Cheukting/mathqa huggingface dataset:
Question (geometry): the length of a rectangle is twice its breadth . if its length is decreased by 5 cm and breadth is increased by 5 cm , the area of the rectangle is increased by 55 sq . cm . find the length of the rectangle .
Options: a ) 16 cm , b ) 18 cm , c ) 15 cm , d ) 20 cm , e ) 23 cm
Rationale: "explanation : let breadth = x . then , length = 2 x . then , ( 2 x - 5 ) ( x + 5 ) - 2 x * x = 55 = > 5 x - 25 = 55 = > x = 16 . length of the rectangle = 16 cm . answer : option a"
Answer: a
Question (geometry): a cylindrical container with 6 meters diameter and a height of 8 meters is filled to capacity with water . if the water is then used to fill several smaller cylinders ( 2 meters radius and 5 meters height ) , how many smaller cylinders can be filled to capacity before the larger cylinder becomes empty ?
Options: a ) 5
b ) 4
c ) 3
d ) 2
e ) 1
Rationale: calculate the volume of the larger cylinder and divide it by the volume of the smaller cylinder . volume of cylinder = π r 2 h larger cylinder volume = 226.19 smaller cylinder volume = 62.83 therefore the number of smaller cylinders can be filled to capacity = 226.19 / 62.83 = 3.6 answer is c only 3 smaller cylinders can be filled to capacity .
Answer: c
Question (geometry): four circular cardboard pieces , each of radius 7 cm are placed in such a way that each piece touches two other pieces . the area of the space encosed by the four pieces is. four circular cardboard pieces , each of radius 7 cm are placed in such a way that each piece touches two other pieces . the area of the space encosed by the four pieces is
Options: a ) 12
b ) 32
c ) 42
d ) 52
e ) 58
Rationale: required area = 14 * 14 - ( 4 * 1 / 4 * 22 / 7 * 7 * 7 ) sq cm = 196 - 154 = 42 sq cm . answer : c
Answer: c
Question (geometry): the roof of an apartment building is rectangular and its length is 5 times longer than its width . if the area of the roof is 720 feet squared , what is the difference between the length and the width of the roof ?
Options: a ) 38 . , b ) 40 . , c ) 42 . , d ) 44 . , e ) 48 .
Rationale: "answer is e : 48 let w be the width , so length is 5 w . therefore : w * 5 w = 720 , solving for , w = 12 , so 5 w - w = 4 w = 4 * 12 = 48"
Answer: e
Question (gain): jaclyn buys $ 10 000 worth of debentures in a company . she earns 9.5 % p . a . simple interest , paid to her quarterly ( that is , every 3 months ) . if the agreed period of the debenture was 18 months : calculate the amount of interest jaclyn will earn for each quarter
Options: a ) 237.5 , b ) 234 , c ) 289.5 , d ) 345 , e ) none of these
Rationale: explanation : i = ( p x r x t ) / 100 = 10000 * 9.5 / 100 * ( 18 / 12 ) ^ 1 / 6 = 237.5 answer : a
Answer: a
Question (physics): two trains each 250 m in length are running on the same parallel lines in opposite directions with the speed of 80 kmph and 40 kmph respectively . in what time will they cross each other completely ?
Options: a ) 15 sec , b ) 19 sec , c ) 12 sec , d ) 10 sec , e ) 11 sec
Rationale: "explanation : d = 250 m + 250 m = 500 m rs = 80 + 40 = 120 * 5 / 18 = 100 / 3 t = 500 * 3 / 100 = 15 sec answer : option a"
Answer: a
Question (other): at garage sale , all of the prices of the items sold were different . if the price of a radio sold at the garage sale was both the 15 th highest price and the 25 th lowest price among the prices of the items sold , how many items were sold at the garage sale ?
Options: a ) 33 , b ) 34 , c ) 35 , d ) 39 , e ) 37
Rationale: "14 + 24 + 1 = 39 answer : d"
Answer: d
Question (general): in a division sum , the quotient is 20 , the divisor 66 and the remainder 55 , find the dividend ?
Options: a ) 1375 , b ) 1376 , c ) 1875 , d ) 1365 , e ) 1345
Rationale: "explanation : 20 * 66 + 55 = 1375 answer : a"
Answer: a
Question (general): a and b are two partially filled buckets of water . if 6 liters are transferred from a to b , then a would contain one - third of the amount of water in b . alternatively , if 6 liters are transferred from b to a , b would contain one - half of the amount of water in a . bucket a contains how many liters of water ?
Options: a ) 66 / 5 , b ) 13 , c ) 17 , d ) 21 , e ) 23
Rationale: let bucket a be a and bucket b be b scenario 1 a - 6 = 1 / 3 ( b + 6 ) - - - - > 3 a - 18 = b + 6 scenario 2 b - 6 = 1 / 2 ( a + 6 ) - - - - - > 2 b - 12 = a + 6 from scenario 1 , b = 3 a - 24 substitute b with this information in stmt 2 2 ( 3 a - 24 ) - 12 = a + 6 - - - - - - > 6 a - 48 - 12 = a + 6 - - - - - - > 6 a - a = 60 + 6 - - - > 5 a = 66 a = 66 / 5 , answer choice a
Answer: a
Question (general): what is the total cost of 2 sandwiches at $ 2.49 each and 4 sodas at $ 1.87 each ?
Options: a ) $ 3.36 , b ) $ 6.85 , c ) $ 8.46 , d ) $ 10.08 , e ) $ 12.46
Rationale: "answer = e 2 * 2.49 + 4 * 1.87 = 2 ( 2.50 - 0.01 ) + 4 ( 2.00 - 0.13 ) = 5 + 8 - 0.02 - 0.52 = 13 - 0.54 = 12.46"
Answer: e
Question (general): the sum of ages of 4 children born 1 years different each is 38 years . what is the age of the elder child ?
Options: a ) 8 , b ) 11 , c ) 10 , d ) 16 , e ) 17
Rationale: "let the ages of children be x , ( x + 1 ) , ( x + 2 ) , ( x + 3 ) years . then , x + ( x + 1 ) + ( x + 2 ) + ( x + 3 ) = 38 4 x = 32 x = 8 . x + 3 = 8 + 3 = 11 answer : b"
Answer: b
Question (geometry): what is the positive integer that can be added by 595 to make it a perfect square ?
Options: a ) 2 * 3 * 6
b ) 3 * 2 * 5
c ) 5 * 3 * 3
d ) 2 * 3
e ) 3 * 5 * 4
Rationale: 596 is added to a number that gives a perfect square nearest perfect square is 625 . so , 625 - 596 = 30 30 = 2 * 3 * 5 option b is answer
Answer: b
Question (general): after a storm deposits 110 billion gallons of water into the city reservoir , the reservoir is 60 % full . if the original contents of the reservoir totaled 220 billion gallons , the reservoir was approximately what percentage full before the storm ?
Options: a ) 40 % , b ) 48 % , c ) 54 % , d ) 58 % , e ) 65 %
Rationale: when the storm deposited 110 billion gallons , volume of water in the reservoir = 220 + 110 = 360 billion gallons if this is only 60 % of the capacity of the reservoir , the total capacity of the reservoir = 330 / 0.6 = 550 billion gallons therefore percentage of reservoir that was full before the storm = ( 220 / 550 ) * 100 = 40 % option a
Answer: a
Question (general): ( 6 ) 6.5 × ( 36 ) 4.5 ÷ ( 216 ) 4.5 = ( 6 ) ?
Options: a ) 1 , b ) 2 , c ) 4 , d ) 6 , e ) 8
Rationale: "explanation : ( 6 ) 6.5 × ( 36 ) 4.5 ÷ ( 216 ) 4.5 = ( 6 ) 6.5 × [ ( 6 ) 2 ] 4.5 ÷ [ ( 6 ) 3 ] 4.5 = ( 6 ) 6.5 × ( 6 ) 9 ÷ ( 6 ) 13.5 = ( 6 ) ( 6.5 + 9 - 13.5 ) = ( 6 ) 2 answer : option b"
Answer: b
Question (geometry): a rectangular grass field is 75 m * 55 m , it has a path of 3.2 m wide all round it on the outside . find the area of the path and the cost of constructing it at rs . 2 per sq m ?
Options: a ) s . 1350 , b ) s . 1327 , c ) s . 1328 , d ) s . 1364 , e ) s . 1927
Rationale: "area = ( l + b + 2 d ) 2 d = ( 75 + 55 + 3.2 * 2 ) 2 * 2.5 = > 682 682 * 2 = rs . 1364 answer : d"
Answer: d
Question (physics): a fill pipe can fill 1 / 2 of cistern in 20 minutes . in how many minutes , it can fill 1 / 2 of the cistern ?
Options: a ) 5 min , b ) 10 min , c ) 15 min , d ) 20 min , e ) 25 min
Rationale: required time = 20 * 2 * 1 / 2 = 20 minutes answer is d
Answer: d
Question (general): what is the average of 120 , 130 , 140 , 510 , 520 , 530 , 1115 , 1120 , and 1125 ?
Options: a ) 419 , b ) 551 , c ) 601 , d ) 590 , e ) 721
Rationale: "add 120 , 130 , 140 , 510 , 520 , 530 , 1115 , 1120 , and 1125 grouping numbers together may quicken the addition sum = 5310 5310 / 9 = 590 . d"
Answer: d
Question (physics): a bus travels from town a to town b . if the bus ' s speed is 50 km / hr , it will arrive in town b 42 min later than scheduled . if the bus increases its speed by 509509 m / sec , it will arrive in town b 30 min earlier than scheduled . find : a ) the distance between the two towns ; b ) the bus ' s scheduled time of arrival in b ; c ) the speed of the bus when it ' s on schedule .
Options: a ) 60 , b ) 37 , c ) 26 , d ) 28 , e ) 11
Rationale: first we will determine the speed of the bus following its increase . the speed is increased by 509509 m / sec = 50 ⋅ 60 ⋅ 6091000 = 50 ⋅ 60 ⋅ 6091000 km / hr = 20 = 20 km / hr . therefore , the new speed is v = 50 + 20 = 70 v = 50 + 20 = 70 km / hr . if xx is the number of hours according to the schedule , then at the speed of 50 km / hr the bus travels from a to b within ( x + 4260 ) ( x + 4260 ) hr . when the speed of the bus is v = 70 v = 70 km / hr , the travel time is x − 3060 x − 3060 hr . then 50 ( x + 4260 ) = 70 ( x − 3060 ) 50 ( x + 4260 ) = 70 ( x − 3060 ) 5 ( x + 710 ) = 7 ( x − 12 ) 5 ( x + 710 ) = 7 ( x − 12 ) 72 + 72 = 7 x − 5 x 72 + 72 = 7 x − 5 x 2 x = 72 x = 7 x = 72 x = 72 hr . so , the bus is scheduled to make the trip in 33 hr 3030 min . the distance between the two towns is 70 ( 72 − 12 ) = 70 ⋅ 3 = 21070 ( 72 − 12 ) = 70 ⋅ 3 = 210 km and the scheduled speed is 210 / 7 / 2 = 60 km / hr . answer : a
Answer: a
Question (general): how many numbers from 10 to 100000 are exactly divisible by 9 ?
Options: a ) 900 , b ) 11110 , c ) 1100 , d ) 1200 , e ) 1400
Rationale: "10 / 9 = 1 and 100000 / 9 = 11111 = = > 11111 - 1 = 11110 . answer : b"
Answer: b
Question (gain): if 10 litres of an oil of rs . 40 per litres be mixed with 5 litres of another oil of rs . 66 per litre then what is the rate of mixed oil per litre ?
Options: a ) rs . 48.66 , b ) rs . 51.03 , c ) rs . 54.17 , d ) rs . 55.33 , e ) none of the above
Rationale: "40 * 10 = 400 66 * 5 = 330 730 / 15 = 48.66 answer : a"
Answer: a
Question (physics): tom wants to buy items costing $ 25.35 , $ 70.69 , and $ 85.96 . he earns $ 6.50 an hour doing odd jobs . if ten percent of his income is put aside for other purposes , how many hours must he work to earn the money he needs for his purchases ? round your answer to the nearest whole hour .
Options: a ) 8 hours , b ) 48 hours , c ) 31 hours , d ) 18 hours , e ) 28 hours
Rationale: $ 6.50 x . 10 = $ . 65 is 10 % of his hourly income $ 6.50 - . 65 = $ 5.85 hourly amount available to spend $ 25.35 + $ 70.69 + $ 85.96 = $ 182 total needed $ 182 ÷ $ 5.85 = 31.11 . . . rounds to 31 hours correct answer c
Answer: c
Question (physics): a 600 meter long train crosses a signal post in 40 seconds . how long will it take to cross a 1.8 kilometer long bridge , at the same speed ?
Options: a ) 4 min , b ) 2 min , c ) 8 min , d ) 9 min , e ) 3 min
Rationale: s = 600 / 40 = 15 mps s = 1800 / 15 = 120 sec = 2 min . answer : b
Answer: b
Question (gain): a small college reduced its faculty by approximately 13 percent to 195 professors . what was the original number of faculty members ?
Options: a ) 182 , b ) 208 , c ) 224 , d ) 254 , e ) 302
Rationale: "f x is the original number of faculty members , then after 13 % reduction in faculty members number is . 87 x but we are given . 87 x = 195 x = 224 so the original number of faculty members is 224 correct answer - c"
Answer: c
Question (general): the probability that a man will be alive for 10 more yrs is 3 / 4 & the probability that his wife will alive for 10 more yrs is 1 / 5 . the probability that none of them will be alive for 10 more yrs , is
Options: a ) 1 / 2 , b ) 1 , c ) 2 / 3 , d ) 1 / 5 , e ) 2
Rationale: "sol . required probability = pg . ) x p ( b ) = ( 1 — d x ( 1 — i ) = : x 1 = 1 / 5 ans . ( d )"
Answer: d
Question (gain): a reduction of 20 % in the price of salt enables a lady to obtain 10 kgs more for rs . 100 , find the original price per kg ?
Options: a ) 2.9 , b ) 2.2 , c ) 2.5 , d ) 2.1 , e ) 2.3
Rationale: "100 * ( 20 / 100 ) = 20 - - - 10 ? - - - 1 = > rs . 2 100 - - - 80 ? - - - 2 = > rs . 2.5 answer : c"
Answer: c
Question (general): a company that ships boxes to a total of 12 distribution centers uses color coding to identify each center . if either a single color or a pair of two different colors is chosen to represent each center and if each center is uniquely represented by that choice of one or two colors , what is the minimum number of colors needed for the coding ? ( assume that the order of the colors in a pair does not matter . )
Options: a ) 4 , b ) 5 , c ) 6 , d ) 12 , e ) 24
Rationale: "let ' s start with 4 minimum number of colors so single color code we can make 4 nos . now if we need to make 2 color combination out of 4 we can do so in 4 ! / 2 ! * 2 ! or 4 * 3 / 2 or 6 so total we can make 4 + 6 = 10 color combinations but we have 12 boxes so let ' s look at 5 we get 5 single color codes and out 5 color choices , we can choose 2 in 5 ! / 2 ! * 3 ! ways or 10 ways . so total we can have 5 + 10 = 15 color combinations . so , minimum number we need will be 5 ans is b . . . . . . ."
Answer: b
Question (gain): the present worth of a sum due sometime hence is rs . 576 and the banker ’ s gain is rs . 16 . the true discount is
Options: a ) rs . 36 , b ) rs . 72 , c ) rs . 48 , d ) rs . 96 , e ) none
Rationale: solution t . d = √ p . w xb . g = √ 576 x 16 = 96 . answer d
Answer: d
Question (physics): two trains are moving in the same direction at 90 kmph and 36 kmph . the faster train crosses a man in the slower train in 29 seconds . find the length of the faster train ?
Options: a ) 425 , b ) 435 , c ) 445 , d ) 455 , e ) 465
Rationale: "relative speed = ( 90 - 36 ) * 5 / 18 = 3 * 5 = 15 mps . distance covered in 29 sec = 29 * 15 = 435 m . the length of the faster train = 435 m . answer : b"
Answer: b
Question (physics): the ratio between the length and the breadth of a rectangular park is 3 : 2 . if a man cycling along the boundary of the park at the speed of 12 km / hr completes one round in 5 minutes , then the area of the park ( in sq . m ) is :
Options: a ) 153601 , b ) 153600 , c ) 153602 , d ) 60000 , e ) 153604
Rationale: "perimeter = distance covered in 5 min . = ( 12000 / 60 ) x 5 m = 1000 m . let length = 3 x metres and breadth = 2 x metres . then , 2 ( 3 x + 2 x ) = 1000 or x = 100 . length = 300 m and breadth = 200 m . area = ( 300 x 200 ) m 2 = 60000 m 2 . answer : d"
Answer: d
Question (gain): the value of a machine depreciates at the rate of 10 % every year . it was purchased 3 years ago . if its present value is rs . 8748 , its purchase price was :
Options: a ) 12003 , b ) 12000 , c ) 12002 , d ) 12289 , e ) 12019
Rationale: "explanation : = rs . 12000 answer : b ) 12000"
Answer: b
Question (general): solve for x the equation log 9 ( x 3 ) = log 2 ( 8 )
Options: a ) 9 , b ) 8 , c ) 7 , d ) 6 , e ) 5
Rationale: log 9 ( x 3 ) = log 2 ( 8 ) : given log 2 ( 23 ) = 3 : simplify right hand side of given equation . log 9 ( x 3 ) = 3 : rewrite the above equation log 9 ( x 3 ) = log 9 ( 93 ) : rewite 3 as a log base 9 . x 3 = 93 : obtain algebraic equation from eqaution d . x = 9 : solve above for x correct answer a
Answer: a
Question (general): there are 6 more women than there are men on a local co - ed softball team . if there are a total of 16 players on the team , what is the ratio of men to women ?
Options: a ) 10 / 16 , b ) 6 / 16 , c ) 4 / 16 , d ) 5 / 11 , e ) 4 / 10
Rationale: "w = m + 6 w + m = 16 m + 6 + m = 16 2 m = 10 m = 5 w = 11 ratio : 5 : 11 ans : d"
Answer: d
Question (gain): salad dressing p is made up of 30 % vinegar and 70 % oil , and salad dressing q contains 10 % vinegar and 90 % oil . if the two dressings are combined to produce a salad dressing that is 25 % vinegar , dressing p comprises what percentage of the new dressing ?
Options: a ) 75 % , b ) 60 % , c ) 40 % , d ) 25 % , e ) 20 %
Rationale: "let x be the percentage of dressing p in the new dressing . 0.3 x + 0.1 ( 1 - x ) = 0.25 0.2 x = 0.15 x = 0.75 = 75 % the answer is a ."
Answer: a
Question (other): water consists of hydrogen and oxygen , and the approximate ratio , by mass , of hydrogen to oxygen is 2 : 16 . approximately how many grams of oxygen are there in 135 grams of water ?
Options: a ) 120 , b ) 116 , c ) 112 , d ) 108 , e ) 104
Rationale: "( 16 / 18 ) * 144 = 120 grams the answer is a ."
Answer: a
Question (physics): a boat can travel with a speed of 16 km / hr in still water . if the rate of stream is 5 km / hr , then find the time taken by the boat to cover distance of 63 km downstream .
Options: a ) 3 hours , b ) 5 hours , c ) 6 hours , d ) 7 hours , e ) 8 hours
Rationale: "explanation : it is very important to check , if the boat speed given is in still water or with water or against water . because if we neglect it we will not reach on right answer . i just mentioned here because mostly mistakes in this chapter are of this kind only . lets see the question now . speed downstream = ( 16 + 5 ) = 21 kmph time = distance / speed = 63 / 21 = 3 hours option a"
Answer: a
Question (physics): john and jacob set out together on bicycle traveling at 15 and 12 miles per hour , respectively . after 40 minutes , john stops to fix a flat tire . if it takes john two hour to fix the flat tire and jacob continues to ride during this time , how many hours will it take john to catch up to jacob assuming he resumes his ride at 15 miles per hour ? ( consider john ' s deceleration / acceleration before / after the flat to be negligible )
Options: a ) 7 , b ) 7 1 / 3 , c ) 7 1 / 2 , d ) 4 , e ) 7 1 / 2
Rationale: "john ' s speed - 15 miles / hr jacob ' s speed - 12 miles / hr after 40 min ( i . e 2 / 3 hr ) , distance covered by john = 15 x 2 / 3 = 10 miles . jacob continues to ride for a total of 2 hour and 40 min ( until john ' s bike is repaired ) . distance covered in 2 hour 40 min ( i . e 8 / 3 hr ) = 12 x 8 / 3 = 32 miles . now , when john starts riding back , the distance between them is 22 miles . jacob and john are moving in the same direction . for john to catch jacob , the effective relative speed will be 15 - 12 = 3 miles / hr . thus , to cover 22 miles at 3 miles / hr , john will take 22 / 3 = 7 1 / 3 hours answer b"
Answer: b
Question (physics): a 1200 m long train crosses a tree in 120 sec , how much time will i take to pass a platform 600 m long ?
Options: a ) 266 sec , b ) 180 sec , c ) 776 sec , d ) 166 sec , e ) 997 sec
Rationale: "l = s * t s = 1200 / 120 s = 10 m / sec . total length ( d ) = 1800 m t = d / s t = 1800 / 10 t = 180 sec answer : b"
Answer: b
Question (probability): two mba admissions committees are to be formed randomly from 6 second year mbas with 3 members each . what is the probability v that jane will be on the same committee as albert ?
Options: a ) 12 % , b ) 20 % , c ) 33 % , d ) 40 % , e ) 50 %
Rationale: "total number of ways to choose 3 member committee - 6 c 3 = ( 6 ! / 3 ! 3 ! ) = 20 no . of ways albert n jane are in same committee : - ( 4 c 1 * 2 ) = 8 probability v = ( 8 / 20 ) * 100 = 40 % . + 1 for me . . : d"
Answer: d
Question (geometry): a rectangular plot 15 m × 10 m , has a path of grass outside it . if the area of grassy pathway is 54 m 2 , find the width of the path .
Options: a ) 4 m
b ) 3 m
c ) 2 m
d ) 1 m
e ) none of these
Rationale: let the width of the path = w m then , length of plot with path = ( 15 + 2 w ) m and breadth of plot with path = ( 10 + 2 w ) m therefore , area of rectangular plot ( without path ) = 15 × 10 = 150 m 2 and area of rectangular plot ( with path ) = 150 + 54 = 204 m 2 hence , ( 15 + 2 w ) × ( 10 + 2 w ) = 204 ⇒ 4 w 2 + 50 w – 54 = 0 ⇒ 2 w 2 + 25 w – 27 = 0 ⇒ ( w – 2 ) ( w + 27 ) = 0 thus w = 2 or – 27 ∴ with of the path = 2 m answer c
Answer: c
Question (physics): if a car had traveled 40 kmh faster than it actually did , the trip would have lasted 30 minutes less . if the car went exactly 120 km , at what speed did it travel ?
Options: a ) 50 kmh , b ) 60 kmh , c ) 70 kmh , d ) 80 kmh , e ) 90 kmh
Rationale: "time = distance / speed difference in time = 1 / 2 hrs 120 / x - 120 / ( x + 40 ) = 1 / 2 substitute the value of x from the options . - - > x = 80 - - > 120 / 80 - 120 / 120 = 3 / 2 - 1 = 1 / 2 answer : d"
Answer: d
Question (general): a grocer has a sale of rs . 3435 , rs . 3927 , rs . 3855 , rs . 4230 and rs . 3562 for 5 consecutive months . how much sale must he have in the sixth month so that he gets an average sale of rs . 3500 ?
Options: a ) s . 1991 , b ) s . 2991 , c ) s . 3991 , d ) s . 4991 , e ) s . 5991
Rationale: "explanation : total sale for 5 months = rs . ( 3435 + 3927 + 3855 + 4230 + 3562 ) = rs . 19009 . required sale = rs . [ ( 3500 x 6 ) â € “ 19009 ] = rs . ( 21000 â € “ 19009 ) = rs . 1991 . answer a"
Answer: a
Question (probability): what is the probability of getting a number less than 4 when a die is rolled ?
Options: a ) 5 / 5 , b ) 1 / 2 , c ) 5 / 1 , d ) 5 / 7 , e ) 5 / 2
Rationale: "total number of outcomes possible when a die is rolled = 6 ( ∵ any one face out of the 6 faces ) i . e . , n ( s ) = 6 e = getting a number less than 4 = { 1 , 2 , 3 } hence , n ( e ) = 3 the probability = 3 / 6 = 1 / 2 . answer : b"
Answer: b
Question (physics): a 270 m long train running at the speed of 120 kmph crosses another train running in opposite direction at the speed of 80 kmph in 9 second . what is the length of the other train ?
Options: a ) 150 m , b ) 230 m , c ) 290 m , d ) 310 m , e ) 420 m
Rationale: relative speed = 120 + 80 = 200 * 5 / 18 = 500 / 9 m / s let the length of the other train be x meters x + 270 / 9 = 500 / 9 x = 230 m answer is b
Answer: b
Question (physics): two trains of equal length , running with the speeds of 60 and 40 kmph , take 40 seconds to cross each other while they are running in the same direction . what time will they take to cross each other if they are running in opposite directions ?
Options: a ) 10 sec , b ) 16 sec , c ) 13 sec , d ) 67 sec , e ) 8 sec
Rationale: "rs = 60 - 40 = 20 * 5 / 18 = 100 / 18 t = 40 d = 40 * 100 / 18 = 2000 / 9 rs = 60 + 40 = 100 * 5 / 18 t = 2000 / 9 * 18 / 500 = 8 sec answer : e"
Answer: e
Question (other): a dog takes 2 leaps for every 3 leaps of a hare . if one leap of the dog is equal to 3 leaps of the hare , the ratio of the speed of the dog to that of the hare is :
Options: a ) 1 : 5 , b ) 2 : 5 , c ) 3 : 5 , d ) 4 : 5 , e ) 6 : 5
Rationale: "explanation : dog : hare = ( 2 * 3 ) leaps of hare : 3 leaps of hare = 6 : 5 . answer : e ) 6 : 5"
Answer: e
Question (general): in a group of pigs and hens , the number of legs are 22 more than twice the number of heads . the number of pigs is
Options: a ) 5 , b ) 7 , c ) 10 , d ) 12 , e ) 11
Rationale: explanation : let the number of pigs be x and the number of hens be y . then , 4 x + 2 y = 2 ( x + y ) + 22 4 x + 2 y = 2 x + 2 y + 22 2 x = 22 x = 11 answer : e
Answer: e
Question (general): x + y = 19 , and x + 3 y = 1 . find the value of x + 2 y
Options: a ) 20 , b ) 18 , c ) 11 , d ) 10 , e ) 5
Rationale: add these two equations 2 x + 4 y = 20 divide by 2 ( to get x + 2 y ) answer will be d . 10
Answer: d
Question (gain): in the fifth grade at parkway elementary school there are 470 students . 300 students are boys and 250 students are playing soccer . 86 % of the students that play soccer are boys . how many girl student are in parkway that is not playing soccer ?
Options: a ) 69 . , b ) 135 . , c ) 81 . , d ) 91 . , e ) 108 .
Rationale: "total students = 470 boys = 300 , girls = 170 total playing soccer = 250 86 % of 250 = 215 are boys who play soccer . girls who play soccer = 35 . total girls who do not play soccer = 170 - 35 = 135 . correct option : b"
Answer: b
Question (physics): how long does a train 110 m long traveling at 60 kmph takes to cross a bridge of 390 m in length ?
Options: a ) 18.9 sec , b ) 88.9 sec , c ) 22.9 sec , d ) 30.00 sec , e ) 72.0 sec
Rationale: "d = 110 + 390 = 500 m s = 60 * 5 / 18 = 50 / 3 t = 500 * 3 / 50 = 30 sec answer : d"
Answer: d
Question (physics): a can finish a work in 24 days , b in 9 days and c in 12 days . b and c start the work but are forced to leave after 3 days . when a done the work ?
Options: a ) 10 days , b ) 12 days , c ) 13 days , d ) 9 days , e ) 14 days
Rationale: "b + c = = > 1 / 9 + 1 / 12 = 7 / 36 b , c = in 3 days = 7 / 36 * 3 = 7 / 12 remaining work = 1 - 7 / 12 = 5 / 12 1 / 24 work is done by a in 1 day 5 / 12 work is done a 24 * 5 / 12 = 10 days answer a"
Answer: a