Cheukting/mathqa huggingface dataset:
Question (general): how much is 60 % of 40 is greater than 4 / 5 of 30 ?
Options: a ) 8 , b ) 3 , c ) 7 , d ) 0 , e ) 1
Rationale: "( 60 / 100 ) * 40 â € “ ( 4 / 5 ) * 30 24 - 24 = 0 answer : d"
Answer: d
Question (physics): a train speeds past a pole in 22 seconds and a platform 140 m long in 33 seconds . its length is ?
Options: a ) 280 , b ) 260 , c ) 300 , d ) 290 , e ) 270
Rationale: "let the length of the train be x meters and its speed be y m / sec . they , x / y = 22 = > y = x / 22 x + 140 / 33 = x / 22 x = 280 m . answer : a"
Answer: a
Question (general): find the greatest number which on dividing 6215 and 7373 , leaves a reminder of 23 and 29 respectively
Options: a ) 125 , b ) 127 , c ) 129 , d ) 131 , e ) 144
Rationale: "explanation : in this type of question , its obvious we need to calculate the hcf , trick is hcf of ( 6215 - 23 ) and ( 7373 - 29 ) = hcf ( 6192 , 7344 ) = 144 option e"
Answer: e
Question (probability): an urn contains 5 red , 6 blue and 8 green balls . 3 balls are randomly selected from the urn , find the probability that the drawn ball are blue ?
Options: a ) 20 / 969 , b ) 20 / 875 , c ) 21 / 876 , d ) 3 / 512 , e ) 2 / 9
Rationale: "sample space = no . of ways 3 balls were drawn from urn = 19 c 3 = 969 no . ways 3 blue balls were drawn from bag = 6 c 3 = 20 probability = 20 / 969 ans - a"
Answer: a
Question (physics): the pinedale bus line travels at an average speed of 60 km / h , and has stops every 5 minutes along its route . yahya wants to go from his house to the pinedale mall , which is 8 stops away . how far away , in kilometers , is pinedale mall away from yahya ' s house ?
Options: a ) 20 km , b ) 30 km , c ) 40 km , d ) 50 km , e ) 60 km
Rationale: "number of stops in an hour : 60 / 5 = 12 distance between stops : 60 / 12 = 5 km distance between yahya ' s house and pinedale mall : 5 x 8 = 40 km imo , correct answer is ` ` c . ' '"
Answer: c
Question (general): the sum of ages of 5 children born at the intervals of 2 years each is 55 years . what is the age of the youngest child ?
Options: a ) 4 , b ) 7 , c ) 6 , d ) 9 , e ) 8
Rationale: "let the ages of children be x , ( x + 2 ) , ( x + 4 ) , ( x + 6 ) and ( x + 8 ) years . then , x + ( x + 2 ) + ( x + 4 ) + ( x + 6 ) + ( x + 8 ) = 50 5 x = 55 - 20 = 35 x = 7 . age of the youngest child = x = 7 years . answer : b"
Answer: b
Question (probability): what is the probability of getting a sum 9 from two throws of dice .
Options: a ) 1 / 3 , b ) 1 / 9 , c ) 1 / 12 , d ) 2 / 9 , e ) none of these
Rationale: "explanation : total number of cases = 6 * 6 = 36 favoured cases = [ ( 3,6 ) , ( 4,5 ) , ( 6,3 ) , ( 5,4 ) ] = 4 so probability = 4 / 36 = 1 / 9 option b"
Answer: b
Question (general): two equally sized jugs full of water are each emptied into two separate unequally sized empty jugs , x and y . now , jug x is 1 / 5 full , while jug y is 4 / 7 full . if water is poured from jug x into jug y until jug y is filled , what fraction of jug x then contains water ?
Options: a ) 0 , b ) 1 / 15 , c ) 2 / 15 , d ) 1 / 20 , e ) 2 / 10
Rationale: "suppose the water in each jug is l liters cx x ( 1 / 5 ) = l cx = 5 l liters cx is capacity of x cy x ( 4 / 7 ) = l cy = 7 l / 4 liters cy is capacity of y now , y is 7 l / 4 - l empty = 3 l / 4 empty so , we can put only 3 l / 4 water in jug y from jug x jug x ' s remaining water = l - 3 l / 4 = l / 4 fraction of x which contains water = water / cx = ( l / 4 ) / 5 l = 1 / 20 answer will be d"
Answer: d
Question (physics): two goods trains each 820 m long are running in opposite directions on parallel tracks . their speeds are 45 km / hr and 30 km / hr respectively . find the time taken by the slower train to pass the driver of the faster one ?
Options: a ) 228 , b ) 27.32 , c ) 76.6 , d ) 78.72 , e ) 21
Rationale: relative speed = 45 + 30 = 75 km / hr . 75 * 5 / 18 = 125 / 6 m / sec . distance covered = 820 + 820 = 1640 m . required time = 1640 * 6 / 125 = 78.72 sec . answer : d
Answer: d
Question (physics): 20 beavers , working together in a constant pace , can build a dam in 3 hours . how many hours c will it take 12 beavers that work at the same pace , to build the same dam ?
Options: a ) 2 . , b ) 4 . , c ) c = 5 . , d ) c = 6 . , e ) 8 .
Rationale: "c . 5 hrs if there were 10 beavers it qould have taken double c = 6 hrs . . so closest to that option is 5 ."
Answer: c
Question (gain): indu gave bindu rs . 1875 on compound interest for 2 years at 4 % per annum . how much loss would indu has suffered had she given it to bindu for 2 years at 4 % per annum simple interest ?
Options: a ) s . 10 , b ) s . 2 , c ) s . 5 , d ) s . 3 , e ) s . 4
Rationale: "1875 = d ( 100 / 4 ) 2 d = 3 answer : d"
Answer: d
Question (general): how many integers are between 7 and 57 / 4 , inclusive ?
Options: a ) 4 , b ) 5 , c ) 7 , d ) 8 , e ) 10
Rationale: "57 / 4 = 14 . xx we are not concerned about the exact value of 57 / 4 as we just need the integers . since the values are small , we can write down the integers . the different integers between 7 and 57 / 4 would be 7 , 8 , 9 , 10 , 11 , 12 , 13,14 total number of integers = 8 option d"
Answer: d
Question (other): a bottle contains a certain solution . in the bottled solution , the ratio of water to soap is 3 : 4 , and the ratio of soap to salt is five times this ratio . the solution is poured into an open container , and after some time , the ratio of water to soap in the open container is halved by water evaporation . at that time , what is the ratio of water to salt in the solution ?
Options: a ) 9 : 32 , b ) 9 : 30 , c ) 32 : 9 , d ) 19 : 32 , e ) 18 : 30
Rationale: "water : soap = 3 : 4 soap : salt = 15 : 20 = > for 15 soap , salt = 20 = > for 4 soap , salt = ( 20 / 15 ) * 4 = 80 / 15 = 16 / 3 so , water : soap : salt = 3 : 4 : 16 / 3 = 9 : 12 : 16 after open container , water : soap : salt = 4.5 : 12 : 16 so , water : salt = 4.5 : 16 = 9 : 32 answer : a"
Answer: a
Question (general): 3 / 5 * [ ( 2 / 3 + 3 / 8 ) / 2 ] - 1 / 16 =
Options: a ) 1 / 4 , b ) 19 / 16 , c ) 15 / 16 , d ) 9 / 13 , e ) 0
Rationale: we need to simplify the expression using pemdas . parentheses exponents multiplication anddivision addition andsubtraction the calculation of an equation or expression must be carried out in the following order : 1 ) operations within parentheses ( or absolute value bars or radicals ) 2 ) exponents 3 ) multiplication and division from left to right 4 ) addition and subtraction from left to right the answer is a .
Answer: a
Question (physics): steve traveled the first 2 hours of his journey at 40 mph and the last 3 hours of his journey at 100 mph . what is his average speed of travel for the entire journey ?
Options: a ) 60 mph , b ) 56.67 mph , c ) 53.33 mph , d ) 64 mph , e ) 76 mph
Rationale: "answer average speed of travel = total distance travelled / total time taken total distance traveled by steve = distance covered in the first 2 hours + distance covered in the next 3 hours . distance covered in the first 2 hours = speed * time = 40 * 2 = 80 miles . distance covered in the next 3 hours = speed * time = 100 * 3 = 300 miles . therefore , total distance covered = 80 + 300 = 380 miles . total time taken = 2 + 3 = 5 hours . hence , average speed = total distance travelled / total time taken = 380 / 5 = 76 miles per hour . choice e"
Answer: e
Question (gain): each of the cucumbers in 100 pounds of cucumbers is composed of 99 % water , by weight . after some of the water evaporates , the cucumbers are now 93 % water by weight . what is the new weight of the cucumbers , in pounds ?
Options: a ) 2 , b ) 15 , c ) 92 , d ) 96 , e ) 98
Rationale: "out of 100 pounds 99 % or 99 pounds is water and 1 pound is non - water . after somewaterevaporates the cucumbers become 93 % water and 7 % of non - water , so now 1 pound of non - water composes 7 % of cucucmbers , which means that the new weight of cucumbers is 1 / 0.07 = 15 pounds . answer : b ."
Answer: b
Question (geometry): the cost of the paint is rs . 50 per kg . if 1 kg of paint covers 20 sq . ft , how much will it cost to paint outside of a cube having 20 feet each side
Options: a ) rs . 962 , b ) rs . 6000 , c ) rs . 546 , d ) rs . 876 , e ) none of these
Rationale: "explanation : surface area of a cube = 6 x 20 ^ 2 = 2400 sq . ft quantity of paint required = ( 2400 / 20 ) = 120 kg cost of painting = 50 x 120 = rs . 6000 answer : b"
Answer: b
Question (physics): a man can row downstream at 25 kmph and upstream at 15 kmph . find the time to reach a destination point at a distance of 50 km along the downstream .
Options: a ) 4 hrs . , b ) 1 hrs . , c ) 3 hrs . , d ) 2 hrs . , e ) 2 1 / 2 hrs .
Rationale: "let the speed of the man in downstream = 25 kmph . distance to be covered along the stream = 50 kmph = > time taken = d / s = 50 / 25 = 2 hrs . answer : d"
Answer: d
Question (physics): a train is 360 meter long is running at a speed of 45 km / hour . in what time will it pass a bridge of 160 meter length ?
Options: a ) 11 seconds , b ) 41.6 seconds , c ) 40 seconds , d ) 88 seconds , e ) 19 seconds
Rationale: "speed = 45 km / hr = 45 * ( 5 / 18 ) m / sec = 25 / 2 m / sec total distance = 360 + 160 = 520 meter time = distance / speed = 520 * ( 2 / 25 ) = 41.6 seconds answer : b"
Answer: b
Question (other): the ratio of three numbers is 1 : 2 : 3 and the sum of their squares is 2016 . the sum of the numbers is ?
Options: a ) a ) 10 , b ) b ) 12 , c ) c ) 15 , d ) d ) 14 , e ) e ) 9
Rationale: "let the numbers be x , 2 x , 3 x then , x ^ 2 + 4 x ^ 2 + 9 x ^ 2 = 2016 14 x ^ 2 = 2016 x ^ 2 = 144 x = 12 answer is b"
Answer: b
Question (gain): a certain airline ' s fleet consisted of 90 type a planes at the beginning of 1980 . at the end of each year , starting with 1980 , the airline retired 3 of the type a planes and acquired 4 new type b plans . how many years did it take before the number of type a planes left in the airline ' s fleet was less than 50 percent of the fleet ?
Options: a ) 11 , b ) 12 , c ) 13 , d ) 14 , e ) 15
Rationale: "let x be the number of years . 4 x > 90 - 3 x 7 x > 90 x > 12 + 6 / 7 the answer is c ."
Answer: c
Question (gain): john makes $ 60 a week from his job . he earns a raise andnow makes $ 78 a week . what is the % increase ?
Options: a ) 16.12 % , b ) 16.66 % , c ) 30 % , d ) 17.66 % , e ) 18.1 %
Rationale: "increase = ( 18 / 60 ) * 100 = ( 3 / 10 ) * 100 = 30 % . c"
Answer: c
Question (geometry): what is the perimeter of a square field whose diagonal is 8 â ˆ š 2 ?
Options: a ) 64 m , b ) 32 m , c ) 30 m , d ) 16 m , e ) 18 m
Rationale: "explanation : a â ˆ š 2 = b â ˆ š 2 - > a = 8 4 a = 32 m answer is b"
Answer: b
Question (general): a jogger running at 9 km / hr along side a railway track is 250 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 ) 37 sec , b ) 89 sec , c ) 36 sec , d ) 87 sec , e ) 45 sec
Rationale: "speed of train relative to jogger = 45 - 9 = 36 km / hr . = 36 * 5 / 18 = 10 m / sec . distance to be covered = 250 + 120 = 370 m . time taken = 370 / 10 = 37 sec . answer : a"
Answer: a
Question (gain): find the simple interest on $ 1000 for 3 years at 10 % per annum ?
Options: a ) $ 250 , b ) $ 300 , c ) $ 500 , d ) $ 600 , e ) $ 1000
Rationale: "si = ptr / 100 = 1000 * 3 * 10 / 100 = $ 300 answer is b"
Answer: b
Question (physics): two pipes a and b can separately fill a cistern in 60 minutes and 75 minutes respectively . there is a third pipe in the bottom of the cistern to empty it . if all the three pipes are simultaneously opened , then the cistern is full in 50 minutes . in how much time , the third pipe alone can empty the cistern ?
Options: a ) 90 min , b ) 100 min , c ) 110 min , d ) 120 min , e ) 130 min
Rationale: "1 / 50 - ( 1 / 60 + 1 / 75 ) = - 1 / 100 third pipe can empty in 100 minutes answer : b"
Answer: b
Question (general): of the 20,210 employees of the anvil factory , 2 / 7 are journeymen . if half of the journeymen were laid off , what percentage of the total remaining employees would be journeymen ?
Options: a ) 14.3 % , b ) 16.67 % , c ) 33 % , d ) 28.6 % , e ) 49.67 %
Rationale: the exam gives us a number that is easily divisible by 7 to pique our curiosity and tempt us into calculating actual numbers ( also because otherwise the ratio would be incorrect ) . since the question is about percentages , the actual numbers will be meaningless , as only the ratio of that number versus others will be meaningful . nonetheless , for those who are curious , each 1 / 7 portion represents ( 14210 / 7 ) 2,030 employees . this in turn means that 4,060 employees are journeymen and the remaining 10,150 are full time workers . if half the journeymen were laid off , that would mean 1 / 7 of the total current workforce would be removed . this statistic is what leads many students to think that since half the journeymen are left , the remaining journeymen would represent half of what they used to be , which means 1 / 7 of the total workforce . if 1 / 7 of the workforce is journeymen , and 1 / 7 is roughly 14.3 % , then answer choice a should be the right answer . in this case , though , it is merely the tempting trap answer choice . what changed between the initial statement and the final tally ? well , you let go of 1 / 7 of the workforce , so the total number of workers went down . the remaining workers are still 1 / 7 of the initial workers , but the group has changed . the new workforce is smaller than the original group , specifically 6 / 7 of it because 1 / 7 was eliminated . the remaining workers now account for 1 / 7 out of 6 / 7 of the force , which if we multiply by 7 gives us 1 out of 6 . this number as a percentage is answer choice b , 49.67 % . using the absolute numbers we calculated before , there were 4,060 journeymen employees out of 14,210 total . if 2,030 of them are laid off , then there are 2,030 journeyman employees left , but now out of a total of ( 14,210 - 2,030 ) 12,180 employees . 2,030 / 12,180 is exactly 1 / 6 , or 16.67 % . the answer will work with either percentages or absolute numbers , but the percentage calculation will be significantly faster and applicable to any similar situation . the underlying principle of percentages ( and , on a related note , ratios ) can be summed up in the brainteaser i like to ask my students : if you ’ re running a race and you overtake the 2 nd place runner just before the end , what position do you end up in ? the correct answer is 2 nd place . percentages , like ratios and other concepts of relative math , depend entirely on the context . whether 100 % more of something is better than 50 % more of something else depends on the context much more than the percentages quoted . when it comes to percentages on the gmat , the goal is to understand them enough to instinctively not fall into the traps laid out for you . e
Answer: e
Question (general): if jimmy drinks 8 ounces of water each time for 8 times a day . how much gallons of water he would have to prepare ahead to drink for 5 days ? ( 1 ounce = 0.0078125 gallon )
Options: a ) 1 , b ) 1.5 , c ) 2 , d ) 2.5 , e ) 3
Rationale: 8 ounces * 8 times / day = 64 ounces of water = 64 * 0.0078125 = 0.5 gallon . 5 days need 0.5 * 5 = 2.5 gallons . correct option : 2.5 answer : d
Answer: d
Question (other): 100 people are attending a newspaper conference . 45 of them are writers and more than 36 are editors . of the people at the conference , x are both writers and editors and 2 x are neither . what is the largest possible number of people who are both writers and editors ?
Options: a ) 26 , b ) 24 , c ) 18 , d ) 20 , e ) 22
Rationale: "{ total } = { writers } + { editors } - { both } + { neither } . { total } = 100 ; { writers } = 45 ; { editors } > 38 ; { both } = x ; { neither } = 2 x ; 100 = 45 + { editors } - x + 2 x - - > x = 55 - { editors } . we want to maximize x , thus we should minimize { editors } , minimum possible value of { editors } is 37 , thus x = { both } = 55 - 37 = 18 . answer : c ."
Answer: c
Question (physics): two trains , a and b , started simultaneously from opposite ends of a 120 - mile route and traveled toward each other on parallel tracks . train a , traveling at a constant rate , completed the 120 - mile trip in 6 hours ; train b , traveling at a constant rate , completed the 120 - mile trip in 4 hours . how many miles had train a traveled when it met train b ?
Options: a ) 28 , b ) 36 , c ) 48 , d ) 50 , e ) 54
Rationale: "as the ratio of the rates of a and b is 4 to 6 then the distance covered at the time of the meeting ( so after traveling the same time interval ) would also be in that ratio , which means that x would cover 4 / ( 4 + 6 ) = 4 / 10 of 120 miles : 120 * 4 / 10 = 48 miles . answer : c ."
Answer: c
Question (gain): if a speaks the truth 55 % 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 ) 0.29 , b ) 0.33 , c ) 0.41 , d ) 0.482 , e ) 0.411
Rationale: "explanation : probability that a speaks truth is 55 / 100 = 0.55 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 ) = 0.55 × 0.6 = 0.33 answer : b"
Answer: b
Question (general): the closest approximation of ( 69.28 × 0.004 ) / 0.03 is
Options: a ) 0.092 , b ) 0.92 , c ) 9.2 , d ) 92 , e ) 920
Rationale: "( 69.28 × 0.004 ) / 0.03 1 . 0.004 = 4 × 10 ^ ( - 3 ) 2 . 0.03 = 3 × 10 ^ ( - 2 ) 3 . ( a × b ) / c = a × ( b / c ) 4 . 0.004 / 0.03 = 4 × 10 ^ ( - 3 ) / ( 3 × 10 ^ ( - 2 ) ) = 4 × 10 ^ ( - 3 - ( - 2 ) ) / 3 = 4 × 10 ^ ( - 1 ) / 3 = ( 4 / 3 ) × 10 ^ ( - 1 ) = 1.333 × 10 ^ ( - 1 ) therefore , ( 69.28 × 0.004 ) / 0.03 = 69.28 × ( 0.004 / 0.03 ) = 69.28 × 1.33 × 10 ^ ( - 1 ) = 69.28 × 1.33 / 10 = 6.928 * 1.33 now , 7 × 2 = 14 7 × 1 = 7 or better : 6.9 × 1 = 6.9 6.9 × 2 = 13.8 hence , 6.9 < 6.928 × 1.33 < 13.8 9.2 is the only answer that satisfies this condition . answer : c"
Answer: c
Question (physics): to complete a work a and b takes 8 days , b and c takes 12 days , a , b and c takes 6 days . how much time a and c will take
Options: a ) 24 days , b ) 16 days , c ) 12 days , d ) 8 days , e ) none of these
Rationale: explanation : a + b 1 day work = 1 / 8 b + c 1 day work = 1 / 12 a + b + c 1 day work = 1 / 6 we can get a work by ( a + b + c ) - ( b + c ) and c by ( a + b + c ) - ( a + b ) so a 1 day work = 1 / 6 − 1 / 12 = 1 / 12 similarly c 1 day work = 1 / 6 − 1 / 8 = 4 − 3 / 24 = 1 / 24 so a and c 1 day work = 1 / 12 + 1 / 24 = 3 / 24 = 1 / 8 so a and c can together do this work in 8 days option d
Answer: d
Question (general): 16 is divided into two parts in such a way that seventh part of first and ninth part of second are equal . find the smallest part ?
Options: a ) 14 , b ) 12 , c ) 11 , d ) 8 , e ) 7
Rationale: "x / 7 = y / 9 = > x : y = 7 : 9 7 / 16 * 16 = 7 answer : e"
Answer: e
Question (physics): maxwell leaves his home and walks toward brad ' s house . one hour later , brad leaves his home and runs toward maxwell ' s house . if the distance between their homes is 34 kilometers , maxwell ' s walking speed is 4 km / h , and brad ' s running speed is 6 km / h . what is the total time it takes maxwell before he meets up with brad ?
Options: a ) 3 , b ) 4 , c ) 5 , d ) 6 , e ) 8
Rationale: "total distance = 34 kms maxwell speed = 4 kms / hr maxwell travelled for 1 hour before brad started , therefore maxwell traveled for 4 kms in 1 hour . time taken = total distance / relative speed total distance after brad started = 30 kms relative speed ( opposite side ) ( as they are moving towards each other speed would be added ) = 6 + 4 = 10 kms / hr time taken to meet brad after brad started = 30 / 10 = 3 hrs distance traveled by maxwell = maxwell ' s speed * time taken = 4 * 3 = 12 + 4 = 16 kms . . . therefore total time taken by maxwell to meet brad = distance travelled by maxwell / maxwell ' s speed = 16 / 4 = 4 hrs . . . answer b"
Answer: b
Question (general): if log 2 x - 5 log x + 6 = 0 , then what would the value / values of x be ?
Options: a ) 5.3296 , b ) 6.3296 , c ) 7.3296 , d ) 8.3296 , e ) 9.3296
Rationale: log ( 2 x ) - 5 log ( x ) + 6 = 0 ( given ) log ( 2 x ) - log ( x ^ 5 ) = - 6 log ( 2 x / x ^ 5 ) = - 6 [ since log ( a ) - log ( b ) = log ( a / b ) ] apply anti log 2 / ( x ^ 4 ) = e ^ - 6 2 / ( x ^ 4 ) = 2.4788 * 10 ^ - 3 x ^ 4 = 806.85 x = 5.3296 answer : a
Answer: a
Question (gain): the salary of a person was reduced by 25 % . by what percent should his reduced salary be raised so as to bring it at par with his original salary ?
Options: a ) 10 % , b ) 33.33 % , c ) 20 % , d ) 25 % , e ) 50 %
Rationale: "let the original salary be $ 100 new salary = $ 75 increase on 75 = 25 increase on 100 = [ ( 25 / 75 ) 100 ] % = 33.33 % answer is b"
Answer: b
Question (physics): if a light flashes every 6 seconds , how many times will it flash in 1 / 3 of an hour ?
Options: a ) 101 , b ) 201 , c ) 301 , d ) 401 , e ) 501
Rationale: "in 1 / 3 of an hour there are 20 * 60 = 1200 seconds the number of 6 - second intervals = 1200 / 6 = 200 after the first flash , there will be 200 more flashes for a total of 201 . the answer is b ."
Answer: b
Question (general): if ( x + 1 ) ( x + 3 ) = x ^ 2 + x , what is a possible value of x ?
Options: a ) 2 , b ) 3 , c ) - 1 / 3 , d ) - 3 , e ) - 1
Rationale: rearranging the given expression : ( x + 1 ) ( x + 3 ) = x ^ 2 + x i . e . x ^ 2 + 4 x + 3 = x ^ 2 + x i . e . 3 x = - 3 i . e . x = - 3 / 3 = - 1 answer : option e had it been a difficult expression to solve further , then we could have used options to check which one satisfies the expression after solving it as further as possible .
Answer: e
Question (gain): a company recently conducted a survey and found that 20,000 of its customers live in rural areas . if the number of customers who live in urban areas is 100 percent greater than the number of customers who live in rural areas , how many customers live in urban areas ?
Options: a ) 40,000 , b ) 45,000 , c ) 50,000 , d ) 55,000 , e ) 60,000
Rationale: "the number of customers in urban areas is 20,000 + 1 * 20,000 = 40,000 . the answer is a ."
Answer: a
Question (general): as a treat for her two children , a mother runs to the freezer in which she has 3 cherry ice pops , 4 orange ice pops , and 4 lemon ice pops . she chooses two at random to bring outside to the children , but realizes as she runs out the door that she can not bring them different flavors without one being jealous of the other and getting even more upset . what is the probability that she has to return to the freezer to make sure that they each receive the same flavor ?
Options: a ) 3 / 5 , b ) 5 / 7 , c ) 8 / 11 , d ) 11 / 15 , e ) 13 / 20
Rationale: p ( 2 cherry ) = 3 / 11 * 2 / 10 = 6 / 110 p ( 2 orange ) = 4 / 11 * 3 / 10 = 12 / 110 p ( 2 lemon ) = 4 / 11 * 3 / 10 = 12 / 110 p ( 2 of the same flavor ) = 30 / 110 p ( 2 different flavors ) = 1 - 30 / 110 = 80 / 110 = 8 / 11 the answer is c .
Answer: c
Question (physics): john traveled 80 % of the way from yellow - town to green - fields by train at an average speed of 80 miles per hour . the rest of the way john traveled by car at an average speed of v miles per hour . if the average speed for the entire trip was 70 miles per hour , what is v in miles per hour ?
Options: a ) 30 , b ) 40 , c ) 50 , d ) 55 , e ) 60
Rationale: "hibunuel the question seems incorrect . it should not be 80 % at the speed of 80 . however if it ' s 20 % at the speed of 80 , answer comes out 55 . the question is correct . here ' s the explanation : let distance be d . we can find the total timeequate it , which comes as : 0.8 d / 80 + 0.2 d / v = d / 70 = > v = 60 ( option e ) ."
Answer: e
Question (physics): a rectangular plot measuring 90 metres by 50 metres is to be enclosed by wire fencing . if the poles of the fence are kept 10 metres apart , how many poles will be needed ?
Options: a ) 28 , b ) 56 , c ) 57 , d ) 58 , e ) none of these
Rationale: "solution perimeter of the plot = 2 ( 90 + 50 ) = 280 m . ∴ number of poles = [ 280 / 10 ] = 28 m answer a"
Answer: a