Cheukting/mathqa huggingface dataset:
Question (geometry): a clock hangs on the wall of a railway station , 71 ft 9 in long and 10 ft 4 in high . those are the dimension of the wall , not the clock ! while waiting for a train we noticed that the hands of the clock were pointing in opposite directions , and were parallel to one of the diagonals of the wall , what was the exact time ?
Options: a ) 7 : 15
b ) 7 : 5
c ) 7 : 25
d ) 7 : 45
e ) 7 : 55
Rationale: it can have four possiblities time could be 7 : 5 1 : 35 11 : 25 5 : 55 answer : b
Answer: b
Question (gain): how much 60 % of 50 is greater than 40 % of 30 ?
Options: a ) 18 , b ) 28 , c ) 26 , d ) 27 , e ) 23
Rationale: "( 60 / 100 ) * 50 – ( 40 / 100 ) * 30 30 - 12 = 18 answer : a"
Answer: a
Question (general): you and your friend spent a total of $ 19 for lunch . your friend spent $ 3 more than you . how much did your friend spend on their lunch ?
Options: a ) $ 9 , b ) $ 3 , c ) $ 4 , d ) $ 6 , e ) $ 11
Rationale: my lunch = l , my friends lunch = l + 3 ( l ) + ( l + 3 ) = 19 l + l + 3 - 3 = 19 - 3 2 l = 16 l = 8 my friends lunch l + 3 = 8 + 3 = $ 11 , the answer is e
Answer: e
Question (gain): by selling 90 pens , a trader gains the cost of 30 pens . find his gain percentage ?
Options: a ) 33.3 % , b ) 32.3 % , c ) 31.3 % , d ) 30.3 % , e ) 29.3 %
Rationale: "let the cp of each pen be rs . 1 . cp of 90 pens = rs . 90 profit = cost of 30 pens = rs . 30 profit % = 30 / 90 * 100 = 33.3 % answer : a"
Answer: a
Question (physics): a cistern is normally filled in 2 hrs , but takes 2 hrs longer to fill because of a leak on its bottom , if cistern is full , how much time citern would empty ?
Options: a ) 4 hours , b ) 20 hours , c ) 30 hours , d ) 40 hours , e ) 50 hours
Rationale: "if leakage / hour = 1 / x , then 1 / 2 - 1 / x = 1 / 4 , solving 1 / x = 1 / 4 so in 4 hours full cistern will be empty . answer : a"
Answer: a
Question (physics): two trains of length 100 m and 200 m are 100 m apart . they start moving towards each other on parallel tracks , at speeds 54 kmph and 72 kmph . in how much time will the trains cross each other ?
Options: a ) 70 / 7 sec , b ) 80 / 7 sec , c ) 40 / 7 sec , d ) 60 / 7 sec , e ) 90 / 7 sec
Rationale: "b relative speed = ( 54 + 72 ) * 5 / 18 = 7 * 5 = 35 mps . the time required = d / s = ( 100 + 100 + 200 ) / 35 = 400 / 35 = 80 / 7 sec ."
Answer: b
Question (gain): effective annual rate of interest corresponding to nominal rate of 6 % per annum compounded half yearly will be
Options: a ) 6.09 % , b ) 6.10 % , c ) 6.12 % , d ) 6.14 % , e ) none of these
Rationale: explanation : let the amount rs 100 for 1 year when compounded half yearly , n = 2 , rate = 6 / 2 = 3 % amount = 100 ( 1 + 3 / 100 ) 2 = 106.09 effective rate = ( 106.09 - 100 ) % = 6.09 % option a
Answer: a
Question (gain): in a certain business school class , p students are accounting majors , q students are finance majors , r students are marketing majors , and s students are strategy majors . if pqrs = 1365 , and if 1 < p < q < r < s , how many students in the class are finance majors ?
Options: a ) 3 , b ) 5 , c ) 8 , d ) 11 , e ) 17
Rationale: "pqrs = 1365 = 3 * 5 * 7 * 13 since 1 < p < q < r < s , the number of students who are finance majors is q = 5 . the answer is b ."
Answer: b
Question (physics): a train 500 m long is running at a speed of 78 km / hr . if it crosses a tunnel in 1 min , then the length of the tunnel is ?
Options: a ) 298 m , b ) 300 m , c ) 800 m , d ) 967 m , e ) 1181 m
Rationale: "speed = 78 * 5 / 18 = 65 / 3 m / sec . time = 1 min = 60 sec . let the length of the train be x meters . then , ( 500 + x ) / 60 = 65 / 3 x = 800 m . answer : c"
Answer: c
Question (general): the average age of 3 men is increased by years when two of them whose ages are 21 years and 23 years are replaced by two new men . the average age of the two new men is
Options: a ) 22 , b ) 30 , c ) 25 , d ) 38 , e ) 27
Rationale: "total age increased = ( 3 * 2 ) years = 6 years . sum of ages of two new men = ( 21 + 23 + 6 ) years = 50 years average age of two new men = ( 50 / 2 ) years = 25 years . answer : c"
Answer: c
Question (geometry): points a , b , and , c have xy - coordinates ( 2,0 ) , ( 8,12 ) , and ( 14,0 ) , respectively . points x , y , and z have xy - coordinates ( 6,0 ) , ( 8,4 ) , and ( 10,0 ) , respectively . what fraction s of the area of triangle abc is the area of triangle xyz ?
Options: a ) 1 / 9 , b ) 1 / 8 , c ) 1 / 6 , d ) 1 / 5 , e ) 1 / 3
Rationale: "if you notice , both triangles abc and xyz have a side on x axis . we can take these sides as bases for each triangle , therefore area of abc is 1 / 2 * 12 * 12 ( height of abc is the y coordinate of the third point ( 8,12 ) ) similarly area of xyz is 1 / 2 * 4 * 4 dividing area of xyz with that of abc gives s = 1 / 9 . a"
Answer: a
Question (physics): a van takes 6 hours to cover a distance of 270 km . how much should the speed in kmph be maintained to cover the same direction in 3 / 2 th of the previous time ?
Options: a ) 50 kmph , b ) 30 kmph , c ) 70 kmph , d ) 80 kmph , e ) 90 kmph
Rationale: "time = 6 distence = 270 3 / 2 of 6 hours = 6 * 3 / 2 = 9 hours required speed = 270 / 9 = 30 kmph b"
Answer: b
Question (physics): working together , printer a and printer b would finish the task in 40 minutes . printer a alone would finish the task in 60 minutes . how many pages does the task contain if printer b prints 4 pages a minute more than printer a ?
Options: a ) 250 , b ) 375 , c ) 450 , d ) 480 , e ) 500
Rationale: 40 * a + 40 * b = x pages in 40 mins printer a will print = 40 / 60 * x pages = 2 / 3 * x pages thus in 40 mins printer printer b will print x - 2 / 3 * x = 1 / 3 * x pages also it is given that printer b prints 4 more pages per min that printer a . in 40 mins printer b will print 160 more pages than printer a thus 2 / 3 * x - 1 / 3 * x = 160 = > x = 480 pages answer : d
Answer: d
Question (physics): if 36 men do a work in 70 days , in how many days will 40 men do it ?
Options: a ) 64 , b ) 63 , c ) 65 , d ) 66 , e ) 67
Rationale: "36 * 70 = 40 * x x = 63 days answer : b"
Answer: b
Question (general): last year , for every 100 million vehicles that traveled on a certain highway , 75 vehicles were involved in accidents . if 6 billion vehicles traveled on the highway last year , how many of those vehicles were involved in accidents ? ( 1 billion = 1,000 , 000,000 )
Options: a ) 2500 , b ) 4500 , c ) 3500 , d ) 4000 , e ) 1300
Rationale: "to solve we will set up a proportion . we know that “ 100 million vehicles is to 75 accidents as 6 billion vehicles is to x accidents ” . to express everything in terms of “ millions ” , we can use 6,000 million rather than 6 billion . creating a proportion we have : 100 / 75 = 6,000 / x cross multiplying gives us : 100 x = 6,000 * 75 x = 60 * 75 = 4500 answer : b"
Answer: b
Question (gain): on a certain road , 10 % of the motorists exceed the posted speed limit and receive speeding tickets , but 60 % of the motorists who exceed the posted speed limit do not receive speeding tickets . what percent of the motorists on that road exceed the posted speed limit ?
Options: a ) 10.5 % , b ) 12.5 % , c ) 15 % , d ) 25 % , e ) 30 %
Rationale: "suppose there are x motorists . 10 % of them exceeded the speed limit and received the ticket , i . e . x / 10 . again , suppose total no . of motorists who exceeded the speed limit are y . 60 % of y exceeded the speed limit but did n ' t received the ticket , i . e . 3 y / 5 . it means 2 y / 5 received the ticket . hence , 2 y / 5 = x / 10 or y / x = 1 / 4 or y / x * 100 = 1 / 4 * 100 = 25 % d"
Answer: d
Question (physics): a and b can do a piece of work in 48 days , a and c can do it in 60 days , b and c can do it 72 days . in what time can c alone do it ?
Options: a ) 84 days , b ) 84 ½ days , c ) 85 days , d ) 87 days , e ) 89 days
Rationale: explanation : ( a + b ) 1 day work = 1 / 48 ( b + c ) 1 day work = 1 / 72 ( a + c ) 1 day work = 1 / 60 by adding 2 ( a + b + c ) = 1 / 48 + 1 / 72 + 1 / 60 = 37 / 720 ( a + b + c ) 1 day work = 37 / 1440 a 1 day work = 37 / 1440 – 1 / 72 = 17 / 1440 = 85 days ( approximately ) answer : option c
Answer: c
Question (general): if x is an integer such that 1 < x < 9 , 2 < x < 15 , 7 > x > – 1 , 4 > x > 0 , and x + 1 < 5 , then x is
Options: a ) 3 , b ) 4 , c ) 5 , d ) 6 , e ) 7
Rationale: "1 < x < 9 , 2 < x < 15 , - 1 < x < 7 0 < x < 4 x + 1 < 5 from above : 2 < x < 4 - - > x = 3 . answer : a ."
Answer: a
Question (general): 1 = 1,2 = 2,3 = 9,4 = 16,5 = 25 , then 9 = ?
Options: a ) 1 , b ) 255 , c ) 3 , d ) 445 , e ) 235
Rationale: "1 = 1,2 = 2,3 = 9,4 = 16,5 = 25 , then 9 = ? 9 = 3 check the third eqn . answer : c"
Answer: c
Question (physics): a train 300 m long can cross an electric pole in 10 sec and then find the speed of the train ?
Options: a ) 88 kmph , b ) 89 kmph , c ) 72 kmph , d ) 16 kmph , e ) 108 kmph
Rationale: "length = speed * time speed = l / t s = 300 / 10 s = 30 m / sec speed = 30 * 18 / 5 ( to convert m / sec in to kmph multiply by 18 / 5 ) speed = 108 kmph answer : e"
Answer: e
Question (gain): if a book is sold at 10 % profit instead of 10 % loss , it would have brought rs 14 more . find out the cost price of the book
Options: a ) 75 , b ) 72 , c ) 60 , d ) 70 , e ) 80
Rationale: "let c . p . of the book be rs . ’ x ’ given , 1.10 x - 0.90 x = 14 = > 0.2 x = 14 = 14 / 0.2 = rs 70 answer : d"
Answer: d
Question (general): in the number 11,0 ab , a and b represent the tens and units digits , respectively . if 11,0 ab is divisible by 55 , what is the greatest possible value of b × a ?
Options: a ) 0 , b ) 5 , c ) 10 , d ) 15 , e ) 25
Rationale: "you should notice that 55 * 2 = 110 so 11,000 is divisible by 55 : 55 * 200 = 11,000 ( or you can notice that 11,000 is obviously divisible by both 5 and 11 so by 55 ) - - > b * a = 0 * 0 = 0 . next number divisible by 55 is 11,000 + 55 = 11,055 : b * a = 5 * 5 = 25 ( next number wo n ' t have 110 as the first 3 digits so we have only two options 0 and 25 ) . answer : e"
Answer: e
Question (gain): how many liters of water must be evaporated from 50 liters of a 3 percent sugar solution to get a 4 percent sugar solution ?
Options: a ) 12.5 , b ) 15.5 , c ) 17.5 , d ) 21.5 , e ) 24.5
Rationale: "let x be the amount that needs to be evaporated . 0.03 ( 50 ) = 0.04 ( 50 - x ) 0.04 x = 2 - 1.5 x = 0.5 / 0.04 = 12.5 liters the answer is a ."
Answer: a
Question (general): the average of marks obtained by 120 candidates was 35 . if the avg of marks of passed candidates was 39 & that of failed candidates was 39 and that of failed candidates was 15 , the no . of candidateswho passed the examination is ?
Options: a ) 50 , b ) 90 , c ) 100 , d ) 120 , e ) 140
Rationale: "let the number of candidate who passed = y then , 39 y + 15 ( 120 - y ) = 120 x 35 ⇒ 24 y = 4200 - 1800 ∴ y = 2400 / 24 = 100 c"
Answer: c
Question (geometry): a squirrel runs up a cylindrical post , in a perfect spiral path making one circuit for each rise of 4 feet . how many feet does the squirrel travels if the post is 16 feet tall and 2 feet in circumference ?
Options: a ) 10 feet , b ) 8 feet , c ) 13 feet , d ) 15 feet , e ) 18 feet
Rationale: "total circuit = 16 / 4 = 4 total feet squirrel travels = 4 * 2 = 8 feet answer : b"
Answer: b
Question (general): if ( t - 8 ) is a factor of t ^ 2 - kt - 46 , then k =
Options: a ) 16 , b ) 12 , c ) 2 , d ) 6 , e ) 14
Rationale: "t ^ 2 - kt - 48 = ( t - 8 ) ( t + m ) where m is any positive integer . if 48 / 8 = 6 , then we know as a matter of fact that : m = + 6 and thus k = 8 - 6 = 14 t ^ 2 - kt - m = ( t - a ) ( t + m ) where a > m t ^ 2 + kt - m = ( t - a ) ( t + m ) where a < m t ^ 2 - kt + m = ( t - a ) ( t - m ) e"
Answer: e
Question (geometry): what will be the cost of building a fence around a rectangular plot with area equal to 289 sq ft , if the price per foot of building the fence is rs . 50 ?
Options: a ) a ) rs . 3944
b ) b ) rs . 3948
c ) c ) rs . 3519.5
d ) d ) rs . 3949
e ) e ) rs . 3923
Rationale: let the side of the rectangle plot be a ft . a * b = 289 = > 1.7 b * b = 289 b = 13.03 a = 22.17 length of the fence = perimeter of the plot = 2 ( a + b ) = 70.39 ft . cost of building the fence = 70.39 * 50 = rs . 3519.5 answer : c
Answer: c
Question (gain): how many liters of water must be evaporated from 50 liters of a 8 - percent sugar solution to get a 10 - percent solution ?
Options: a ) 8 , b ) 10 , c ) 12 , d ) 14 , e ) 16
Rationale: "8 % of a 50 liter solution is 4 l which is 10 % of the solution at the end . the solution at the end must be 40 l . we need to evaporate 10 liters . the answer is b ."
Answer: b
Question (gain): . in a certain city , 60 percent of the registered voters are democrats and the rest are republicans . in a mayoral race , if 70 percent of the registered voters who are democrats and 20 percent of the registered voters who are republicans are expected to vote for candidate a , what percent of the registered voters are expected to vote for candidate a ?
Options: a ) 50 % , b ) 53 % , c ) 54 % , d ) 55 % , e ) 57 %
Rationale: registered voters = 100 d = 60 r = 40 70 % of d ( 60 ) = 42 20 % of r ( 40 ) = 8 total voter % of registered voters = 50 / 100 50 % ans a
Answer: a
Question (general): a box contains 12 apples , 11 of which are red . an apple is drawn from the box and its color is noted before it is eaten . this is done a total of n times , and the probability that a red apple is drawn each time is less than 0.5 . what is the smallest possible value of n ?
Options: a ) 3 , b ) 4 , c ) 5 , d ) 6 , e ) 7
Rationale: "p ( choosing a red apple 7 times in a row ) = 11 / 12 * 10 / 11 * 9 / 10 * 8 / 9 * 7 / 8 * 6 / 7 * 5 / 6 = 5 / 12 < 0.5 the answer is e ."
Answer: e
Question (physics): a train 110 meters long completely crosses a 280 meters long bridge in 38 seconds . what is the speed of the train is ?
Options: a ) 32 , b ) 45 , c ) 40 , d ) 66 , e ) 09
Rationale: "s = ( 110 + 280 / 38 = 390 / 38 * 18 / 5 = 40 answer : c"
Answer: c
Question (general): in a market , a dozen eggs cost as much as a pound of rice , and a half - liter of kerosene costs as much as 8 eggs . if the cost of each pound of rice is $ 0.33 , then how many f cents does a liter of kerosene cost ? [ one dollar has 100 cents . ]
Options: a ) 0.33 , b ) 0.44 , c ) 0.55 , d ) 44 , e ) 55
Rationale: "main thing to remember is answer is asked in cents , however when we calculate , it comes up as 0.44 $ just multiply by 100 , answer f = 44 . d"
Answer: d
Question (general): paulson spends 75 % of his income . his income is increased by 20 % and he increased his expenditure by 10 % . find the percentage increase in his savings
Options: a ) 30 % , b ) 35 % , c ) 40 % , d ) 45 % , e ) 50 %
Rationale: "let the original income = rs . 100 . then , expenditure = rs . 75 and savings = rs . 25 new income = rs . 120 , new expenditure = rs . ( ( 110 / 100 ) * 75 ) = rs . 165 / 2 new savings = rs . ( 120 - ( 165 / 2 ) ) = rs . 75 / 2 increase in savings = rs . ( ( 75 / 2 ) - 25 ) = rs . 25 / 2 increase % = ( ( 25 / 2 ) * ( 1 / 25 ) * 100 ) % = 50 % . answer e 50 %"
Answer: e
Question (general): if ( 1 – 1.5 ) n = 1 , then n =
Options: a ) − 400 , b ) − 140 , c ) − 2 , d ) 4 , e ) 400
Rationale: "( 1 – 1.5 ) n = 1 simplify to get : - 0.5 n = 1 rewrite as ( - 1 / 2 ) n = 1 multiply both sides by - 2 to get : n = - 2 answer : c"
Answer: c
Question (other): in a college , the ratio of the number of boys to girls is 8 : 5 . if there are 160 girls , the total number of students in the college is
Options: a ) 2447 , b ) 377 , c ) 667 , d ) 416 , e ) 871
Rationale: "explanation : let the number of boys and girls be 8 x and 5 x . total number of students = 13 x = 13 * 32 = 416 . answer : d"
Answer: d
Question (general): the average weight of 5 students decreases by 12 kg when one of them weighing 72 kg is replaced by a new student . the weight of the student is
Options: a ) 12 kg , b ) 10 kg , c ) 20 kg , d ) 72 kg , e ) none of these
Rationale: "explanation : let the weight of student be x kg . given , difference in average weight = 12 kg = > ( 72 - x ) / 5 = 12 = > x = 12 answer : a"
Answer: a
Question (general): find the least multiple of 23 , which when divided by 1821 and 24 leaves remainders 710 and 13 respectively .
Options: a ) 3002 , b ) 3013 , c ) 3024 , d ) 3036 , e ) none of these
Rationale: solution here ( 18 - 7 ) = 11 , ( 21 - 10 ) = 11 and ( 24 - 13 ) = 11 . l . c . m . of 1821 and 24 is 504 . let required number be 504 k - 11 . least value of k for which ( 504 k - 11 ) is divisible 23 is k = 6 . so , required number = 504 × 6 - 11 = 3024 - 11 = 3013 . answer b
Answer: b
Question (physics): a boy is travelling from his home to school at 5 km / hr and reached 7 min late . next day he traveled at 10 km / hr and reached 8 min early . distance between home and school ?
Options: a ) 2.5 km , b ) 3.5 km , c ) 4.5 km , d ) 5.5 km , e ) 6.5 km
Rationale: let the distance be x t 1 = x / 5 hr t 2 = x / 10 hr difference in time = 7 + 8 = 15 = 1 / 4 hr x / 5 - x / 10 = 1 / 4 x / 10 = 1 / 4 x = 2.5 km answer is a
Answer: a
Question (other): how many of the positive factors of 16 are not factors of 20
Options: a ) 2 , b ) 3 , c ) 4 , d ) 1 , e ) 5
Rationale: "factors of 16 - 1 , 2 , 4 , 8 , 16 factors of 20 - 1 , 2 , 4 , 5 , 10 , 20 . comparing both , we have 2 factors of 16 which are not factors of 20 - 8,16 answer : a"
Answer: a
Question (gain): an investor deposited $ 10,000 to open a new savings account that earned 8 percent annual interest , compounded quarterly . if there were no other transactions in the account , what was the amount of money in the account 6 months after the account was opened ?
Options: a ) $ 10,200 , b ) $ 10,202 , c ) $ 10,400 , d ) $ 10,404 , e ) $ 10,800
Rationale: "the amount in the account after 6 months is 1.02 * 1.02 ( $ 10,000 ) = $ 10,404 . the answer is d ."
Answer: d
Question (physics): a pipe can fill a cistern in 77 minutes . find the time in which 1 / 11 part of the cistern will be filled ?
Options: a ) 5 min , b ) 2 min , c ) 3 min , d ) 1 min , e ) 7 min
Rationale: "full cistern filled in = 77 minutes 1 / 11 part filled in = 77 * 1 / 11 = 7 minutes answer is e"
Answer: e
Question (physics): a can do a job in 10 days and b in 20 days . if they work on it together for 4 days , then the fraction of the work that is left is ?
Options: a ) 2 / 5 , b ) 8 / 15 , c ) 3 / 11 , d ) 1 / 12 , e ) 6 / 13
Rationale: "a ' s 1 day work = 1 / 10 b ' s 1 day work = 1 / 20 a + b 1 day work = 1 / 10 + 1 / 20 = 3 / 20 a + b 4 days work = 3 / 20 * 4 = 3 / 5 remaining work = 1 - 3 / 5 = 2 / 5 answer is a"
Answer: a
Question (physics): a trader sells 20 meters of cloth for rs . 4500 at the profit of rs . 10 per metre of cloth . what is the cost price of one metre of cloth ?
Options: a ) rs . 380 , b ) rs . 215 , c ) rs . 190 , d ) rs . 395 , e ) none of these
Rationale: "sp of 1 m of cloth = 4500 / 20 = rs . 225 cp of 1 m of cloth = sp of 1 m of cloth - profit on 1 m of cloth = rs . 225 - rs . 10 = rs . 215 . answer : c"
Answer: c
Question (gain): sahil purchased a machine at rs 10000 , then got it repaired at rs 5000 , then gave its transportation charges rs 1000 . then he sold it with 50 % of profit . at what price he actually sold it .
Options: a ) rs . 22000 , b ) rs . 24000 , c ) rs . 26000 , d ) rs . 28000 , e ) none of these
Rationale: "explanation : question seems a bit tricky , but it is very simple . just calculate all cost price , then get 150 % of cp . c . p . = 10000 + 5000 + 1000 = 16000 150 % of 16000 = 150 / 100 * 16000 = 24000 option b"
Answer: b
Question (general): the ages of 2 persons differ by 35 years . if 10 years ago the elder one be 6 times as old as the younger one , find the present age of elder person .
Options: a ) 30 , b ) 48.5 , c ) 52 , d ) 50 , e ) 55
Rationale: "age of the younger person = x age of the elder person = x + 35 6 ( x - 10 ) = x + 35 - 10 x = 15 age of elder person = 15 + 35 = 50 answer is d"
Answer: d
Question (general): tom reads at an average rate of 30 pages per hour , while jan reads at an average rate of 38 pages per hour . if tom starts reading a novel at 4 : 30 , and jan begins reading an identical copy of the same book at 5 : 18 , at what time will they be reading the same page ?
Options: a ) 7 : 48 , b ) 8 : 18 , c ) 8 : 48 , d ) 9 : 18 , e ) 9 : 48
Rationale: "since tom reads an average of 1 page every 2 minutes , tom will read 24 pages in the first 48 minutes . jan can catch tom at a rate of 8 pages per hour , so it will take 3 hours to catch tom . the answer is b ."
Answer: b
Question (general): for any positive integer n , the sum of the first n positive integers equals n ( n + 1 ) / 2 . what is the sum of all the integers between 1 and 50 ?
Options: a ) 1275 , b ) 1542 , c ) 985 , d ) 1024 , e ) 1125
Rationale: "sum = 50 * 51 / 2 = 25 * 51 = 1275 answer is a"
Answer: a
Question (general): simplify : 896 x 896 - 204 x 204
Options: a ) 761200 , b ) 761400 , c ) 761800 , d ) 761500 , e ) none of them
Rationale: "( 896 ) ^ 2 - ( 204 ) ^ 2 = ( 896 + 204 ) ( 896 - 204 ) = 1100 x 692 = 761200 . answer is a ."
Answer: a
Question (physics): a searchlight on top of the watch - tower makes 2 revolutions per minute . what is the probability that a man appearing near the tower will stay in the dark for at least 5 seconds ?
Options: a ) 1 / 4 , b ) 1 / 3 , c ) 1 / 2 , d ) 2 / 3 , e ) 5 / 6
Rationale: 2 revolutions per minute = 1 revolution every 30 seconds so no matter what anybody appearing at the tower can not stay in the dark for more than 30 seconds . this will be our total number of possibilities i . e the denominator . p ( man in dark for at least 5 seconds ) = 1 - p ( man in dark for max of 5 seconds ) = 1 - 5 / 30 = 1 - 1 / 6 = 5 / 6 or the other way would be : p ( man in dark for at least 5 seconds ) is like saying he can be in dark for 5 , 6,7 . . . all the way to 30 seconds because that is the max . in this approach it would be 25 / 30 seconds = 5 / 6 . answer is e
Answer: e
Question (general): { - 10 , - 6 , - 5 , - 4 , - 2.5 , - 1 , 0 , 2.5 , 4 , 6 , 7 , 10 } a number is to be selected at random from the set above . what is the probability that the number selected will be a solution of the equation ( x - 5 ) ( x + 10 ) ( 2 x - 5 ) = 0 ?
Options: a ) 1 / 12 , b ) 1 / 6 , c ) 1 / 4 , d ) 1 / 3 , e ) 1 / 2
Rationale: roots of the equation ( x - 5 ) ( x + 10 ) ( 2 x - 5 ) = 0 are x = 5 , x = - 10 and x = 5 / 2 = 2.5 . so , two solutions present in our set of 12 distinct numbers , therefore p = 2 / 12 = 1 / 6 . answer : b .
Answer: b
Question (probability): a bag contains 10 red jellybeans and 10 blue jellybeans . if 3 jellybeans are removed one at a time , at random and are not replaced , what is the probability y that all 3 jellybeans removed from the bag are blue ?
Options: a ) 9 / 100 , b ) 2 / 19 , c ) 1 / 8 , d ) 3 / 20 , e ) 3 / 10
Rationale: "method - 1 10 red jellybeans and 10 blue jellybeans total outcomes = no . of ways to choose 3 jelly bean at random out of a total 20 jellybeans = 20 c 3 = 1140 favourable outcomes = no . of ways to choose 3 jelly bean such that they are all blue out of 10 blue = 10 c 3 = 120 probability = favourable outcomes / total outcomes = 10 c 3 / 20 c 3 probability y = 120 / 1140 = 2 / 19 answer : option b method - 2 probability of first jelly bean to be blue = 10 / 20 [ total 10 blue out of total 20 jellybeans ] probability of second jelly bean to be blue = 9 / 19 [ total 9 blue remaining out of total 19 jellybeans remaining ] probability of third jelly bean to be blue = 8 / 18 [ total 8 blue remaining out of total 18 jellybeans remaining ] required probability = ( 10 / 20 ) * ( 9 / 19 ) * ( 8 / 18 ) = 2 / 19 answer : option b"
Answer: b
Question (other): how many positive factors of 42 are not factors of 56 ?
Options: a ) 1 , b ) 2 , c ) 3 , d ) 4 , e ) 5
Rationale: "42 = 2 * 3 * 7 . so , total number of factors for 42 = 2 * 2 * 2 = 8 factors for 42 = 1 , 2,3 , 6,7 , 14,21 and 42 56 = 2 * 2 * 2 * 7 so , total number of factors for 56 = 4 * 2 = 8 factors of 56 = 1 , 2,4 , 7,8 , 14,28 and 56 . factors same in 42 and 56 are 1 , 2,7 and 14 . hence , answer will be d ."
Answer: d