Cheukting/mathqa huggingface dataset:
Question (general): what is the greatest positive integer x such that 3 ^ x is a factor of 9 ^ 8 ?
Options: a ) 5 , b ) 9 , c ) 16 , d ) 20 , e ) 30
Rationale: "what is the greatest positive integer x such that 3 ^ x is a factor of 9 ^ 8 ? 9 ^ 8 = ( 3 ^ 2 ) ^ 8 = 3 ^ 16 c . 16"
Answer: c
Question (general): find the average of all the numbers between 11 and 36 which are divisible by 5
Options: a ) 15 , b ) 20 , c ) 25 , d ) 30 , e ) 35
Rationale: "explanation : average = ( 15 + 20 + 25 + 30 + 35 ) / 5 = 125 / 5 = 25 answer c"
Answer: c
Question (general): a , b , c subscribe rs . 50000 for a business . a subscribes rs . 4000 more than b and b rs . 5000 more than c . out of a total profit of rs . 35000 a receives :
Options: a ) rs . 11900 , b ) rs . 8400 , c ) rs . 14700 , d ) rs . 13600 , e ) rs . 14600
Rationale: "let c = x . then b = x + 5000 and a + x + 5000 + 4000 = x + 9000 therefore , x + x + 5000 + x + 9000 = 50000 û x = 12000 . therefore , a : b : c = 21000 : 17000 : 12000 = 21 : 17 : 12 therefore , a ’ s share = rs ( 35000 * 21 / 50 ) = rs . 14700 answer : c"
Answer: c
Question (physics): one hour before john started walking from p to q , a distance of 28 miles , ann had started walking along the same road from q to p . ann walked at a constant speed of 3 miles per hour and john at 2 miles per hour . how many miles had ann walked when they met ?
Options: a ) 6 miles , b ) 8,4 miles , c ) 9 miles , d ) 9,6 miles , e ) 18 miles
Rationale: "ann walks from q to p at a speed of 3 miles / hr for one hour . she covers 3 miles in 1 hour and now distance between john and ann is 28 - 3 = 25 miles . ann walks at 3 mph and john at 2 mph so their relative speed is 3 + 2 = 5 mph . they have to cover 25 miles so it will take them 25 / 5 = 5 hours to meet . in 5 hrs , ann would have covered 5 hrs * 3 miles per hour = 15 miles . adding this to the 3 miles she covered before john , ann covered a total of 3 + 15 = 18 miles . answer ( e )"
Answer: e
Question (general): roses can be purchased individually for $ 4.50 , one dozen for $ 36 , or two dozen for $ 50 . what is the greatest number of roses that can be purchased for $ 680 ?
Options: a ) 156 , b ) 162 , c ) 318 , d ) 324 , e ) 325
Rationale: buy as many $ 50 deals as possible . we can by 650 / 50 = 13 two dozen roses , thus total of 13 * 24 = 312 roses . we are left with 680 - 650 = $ 30 . we can buy 30 / 4.5 = ~ 6 roses for that amount . total = 312 + 6 = 318 . answer : c .
Answer: c
Question (gain): the population of a town is 10000 . it increases annually at the rate of 10 % p . a . what will be its population after 2 years ?
Options: a ) 12100 , b ) 14400 , c ) 14500 , d ) 14600 , e ) 14700
Rationale: "formula : 10000 × 110 / 100 × 110 / 100 = 12100 answer : a"
Answer: a
Question (general): set a contains all the even numbers between 8 and 50 inclusive . set b contains all the even numbers between 108 and 150 inclusive . what is the difference between the sum of elements of set b and the sum of the elements of set a ?
Options: a ) 2200 , b ) 2550 , c ) 5050 , d ) 6275 , e ) 11325
Rationale: "set a contains 8 , 10 , 12 . . . 50 set b contains 108 , 110 , 112 . . . 150 number of terms in each set = 22 difference between corresponding terms in set a and b = 100 difference between sum of set b and set a = 100 * 22 = 2200 answer a"
Answer: a
Question (gain): john makes $ 45 a week from his job . he earns a raise andnow makes $ 75 a week . what is the % increase ?
Options: a ) 16 % , b ) 46.66 % , c ) 44.44 % , d ) 36.98 % , e ) 17 %
Rationale: "increase = ( 20 / 45 ) * 100 = ( 4 / 9 ) * 100 = 44.44 % . c"
Answer: c
Question (physics): pipe a can fill a tank in 12 hours . due to a leak at the bottom it takes 20 hours to fill the tank . in what time the leak alone can empty the full tank ?
Options: a ) 18 hours , b ) 23 hours , c ) 28 hours , d ) 30 hours , e ) 40 hours
Rationale: "let leak can empty the full tank in x hours . 1 / 12 - 1 / x = 1 / 20 = > 1 / 12 – 1 / 20 = 1 / x 1 / x = 5 - 3 / 60 = 1 / 30 x = 30 hours answer : d"
Answer: d
Question (gain): find 30 % of 240
Options: a ) 72 , b ) 94 , c ) 86 , d ) 74 , e ) 110
Rationale: "we know that r % of m is equal to r / 100 × m . so , we have 30 % of 240 30 / 100 × 240 = 72 answer : a"
Answer: a
Question (physics): 11 cubic centimetres of silver is drawn into a wire 1 mm in diameter . the length of the wire in metres will be :
Options: a ) 84 m , b ) 88 m , c ) 14 m , d ) 137 m , e ) none
Rationale: "sol . let the length of the wire b h . radius = 1 / 2 mm = 1 / 20 cm . then , 22 / 7 * 1 / 20 * 1 / 20 * h = 11 ⇔ = [ 11 * 20 * 20 * 7 / 22 ] = 1400 cm = 14 m . answer c"
Answer: c
Question (geometry): the length of a rectangle is one - fourth of the radius of a circle . the radius of the circle is equal to the side of the square , whose area is 1225 sq . units . what is the area ( in sq . units ) of the rectangle if the rectangle if the breadth is 10 units ?
Options: a ) 350 sq . units
b ) 250 sq . units
c ) 300 sq . units
d ) 200 sq . units
e ) 100 sq . units
Rationale: given that the area of the square = 6400 sq . units = > side of square = √ 6400 = 80 units the radius of the circle = side of the square = 35 units length of the rectangle = 1 / 4 * 80 = 20 units given that breadth = 10 units area of the rectangle = lb = 20 * 10 = 200 sq . units answer : d
Answer: d
Question (gain): what sum of money will produce rs . 70 as simple interest in 4 years at 2 1 / 2 percent ?
Options: a ) 337 , b ) 500 , c ) 700 , d ) 288 , e ) 211
Rationale: "70 = ( p * 4 * 5 / 2 ) / 100 p = 700 answer : c"
Answer: c
Question (general): if 2 / z = 2 / ( z + 1 ) + 2 / ( z + 16 ) which of these integers could be the value of z ?
Options: a ) 0 , b ) 1 , c ) 2 , d ) 3 , e ) 4
Rationale: "solving for z algebraically in this problem would not be easy . instead , we can follow the hint in the question ( “ which of these integers … ” ) and test each answer choice : a . 2 / 0 = 2 / 1 + 2 / 16 incorrect ( division by zero ) a . 2 / 1 = 2 / 2 + 2 / 17 incorrect a . 2 / 2 = 2 / 3 + 2 / 18 incorrect a . 2 / 3 = 2 / 4 + 2 / 19 incorrect a . 2 / 4 = 2 / 5 + 2 / 20 correct the correct answer is e , because it contains the only value that makes the equation work . notice how quickly this strategy worked in this case"
Answer: e
Question (geometry): the area of a square is equal to five times the area of a rectangle of dimensions 50 cm * 10 cm . what is the perimeter of the square ?
Options: a ) 289 cm , b ) 200 cm , c ) 829 cm , d ) 288 cm , e ) 289 cm
Rationale: "area of the square = s * s = 5 ( 50 * 10 ) = > s = 50 = 50 cm perimeter of the square = 4 * 50 = 200 cm . answer : b"
Answer: b
Question (physics): a truck covers a distance of 360 km at a certain speed in 8 hours . how much time would a car take at an average speed which is 18 kmph more than that of the speed of the truck to cover a distance which is 14 km more than that travelled by the truck ?
Options: a ) 6 hours , b ) 5 hours , c ) 7 hours , d ) 8 hours , e ) none
Rationale: "explanation : speed of the truck = distance / time = 360 / 8 = 45 kmph now , speed of car = ( speed of truck + 18 ) kmph = ( 45 + 18 ) = 63 kmph distance travelled by car = 360 + 81 = 441 km time taken by car = distance / speed = 441 / 63 = 8 hours . answer – d"
Answer: d
Question (physics): the average speed of a car decreased by 3 miles per hour every successive 8 - minutes interval . if the car traveled 3.6 miles in the fifth 8 - minute interval , what was the average speed of the car , in miles per hour , in the first 8 minute interval ?
Options: a ) 31 , b ) 35 , c ) 39 , d ) 43 , e ) 47
Rationale: ( 3.6 miles / 8 minutes ) * 60 minutes / hour = 27 mph let x be the original speed . x - 4 ( 3 ) = 27 x = 39 mph the answer is c .
Answer: c
Question (geometry): a took 15 seconds to cross a rectangular field diagonally walking at the rate of 52 m / min and b took the same time to cross the same field along its sides walking at the rate of 68 m / min . the area of the field is ?
Options: a ) 33
b ) 60
c ) 88
d ) 27
e ) 26
Rationale: explanation : length of the diagonal = 52 * ( 15 / 60 ) = 13 m sum of length and breadth = 68 * ( 15 / 60 ) = 17 m \ inline { \ color { black } \ sqrt { l ^ { 2 } + b ^ { 2 } } = 13 \ ; or \ ; l + b = 17 } area = lb = 1 / 2 [ ( 2 lb ) ] = 1 / 2 [ ( l + b ) ² - ( l ² + b ² ) ] = 1 / 2 [ 17 ² - 169 ] = 1 / 2 * 120 = 60 sq meter answer : b ) 60
Answer: b
Question (geometry): a geometric shape is obtained by combining a square of side 8 cm and a semicircle of diameter 8 cm . what is the perimeter of the shape obtained ?
Options: a ) 28.32
b ) 36.57
c ) 44.57
d ) 48.93
e ) 54.24
Rationale: circumference of the semicircle = ï € xd / 2 = ( 22 / 7 ) x 4 = 12.57 perimeter of the square plot = 3 x 8 = 24 perimeter of the shape = 36.57 cm answer : b
Answer: b
Question (gain): the simple interest on a certain sum of money for 2 years at 10 % per annum is half the compound interest on $ 100 for 2 years at 5 % per annum . the sum placed on simple interest is ?
Options: a ) $ 602.5 , b ) $ 625.8 , c ) $ 710.6 , d ) $ 745 , e ) $ 790.3
Rationale: "c . i . = 100 * ( 1 + 5 / 100 ) ^ 2 - 100 = 100 * 21 / 20 * 21 / 20 - 100 = $ 120.5 sum = 120.5 * 100 / 2 * 10 = $ 602.5 answer is a"
Answer: a
Question (gain): redo ’ s manufacturing costs for sets of horseshoes include a $ 10,500 initial outlay , and $ 15 per set . they can sell the sets $ 40 . if profit is revenue from sales minus manufacturing costs , and the company producessells 500 sets of horseshoes , what was their profit ?
Options: a ) $ 2100 , b ) $ 2000 , c ) $ 2050 , d ) $ 2070 , e ) $ 2500
Rationale: "total manufacturing cost = 10500 + 500 * 15 = 18000 total selling cost = 500 * 40 = 20000 profit = 20000 - 18000 = 2000 answer : b"
Answer: b
Question (general): find the highest value of ' a ' so that 365 a 16 is divisible by 8 .
Options: a ) 9 , b ) 8 , c ) 0 , d ) 2 , e ) 1
Rationale: explanation : given , number is divisible by 8 only if ' a 16 ' is divisible by 8 . . : highest value of a is ' 8 ' . answer : option b
Answer: b
Question (physics): if 15 men can reap 80 hectares in 24 days , then how many hectares can 36 men reap in 30 days ?
Options: a ) 127 , b ) 240 , c ) 287 , d ) 450 , e ) 281
Rationale: explanation : let the required no of hectares be x . then men - - - hectares - - - days 15 - - - - - - - - - 80 - - - - - - - - - 24 36 - - - - - - - - - x - - - - - - - - - 30 more men , more hectares ( direct proportion ) more days , more hectares ( direct proportion ) x = 36 / 15 * 30 / 24 * 80 x = 240 answer : b
Answer: b
Question (general): in a office work is distribute between p persons . if 1 / 8 members are absent then work increased for each person is ?
Options: a ) 13.28 % , b ) 14.28 % , c ) 15.28 % , d ) 16.28 % , e ) 17.28 %
Rationale: "let total % of work is 100 % total person = p 1 / 8 person are absent of total person . so absent person is 1 / 8 p ie p / 8 . left person is , p - p / 8 = 7 p / 8 . p person do the work 100 % 1 person do the work 100 * p % 7 p / 8 person do the work ( 100 * p * 8 ) / 7 p % = 114.28 % work increased for each person is = ( 114.28 - 100 ) % = 14.28 % answer : b"
Answer: b
Question (general): if a * b * c = 65 , b * c * d = 65 , c * d * e = 1000 and d * e * f = 250 the ( a * f ) / ( c * d ) = ?
Options: a ) 1 / 2 , b ) 1 / 4 , c ) 3 / 4 , d ) 2 / 3 , e ) none of these
Rationale: "explanation : a â ˆ — b â ˆ — c / b â ˆ — c â ˆ — d = 65 / 65 = > a / d = 1 d â ˆ — e â ˆ — f / c â ˆ — d â ˆ — e = 250 / 1000 = > f / c = 1 / 4 a / d * f / c = 1 * 1 / 4 = 1 / 4 answer : b"
Answer: b
Question (gain): a man buys a cycle for rs . 1400 and sells it at a loss of 20 % . what is the selling price of the cycle ?
Options: a ) rs . 1090 , b ) rs . 1160 , c ) rs . 1120 , d ) rs . 1202 , e ) none
Rationale: "solution s . p = 80 % of rs . 1400 = rs . ( 80 / 100 × 1400 ) rs . 1120 . answer c"
Answer: c
Question (gain): in one alloy there is 12 % chromium while in another alloy it is 8 % . 15 kg of the first alloy was melted together with 35 kg of the second one to form a third alloy . find the percentage of chromium in the new alloy .
Options: a ) 8.8 % , b ) 9 % , c ) 9.2 % , d ) 8.6 % , e ) 8.4 %
Rationale: the amount of chromium in the new 15 + 35 = 50 kg alloy is 0.12 * 15 + 0.08 * 35 = 4.6 kg , so the percentage is 4.6 / 50 * 100 = 9.2 % . answer : c .
Answer: c
Question (general): in may mrs lee ' s earnings were 90 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 ) 92 , b ) 35 , c ) 64 , d ) 46 , e ) 355
Rationale: "lets say the family income is 100 in may , lee earned 90 family income is 10 in june , lee earned 20 % more than may , so it is ( 90 + 20 * 90 / 100 = 108 ) family income is same 10 in june lee ' s income percent is 108 * 100 / 118 ~ 92 ans is a"
Answer: a
Question (gain): ? % of 360 = 165.6
Options: a ) 277 , b ) 36 , c ) 64 , d ) 72 , e ) 46
Rationale: "? % of 360 = 165.6 or , ? = 165.6 × 100 / 360 = 46 answer e"
Answer: e
Question (gain): find the simple interest on $ 6000 at 15 % per annum for 9 months ?
Options: a ) $ 492 , b ) $ 512 , c ) $ 675 , d ) $ 745 , e ) $ 1020
Rationale: "p = $ 6000 r = 15 % t = 9 / 12 years = 3 / 4 years s . i . = p * r * t / 100 = 6000 * 15 * 3 / 400 = $ 675 answer is c"
Answer: c
Question (general): how many integers between 324,805 and 458,705 have tens digit 1 and units digit 3 ?
Options: a ) 1,349 , b ) 1,353 , c ) 10,040 , d ) 1,354 , e ) 10,400
Rationale: "there is one number in hundred with 1 in the tens digit and 3 in the units digit : 13 , 113 , 213 , 313 , . . . the difference between 324,805 and 458,705 is 458,705 - 324,805 = 134,900 - one number per each hundred gives 134,900 / 100 = 1,349 numbers . answer : a ."
Answer: a
Question (general): a container contains 40 liters of milk , from this container 4 liters of milk was taken out and replaced by water . this process was repeated further 2 times . how much milk is now contained by the container ?
Options: a ) 25.5 liters , b ) 29.16 liters , c ) 30.98 liters , d ) 42.15 liters , e ) 48.32 liters
Rationale: "amount of milk left after 3 operations = 40 ( 1 - 4 / 40 ) ^ 3 = 40 * 9 / 10 * 9 / 10 * 9 / 10 = 29.16 liters answer is b"
Answer: b
Question (gain): solve the quickfire maths brain teaser â ˆ š 25 % = ?
Options: a ) 30 % , b ) 40 % , c ) 50 % , d ) 19 % , e ) 29 %
Rationale: "â ˆ š 25 % = > â ˆ š 25 / â ˆ š 100 = > 5 / 10 = > 50 / 100 = > 50 % c"
Answer: c
Question (general): a satellite is composed of 24 modular units , each of which is equipped with a set of sensors , some of which have been upgraded . each unit contains the same number of non - upgraded sensors . if the number of non - upgraded sensors on one unit is 1 / 3 the total number of upgraded sensors on the entire satellite , what fraction of the sensors on the satellite have been upgraded ?
Options: a ) 5 / 6 , b ) 1 / 5 , c ) 1 / 6 , d ) 1 / 9 , e ) 1 / 24
Rationale: let x be the number of upgraded sensors on the satellite . the number of non - upgraded sensors per unit is x / 3 . the number of non - upgraded sensors on the whole satellite is 24 ( x / 3 ) = 8 x . the fraction of sensors which have been upgraded is x / ( x + 8 x ) = x / 9 x = 1 / 9 the answer is d .
Answer: d
Question (physics): tom drives from town a to town b , driving at a constant speed of 60 miles per hour . from town b tom immediately continues to town c . the distance between a and b is twice the distance between b and c . if the average speed of the whole journey was 36 mph , then what is tom ' s speed driving from b to c in miles per hour ?
Options: a ) 12 , b ) 20 , c ) 24 , d ) 30 , e ) 36
Rationale: let ' s assume that it takes 4 hours to go from point a to b . then the distance between them becomes 240 which makes distance between b and c 120 . ( 240 + 120 ) / ( 4 + x ) gives us the average speed which is 36 . you find x = 6 . so the question simplifies itself to 120 / 6 = 20 hence the answer is b
Answer: b
Question (general): the average ( arithmetic mean ) of 22 , 33 , and 53 is 8 less than the average of 30 , 56 , and x . what is x ?
Options: a ) 42 , b ) 44 , c ) 46 , d ) 48 , e ) 50
Rationale: "the average of 22 , 33 , and 53 is 108 / 3 = 36 . the average of 30 , 56 and x is 44 . then 30 + 56 + x = 132 . x = 46 . the answer is c ."
Answer: c
Question (general): how many 3 - digit numbers are completely divisible 6 ?
Options: a ) 100 , b ) 150 , c ) 200 , d ) 250 , e ) 300
Rationale: "3 - digit number divisible by 6 are : 102 , 108 , 114 , . . . , 996 this is an a . p . in which a = 102 , d = 6 and l = 996 let the number of terms be n . then tn = 996 . a + ( n - 1 ) d = 996 102 + ( n - 1 ) x 6 = 996 6 x ( n - 1 ) = 894 ( n - 1 ) = 149 n = 150 number of terms = 150 . b )"
Answer: b
Question (general): 1 , 6 , 16 , 31 , 51 , ( . . . . )
Options: a ) 61 , b ) 66 , c ) 76 , d ) 86 , e ) 83
Rationale: "explanation : the pattern is 5 , 10 , 15 , 20 , 25 , etc hence 25 = 66 answer : b"
Answer: b
Question (gain): in a public show 60 % of the seats were filled . if there were 600 seats in the hall , how many seats were vacant ?
Options: a ) 100 , b ) 110 , c ) 120 , d ) 140 , e ) 240
Rationale: "75 % of 600 = 60 / 100 × 600 = 360 therefore , the number of vacant seats = 600 - 360 = 240 . answer : e"
Answer: e
Question (general): what is the decimal equivalent of ( 1 / 10 ) ^ 2 ?
Options: a ) 0.0016 , b ) 0.0625 , c ) 0.16 , d ) 0.25 , e ) 0.01
Rationale: "( 1 / 10 ) ² = ( 1 / 10 ) ( 1 / 10 ) = 1 / 100 approach # 1 : use long division to divide 100 into 1 to get 1 / 100 = 0.01 e"
Answer: e
Question (general): for a bake sale , simon baked 2 n more pies than theresa . theresa baked half as many pies as roger , who baked 1313 n pies . no other pies were baked for the sale . what fraction of the total pies for sale did roger bake ?
Options: a ) 1 / 16 , b ) 1 / 8 , c ) 3 / 16 , d ) 3 / 8 , e ) 13 / 16
Rationale: s : simon t : theresa r : roger let theresa baked a . as per question , we have s = a + 2 n r = 2 a = n / 3 or a = n / 6 now , total = a + ( a + 2 n ) + 2 a = 8 n / 3 fraction , ( n / 3 ) / ( 8 n / 3 ) = 1 / 8 answer : b
Answer: b
Question (physics): sarah is driving to the airport . after driving at 50 miles per hour for one hour , she realizes that if she continues at that same average rate she will be an hour late for her flight . she then travels 100 miles per hour for the rest of the trip , and arrives 30 minutes before her flight departs . how many miles did she drive in all ?
Options: a ) 140 , b ) 175 , c ) 200 , d ) 245 , e ) 280
Rationale: "after driving at 50 miles per hourfor one hour , this distance left to cover is d - 50 . say this distance is x miles . now , we know that the difference in time between covering this distance at 50 miles per hour and 100 miles per hour is 1 + 1 / 2 = 3 / 2 hours . so , we have that x / 50 - x / 100 = 3 / 2 - - > 2 x / 100 - x / 100 = 3 / 2 - - > x / 100 = 3 / 2 - - > x = 150 total distance = x + 50 = 200 miles . answer : c ."
Answer: c
Question (physics): two trains a and b are 225 m and 150 m long and are moving at one another at 54 km / hr and 36 km / hr respectively . arun is sitting on coach b 1 of train a . calculate the time taken by arun to completely cross train b .
Options: a ) 10 s , b ) 15 s , c ) 4 s , d ) 8 s , e ) 12 s
Rationale: "detailed solution speed of a = 54 ∗ 1000 / 60 ∗ 60 = 15 m / s speed of b = 36 ∗ 1000 / 60 ∗ 60 = 10 m / s relative speed = s 1 + s 2 = 15 + 10 m / s = 25 m / s the length that needs to be crossed = length of train b = 150 m . therefore time taken = 150 / 25 = 6 s . what is the time taken for trains to completely cross each other ? the length that needs to be crossed = 225 + 150 = 375 m . time taken = 375 / 25 = 15 s . correct answer b ."
Answer: b
Question (geometry): a gardener grows cabbages in her garden that is in the shape of a square . each cabbage takes 1 square feet of area in her garden . this year , she has increased her output by 199 cabbages as compared to last year . the shape of the area used for growing the cabbages has remained a square in both these years . how many cabbages did she produce this year ?
Options: a ) 10,000 , b ) 11,025 , c ) 14,400 , d ) 12,696 , e ) can not be determined
Rationale: "let the side for growing cabbages this year be x ft . thus the area is x ^ 2 . let the side for growing cabbages last year be y ft . thus , the area was y ^ 2 . the area would have increased by 199 sq ft as each cabbage takes 1 sq ft space . x ^ 2 - y ^ 2 = 199 ( x + y ) ( x - y ) = 199 199 is a prime number and thus it will be ( 100 + 99 ) * ( 100 - 99 ) . thus x = 100 and y = 99 x ^ 2 = 100 ^ 2 = 10,000 the answer is a ."
Answer: a
Question (general): if x , y , and z are positive integers and x = 4 y = 7 z , then the least possible value of x - y - z is
Options: a ) 33 , b ) 17 , c ) 49 , d ) 16 , e ) 23
Rationale: x - y - z = x - x / 4 - x / 7 = ( 28 - 7 - 4 ) x / 28 = 17 x / 28 17 is not divisible by 28 ( it ' s a prime # ) , so for least value , x = 28 answer - b
Answer: b
Question (physics): one hour after yolanda started walking from x to y , a distance of 80 miles , bob started walking along the same road from y to x . if yolanda â s walking rate was 8 miles per hour and bob â s was 9 miles per hour , how many miles had bob walked when they met ?
Options: a ) 38.07 , b ) 40 , c ) 42 , d ) 39 , e ) 40.07
Rationale: "let t be the number of hours that bob had walked when he met yolanda . then , when they met , bob had walked 4 t miles and yolanda had walked 8 ( t + 1 ) miles . these distances must sum to 80 miles , so 9 t + 8 ( t + 1 ) = 80 , which may be solved for t as follows 9 t + 8 ( t + 1 ) = 80 9 t + 8 t + 8 = 80 17 t = 72 t = 4.23 ( hours ) therefore , bob had walked 9 t = 9 ( 4.23 ) = 38.07 miles when they met . the best answer is a ."
Answer: a
Question (physics): a boat can travel with a speed of 13 km / hr in still water . if the speed of the stream is 5 km / hr . find the time taken by the boat to go 68 km downstream ?
Options: a ) 2 hours , b ) 3 hours , c ) 3 hours 48 minutes , d ) 5 hours , e ) none
Rationale: "solution speed downstream = ( 13 + 5 ) km / hr = 18 km / hr . time taken to travel 68 km downstream = ( 68 / 18 ) hrs = 3 hrs 48 minutes . answer c"
Answer: c
Question (physics): the speed of a train is 94 kmph . what is the distance covered by it in 12 minutes ?
Options: a ) 15 kmph , b ) 11 kmph , c ) 88 kmph , d ) 19 kmph , e ) 12 kmph
Rationale: "94 * 12 / 60 = 18.8 kmph answer : d"
Answer: d
Question (physics): if 5 machines can produce 20 units in 10 hours , how long would it take 20 machines to produce 180 units ?
Options: a ) 50 hours , b ) 40 hours , c ) 22.5 hours , d ) 12 hours , e ) 8 hours
Rationale: "here , we ' re told that 5 machines can produce 20 units in 10 hours . . . . that means that each machine works for 10 hours apiece . since there are 5 machines ( and we ' re meant to assume that each machine does the same amount of work ) , then the 5 machines equally created the 20 units . 20 units / 5 machines = 4 units are made by each machine every 10 hours now that we know how long it takes each machine to make 4 units , we can break this down further if we choose to . . . 10 hours / 4 units = 2.5 hours per unit when 1 machine is working . the prompt asks us how long would it take 20 machines to produce 180 units . if 20 machines each work for 2.5 hours , then we ' ll have 20 units . since 180 units is ' 9 times ' 20 , we need ' 9 times ' more time . ( 2.5 hours ) ( 9 times ) = 22.5 hours final answer : [ reveal ] spoiler : c"
Answer: c
Question (physics): a worker ' s daily wage is increased by 50 % and the new wage is $ 51 per day . what was the worker ' s daily wage before the increase ?
Options: a ) $ 28 , b ) $ 32 , c ) $ 34 , d ) $ 35 , e ) $ 40
Rationale: "let x be the daily wage before the increase . 1.5 x = $ 51 x = $ 34 the answer is c ."
Answer: c