill . amy makes twice as many trips and carries one and a half times as many crumbs per trip as arthur . if arthur carries a total of z crumbs to the anthill , how many crumbs will amy bring to the anthill , in terms of z ?
Options: a ) z / 2 , b ) z , c ) 3 z / 2 , d ) 2 z , e ) 3 z
Rationale: "lets do it by picking up numbers . let arthur carry 2 crumbs per trip , this means amy carries 3 crumbs per trip . also let arthur make 2 trips and so amy makes 4 trips . thus total crumbs carried by arthur ( z ) = 2 x 2 = 4 , total crumbs carried by amy = 3 x 4 = 12 . 12 is 3 times 4 , so e"
Answer: e
Question (general): a , b and c rents a pasture for rs . 435 . a put in 12 horses for 8 months , b 16 horses for 9 months and 18 horses for 6 months . how much should c pay ?
Options: a ) 135 , b ) 227 , c ) 268 , d ) 198 , e ) 176
Rationale: "12 * 8 : 16 * 9 = 18 * 6 8 : 12 : 9 9 / 29 * 435 = 135 answer : a"
Answer: a
Question (general): a waiter ' s salary consists of his salary and tips . during one week his tips were 3 / 4 of his salary . what fraction of his income came from tips ?
Options: a ) 3 / 7 , b ) 5 / 4 , c ) 5 / 8 , d ) 5 / 9 , e ) 6 / 9
Rationale: "income = salary ( s ) + tips = s + s * 3 / 4 = s * 7 / 4 tips = s * 3 / 4 fraction of his income came from tips = ( s * 3 / 4 ) / ( s * 7 / 4 ) = 3 / 7 answer : a"
Answer: a
Question (general): the least number which must be subtracted from 509 to make it exactly divisible by 9 is :
Options: a ) a ) 2 , b ) b ) 3 , c ) c ) 5 , d ) d ) 5 , e ) e ) 6
Rationale: on dividing 509 by 9 , we get remainder = 5 therefore , required number to be subtracted = 5 answer : c
Answer: c
Question (general): if x / y = 9 / 8 , then ( 8 x + 7 y ) / ( 8 x â € “ 7 y ) = ?
Options: a ) 8 , b ) 7 , c ) 10 , d ) 9 , e ) 6
Rationale: "answer dividing numerator as well as denominator by y , we get given exp . = ( 8 x + 7 y ) / ( 8 x â € “ 7 y ) = ( 8 x / y + 7 ) / ( 8 x / y â € “ 7 ) since x / y = 9 / 8 this implies that = [ ( 8 * 9 ) / 8 + 7 ] / [ ( 8 * 9 ) / 8 - 7 ) ] = ( 9 + 7 ) / ( 9 - 7 ) = 8 option : a"
Answer: a
Question (physics): a train 140 m long , running with a speed of 63 km / hr will pass a tree in ?
Options: a ) 15 sec , b ) 16 sec , c ) 18 sec , d ) 11 sec , e ) 8 sec
Rationale: "speed = 63 * 5 / 18 = 35 / 2 m / sec time taken = 140 * 2 / 35 = 8 sec answer : e"
Answer: e
Question (gain): a person borrows rs . 8000 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 rs , b ) 150 rs , c ) 160 rs , d ) 180 rs , e ) 200 rs
Rationale: "gain in 2 years = [ ( 8000 * 6 * 2 ) / 100 ] - [ ( 8000 * 4 * 2 ) / 100 ] 960 - 640 = 320 gain in 1 year = ( 320 / 2 ) = 160 rs answer : c"
Answer: c
Question (general): the ages of two persons differ by 16 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 ) 20,10 , c ) 25,9 , d ) 30,10 , e ) none of these
Rationale: "explanation : let their ages be x and ( x + 16 ) years . 5 ( x - 5 ) = ( x + 16 - 5 ) or 4 x = 36 or x = 9 . their present ages are 25 years and 9 years option c"
Answer: c