Cheukting/mathqa huggingface dataset:
Question (physics): in a survey of 340 employees , 104 of them are uninsured , 54 work part time , and 12.5 percent of employees who are uninsured work part time . if a person is to be randomly selected from those surveyed , what is the probability that the person will neither work part time nor be uninsured ?
Options: a ) 7 / 12 , b ) 8 / 41 , c ) 39 / 68 , d ) 1 / 8 , e ) 41 / 91
Rationale: - - - - - - - - - ui - - - - - - - - - - - - - - - - nui - - - - - - - total pt - - - - ( 12.5 / 100 ) * 104 = 13 - - - - - - - - - - - - - 54 npt - - - 104 - 13 - - - - - - - - - - - - - - x - - - - - - - - 286 total - - 104 - - - - - - - - - - - - - - - - - - - - - - - - - - - - 340 we have to find not part time and not uninsured . in other words not part time and insured = x / 340 = ( 286 - 104 + 13 ) / 340 = 39 / 68 answer is c .
Answer: c
Question (general): a ( 3 , w ^ 3 ) is the ( x , y ) coordinate of point located on the parabola y = x ^ 2 - 1 . what is the value of w ?
Options: a ) 2 . , b ) 4 . , c ) 5 . , d ) 6 . , e ) 9 .
Rationale: y = x ^ 2 - 1 w ^ 3 = 3 ^ 2 - 1 w ^ 3 = 8 w = 2 answer a
Answer: a
Question (general): in x game of billiards , x can give y 20 points in 60 and he can give z 30 points in 60 . how many points can y give z in x game of 120 ?
Options: a ) 30 , b ) 20 , c ) 25 , d ) 40 , e ) 50
Rationale: x scores 60 while y score 40 and z scores 30 . the number of points that z scores when y scores 120 = ( 120 * 30 ) / 40 = 90 . in x game of 100 points , y gives ( 120 - 90 ) = 30 points to c . a
Answer: a
Question (general): a house wife saved $ 2.50 in buying an item on sale . if she spent $ 25 for the item , approximately how much percent she saved in the transaction ?
Options: a ) 8 % , b ) 9 % , c ) 10 % , d ) 11 % , e ) 12 %
Rationale: actual price = 25 + 2.50 = $ 27.50 saving = 2.50 / 27.50 * 100 = 100 / 11 = 9 % approximately answer is b
Answer: b
Question (gain): after successive discounts of 20 % , 10 % and 5 % a certain good is sold for rs . 6700 . find the actual price of the good .
Options: a ) s . 6000 , b ) s . 9000 , c ) s . 10800 , d ) s . 9795 , e ) s . 9980
Rationale: let actual price was 100 . after three successive discount this will become , 100 = = 20 % discount = > 80 = = 10 % discount = > 72 = = 5 % discount = 68.4 now compare , 68.4 = 6700 1 = 6700 / 68.4 100 = ( 6700 * 100 ) / 68.4 = rs . 9795 . answer : option d
Answer: d
Question (physics): a not - so - good clockmaker has four clocks on display in the window . clock # 1 loses 25 minutes every hour . clock # 2 gains 15 minutes every hour relative to clock # 1 ( i . e . , as clock # 1 moves from 12 : 00 to 1 : 00 , clock # 2 moves from 12 : 00 to 1 : 15 ) . clock # 3 loses 20 minutes every hour relative to clock # 2 . finally , clock # 4 gains 20 minutes every hour relative to clock # 3 . if the clockmaker resets all four clocks to the correct time at 12 noon , what time will clock # 4 display after 6 actual hours ( when it is actually 6 : 00 pm that same day ) ?
Options: a ) 5 : 00 , b ) 5 : 34 , c ) 5 : 42 , d ) 6 : 00 , e ) 6 : 24
Rationale: "c 1 loses 15 minutes every hour . so after 60 minutes have passed , c 1 displays that 60 - 15 = 45 minutes have passed . c 2 gains 15 minutes for every 60 minutes displayed on c 1 . thus , the time displayed on c 2 is 75 / 60 = 5 / 4 the time displayed on c 1 . so after 60 minutes have passed , c 2 displays the passing of ( 5 / 4 * 45 ) minutes . c 3 loses 20 minutes for every 60 minutes displayed on c 2 . thus , the time displayed on c 3 is 40 / 60 = 2 / 3 the time displayed on c 2 . so after 60 minutes have passed , c 3 displays the passing of ( 2 / 3 * 5 / 4 * 45 ) minutes . c 4 gains 20 minutes for every 60 minutes displayed on c 3 . thus , the time displayed on c 4 is 80 / 60 = 4 / 3 the time displayed on clock 3 . so after 60 minutes have passed , c 4 displays the passing of 4 / 3 * 2 / 3 * 5 / 4 * 45 = 50 minutes . c 4 loses 10 minutes every hour . in 6 hours , c 4 will lose 6 * 10 = 60 minutes = 1 hour . since the correct time after 6 hours will be 6 pm , c 4 will show a time of 6 - 1 = 5 : 42 pm . the correct answer is c ."
Answer: c
Question (general): in a factory , an average of 60 tv ' s are produced per day for the fist 25 days of the months . a few workers fell ill for the next 5 days reducing the daily avg for the month to 58 sets / day . the average production per day for day last 5 days is ?
Options: a ) 20 , b ) 36 , c ) 48 , d ) 50 , e ) 59
Rationale: production during these 5 days = total production in a month - production in first 25 days . = 30 x 58 - 25 x 60 = 240 ∴ average for last 5 days = 240 / 5 = 48 c
Answer: c
Question (general): a collection of books went on sale , and 2 / 3 of them were sold for $ 4.25 each . if none of the 30 remaining books were sold , what was the total amount received for the books that were sold ?
Options: a ) $ 260 , b ) $ 255 , c ) $ 285 , d ) $ 290 , e ) $ 275
Rationale: "if 30 books constitute 1 / 3 rd of the total , then 2 / 3 rd of the total = 60 books amount received for sold books = 60 * 4.25 = $ 255 answer : b"
Answer: b
Question (other): the ratio between the present ages of a and b is 5 : 3 respectively . the ratio between a ' s age 4 years ago and b ' s age 4 years hence is 1 : 1 . what is the ratio between a ' s age 4 years hence and b ' s age 4 years ago ?
Options: a ) 3 : 9 , b ) 3 : 6 , c ) 3 : 1 , d ) 3 : 4 , e ) 3 : 2
Rationale: "let the present ages of a and b be 5 x and 3 x years respectively . then , ( 5 x - 4 ) / ( 3 x + 4 ) = 1 / 1 2 x = 8 = > x = 4 required ratio = ( 5 x + 4 ) : ( 3 x - 4 ) = 24 : 8 = 3 : 1 answer : c"
Answer: c
Question (general): when jessica withdrew $ 200 from her bank account , her account balance decreased by 2 / 5 . if she deposits an amount equal to 2 / 3 of the remaining balance , what will be the final balance in her bank account ?
Options: a ) 300 , b ) 375 , c ) 400 , d ) 500 , e ) 575
Rationale: "as per the question 200 = 2 a / 5 thus - a which is the total amount = 500 the amount thus left = 300 she then deposited 2 / 3 of 300 = 200 total amount in her account = 500 answer d"
Answer: d
Question (general): in n is a positive integer less than 200 , and 14 n / 60 is an integer , then n has how many different positive prime factors s ?
Options: a ) 2 , b ) 3 , c ) 5 , d ) 6 , e ) 8
Rationale: "i like to put the numbers in prime factors so it is easier and faster to visualize . 14 * n / 60 if we write the factors of 14 - - > 2 , 7 , and the factors of 60 - - > 2 , 2 , 3 , 5 , we have ( 2 * 7 * n ) / ( 2 ^ 2 * 3 * 5 ) simplifying 7 * n / ( 2 * 3 * 5 ) the only way the equation above has an integer value is if n has at least the factors 2 , 3 and 5 , so we can simplify again and we have the number 7 . the number could be 2 * 3 * 5 , or 2 * 3 * 5 * 2 , or 2 * 3 * 5 * . . . . . however to be less than 200 we can not add any prime number . 2 * 3 * 5 = 120 if we added the next prime factor 7 , we would have s = 2 * 3 * 5 * 7 = 840 thus , answer b"
Answer: b
Question (geometry): an equilateral triangle t 2 is formed by joining the mid points of the sides of another equilateral triangle t 1 . a third equilateral triangle t 3 is formed by joining the mid - points of t 2 and this process is continued indefinitely . if each side of t 1 is 40 cm , find the sum of the perimeters of all the triangles .
Options: a ) 180 cm
b ) 220 cm
c ) 240 cm
d ) 270 cm
e ) 300 cm
Rationale: we have 40 for first triangle , when we join mid - points of first triangle we get the second equilateral traingle then the length of second one is 20 and continues . so we have 40 , 20,10 , . . . we have ratio = 1 / 2 , and it is gp type . sum of infinite triangle is a / 1 - r = 40 / 1 - ( 1 / 2 ) = 80 equilateral triangle perimeter is 3 a = 3 * 80 = 240 . so option c .
Answer: c
Question (physics): two pipes a and b can fill a tank in 10 hours and 20 hours respectively . if both the pipes are opened simultaneously , how much time will be taken to fill the tank ?
Options: a ) 10 / 3 , b ) 20 / 3 , c ) 15 / 7 , d ) 11 / 17 , e ) 1 / 4
Rationale: "part filled by a in 1 hour = 1 / 10 part filled by b in 1 hour = 1 / 20 part filled by ( a + b ) in 1 hour = 1 / 10 + 1 / 20 = 3 / 20 both the pipes together fill the tank in 20 / 3 hours answer is b"
Answer: b
Question (general): the number obtained by interchanging the digits of a two - digit number is less than the original number by 36 . the sum of the digits of the number is 8 . what is the original number ?
Options: a ) 71 , b ) 62 , c ) 53 , d ) 35 , e ) 45
Rationale: explanation : let the number be 10 x + y . ∴ x + y = 8 . . . . . ( i ) 10 x + y - ( 10 y + x ) = 36 ∴ 9 ( x - y ) = 3 ∴ x - y = 4 . . . . . . . ( ii ) from equation ( i ) and ( ii ) : x = 6 , y = 2 ∴ number = 62 answer : option b
Answer: b
Question (gain): in one alloy there is 10 % chromium while in another alloy it is 6 % . 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 ) 7.2 % , 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 0.10 * 15 + 0.06 * 35 = 3.6 kg , so the percentage is 3.6 / 50 * 100 = 7.2 % . answer : a ."
Answer: a
Question (physics): the food in a camp lasts for 10 men for 20 days . if 30 more men join , how many days will the food last ?
Options: a ) 8 days , b ) 4 days , c ) 5 days , d ) 10 days , e ) 17 days
Rationale: "one man can consume the same food in 10 * 20 = 200 days . 30 more men join , the total number of men = 40 the number of days the food will last = 200 / 40 = 5 days . answer : c"
Answer: c
Question (geometry): surface area of a sphere is 2464 cm 2 . if its radius is doubled , then the surface area of the new sphere will be
Options: a ) 4920 cm 2
b ) 4727 cm 2
c ) 9856 cm 2
d ) 19712 cm 2
e ) none
Rationale: sol . let the original radius be r . then , original surface area = 4 π r 2 = 2464 cm 2 ( given ) . new radius = 2 r . ∴ new surface area = 4 π ( 2 r ) 2 = 4 x 4 π r 2 = ( 4 x 2464 ) cm 2 = 9856 cm 2 answer c
Answer: c
Question (physics): how long does a train 100 m long travelling at 60 kmph takes to cross a bridge of 80 m in length ?
Options: a ) 15.8 sec , b ) 14.9 sec , c ) 12.4 sec , d ) 10.8 sec , e ) 11.8 sec
Rationale: "d 16.8 sec d = 100 + 80 = 180 m s = 60 * 5 / 18 = 50 / 3 t = 180 * 3 / 50 = 10.8 sec"
Answer: d
Question (general): - 74 x 29 + 265 = ?
Options: a ) 2436 , b ) - 1881 , c ) - 2801 , d ) - 2071 , e ) none of them
Rationale: "given exp . = - 74 x ( 30 - 1 ) + 265 = - ( 74 x 30 ) + 74 + 265 = - 2220 + 339 = - 1881 answer is b"
Answer: b
Question (general): the population of 6 villages is 803 , 9001100 , 1023945 and 980 . what is the population of the seventh village if the average population of the 7 villages is 1000 ?
Options: a ) 1134 , b ) 1238 , c ) 1348 , d ) 1500 , e ) 1249
Rationale: population of seventh village = 7 * 1000 - ( 803 + 900 + 1100 + 1023 + 945 + 980 ) = 1249 answer is e
Answer: e
Question (general): if 625 ^ ( - x ) + 25 ^ ( - 2 x ) + 5 ^ ( - 4 x ) = 14 , what is the value of x ?
Options: a ) - 4 , b ) - 1 / 4 , c ) 0 , d ) 1 / 4 , e ) 4
Rationale: "we ' re told that 625 ^ ( - x ) + 25 ^ ( - 2 x ) + 5 ^ ( - 4 x ) = 15 . we ' re asked for the value of x . since each of the calculated terms must be positive ( regardless of what the exponent is ) , we can use thebasesto our advantage . . . . . with answer a , we ' d have 625 ^ 4 , which is much bigger than 15 ( and we ' d be adding to that big number ) . eliminate a . with answer e , we ' d have 625 ^ ( - 4 ) , which would create a tiny fraction ( and we ' d add some other fractions to it , so the total would be much too small ) . eliminate e . with answer d , we ' d have 625 ^ ( - 1 / 4 ) , which will also be a fraction ( just not as tiny as the one in answer e ) , but the total would still be too small . eliminate d . with answer c , anything to the ' 0 power ' is 1 , so we ' d have 1 + 1 + 1 = 3 . this is not 15 . eliminate c . d"
Answer: d
Question (physics): the radius of the wheel of a bus is 70 cms and the speed of the bus is 66 km / h , then the r . p . m . ( revolutions per minutes ) of the wheel is
Options: a ) 200 , b ) 250 , c ) 300 , d ) 330 , e ) none of these
Rationale: "radius of the wheel of bus = 70 cm . then , circumference of wheel = 2 π r = 140 π = 440 cm distance covered by bus in 1 minute = 66 ⁄ 60 × 1000 × 100 cms distance covered by one revolution of wheel = circumference of wheel = 440 cm ∴ revolutions per minute = 6600000 / 60 × 440 = 250 answer b"
Answer: b
Question (physics): harry started a 4 - mile hike with a full 6 - cup canteen of water and finished the hike in 2 hours with 1 cup of water remaining in the canteen . if the canteen leaked at the rate of 1 cup per hour and harry drank 1 cups of water during the last mile , how many cups did he drink per mile during the first 3 miles of the hike ?
Options: a ) 1 / 3 , b ) 2 / 3 , c ) 3 / 4 , d ) 5 / 4 , e ) 4 / 3
Rationale: no of cups leaked during the trip = 2 cups . no of cups harry drank = 3 cups . no of cups harry drank during the first 3 miles = 2 . drink / mile = 2 / 3 answer : b
Answer: b
Question (general): in a room filled with 7 people , 2 people have exactly 1 sibling in the room and 5 people have exactly 2 siblings in the room . if two individuals are selected from the room at random , what is the probability that those two individuals are not siblings ?
Options: a ) 5 / 21 , b ) 3 / 7 , c ) 4 / 7 , d ) 5 / 7 , e ) 16 / 21
Rationale: "there are suppose a b c d e f g members in the room 4 people who have exactly one sibling . . . . a b c d . . . . ( a is bs ∘ sssibl ∈ g ∘ ssand ∘ ssviceversa ) ∘ ss ( c ∘ ssis ∘ ssds ∘ sssibl ∈ g ∘ ssand ∘ ssviceversa ) ∘ ss ( c ∘ ssis ∘ ssdssibl ∈ gandviceversa ) ( cisds sibling and viceversa ) ( c is ds sibling and viceversa ) . . . now remaning efg are 5 people who have exactly 2 siblings . . . . ( e has f and g as his / her sibling and so on . . ) there are now 3 different set of siblings ( a and b ) ( c and d ) ; ( efg ) now first selecting 2 people out of 7 is 7 c 2 = 21 first sibling pair - - - - ( a and b ) - - selecting 2 people - - 2 c 2 = 1 second sibling pair ( c and d ) - - selecting 2 people - - 2 c 2 = 1 third sibling pair ( e f g ) - - selecting 2 out of 5 - - 5 c 2 = 10 total = 1 + 1 + 10 = 12 but , a / c to formula p ( success ) - 1 - p ( fail ) here , p ( failure ) is selecting 2 people who are siblings = 12 / 21 ( 21 is 7 c 2 ) = 1 - 12 / 21 = 9 / 21 = 3 / 7 ans b"
Answer: b
Question (physics): two taps a and b can fill a cistern in 12 minutes and 18 minutes respectively . they are turned on at the same time . if the tap a is turned off after 4 minutes , how long will tap b take to fill the rest of the cistern ?
Options: a ) 8 min . , b ) 9 min . , c ) 10 min . , d ) 7 min . , e ) none of these
Rationale: in one min , ( a + b ) fill the cistern = 1 ⁄ 12 + 1 ⁄ 18 = 5 ⁄ 36 th in 4 min , ( a + b ) fill the cistern = 5 ⁄ 36 × 4 = 5 ⁄ 9 th rest part = 1 - 5 ⁄ 9 = 4 ⁄ 9 th ∵ 1 ⁄ 18 th part is filled by b in one min . ∴ 4 ⁄ 9 th part is filled by b in 18 × 4 ⁄ 9 = 8 min answer a
Answer: a
Question (general): how many digits are in ( 8 × 10 ^ 18 ) ( 10 × 10 ^ 10 ) ?
Options: a ) 24 , b ) 25 , c ) 26 , d ) 27 , e ) 30
Rationale: "the question simplfies to ( 8 × 10 ^ 18 ) ( 10 ^ 11 ) = > 8 * 10 ^ 29 = > will contain 29 zeros + 1 digit 8 = > 30 ans e"
Answer: e
Question (physics): jack and christina are standing 240 feet apart on a level surface . their dog , lindy , is standing next to christina . at the same time , they all begin moving toward each other . jack walks in a straight line toward christina at a constant speed of 3 feet per second and christina walks in a straight line toward jack at a constant speed of 3 feet per second . lindy runs at a constant speed of 10 feet per second from christina to jack , back to christina , back to jack , and so forth . what is the total distance , in feet , that lindy has traveled when the three meet at one place ?
Options: a ) 340 , b ) 360 , c ) 380 , d ) 400 , e ) 420
Rationale: "the relative speed of jack and christina is 3 + 3 = 6 feet per second . the distance between them is 210 feet , hence they will meet in ( time ) = ( distance ) / ( relative speed ) = 240 / 6 = 40 seconds . for all this time lindy was running back and forth , so it covered ( distance ) = ( speed ) * ( time ) = 10 * 40 = 400 feet . answer : d ."
Answer: d
Question (physics): the speed of a boat in still water is 60 kmph and the speed of the current is 17 kmph . find the speed downstream and upstream ?
Options: a ) 77,43 kmph , b ) 80,80 kmph , c ) 80,42 kmph , d ) 80,40 kmph , e ) 83,40 kmph
Rationale: speed downstream = 60 + 17 = 77 kmph speed upstream = 60 - 17 = 43 kmph . answer : a
Answer: a
Question (general): a solution of 70 litres contains oil and water in the ratio 9 : x . if 6 litres of water is added to the solution , the ratio becomes 6 : 4 , find the value of x ?
Options: a ) 6 , b ) 8.5 , c ) 9 , d ) 6.5 , e ) 5
Rationale: exp . total new quantity = original sol + water = 70 + 6 = 76 new ratio = 6 : 4 , new quantity of oil = 6 / 10 * 76 = 45.6 lit , new quantity of water = 4 / 10 * 76 = 30.4 lit water present initially = ( 30.4 - 6 ) = 24.4 lit ratio = 45.6 / 24.4 = 9 / x there for x = 4.81 approx 5 answer : e
Answer: e
Question (gain): if an article is sold at 18 % profit instead of 11 % profit , then the profit would be $ 56 more . what is the cost price ?
Options: a ) $ 600 , b ) $ 800 , c ) $ 1000 , d ) $ 1200 , e ) $ 1400
Rationale: "7 % * cost price = $ 56 1 % * cost price = $ 56 / 7 = $ 8 the cost price is $ 800 . the answer is b ."
Answer: b
Question (general): if a , b , c , d , e and f are integers and ( ab + cdef ) < 0 , then what is the maximum number d of integers that can be negative ?
Options: a ) 2 , b ) 3 , c ) 4 , d ) 5 , e ) 6
Rationale: "minimuum should be 1 maximum should be 4 : 1 out of a or b to make the multiplication negative 3 out of c , d , e or f to make the multiplication negative . negative + negative < 0 answer : c maximum will be 5 . . you dont require both the multiplicatin to be negative for entire equation to be negative . . . any one a or b can be negative to make ab negative and it can still be more ( away from 0 ) than the multiplication of 4 other - ve numbers . . . actually by writing minimum required as 1 out of 6 , you are actually meaning 5 out of 6 also possible as you will see d = 5 or 1 will give you same equation . . ans d"
Answer: d
Question (gain): a jar full of whisky contains 40 % alcohol . a part of this whisky is replaced by another containg 17 % alcohol and now the percentage of alcohol was found to be 26 % . what quantity of whisky is replaced ?
Options: a ) 1 / 3 , b ) 2 / 3 , c ) 2 / 5 , d ) 3 / 5 , e ) 4 / 5
Rationale: "let us assume the total original amount of whiskey = 10 ml - - - > 4 ml alcohol and 6 ml non - alcohol . let x ml be the amount removed - - - > total alcohol left = 4 - 0.4 x new quantity of whiskey added = x ml out of which 0.19 is the alcohol . thus , the final quantity of alcohol = 4 - 0.4 x + 0.19 x - - - - > ( 4 - 0.21 x ) / 10 = 0.26 - - - > x = 20 / 3 ml . per the question , you need to find the x ml removed as a ratio of the initial volume - - - > ( 20 / 3 ) / 10 = 2 / 5 . hence , c is the correct answer ."
Answer: c
Question (geometry): the length of the rectangular field is double its width . inside the field there is square shaped pond 6 m long . if the area of the pond is 1 / 8 of the area of the field . what is the length of the field ?
Options: a ) 24 , b ) 32 , c ) 75 , d ) 28 , e ) 11
Rationale: "a / 8 = 6 * 6 = > a = 6 * 6 * 8 x * 2 x = 6 * 6 * 8 x = 12 = > 2 x = 24 answer : a"
Answer: a
Question (geometry): the area of a triangle is with base 2 m and height 3 m ?
Options: a ) 11 , b ) 10 , c ) 787 , d ) 3 , e ) 12
Rationale: "1 / 2 * 2 * 3 = 3 m 2 answer : d"
Answer: d
Question (general): if the price of a certain computer increased 30 percent from c dollars to 351 dollars , then 2 c =
Options: a ) 540 , b ) 570 , c ) 619 , d ) 649 , e ) 700
Rationale: "before price increase price = c after 30 % price increase price = c + ( 30 / 100 ) * c = 1.3 c = 351 ( given ) i . e . c = 351 / 1.3 = $ 270 i . e . 2 c = 2 * 270 = 540 answer : option a"
Answer: a
Question (gain): the purchase price of an article is $ 48 . in order to include 5 % of cost for overhead and to provide $ 12 of net profit , the markup should be
Options: a ) 15 % , b ) 25 % , c ) 30 % , d ) 40 % , e ) 45 %
Rationale: "cost price of article = 48 $ % of overhead cost = 5 net profit = 12 $ we need to calculate % markup net profit as % of cost price = ( 12 / 48 ) * 100 = 25 % total markup should be = 25 + 5 = 30 % answer c"
Answer: c
Question (gain): a store reduced the price of all items in the store by 12 % on the first day and by another 10 % on the second day . the price of items on the second day was what percent of the price before the first reduction took place ?
Options: a ) 80.0 , b ) 79.2 , c ) 81.0 , d ) 81.1 , e ) 81.9
Rationale: "consider price of the all items as $ 100 after a initial reduction of 12 % price becomes = 0.88 * 100 = $ 88 after the final reduction of 10 % price becomes = 0.9 * 88 = $ 79.2 price of all items on second day is 79.2 % of price on first day correct answer option b"
Answer: b
Question (physics): darcy lives 1.5 miles from work . she can walk to work at a constant rate of 3 miles per hour , or she can ride the train to work at a constant rate of 20 miles per hour . if she rides the train , there is an additional x minutes spent walking to the nearest train station , waiting for the train , and walking from the final train station to her work . if it takes darcy a total of 10 more minutes to commute to work by walking than it takes her to commute to work by riding the train , what is the value of x ?
Options: a ) 10.5 , b ) 15 , c ) 15.5 , d ) 30 , e ) 60
Rationale: "the time it takes darcy to walk to work is ( 1.5 / 3 ) * 60 = 30 minutes the time it takes darcy to take the train is ( 1.5 / 20 ) * 60 + x = 4.5 + x minutes it takes 15 minutes longer to walk , so 30 = 4.5 + x + 10 x = 15.5 minutes answer : c"
Answer: c
Question (general): when the smallest of 3 consecutive odd integers is added to 4 times the largest , it produces a result 732 more than 4 times the middle integer . find the numbers ?
Options: a ) 732 , b ) 678 , c ) 698 , d ) 710 , e ) 729
Rationale: x + 4 ( x + 4 ) = 732 + 4 ( x + 2 ) solve for x and find all three numbers x + 4 x + 16 = 732 + 4 x + 8 x = 724 x + 2 = 726 x + 4 = 728 check : the smallest is added to four times the largest 724 + 4 * 728 = 3636 four times the middle 4 * 726 = 2904 3636 is more than 2904 by 3636 - 2904 = 732 a
Answer: a
Question (physics): in a particular city there are 100 homes numbered from 1 , 23 , . . , 100 . the city was build by a builder from chennai . there was 4 to 5 shops in the town which was build by a builder from mumbai . the 2 nd builder can build in 1 ½ times as compared to time by 1 st builder . the 2 nd builder builds in 15 days , then how many 2 ' s are used by the builder from chennai in numbering the 100 homes ?
Options: a ) 17 , b ) 18 , c ) 19 , d ) 20 , e ) 21
Rationale: in the last line it should be given the builder from chennai in numbering the 100 homes ? then ans is 20 answer : d
Answer: d
Question (physics): p and q can complete a work in 40 days and 24 days respectively . p alone started the work and q joined him after 8 days till the completion of the work . how long did the work last ?
Options: a ) 5 days , b ) 10 days , c ) 14 days , d ) 20 days , e ) 26 days
Rationale: "explanation : work done by p in 1 day = 1 / 40 work done by q in 1 day = 1 / 24 work done by p in 8 days = 8 ã — ( 1 / 40 ) = 1 / 5 remaining work = 1 â € “ 1 / 5 = 4 / 5 work done by p and q in 1 day = 1 / 40 + 1 / 24 = 1 / 15 number of days p and q take to complete the remaining work = ( 4 / 5 ) / ( 1 / 15 ) = 12 total days = 8 + 12 = 20 answer : option d"
Answer: d