Cheukting/mathqa huggingface dataset:
Question (general): working simultaneously and independently at an identical constant rate , 4 machines of a certain type can produce a total of x units of product p in 6 days . how many of these machines , working simultaneously and independently at this constant rate , can produce a total of 3 x units of product p in 6 days ?
Options: a ) 24 , b ) 18 , c ) 16 , d ) 12 , e ) 8
Rationale: "4 machines do x units in 6 days we have x / 6 = > rate of the 4 machines we know that we need to have 4 x units in 6 days therefore , we need to get to 4 x / 6 rate of the machines . rate of one machine is x / 6 * 1 / 4 = x / 24 . now , we need to know how many machines need to work simultaneously , to get 3 x done in 6 days . 3 x / 6 work needs to be done by machines that work at x / 24 rate . let ' s assign a constant y for the number of machines : ( x / 24 ) * y = 3 x / 6 y = 3 x / 6 * 24 / x cancel 6 with 24 , and x with x and get - > 12 . answer choice d"
Answer: d
Question (other): how many factors of 270 are odd numbers greater than 1 ?
Options: a ) 3 , b ) 4 , c ) 5 , d ) 6 , e ) 9
Rationale: "prime factors of 810 are 2 ^ 1,3 ^ 4,5 ^ 1 total divisors = ( power if a prime factor + 1 ) total no . of odd factors ( 3,5 , ) = ( 4 + 1 ) ( 1 + 1 ) = 10 since we need odd divisors other than 1 = > 10 - 1 = 9 odd divisors e is the answer"
Answer: e
Question (general): a batsman in his 12 th innings makes a score of 65 and thereby increases his average by 2 runs . what is his average after the 12 th innings if he had never been ‘ not out ’ ?
Options: a ) 42 , b ) 43 , c ) 44 , d ) 45 , e ) 46
Rationale: "let ‘ x ’ be the average score after 12 th innings ⇒ 12 x = 11 × ( x – 2 ) + 65 ∴ x = 43 answer b"
Answer: b
Question (general): what is the unit digit in 7 ^ 105
Options: a ) 7 , b ) 0 , c ) 2 , d ) 3 , e ) 5
Rationale: "explanation : unit digit in 7 ^ 105 = unit digit in [ ( 7 ^ 4 ) 26 x 7 ] but , unit digit in ( 7 ^ 4 ) 26 = 1 unit digit in 7105 = ( 1 x 7 ) = 7 a"
Answer: a
Question (general): if the number is decreased by 5 and divided by 7 the result is 7 . what would be the result if 14 is subtracted and divided by 10 ?
Options: a ) 4 , b ) 7 , c ) 8 , d ) 5 , e ) 3
Rationale: "explanation : let the number be x . then , ( x - 5 ) / 7 = 7 = > x - 5 = 49 x = 54 . : ( x - 14 ) / 10 = ( 54 - 14 ) / 10 = 4 answer : option a"
Answer: a
Question (general): when the number 1 y 92355 is exactly divisible by 11 , then the smallest whole number in place of y is ?
Options: a ) 1 , b ) 3 , c ) 7 , d ) 9 , e ) 0
Rationale: the given number = 1 y 92355 sum of the odd places = 5 + 3 + 9 + 1 = 18 sum of the even places = 5 + 2 + y ( sum of the odd places ) - ( sum of even places ) = number ( exactly divisible by 11 ) 18 - ( 7 + y ) = divisible by 11 11 � y = divisible by 11 . y must be 0 , to make given number divisible by 11 . e
Answer: e
Question (physics): how many liters of oil at rs . 40 per liter should be mixed with 240 liters of a second variety of oil at rs . 60 per liter so as to get a mixture whose cost is rs . 52 per liter ?
Options: a ) 120 , b ) 150 , c ) 160 , d ) 180 , e ) 200
Rationale: 8 : 12 = 2 : 3 if 240 lrs of the 2 nd variety taken then the 1 st variety should be taken as 160 lr answer c
Answer: c
Question (general): if w / x = 1 / 3 and w / y = 2 / 3 , then ( x + y ) / y =
Options: a ) 2 , b ) 4 , c ) 5 , d ) 3 , e ) 7
Rationale: "ratio 1 : 3 w = x ratio 2 : 3 w = 2 y x = 2 y ( x + y ) / y = ( 2 y + y ) / y = y ( 2 + 1 ) / y = 3 answer is d"
Answer: d
Question (physics): two trains running in opposite directions cross a man standing on the platform in 25 seconds and 18 seconds respectively and they cross each other in 20 seconds . the ratio of their speeds is :
Options: a ) 3 : 1 , b ) 3 : 2 , c ) 3 : 8 , d ) 2 : 5 , e ) 3 : 4
Rationale: "let the speeds of the two trains be x m / sec and y m / sec respectively . then , length of the first train = 25 x meters , and length of the second train = 18 y meters . ( 25 x + 18 y ) / ( x + y ) = 20 = = > 25 x + 18 y = 20 x + 20 y = = > 5 x = 2 y = = > x / y = 2 / 5 answer : option d"
Answer: d
Question (general): in how many no . between 100 and 1000 at least one of their digits is 7 ?
Options: a ) 900 , b ) 648 , c ) 720 , d ) 252 , e ) 729
Rationale: "let ' s count the number of occurrences with only one 7 : ( 1 ) 7 xx : 1 * 9 * 9 = 81 ( 2 ) x 7 x : 8 * 1 * 9 = 72 ( 3 ) xx 7 : 8 * 9 * 1 = 72 81 + 72 + 72 = 225 at this point we can already see that the answer must be d since the choice are very dispersed . anyways , let ' s count number of occurrences with two 7 s : ( 1 ) 77 x : 1 * 1 * 9 = 9 ( 2 ) x 77 : 8 * 1 * 1 = 8 ( 3 ) 7 x 7 : 1 * 9 * 1 = 9 9 + 8 + 9 = 26 number 777 is missing . so the total becomes 225 + 26 + 1 = 252 d is the correct answer ."
Answer: d
Question (gain): the charge for a single room at hotel p is 25 percent less than the charge for a single room at hotel r and 10 percent less than the charge for a single room at hotel g . the charge for a single room at hotel r is what percent greater than the charge for a single room at hotel g ?
Options: a ) 15 % , b ) 20 % , c ) 40 % , d ) 50 % , e ) 150 %
Rationale: "let rate in r = 100 x then p = 75 x g = 100 y p = 90 y thus 75 x = 90 y or x = 1.20 y ans r = 120 y so increase = 20 % answer : b ."
Answer: b
Question (general): farm tax is levied on the 60 % of the cultivated land . the tax department collected total $ 4000 through the farm tax from the village of mr . willam . mr . willam paid only $ 500 as farm tax . the percentage of total land of mr . willam over the total taxable land of the village is :
Options: a ) 15 % , b ) 25 % , c ) 12.5 % , d ) 20.83 % , e ) none
Rationale: "only trick n this question is to ignore 60 % information as farm tax is levied uniformly in the village and that includes mr william ' s land . what percentage of tax mr william paid ? this will be equal to the percentage of total cultivated land he holds over the total cultivated land in the village . that leads to ( 500 / 4000 ) x 100 = 12.5 % in percentage terms . but the question asks ratio between his total land to total cultivated land . hence the answer is 12.5 % x ( 100 / 60 ) = 20.833 % and the answer is not there in the options . the correct answer is ( d ) ."
Answer: d
Question (gain): the s . i . on a certain sum of money for 2 years at 6 % per annum is half the c . i . on rs . 4000 for 2 years at 10 % per annum . the sum placed on s . i . is ?
Options: a ) 2197 , b ) 1267 , c ) 3500 , d ) 2267 , e ) 1262
Rationale: "explanation : c . i . = [ 4000 * ( 1 + 10 / 100 ) 2 - 4000 ] = ( 4000 * 11 / 10 * 11 / 10 - 4000 ) = rs . 840 . sum = ( 420 * 100 ) / ( 2 * 6 ) = rs . 3500 answer : c"
Answer: c
Question (general): the avg weight of a , b & c is 60 kg . if d joins the group , the avg weight of the group becomes 65 kg . if another man e who weights is 3 kg more than d replaces a , then the avgof b , c , d & e becomes 64 kg . what is the weight of a ?
Options: a ) 56 , b ) 65 , c ) 75 , d ) 89 , e ) 87
Rationale: "a + b + c = 3 * 60 = 180 a + b + c + d = 4 * 65 = 260 - - - - ( i ) so , d = 80 & e = 80 + 3 = 83 b + c + d + e = 64 * 4 = 256 - - - ( ii ) from eq . ( i ) & ( ii ) a - e = 260 – 256 = 4 a = e + 4 = 83 + 4 = 87 answer : e"
Answer: e
Question (gain): a reduction of 40 % in the price of bananas would enable a man to obtain 66 more for rs . 40 , what is reduced price per dozen ?
Options: a ) 1.91 , b ) 2.91 , c ) 4.91 , d ) 3.91 , e ) 5.91
Rationale: "40 * ( 40 / 100 ) = 16 - - - 66 ? - - - 12 = > rs . 2.91 answer : b"
Answer: b
Question (general): a car travels uphill at 30 km / hr and downhill at 80 km / hr . it goes 100 km uphill and 50 km downhill . find the average speed of the car ?
Options: a ) 38 kmph , b ) 33 kmph , c ) 34 kmph , d ) 35 kmph , e ) 36 kmph
Rationale: "avg speed = total distance / total time . total distance traveled = 100 + 50 = 150 km ; time taken for uphill journey = 100 / 30 = 10 / 3 ; time taken for down hill journey = 50 / 80 = 5 / 8 ; avg speed = 150 / ( 10 / 3 + 5 / 8 ) = 38 kmph answer : a"
Answer: a
Question (physics): convert the 8 / 26 m / s into kilometers per hour ?
Options: a ) 3.5 kmph . , b ) 2.5 kmph . , c ) 1.2 kmph . , d ) 1.1 kmph . , e ) 1.9 kmph .
Rationale: "8 / 26 m / s = 8 / 26 * 18 / 5 = 1 ( 1 / 10 ) = 1.1 kmph . answer : d"
Answer: d
Question (probability): jane and thomas are among the 7 people from which a committee of 4 people is to be selected . how many different possible committees of 4 people can be selected from these 7 people if at least one of either jane or thomas is to be selected ?
Options: a ) 30 , b ) 45 , c ) 55 , d ) 65 , e ) 70
Rationale: "the total number of ways to choose 4 people from 7 is 7 c 4 = 35 . the number of committees without jane or thomas is 5 c 4 = 5 . there are 35 - 5 = 30 possible committees which include jane and / or thomas . the answer is a ."
Answer: a
Question (general): jack , jill , and sandy each have one try to make a basket from half court . if their individual probabilities of making the basket are 1 / 6 , 1 / 7 , and 1 / 8 respectively , what is the probability that jack and jill will make a basket but sandy will miss ?
Options: a ) 1 / 8 , b ) 1 / 16 , c ) 1 / 48 , d ) 1 / 96 , e ) 1 / 168
Rationale: "the probability that jack and jill will make a basket but sandy will miss is 1 / 6 * 1 / 7 * 7 / 8 = 1 / 48 . the answer is c ."
Answer: c
Question (gain): you hold some gold in a vault as an investment . over the past year the price of gold increases by 42 % . in order to keep your gold in the vault , you must pay 4 % of the total value of the gold per year . what percentage has the value of your holdings changed by over the past year .
Options: a ) 38 % , b ) 46 % , c ) 47.68 % , d ) 44.32 % , e ) 36.32 %
Rationale: "( 100 % + 42 % ) * ( 100 % - 4 % ) = 1.42 * 0.96 = 136.32 % an increase of 36.32 % your gold holdings have increased in value by 36.32 % . the answer is e"
Answer: e
Question (gain): calculate how many seconds it eill take for 4 bells to toll together again , given that they begin to toll together respectively at the intervals of 2 , 5 , 8 and 11 seconds . ?
Options: a ) 440 , b ) 420 , c ) 410 , d ) 442 , e ) 422
Rationale: "lcm of 2 , 5 , 8 and 11 is 440 lcm = 440 answer : a"
Answer: a
Question (general): the sum of the ages of 5 children born at the intervals of 1 year each is 50 years . what is the age of the youngest child ?
Options: a ) 22 , b ) 8 , c ) 10 , d ) 99 , e ) 38
Rationale: "let x = the youngest child . each of the other four children will then be x + 1 , x + 2 , x + 3 , x + 4 . we know that the sum of their ages is 50 . so , x + ( x + 1 ) + ( x + 2 ) + ( x + 3 ) + ( x + 4 ) = 50 therefore the youngest child is 8 years old answer : b"
Answer: b
Question (general): if 15 machine can finish a job in 36 days , then how many more machines would be needed to finish the job in one - fourth less time ?
Options: a ) a . 5 , b ) b . 8 , c ) c . 10 , d ) d . 12 , e ) e . 16
Rationale: "you might think of this in a management context - we can use the principle of ' person - hours ' to solve any problem where we have identical workers . so , using simpler numbers , suppose you know that 6 identical employees , working simultaneously , would finish a job in 5 hours . then that job requires 6 * 5 = 30 total hours of person - work . if instead you wanted the job done in 3 hours , you ' d assign 30 / 3 = 10 employees to do the job , because you want to get a total of 30 hours of work from the employees . we can solve this problem identically . if 15 machines ( identical ones , i assume ) work simultaneously for 36 days , they will do a total of 15 * 36 machine - days of work . so the job requires 15 * 36 days of machine work in total . we instead want the job done in 1 / 4 less time , so in 27 days . so we ' ll need 15 * 36 / 27 = 20 machines , or 5 additional machines . a"
Answer: a
Question (general): if a randomly selected non - negative single digit integer is added to { 2 , 3 , 6 , 8 } . what is the probability that the median of the set will increase but the range still remains the same ?
Options: a ) 0.2 , b ) 0.3 , c ) 0.4 , d ) 0.5 , e ) 0.6
Rationale: "we are selecting from non - negative single digit integers , so from { 0 , 1 , 2 , 3 , 4 , 5 , 6 , 7 , 8 , 9 } . these 10 digits represent the total number of outcomes . hence , the total number of outcomes is 10 . we need to find the probability that the median of the set will increase but the range still remains the same . the median of the set is ( 3 + 6 ) / 2 = 4.5 , thus the number selected must be 5 or greater . for the range to remain the same , the number must be between 2 and 8 inclusive . to satisfy both conditions , the number selected must be 5 , 6 , 7 , or 8 . the probability is 4 / 10 = 0.4 the answer is c ."
Answer: c
Question (physics): in what time will a train 140 m long cross an electric pole , it its speed be 108 km / hr ?
Options: a ) 2.5 , b ) 4.7 , c ) 2.9 , d ) 2.3 , e ) 2.1
Rationale: "speed = 108 * 5 / 18 = 30 m / sec time taken = 140 / 30 = 4.7 sec . answer : b"
Answer: b
Question (physics): a small water pump would take 2 hours to fill an empty tank . a larger pump would take 1 / 3 hour to fill the same tank . how many hours would it take both pumps , working at their respective constant rates , to fill the empty tank if they began pumping at the same time ?
Options: a ) 3 / 7 , b ) 2 / 7 , c ) 1 / 4 , d ) 2 / 3 , e ) 5 / 7
Rationale: "rate of the small pump is 1 / 2 tank / hour rate of the larger pump is 1 / ( 1 / 3 ) or 3 tank / hour ; combined rate of the two pumps is 1 / 2 + 3 = 7 / 2 tank / hour , together they will fill the empty tank in 1 / ( 7 / 2 ) = 2 / 7 hours ( time = job / rate ) . answer : b"
Answer: b
Question (gain): in a certain company 20 % of the men and 40 % of the women attended the annual company picnic . if 45 % of all the employees are men . what % of all the employee went to the picnic ?
Options: a ) 31 % , b ) 34 % , c ) 35 % , d ) 36 % , e ) 37 %
Rationale: "total men in company 45 % means total women in company 55 % ( assume total people in company 100 % ) no of men employees attended picnic = 45 x ( 20 / 100 ) = 9 no of women employees attend picnic = 55 x ( 40 / 100 ) = 22 total percentage of employees attend the picnic = 9 + 22 = 31 % answer : a"
Answer: a
Question (other): the ratio by weight , measured in pounds , of books to clothes to electronics in a suitcase initially stands at 5 : 4 : 2 . someone removes 7 pounds of clothing from the suitcase , thereby doubling the ratio of books to clothes . how many pounds do the electronics in the suitcase weigh ?
Options: a ) 6 , b ) 7 , c ) 8 , d ) 9 , e ) 10
Rationale: "the weights of the items in the suitcase are 5 k , 4 k , and 2 k . if removing 7 pounds of clothes doubles the ratio of books to clothes , then 7 pounds represents half the weight of the clothes . 2 k = 7 pounds and then k = 3.5 pounds . the electronics weigh 2 ( 3.5 ) = 7 pounds . the answer is b ."
Answer: b
Question (gain): martin bought 10 concert tickets , some at the full price of $ 2.00 per ticket , and some at a discounted price of $ 1.60 per ticket . if he spent a total of $ 17.20 , how many discounted tickets did he buy ?
Options: a ) 3 , b ) 4 , c ) 5 , d ) 6 , e ) 7
Rationale: "let x be the number of tickets he bought at $ 2 per ticket . then 2 x + ( 10 - x ) 1.6 = 17.2 0.4 x = 1.2 = > x = 3 discounted tickets = 10 - x = 7 ans : e"
Answer: e
Question (general): if 625 ^ ( - x ) + 25 ^ ( - 2 x ) + 5 ^ ( - 4 x ) = 10 , 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 . c"
Answer: c
Question (general): if a # b = ab – b + b ^ 2 , then 2 # 3 =
Options: a ) 2 , b ) 8 , c ) 12 , d ) 21 , e ) 35
Rationale: "solution - simply substitute 2 and 3 in equation in the place of a and b respectively . 2 # 3 = 2 * 3 - 3 + 3 ^ 2 = 6 - 3 + 9 = 12 . ans c"
Answer: c
Question (general): andy solves problems 70 to 125 inclusive in a math exercise . how many problems does he solve ?
Options: a ) 56 , b ) 52 , c ) 51 , d ) 50 , e ) 49
Rationale: 125 - 70 + 1 = 56 ' a ' is the answer
Answer: a
Question (other): share rs . 4200 among john , jose & binoy in the ration 2 : 4 : 6 . find the amount received by john ?
Options: a ) 900 , b ) 980 , c ) 1200 , d ) 1240 , e ) 1400
Rationale: "amount received by sanjay . 4 / 12 x 4200 = 1400 = ( related ratio / sum of ratio ) x total amount so , the amount received by sanjay is 1400 . e"
Answer: e
Question (general): if k is a non - negative integer and 21 ^ k is a divisor of 435,961 then 7 ^ k - k ^ 7 =
Options: a ) 0 , b ) 1 , c ) 42 , d ) 118 , e ) 242
Rationale: "4 + 3 + 5 + 9 + 6 + 1 = 28 , so this number is not divisible by 3 and thus not divisible by 21 . therefore , k = 0 7 ^ k - k ^ 7 = 1 - 0 = 1 the answer is b ."
Answer: b
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 60 kilometers , maxwell ' s walking speed is 4 km / h , and brad ' s running speed is 6 km / h , what is the distance traveled by brad ?
Options: a ) 16 , b ) 36 , c ) 20 , d ) 24 , e ) 30
Rationale: "time taken = total distance / relative speed total distance = 60 kms relative speed ( opposite side ) ( as they are moving towards each other speed would be added ) = 6 + 4 = 10 kms / hr time taken = 60 / 10 = 6 hrs distance traveled by brad = brad ' s speed * time taken = 6 * 6 = 36 kms . . . answer - b"
Answer: b
Question (physics): a train 90 meters long completely crosses a 200 meters long bridge in 36 seconds . what is the speed of the train is ?
Options: a ) 29 , b ) 40 , c ) 25 , d ) 66 , e ) 09
Rationale: "s = ( 90 + 200 ) / 36 = 290 / 36 * 18 / 5 = 29 answer : a"
Answer: a
Question (geometry): a circular plate with a diameter of 10 inches is kept on another plate of 12 inches diameter . what fraction of the big plate ' s surface is not covered by the small plate ?
Options: a ) 11 / 36
b ) 23 / 10
c ) 5 / 14
d ) 22 / 11
e ) 3 / 4
Rationale: the questions asks us to find the surface which is not covered by the plate i . e . , area of the surface not covered . where as circumference is the length along the edge of the circle , 2 * pi * r implies the length of the curve pi * r ^ 2 implies area enclosed by that curve . . hence area of the circle is considered for this problem area of the big plate = pi * r ^ 2 , where r = 6 = > pi * 36 area of the small plate = pi * 25 surface not covered by the plate = pi * 36 - pi * 25 = pi * 11 fraction of big plate ' s surface is not covered by small plate = pi * 11 / total area of the big plate = > pi * 11 / pi * 36 answer a
Answer: a
Question (physics): a contractor undertakes to do a job within 100 days and hires 10 people to do it . after 20 days , he realizes that one fourth of the work is done so he fires 2 people . in how many more days b will the work get over ?
Options: a ) 60 , b ) 70 , c ) b = 75 , d ) b = 80 , e ) 100
Rationale: "we can also use the concept of man - days here 100 days - - > 10 men so the job includes 100 * 10 = 1000 man - days after 20 days 1 / 4 of job is completed so 1 / 4 x 1000 man - days = 250 man - days job is done now the balance job = 1000 - 250 = 750 man - days worth of job since 2 men are fired so b / l men = 8 therefore total no . of days of job = 750 man - day / 8 days = 375 / 4 = 94 days ( approx . ) now since this is total and ques . is asking for additional no . of days , so 94 - 20 = 74 days the nearest approx . to answer is 75 ans : c ( 75 days )"
Answer: c
Question (gain): if the cost price is 25 % of selling price . then what is the profit percent
Options: a ) 238 , b ) 278 , c ) 300 , d ) 166 , e ) 129
Rationale: "explanation : let the s . p = 100 then c . p . = 25 profit = 75 profit % = ( 75 / 25 ) * 100 = 300 % answer : c"
Answer: c
Question (physics): a man rows downstream 32 km and 14 km upstream . if he takes 6 hours to cover each distance , then the velocity ( in kmph ) of the current is :
Options: a ) 1.5 kmph , b ) 1.75 kmph , c ) 2 kmph , d ) 3 kmph , e ) none
Rationale: sol . rate downstream = [ 32 / 6 ] kmph ; rate upstream = [ 14 / 6 ] kmph . ∴ velocity of current = 1 / 2 [ 32 / 6 - 14 / 6 ] kmph = 3 / 2 kmph = 1.5 kmph . answer a
Answer: a
Question (general): the average weight of 10 person ' s increases by 4 kg when a new person comes in place of one of them weighing 70 kg . what is the weight of the new person ?
Options: a ) 85 , b ) 86.5 , c ) 90 , d ) 88.5 , e ) 110
Rationale: "total increase in weight = 10 x 4 = 40 if x is the weight of the new person , total increase in weight = x − 70 = > 40 = x - 70 = > x = 40 + 70 = 110 answer : e"
Answer: e
Question (gain): the price of rice falls by 20 % . how much rice can be bought now with the money that was sufficient to buy 20 kg of rice previously ?
Options: a ) 5 kg , b ) 15 kg , c ) 25 kg , d ) 30 kg , e ) none
Rationale: "solution : let rs . 100 be spend on rice initially for 20 kg . as the price falls by 20 % , new price for 20 kg rice , = ( 100 - 20 % of 100 ) = 80 new price of rice = 80 / 20 = rs . 4 per kg . rice can bought now at = 100 / 4 = 25 kg . answer : option c"
Answer: c
Question (physics): a boat takes 90 minutes less to travel 36 miles downstream than to travel the same distance upstream . if the speed of the boat in still water is 10 mph , the speed of the stream is
Options: a ) 2 mph , b ) 2.5 mph , c ) 3 mph , d ) 4 mph , e ) none
Rationale: "solution speed downstreams = ( 10 + x ) mph . speed upstreams = ( 10 - x ) mph . = 18 kmph . 36 / ( 10 - x ) - 36 / ( 10 + x ) = 90 / 60 = 72 x × 60 = 90 ( 100 - x ² ) x ² + 48 x + 100 = 0 . x = 2 mph . answer a"
Answer: a
Question (general): if 2 + 3 = 10 ; 2 + 5 = 27 ; 2 + 7 = 53 then 2 + 11 = ?
Options: a ) 124 , b ) 129 , c ) 128 , d ) 125 , e ) 120
Rationale: "2 ^ 0 + 3 ^ 2 = 1 + 9 = 10 2 ^ 1 + 5 ^ 2 = 2 + 25 = 27 2 ^ 2 + 7 ^ 2 = 4 + 49 = 53 and 2 ^ 3 + 11 ^ 2 = 8 + 121 = 129 answer : b"
Answer: b
Question (geometry): if the sides of a cube are in the ratio 7 : 3 . what is the ratio of their diagonals ?
Options: a ) 9 : 4 , b ) 8 : 4 , c ) 7 : 4 , d ) 7 : 3 , e ) 6 : 4
Rationale: "explanation : diagonal of a cube = a √ 3 where a is side a 1 : a 2 = 7 : 3 d 1 : d 2 = 7 : 3 where √ 3 cancelled both side answer : d"
Answer: d
Question (physics): the sum of two consecutive integers is 31 . find the numbers .
Options: a ) 17 , 18 , b ) 7 , 8 , c ) 15 , 16 , d ) 1 , 2 , e ) 8 , 9
Rationale: "n + ( n + 1 ) = 31 2 n + 1 = 31 2 n = 30 n = 15 answer : c"
Answer: c
Question (general): the average of 4 consecutive odd numbers is 24 . find the largest number
Options: a ) 25 , b ) 27 , c ) 29 , d ) 31 , e ) 32
Rationale: explanation : let the numbers are x , x + 2 , x + 4 , x + 6 , then = > x + ( x + 2 ) + ( x + 4 ) + ( x + 6 ) / 4 = 24 = > 4 x + 12 ) / 4 = 24 = > x + 3 = 24 = > x = 21 so largest number is 21 + 6 = 27 option b
Answer: b
Question (general): what is the smallest integer that is multiple of 8,7 and 20
Options: a ) 141 , b ) 180 , c ) 130 , d ) 122 , e ) 280
Rationale: correct answer : e it is the lcm of 8,7 and 20 which is 280
Answer: e