Cheukting/mathqa huggingface dataset:
Question (general): john was 43 years old when he married betty . they just celebrated their fifth wedding anniversary , and betty ' s age is now 7 / 8 of john ' s . how old is betty ?
Options: a ) 24 , b ) 26 , c ) 42 , d ) 30 , e ) 32
Rationale: "assume betty ' s age on marriage = x years . john ' s age on marriage = 43 john ' s age after 5 years = 48 years . betty ' s age after 5 years = x + 5 given : x + 5 = 7 / 8 ( 48 ) = 42 therefore betty ' s current age = 42 option c"
Answer: c
Question (gain): what is 120 % of 13 / 24 of 720 ?
Options: a ) 372 , b ) 434 , c ) 468 , d ) 512 , e ) 564
Rationale: "120 % * 13 / 24 * 360 = 1.2 * 13 * 30 = 468 the answer is c ."
Answer: c
Question (general): a “ palindromic integer ” is an integer that remains the same when its digits are reversed . so , for example , 43334 and 516615 are both examples of palindromic integers . how many 6 - digit palindromic integers are both even and greater than 700,000 ?
Options: a ) 60 , b ) 100 , c ) 180 , d ) 240 , e ) 300
Rationale: "the first digit and last digit are the same so the only possibility is 8 . the second and third digits can be any number from 0 to 9 . the total number of palindromic integers is 1 * 10 * 10 = 100 the answer is b ."
Answer: b
Question (geometry): the area of a side of a box is 120 sq cm . the area of the other side of the box is 72 sq cm . if the area of the upper surface of the box is 60 sq cm then find the volume of the box .
Options: a ) 259200 cm 3
b ) 86400 cm 3
c ) 720 cm 3
d ) can not be determined
e ) none of these
Rationale: volume of the box = √ 120 × 72 × 60 = 720 cm 3 answer c
Answer: c
Question (general): mike took a taxi to the airport and paid $ 2.50 to start plus $ 0.25 per mile . annie took a different route to the airport and paid $ 2.50 plus $ 5.00 in bridge toll fees plus $ 0.25 per mile . if each was charged exactly the same amount , and annie ' s ride was 16 miles , how many miles was mike ' s ride ?
Options: a ) 32 , b ) 36 , c ) 40 , d ) 44 , e ) 48
Rationale: "the cost of annie ' s ride was 2.5 + 5 + ( 0.25 * 16 ) = $ 11.50 let x be the distance of mike ' s ride . the cost of mike ' s ride is 2.5 + ( 0.25 * x ) = 11.5 0.25 * x = 9 x = 36 miles the answer is b ."
Answer: b
Question (physics): if a man walks at a rate of 5 kmph , he misses a train by 7 minutes . however , if he walks at the rate of 6 kmph , he reaches the station 5 minutes before the arrival of the train . find the distance covered by him to reach the station .
Options: a ) 8 , b ) 4 , c ) 15 , d ) 6 , e ) 12
Rationale: let the required distance x km difference in the times taken at two speeds = 12 min = 1 / 5 hr ( x / 5 ) - ( x / 6 ) = 1 / 5 x = 6 the required distance is 6 km answer is d
Answer: d
Question (general): the milk level in a rectangular box measuring 62 feet by 25 feet is to be lowered by 6 inches . how many gallons of milk must be removed ? ( 1 cu ft = 7.5 gallons )
Options: a ) 100 , b ) 250 , c ) 750 , d ) 5812.5 , e ) 5835.5
Rationale: "6 inches = 1 / 2 feet ( there are 12 inches in a foot . ) , so 62 * 25 * 1 / 2 = 775 feet ^ 3 of milk must be removed , which equals to 775 * 7.5 = 5812.5 gallons . answer : d ."
Answer: d
Question (physics): the radius of a wheel is 22.4 cm . what is the distance covered by the wheel in making 320 resolutions ?
Options: a ) 724 m , b ) 704 m , c ) 287 m , d ) 450.6 m , e ) 927 m
Rationale: "in one resolution , the distance covered by the wheel is its own circumference . distance covered in 320 resolutions . = 320 * 2 * 22 / 7 * 22.4 = 45056 cm = 450.6 m answer : d"
Answer: d
Question (general): what is 10 - 8 + 6 - 4 + . . . + ( - 12 ) ?
Options: a ) 8 , b ) 10 , c ) 12 , d ) 14 , e ) 16
Rationale: "the expression considers all even numbers between 10 and - 12 with alternate addition and subtraction of the numbers . the numbers to be used are : 10 , 8 , 6 , 4 , 2 , 0 , - 2 , - 4 , - 6 , - 8 , - 10 , and - 12 now , the first term is positive and the next term is subtracted . so , the required expression becomes , 10 - 8 + 6 - 4 + 2 - 0 + ( - 2 ) - ( - 4 ) + ( - 6 ) - ( - 8 ) + ( - 10 ) - ( - 12 ) = 10 - 8 + 6 - 4 + 2 - 0 - 2 + 4 - 6 + 8 - 10 + 12 = 42 - 30 = 12 hence the correct answer choice is c ."
Answer: c
Question (physics): maxwell leaves his home and walks toward brad ' s house at the same time that brad leaves his home and runs toward maxwell ' s house . if the distance between their homes is 36 kilometers , maxwell ' s walking speed is 2 km / h , and brad ' s running speed is 4 km / h . what is the distance traveled by maxwell when they meet in the middle ?
Options: a ) 10 , b ) 11 , c ) 12 , d ) 13 , e ) 9
Rationale: "consider max starts from point a and brad starts from point b and move towards each other . assume they shall meet at point o after time ' t ' . the question asks us to find oa . from the question stem we can make out : - distance oa = 50 km - distance ob = > 2 xt = 36 - 4 xt ( i . e distance = speed x time ) = > 6 t = 36 hence t = 6 oa = 2 x 6 = 12 km answer : c"
Answer: c
Question (general): if 20 % of ( x - y ) = 15 % of ( x + y ) , then what percent of x is y ?
Options: a ) 50.5 % , b ) 44.4 % , c ) 22.2 % , d ) 14.3 % , e ) 25 %
Rationale: "20 % of ( x - y ) = 15 % of ( x + y ) 20 / 100 ( x - y ) = 15 / 100 ( x + y ) 5 x = 35 y required percentage = y / x * 100 = 5 y / 35 y * 100 = 14.28 % answer is d"
Answer: d
Question (general): if a tap could fill entire tank in 18 hrs due to leakage , then in how much time tank can be emptied by leakage if tap can fill entire tank in 12 hrs without leakage ?
Options: a ) 35 hrs , b ) 36 hrs , c ) 37 hrs , d ) 38 hrs , e ) 39 hrs
Rationale: if a tap could fill entire tank in 18 hrs due to leakage , tap can fill entire tank in 12 hrs without leakage . tank emptied in 0 ne hr by leakage = 1 / 12 - 1 / 18 = ( 6 - 4 ) / 72 = 2 / 72 = 1 / 36 . full tank can be emptied in 36 hrs . answer : b
Answer: b
Question (geometry): what is the percentage increase in the area of a rectangle , if each of its sides is increased by 20 % ?
Options: a ) 42 % , b ) 43 % , c ) 45 % , d ) 44 % , e ) 46 %
Rationale: let original length = l original breadth = b then original area = lb length is increased by 20 % ⇒ new length = l × 120100 = 1.2 l breadth is increased by 20 % ⇒ new breadth = b × 120100 = 1.2 b new area = 1.2 l × 1.2 b = 1.44 lb increase in area = new area - original area = 1.44 lb − lb = 0.44 lb percentage increase in area = increase in areaoriginal area × 100 = 0.44 lblb × 100 = 44 % answer is d .
Answer: d
Question (physics): the megatek corporation is displaying its distribution of employees by department in a circle graph . the size of each sector of the graph representing a department is proportional to the percentage of total employees in that department . if the section of the circle graph representing the manufacturing department takes up 252 ° of the circle , what percentage of megatek employees are in manufacturing ?
Options: a ) 20 % , b ) 25 % , c ) 30 % , d ) 35 % , e ) 70 %
Rationale: "answer : e 252 ° divided by 360 ° equals 0.7 , therefore the sector is equal to 70 % of the total"
Answer: e
Question (physics): in a 100 m race , a beats b by 10 m and c by 13 m . in a race of 180 m , b will beat c by :
Options: a ) 3 , b ) 7 , c ) 8 , d ) 6 , e ) 0
Rationale: a : b = 100 : 90 . a : c = 100 : 87 . \ inline \ fn _ jvn { \ color { black } \ therefore \ frac { b } { c } = \ left ( \ frac { b } { a } \ times \ frac { a } { c } \ right ) = \ left ( \ frac { 90 } { 100 } \ times \ frac { 100 } { 87 } \ right ) = \ frac { 30 } { 29 } } when b runs 30 m , c runs 29 m . when b runs 180 m , c runs \ inline \ fn _ jvn { \ color { black } \ left ( \ frac { 29 } { 30 } \ times 180 \ right ) m } = 174 m \ inline \ fn _ jvn { \ color { blue } \ therefore } b beats c by ( 180 - 174 ) m = 6 m . answer : d ) 6 m
Answer: d
Question (geometry): the points a ( 0 , 0 ) , b ( 0 , 4 a - 5 ) and c ( 2 a + 3 , 2 a + 6 ) form a triangle . if angle abc = 90 , what is the area of triangle abc ?
Options: a ) 114 , b ) 116 , c ) 118 , d ) 119 , e ) 120
Rationale: "1 / 2 bh = 1 / 2 ( 2 a + 3 ) ( 2 a + 6 ) now 4 a - 5 = 2 a + 6 2 a = 11 therefore , a ( 0,0 ) ; b ( 0,17 ) ; c ( 14,17 ) 1 / 2 * 14 * 17 = 119 answer : d"
Answer: d
Question (geometry): in a rectangular coordinate system , what is the area of a triangle whose vertices have the coordinates ( 3 , 0 ) , ( 6 , 3 ) , and ( 6 , - 3 ) ?
Options: a ) 9
b ) 10
c ) 11
d ) 12
e ) 13
Rationale: the triangle is symmetric about the x - axis . the part above the x - axis forms a triangle with a base of 3 and a height of 3 . the area of this part is ( 1 / 2 ) ( 3 ) ( 3 ) . we can double this to find the area of the whole triangle . the total area is ( 2 ) ( 1 / 2 ) ( 3 ) ( 3 ) = 9 . the answer is a .
Answer: a
Question (general): jill works as a waitress at the local diner where she earns an hourly wage of $ 4.00 per hour and a standard tip rate of 15 % of the cost of the orders she serves . if she worked 3 8 - hour shifts this week and averaged $ 40 in orders per hour , how much did jill earn this week ?
Options: a ) 280 , b ) 300 , c ) 240 , d ) 350 , e ) 400
Rationale: jill earns 4 dollars / hour and the hourly tip is ( 3 / 20 ) * 40 . jill thus earns 4 * 8 + 8 * 2 * 3 per day ( or 4 ( 8 ) + 6 ( 8 ) = 10 ( 8 ) = 80 ) . jill has worked for 3 days - > 80 * 3 = 240 . this matches answer choice c .
Answer: c
Question (gain): if a speaks the truth 85 % of the times , b speaks the truth 60 % of the times . what is the probability that they tell the truth at the same time
Options: a ) 0.49 , b ) 0.48 , c ) 0.41 , d ) 0.482 , e ) 0.51
Rationale: "explanation : probability that a speaks truth is 85 / 100 = 0.85 probability that b speaks truth is 60 / 100 = 0.6 since both a and b are independent of each other so probability of a intersection b is p ( a ) × p ( b ) = 0.85 × 0.6 = 0.51 answer : e"
Answer: e
Question (general): there are , in a certain league , 14 teams , and each team face another team for a total of 5 times . how many games are played in the season ?
Options: a ) 455 , b ) 525 , c ) 1400 , d ) 180 , e ) 560
Rationale: "by using the formula , t [ n ( n - 1 ) / 2 ] , where t = no . of games between two teams and n = total no . of teams , we get : 455 option a ."
Answer: a
Question (general): 10 is added to a certain number , the sum is multiplied by 7 , the product is divided by 5 and 5 is subtracted from the quotient . the remainder left is half of 88 . what is the number ?
Options: a ) 21 , b ) 20 , c ) 25 , d ) 30 , e ) 45
Rationale: "let number is x . when 10 added to it , = ( x + 10 ) 7 multiplied to sum , = 7 * ( x + 10 ) now , = [ { 7 * ( x + 10 ) } / 5 ] and , = [ { 7 * ( x + 10 ) } / 5 ] - 5 according to question , [ { 7 * ( x + 10 ) } / 5 ] - 5 = half of 88 [ ( 7 x + 70 ) / 5 ) = 44 + 5 7 x + 70 = 49 * 5 x + 10 = 7 * 5 x + 10 = 35 x = 35 - 10 x = 25 so , required number is : 25 . answer : c"
Answer: c
Question (gain): on a certain transatlantic crossing , 25 percent of a ship ' s passengers held round - trip tickets and also took their cars abroad the ship . if 60 percent of the passengers with round - trip tickets did not take their cars abroad the ship , what percent of the ship ' s passengers held round - trip tickets ?
Options: a ) 33.3 % , b ) 40 % , c ) 50 % , d ) 60 % , e ) 62.5 %
Rationale: "0.25 p = rt + c 0.6 ( rt ) = no c = > 0.40 ( rt ) had c 0.25 p = 0.40 ( rt ) rt / p = 62.5 % answer - e"
Answer: e
Question (physics): two cars are traveling in the same direction along the same route . the red car travels at a constant speed of 40 miles per hour , and the black car is traveling at a constant speed of 50 miles per hour . if the red car is 10 miles ahead of the black car , how many hours will it take the black car to overtake the red car ?
Options: a ) 0.1 , b ) 0.6 , c ) 1 , d ) 1.2 , e ) 2
Rationale: "option c 10 + 40 t = 50 t t = 1"
Answer: c
Question (general): the average of 25 results is 19 . the average of first 12 of those is 14 and the average of last 12 is 17 . what is the 13 th result ?
Options: a ) 74 , b ) 75 , c ) 103 , d ) 78 , e ) 45
Rationale: "solution : sum of 1 st 12 results = 12 * 14 sum of last 12 results = 12 * 17 13 th result = x ( let ) now , 12 * 14 + 12 * 17 + x = 25 * 19 or , x = 103 . answer : option c"
Answer: c
Question (gain): in town p , 70 percent of the population are employed , and 21 percent of the population are employed males . what percent of the employed people in town p are females ?
Options: a ) 46 % , b ) 52 % , c ) 58 % , d ) 64 % , e ) 70 %
Rationale: the percent of the population who are employed females is 70 - 21 = 49 % the percent of employed people who are female is 49 % / 70 % = 70 % . the answer is e .
Answer: e
Question (general): mysoon collects glass ornaments . 10 more than 1 / 6 of the ornaments in her collection are handmade , and 1 / 2 of the handmade ornaments are antiques . if 1 / 3 of the ornaments in her collection are handmade antiques , how many ornaments are in her collection ?
Options: a ) 20 , b ) 60 , c ) 108 , d ) 144 , e ) 180
Rationale: the number of ornaments = a ten more than 1 / 6 of the ornaments in her collection are handmade = > handmade = 10 + a / 6 1 / 2 of the handmade ornaments are antiques = > handmade ornaments = 1 / 2 * ( 10 + a / 6 ) = 5 + a / 12 1 / 3 of the ornaments in her collection are handmade antiques = > handmade ornaments = a / 3 = > 5 + a / 12 = a / 3 = > a = 200 ans : a
Answer: a
Question (physics): a train speeds past a pole in 12 seconds and a platform 160 m long in 17 seconds . its length is ?
Options: a ) 384 , b ) 360 , c ) 324 , d ) 390 , e ) 395
Rationale: "let the length of the train be x meters and its speed be y m / sec . they , x / y = 12 = > y = x / 12 x + 160 / 17 = x / 12 x = 384 m . answer : a"
Answer: a
Question (general): a picnic attracts 240 persons . there are 40 more men than women , and 40 more adults than children . how many men are at this picnic ?
Options: a ) 240 , b ) 75 , c ) 110 , d ) 90 , e ) 200
Rationale: "adult + children = 240 let , children = y then , adult = y + 40 i . e . y + ( y + 40 ) = 240 i . e . y = 100 i . e . adult = 100 + 40 = 140 adults include only men and women i . e . men + women = 140 let women , w = x then men , m = x + 40 i . e . x + ( x + 40 ) = 2 x + 40 = 140 i . e . x = 54 i . e . men , m = 54 + 40 = 90 answer : option d"
Answer: d
Question (other): two vessels contains equal number of mixtures milk and water in the ratio 4 : 1 and 7 : 3 . both the mixtures are now mixed thoroughly . find the ratio of milk to water in the new mixture so obtained ?
Options: a ) 2 : 1 , b ) 4 : 1 , c ) 3 : 1 , d ) 2 : 3 , e ) 4 : 3
Rationale: the ratio of milk and water in the new vessel is = ( 4 / 5 + 7 / 10 ) : ( 1 / 5 + 3 / 10 ) = 3 / 2 : 1 / 2 = 3 : 1 answer is c
Answer: c
Question (general): if x : y is 1 : 2 and y : z is 2 : 5 then x : z is equal to
Options: a ) 2 : 5 , b ) 3 : 5 , c ) 1 : 5 , d ) 4 : 5 , e ) 1 : 3
Rationale: "the two ratios given are having the same number 2 for y in both the ratios . hence - x : y = 1 : 2 y : z = 2 : 5 = > x : z = 1 : 5 answer c"
Answer: c
Question (general): if | x - 16 | = 2 x , then x = ?
Options: a ) 10 , b ) 15 , c ) - 16 , d ) 16 , e ) 5
Rationale: "| x - 16 | = 2 x . . . ( given ) x ^ 2 - 32 x + 256 = 4 x ^ 2 3 * x ^ 2 + 32 * x - 256 = 0 . . . . ( by solving above eq . we get ) , x = - 16 or 5.33 = = = > ans - c"
Answer: c
Question (physics): in a 200 meter race a beats b by 35 meters in 7 seconds . a ' s time over the cause is ?
Options: a ) 47 sec , b ) 40 sec , c ) 45 sec , d ) 33 sec , e ) 35 sec
Rationale: b covers 35 m in 7 seconds b take time = ( 200 * 7 ) / 35 = 40 a takes time = 40 - 7 = 33 sec answer : d
Answer: d
Question (probability): a life insurance company insured 25,000 young boys , 14,000 young girls and 16,000 young adults . the probability of death within 10 years of a young boy , young girl and a young adult are 0.02 , 0.03 and 0.15 respectively . one insured person dies . what is the probability that the dead person is a young boy ?
Options: a ) 36 / 165 , b ) 25 / 166 , c ) 26 / 165 , d ) 32 / 165 , e ) 33 / 165
Rationale: the number of young boys that will die = 0.02 x 25,000 = 500 the number of young girls that will die = 0.03 x 14,000 = 420 the number of young adults that will die = 0.15 x 16,000 = 2400 the required probability = the number of young boys who will die / the total number of people who will die . = 500 / ( 500 + 420 + 2400 ) = 25 / 166 answer : b
Answer: b
Question (geometry): triangle a ’ s base is 10 % greater than the base of triangle b , and a ’ s height is 10 % less than the height of triangle b . the area of triangle a is what percent less or more than the area of triangle b ?
Options: a ) 9 % less
b ) 1 % less
c ) equal to each other
d ) 1 % more
e ) 9 % more
Rationale: base of a = 11 / 10 * base of b height of a = 9 / 10 * height of b area of a = ( 1 / 2 ) * base of a * height of a = 11 / 10 * 9 / 10 * area of b = 99 / 100 * area of b area of a is 1 % less than the area of b . answer ( b )
Answer: b
Question (general): peter and tom shared the driving on a certain trip . if peter and tom both drove for the same amount of time , but peter only drove 3 / 5 of the total distance , what was the ratio of peter ' s average speed to tom ' s average speed ?
Options: a ) 1 : 5 , b ) 3 : 2 , c ) 1 : 2 , d ) 3 : 5 , e ) 2 : 3
Rationale: "the answer is suppose to be b . 3 : 2 . it ' s from the gmatprep answer : option b"
Answer: b
Question (physics): jack and jill are marathon runners . jack can finish a marathon ( 42 km ) in 2.5 hours and jill can run a marathon in 4.2 hours . what is the ratio of their average running speed ? ( jack : jill )
Options: a ) 41 / 25 , b ) 15 / 14 , c ) 4 / 5 , d ) 5 / 4 , e ) can not be determined
Rationale: "average speed of jack = distance / time = 42 / ( 5 / 2 ) = 84 / 5 average speed of jill = 42 / ( 4.2 ) = 10 ratio of average speed of jack to jill = ( 84 / 5 ) / 10 = 84 / 50 = 41 / 25 answer a"
Answer: a
Question (general): in a store , the total price for 20 shirts is $ 360 and the total price for 45 sweaters is $ 900 . by how much does the average ( arithmetic mean ) price of a sweater exceed that of a shirt in this store ?
Options: a ) $ 1 , b ) $ 2 , c ) $ 3 , d ) $ 4 , e ) $ 5
Rationale: "the average price of a shirt is : $ 360 / 20 = $ 18 . the average price of a sweater is : $ 900 / 45 = $ 20 . the difference in price is : $ 20 - $ 18 = $ 2 . the answer is b ."
Answer: b
Question (gain): a certain college ' s enrollment at the beginning of 1992 was 20 percent greater than it was at the beginning of 1991 , and its enrollment at the beginning of 1993 was 10 percent greater than it was at the beginning of 1992 . the college ' s enrollment at the beginning of 1993 was what percent greater than its enrollment at the beginning of 1991 ?
Options: a ) 17.5 % , b ) 24 % , c ) 30 % , d ) 32 % , e ) 38 %
Rationale: "suppose enrollment in 1991 was 100 then enrollment in 1992 will be 120 and enrollment in 1993 will be 120 * 1.10 = 132 increase in 1993 from 1991 = 132 - 100 = 32 answer : d"
Answer: d
Question (general): the average expenditure of a labourer for 8 months was 85 and he fell into debt . in the next 4 months by reducing his monthly expenses to 60 he not only cleared off his debt but also saved 30 . his monthly income is
Options: a ) 80 , b ) 85 , c ) 75 , d ) 95 , e ) 100
Rationale: "income of 8 months = ( 8 × 85 ) – debt = 680 – debt income of the man for next 4 months = 4 × 60 + debt + 30 = 270 + debt ∴ income of 10 months = 950 average monthly income = 950 ÷ 10 = 95 answer d"
Answer: d
Question (general): in a fuel station the service costs $ 2.05 per car , every liter of fuel costs 0.6 $ . assuming that you fill up 3 mini - vans and 2 trucks , how much money will the fuel cost to all the cars owners total , if a mini - van ' s tank is 65 liters and a truck ' s tank is 140 % bigger and they are all empty - ?
Options: a ) 122.6 $ , b ) 128.9 $ , c ) 243.7 $ , d ) 298.85 $ , e ) 314.45 $
Rationale: "service cost of 3 van and 2 truck = 2.05 * ( 3 + 2 ) = 10.5 fuel in 3 van = 3 * 65 = 195 litre fuel in 2 trucks = 2 * 65 ( 1 + 140 / 100 ) = 312 total fuel ( van + truck ) = 507 litre total fuel cost = 507 * 0.6 = 304.2 total cost = fuel + service = 304.2 + 10.25 = 314.45 answer is e"
Answer: e
Question (physics): 66 cubic centimetres of silver is drawn into a wire 1 mm in diameter . the length of the wire in metres will be :
Options: a ) 66 , b ) 84 , c ) 80 , d ) 72 , e ) 68
Rationale: "let the length of the wire be h . radius = 1 / 2 mm = 1 / 20 cm . then , ( 22 / 7 ) x ( 1 / 20 ) x ( 1 / 20 ) x h = 66 . h = ( 66 x 20 x 20 x 7 ) / 22 = 8400 cm = 84 m . answer b"
Answer: b
Question (gain): if the cost price of 58 articles is equal to the selling price of 50 articles , then what is the percent profit ?
Options: a ) 12 % , b ) 16 % , c ) 20 % , d ) 24 % , e ) 28 %
Rationale: "let x be the cost price of one article . let y be the selling price of one article . 50 y = 58 x y = 1.16 x the answer is b ."
Answer: b
Question (physics): a person is traveling at 20 km / hr and reached his destiny in 8 hr then find the distance ?
Options: a ) 180 km , b ) 200 km , c ) 160 km , d ) 220 km , e ) 240 km
Rationale: "t = 8 hrs d = t * s = 20 * 8 = 160 km answer is c"
Answer: c
Question (general): at the wholesale store you can buy an 8 - pack of hot dogs for $ 1.55 , a 20 - pack for $ 3.05 , and a 250 - pack for $ 22.95 . what is the greatest number of hot dogs you can buy at this store with $ 300 ?
Options: a ) 3,108 , b ) 3,100 , c ) 3,108 , d ) 3,124 , e ) 3,250
Rationale: "to maximize number of hot dogs with 300 $ total number of hot dogs bought in 250 - pack = 22.95 * 13 = 298.35 $ amount remaining = 300 - 298.35 = 1.65 $ this amount is too less to buy any 8 - pack . greatest number of hot dogs one can buy with 300 $ = 250 * 13 = 3250 answer e"
Answer: e
Question (physics): a train 400 m long can cross an electric pole in 20 sec and then find the speed of the train ?
Options: a ) 87 kmph , b ) 28 kmph , c ) 72 kmph , d ) 18 kmph , e ) 29 kmph
Rationale: "length = speed * time speed = l / t s = 400 / 20 s = 20 m / sec speed = 20 * 18 / 5 ( to convert m / sec in to kmph multiply by 18 / 5 ) speed = 72 kmph answer : c"
Answer: c
Question (physics): two diesel trains of length 120 m and 280 m are running towards each other on parallel lines at 42 kmph and 30 kmph respectively . in what time will they be clear of each other from the moment they meet ?
Options: a ) 10 sec , b ) 30 sec , c ) 40 sec , d ) 20 s , e ) 50 sec
Rationale: d relative speed = ( 42 + 30 ) * 5 / 18 = 4 * 5 = 20 mps . distance covered in passing each other = 120 + 280 = 400 m . the time required = d / s = 400 / 20 = 20 sec .
Answer: d
Question (physics): two trains start simultaneously from opposite ends of a 180 - km route and travel toward each other on parallel tracks . train x , traveling at a constant rate , completes the 180 - km trip in 5 hours . train y , travelling at a constant rate , completes the 180 - km trip in 4 hours . how many kilometers had train x traveled when it met train y ?
Options: a ) 72 , b ) 74 , c ) 76 , d ) 78 , e ) 80
Rationale: if the two trains cover a total distance d , then train x travels ( 4 / 9 ) * d while train y travels ( 5 / 9 ) * d . if the trains travel 180 km to the meeting point , then train x travels ( 4 / 9 ) * 180 = 80 km . the answer is e .
Answer: e
Question (general): maria bought 10 notebooks and 5 pens costing 2 dollars each . how much did maria pay ?
Options: a ) $ 10 , b ) $ 20 , c ) $ 30 , d ) $ 40 , e ) $ 50
Rationale: 2 × ( 10 + 5 ) = 2 × 10 + 2 × 5 = 20 + 10 = 30 dollars correct answer is c ) $ 30
Answer: c
Question (general): a jogger running at 9 km / hr along side a railway track is 280 m ahead of the engine of a 120 m long train running at 45 km / hr in the same direction . in how much time will the train pass the jogger ?
Options: a ) 67 sec , b ) 89 sec , c ) 36 sec , d ) 87 sec , e ) 40 sec
Rationale: "speed of train relative to jogger = 45 - 9 = 36 km / hr . = 36 * 5 / 18 = 10 m / sec . distance to be covered = 280 + 120 = 400 m . time taken = 400 / 10 = 40 sec . answer : e"
Answer: e