Cheukting/mathqa huggingface dataset:
Question (physics): jonathan can type a 30 page document in 40 minutes , susan can type it in 30 minutes , and jack can type it in 24 minutes . working together , how much time will it take them to type the same document ?
Options: a ) 5 minutes , b ) 10 minutes , c ) 15 minutes , d ) 18 minutes , e ) 20 minutes
Rationale: "you may set up common equation like this : job / a + job / b + job / c = job / x memorize this universal formula , you will need it definitely for gmat . and find x from this equation in this specific case , the equation will look like this : 30 / 40 + 30 / 30 + 30 / 24 = 30 / x if you solve this equation , you get the same answer b ( 10 )"
Answer: b
Question (geometry): the measure of the side of a square is multiplied by 7 . if x represents the perimeter of the original square , what is the value of the new perimeter ?
Options: a ) 3 x , b ) 4 x , c ) 7 x , d ) 12 x , e ) 27 x
Rationale: "original perimeter = x hence original side = x / 4 new side = 7 x / 4 new perimeter = 4 * 7 x / 4 = 7 x correct option : c"
Answer: c
Question (general): a box contains 10 tablets of medicine a and 17 tablets of medicine b . what is the least number of tablets that should be taken from the box to ensure that at least two tablets of each kind are among the extracted .
Options: a ) 12 , b ) 15 , c ) 17 , d ) 19 , e ) 21
Rationale: "the worst case scenario will be if we remove all 17 tablets of medicine b first . the next 2 tablets we remove have to be of medicine a , so to guarantee that at least two tablets of each kind will be taken we should remove minimum of 17 + 2 = 19 tablets . answer : d ."
Answer: d
Question (general): the milk level in a rectangular box measuring 60 feet by 25 feet is to be lowered by 6 inches . how many gallons of milk must be removed ? ( 1 cu ft = 7.5 gallons )
Options: a ) 100 , b ) 250 , c ) 750 , d ) 5625 , e ) 5635
Rationale: "6 inches = 1 / 2 feet ( there are 12 inches in a foot . ) , so 60 * 25 * 1 / 2 = 750 feet ^ 3 of milk must be removed , which equals to 750 * 7.5 = 5625 gallons . answer : d ."
Answer: d
Question (probability): from a group of 4 boys and 4 girls , 2 children are to be randomly selected . what is the probability that 1 boy and 1 girl will be selected ?
Options: a ) 1 / 2 , b ) 2 / 3 , c ) 3 / 5 , d ) 4 / 7 , e ) 5 / 9
Rationale: "the total number of ways to choose 2 children from 8 is 8 c 2 = 28 the number of ways to choose 1 boy and 1 girl is 4 * 4 = 16 p ( 1 boy and 1 girl ) = 16 / 28 = 4 / 7 the answer is d ."
Answer: d
Question (probability): rhonda picked 2 pen from the table , if there were 7 pens on the table and 5 belongs to jill , what is the probability that the 2 pen she picked does not belong to jill ? .
Options: a ) 5 / 42 , b ) 2 / 42 , c ) 7 / 42 , d ) 2 / 7 , e ) 5 / 7
Rationale: since jill owns 5 of the pen , the subset from which the 2 pens hould be chosen are the 2 pens not owned by jill fom the universe of 7 . the first pen can be one of the 2 from the 7 with probability 2 / 7 . the second pen can be one of the 1 from the 6 remaining with probability 1 / 6 , the total probability will be 2 / 7 × 1 / 6 . on cancellation , this comes to 2 / 42 . thus , the answer is b - 2 / 42 .
Answer: b
Question (gain): a merchant sells an item at a 20 % discount , but still makes a gross profit of 20 percent of the cost . what percent w of the cost would the gross profit on the item have been if it had been sold without the discount ?
Options: a ) 20 % , b ) 40 % , c ) 50 % , d ) 60 % , e ) 75 %
Rationale: "let the market price of the product is mp . let the original cost price of the product is cp . selling price ( discounted price ) = 100 % of mp - 20 % mp = 80 % of mp . - - - - - - - - - - - - - - - - ( 1 ) profit made by selling at discounted price = 20 % of cp - - - - - - - - - - - - - - ( 2 ) apply the formula : profit w = selling price - original cost price = > 20 % of cp = 80 % of mp - 100 % cp = > mp = 120 cp / 80 = 3 / 2 ( cp ) now if product is sold without any discount , then , profit = selling price ( without discount ) - original cost price = market price - original cost price = mp - cp = 3 / 2 cp - cp = 1 / 2 cp = 50 % of cp thus , answer should bec ."
Answer: c
Question (general): country x taxes each of its citizens an amount equal to 13 percent of the first $ 40,000 of income , plus 20 percent of all income in excess of $ 40,000 . if a citizen of country x is taxed a total of $ 8,000 , what is her income ?
Options: a ) $ 54,000 , b ) $ 56,000 , c ) $ 64,000 , d ) $ 66,667 , e ) $ 80,000
Rationale: "equation is correct , so math must be a problem . 0.13 * 40,000 + 0.2 * ( x - 40,000 ) = 8,000 - - > 5,200 + 0.2 x - 8,000 = 8,000 - - > 0.2 x = 10,800 - - > x = 54,000 . answer : a ."
Answer: a
Question (general): a number when divided by 4 , gives 40 as quotient and 0 as remainder . what will be the remainder when dividing the same number by 3
Options: a ) a ) 1 , b ) b ) 3 , c ) c ) 4 , d ) d ) 6 , e ) e ) 7
Rationale: "explanation : p ÷ 4 = 40 = > p = 40 * 4 = 160 p / 3 = 160 / 3 = 53 , remainder = 1 answer : option a"
Answer: a
Question (geometry): the surface of a cube is 294 sq cm . find its volume ?
Options: a ) 8 cc , b ) 9 cc , c ) 2 cc , d ) 343 cc , e ) 6 cc
Rationale: "6 a 2 = 294 = 6 * 49 a = 7 = > a 3 = 343 cc answer : d"
Answer: d
Question (general): of 30 applicants for a job , 16 had at least 4 years ' experience , 21 had degrees , and 5 had less than 4 years ' experience and did not have a degree . how many of the applicants had at least 4 years ' experience and a degree ?
Options: a ) 12 , b ) 10 , c ) 9 , d ) 7 , e ) 5
Rationale: "set a : people with more than 4 years exp set b : people with degree aub = total - ( less than 4 exp and no degree ) aub = 30 - 5 = 25 aub = a + b - aib aib = 21 + 16 - 25 = 12 answer a"
Answer: a
Question (general): the average marks of 20 students in a class is 100 . but a student mark is wrongly noted as 50 instead of 10 then find the correct average marks ?
Options: a ) 78 , b ) 82 , c ) 98 , d ) 91 , e ) 85
Rationale: "correct avg marks = 100 + ( 10 - 50 ) / 20 avg = 100 - 2 = 98 answer is c"
Answer: c
Question (general): a parking garage rents parking spaces for $ 10 per week or $ 20 per month . how much does a person save in a year by renting by the month rather than by the week ?
Options: a ) $ 140 , b ) $ 160 , c ) $ 220 , d ) $ 240 , e ) $ 280
Rationale: "10 $ per week ! an year has 52 weeks . annual charges per year = 52 * 10 = 520 $ 30 $ per month ! an year has 12 months . annual charges per year = 12 * 20 = 240 $ 520 - 240 = 280 ans e"
Answer: e
Question (physics): jerry travels 8 miles at an average speed of 40 miles per hour , stops for 14 minutes , and then travels another 20 miles at an average speed of 60 miles per hour . what is jerry ’ s average speed , in miles per hour , for this trip ?
Options: a ) 36 , b ) 42.5 , c ) 44 , d ) 50 , e ) 52.5
Rationale: "total time taken by jerry = ( 8 / 40 ) * 60 minutes + 14 minutes + ( 20 / 60 ) * 60 minutes = 46 minutes average speed = total distance / total time = ( 8 + 20 ) miles / ( 46 / 60 ) hours = 28 * 60 / 46 = 36 miles per hour answer : option a"
Answer: a
Question (geometry): the total surface area of a cuboid length 12 m , breadth 10 m and height 8 m .
Options: a ) 576
b ) 566
c ) 596
d ) 556
e ) 586
Rationale: total surface area of cuboid = 2 ( lb + bh + lh ) = 2 ( 120 + 80 + 96 ) = 2 ( 296 ) = > 596 m ( power 2 ) answer is c .
Answer: c
Question (general): the average salary per head of the entire staff of an office including the officers and clerks is rs . 90 . the average salary of officers is rs . 500 and that of the clerks is rs . 84 . if the number of officers is 2 , find the number of officers in the office ?
Options: a ) 620 , b ) 720 , c ) 820 , d ) 920 , e ) 1020
Rationale: "500 84 \ / 90 / \ 6 410 3 : 205 3 - > 12 205 - > ? 820 answer : c"
Answer: c
Question (general): what is the least integer greater than – 4 + 0.5 ?
Options: a ) – 3 , b ) – 1 , c ) 0 , d ) 1 , e ) 2
Rationale: "this question is just about doing careful arithmetic and remembering what makes a numberbiggerorsmallercompared to another number . first , let ' s take care of the arithmetic : ( - 4 ) + ( 0.5 ) = - 3.5 on a number line , since we ' re adding + . 5 to a number , the total moves to the right ( so we ' re moving from - 4 to - 3.5 ) . next , the question asks for the least integer that is greater than - 3.5 again , we can use a number line . numbers become greater as you move to the right . the first integer to the right of - 3.5 is - 3 . final answer : a"
Answer: a
Question (general): if â € œ * â €  is called â € œ + â €  , â € œ / â €  is called â € œ * â €  , â € œ - â €  is called â € œ / â €  , â € œ + â €  is called â € œ - â €  . 240 / 80 â € “ 60 * 40 - 10 = ?
Options: a ) 355 , b ) 341 , c ) 323.2 , d ) 425.6 , e ) 225.7
Rationale: "explanation : given : 240 / 80 â € “ 60 * 40 - 10 = ? substituting the coded symbols for mathematical operations , we get , 240 * 80 / 60 + 40 / 10 = ? 240 * 1.33 + 4 = ? 319.2 + 4 = 323.2 answer : c"
Answer: c
Question (physics): 60 boys can complete a work in 24 days . how many men need to complete twice the work in 20 days
Options: a ) 144 , b ) 170 , c ) 180 , d ) 190 , e ) 200
Rationale: "one man can complete the work in 24 * 60 = 1440 days = one time work to complete the work twice it will be completed in let m be the no . of worker assign for this therefore the eqn becomes m * 20 = 2 * 1440 m = 144 workers answer : a"
Answer: a
Question (general): jill has 21 gallons of water stored in quart , half - gallon , and one gallon jars . she has equal numbers of each size jar holding the liquid . what is the total number of water filled jars ?
Options: a ) 3 , b ) 6 , c ) 9 , d ) 36 , e ) 14
Rationale: let the number of each size of jar = wthen 1 / 4 w + 1 / 2 w + w = 21 1 3 / 4 w = 21 w = 12 the total number of jars = 3 w = 36 answer : d
Answer: d
Question (general): jacob is 12 years old . he is 3 times as old as his brother . how old will jacob be when he is twice as old ?
Options: a ) 13 , b ) 14 , c ) 15 , d ) 16 , e ) 17
Rationale: "j = 12 ; j = 3 b ; b = 12 / 3 = 4 ; twice as old so b = 4 ( now ) + ( 4 ) = 8 ; jacob is 12 + 4 = 16 answer : d"
Answer: d
Question (probability): if two integers x , y ( x > y ) are selected from - 10 to 1 ( inclusive ) , how many possible cases are there ?
Options: a ) 150 , b ) 66 , c ) 190 , d ) 210 , e ) 240
Rationale: "if two integers x , y ( x > y ) are selected from - 10 to 9 ( inclusive ) , how many possible cases are there ? a . 150 b . 180 c . 190 d . 210 e . 240 - - > 12 c 2 = 12 * 11 / 2 = 66 . therefore , the answer is b ."
Answer: b
Question (gain): a trader sells 40 metres of cloth for rs . 8200 at a profit of rs . 20 per metre of cloth . how much profit will the trder earn on 40 metres of cloth ?
Options: a ) rs . 800 , b ) rs . 1500 , c ) rs . 1000 , d ) rs . 1200 , e ) none of these
Rationale: "explanation : sp of 1 metre cloth = 8200 / 40 = rs . 205 . cp of 1 metre cloth = rs . 205 – 20 = rs . 185 cp on 40 metres = 185 x 40 = rs . 7400 profit earned on 40 metres cloth = rs . 8200 – rs . 7400 = rs . 800 . answer : option a"
Answer: a
Question (general): what least value must be given to * so that the number 451 * 603 is exactly divisible by 9 ?
Options: a ) 2 , b ) 5 , c ) 7 , d ) 8 , e ) 9
Rationale: sum of digits = ( 4 + 5 + 1 + x + 6 + 0 + 3 ) = 19 + x divisible by 9 clearly x = 9 answer e 9
Answer: e
Question (physics): 24 machines can do a work in 10 days . how many machines are needed to complete the work in 40 days ?
Options: a ) 10 , b ) 6 , c ) 4 , d ) 7 , e ) 5
Rationale: "required number of machines = 24 * 10 / 40 = 6 answer is b"
Answer: b
Question (geometry): in a company of 170 employees , 110 are females . a total of 80 employees have advanced degrees and the rest have a college degree only . if 25 employees are males with college degree only , how many employees are females with advanced degrees ?
Options: a ) 40 , b ) 45 , c ) 50 , d ) 55 , e ) 60
Rationale: the number of males is 170 - 110 = 60 . the number of males with advanced degrees is 60 - 25 = 35 . the number of females with advanced degrees is 80 - 35 = 45 . the answer is b .
Answer: b
Question (gain): at a particular graduation party with 300 guests , 70 % of the guests brought gifts , and 40 % of the female guests brought gifts . if 36 males did not bring gifts to the party , how many females did bring gifts ?
Options: a ) 18 , b ) 36 , c ) 42 , d ) 68 , e ) 70
Rationale: "the correct method total = 300 . . 70 % of 300 = 210 got gifts . . 90 did not get gift , out of which 48 are males , so remaining 90 - 36 = 54 are females . . but 40 % females brought gift , so 60 % did not get it . . so 60 % = 54 , 100 % = 54 * 100 / 60 = 90 . . ans 40 % of 90 = 36 b"
Answer: b
Question (general): if 8 a = 9 b and ab ≠ 0 , what is the ratio of a / 9 to b / 8 ?
Options: a ) 64 / 81 , b ) 8 / 9 , c ) 1 , d ) 9 / 8 , e ) 81 / 64
Rationale: "if ab ≠ 0 then a and b has two integer sets of pair if a = 9 then b = 8 and if a = - 9 then b = - 8 also in fraction if a = 1 / 8 then b = 1 / 9 any of the pair we check the ratio 8 a / 9 b = 1 answer : c"
Answer: c
Question (general): in a theater , the first row has 17 seats and each row has 3 more seats than previous row . if the last row has 44 seats , what is the total number of seats in the theater ?
Options: a ) 265 , b ) 275 , c ) 285 , d ) 295 , e ) 305
Rationale: "the number of seats in the theater is 17 + ( 17 + 3 ) + . . . + ( 17 + 27 ) = 10 ( 17 ) + 3 ( 1 + 2 + . . . + 9 ) = 10 ( 17 ) + 3 ( 9 ) ( 10 ) / 2 = 170 + 135 = 305 the answer is e ."
Answer: e
Question (gain): the list price of an article is rs . 69 . a customer pays rs . 56.16 for it . he was given two successive discounts , one of them being 10 % . the other discount is ?
Options: a ) 9.33 % , b ) 9.44 % , c ) 9.45 % , d ) 9.56 % , e ) 9.67 %
Rationale: "69 * ( 90 / 100 ) * ( ( 100 - x ) / 100 ) = 56.16 x = 9.56 % answer : d"
Answer: d
Question (physics): how many seconds will a 200 m long train take to cross a man walking with a speed of 3 km / hr in the direction of the moving train if the speed of the train is 63 km / hr ?
Options: a ) 26 sec , b ) 30 sec , c ) 12 sec , d ) 19 sec , e ) 12 sec
Rationale: "speed of train relative to man = 63 - 3 = 60 km / hr . = 60 * 5 / 18 = 50 / 3 m / sec . time taken to pass the man = 200 * 3 / 50 = 12 sec . answer : c"
Answer: c
Question (geometry): the radius of a cone is 4 m , height 5 m . find the curved surface area ?
Options: a ) 1 , b ) 3 , c ) 5 , d ) 7 , e ) 9
Rationale: "cone curved surface area = π rl = 22 / 7 × 4 × 5 = 440 / 7 = 62 6 / 7 slant height ( l ) = √ r ( power 2 ) + h ( power 2 ) = √ 16 + 9 = √ 25 = 5"
Answer: c
Question (physics): a constructor estimates that 8 people can paint mr khans house in 3 days . if he uses 4 people instead of 8 , how long will they take to complete the job ?
Options: a ) 6 , b ) 8 , c ) 3 , d ) 4 , e ) 0
Rationale: "explanation : use formula for a work members ã — days = constant 8 ã — 3 = 4 ã — a a = 6 so answer is 6 days answer : a"
Answer: a
Question (physics): the radius of a semi circle is 70 cm then its perimeter is ?
Options: a ) 32.8 , b ) 32.4 , c ) 360 , d ) 32.2 , e ) 32.9
Rationale: "diameter = 140 cm 1 / 2 * 22 / 7 * 140 + 140 = 360 answer : c"
Answer: c
Question (physics): a cistern of capacity 8000 litres measures externally 3.3 m by 2.6 m by 1.3 m and its walls are 5 cm thick . the thickness of the bottom is :
Options: a ) 90 cm , b ) 3 dm , c ) 1 m , d ) 1.1 cm , e ) none of these
Rationale: "explanation : let the thickness of the bottom be x cm . then , [ ( 330 - 10 ) × ( 260 - 10 ) × ( 130 - x ) ] = 8000 × 1000 = > 320 × 250 × ( 130 - x ) = 8000 × 1000 = > ( 130 - x ) = 8000 × 1000 / 320 = 100 = > x = 30 cm = 3 dm . answer : b"
Answer: b
Question (general): operation # is defined as adding a randomly selected two digit multiple of 12 to a randomly selected two digit prime number and reducing the result by half . if operation # is repeated 10 times , what is the probability that it will yield at least two integers ?
Options: a ) 0 % , b ) 10 % , c ) 20 % , d ) 30 % , e ) 40 %
Rationale: "any multiple of 12 is even . any two - digit prime number is odd . ( even + odd ) / 2 is not an integer . thus # does not yield an integer at all . therefore p = 0 . answer : a ."
Answer: a
Question (general): running at their respective constant rate , machine x takes 2 days longer to produce w widgets than machines y . at these rates , if the two machines together produce 5 w / 4 widgets in 3 days , how many days would it take machine x alone to produce 6 w widgets .
Options: a ) 4 , b ) 36 , c ) 8 , d ) 10 , e ) 12
Rationale: i am getting 12 . e . hope havent done any calculation errors . . approach . . let y = no . of days taken by y to do w widgets . then x will take y + 2 days . 1 / ( y + 2 ) + 1 / y = 5 / 12 ( 5 / 12 is because ( 5 / 4 ) w widgets are done in 3 days . so , x widgets will be done in 12 / 5 days or 5 / 12 th of a widget in a day ) solving , we have y = 4 = > x takes 6 days to doing x widgets . so , he will take 36 days to doing 6 w widgets . answer : b
Answer: b
Question (gain): the cost price of a radio is rs . 1500 and it was sold for rs . 1230 , find the loss % ?
Options: a ) 18 % , b ) 19 % , c ) 68 % , d ) 19 % , e ) 38 %
Rationale: "1500 - - - - 270 100 - - - - ? = > 18 % answer : a"
Answer: a
Question (physics): among the two clocks , clock a gains 20 seconds per minute . if clock a and b are set at 2 0 ' clock , when clock a is at 7 : 20 , what does clock b show ?
Options: a ) 5 : 30 , b ) 6 : 00 , c ) 5 : 45 , d ) 6 : 20 , e ) 3 : 30
Rationale: clock a gains 20 seconds per minute , 1200 seconds per hour or 20 minutes per hour . the two clocks show 2 : 00 at 2 0 ' clock at 3 : 00 - clock b is at 3 : 00 clock a is at 3 : 20 ( 1 hour + gains 20 minutes ) at 4 : 00 - clock b is at 4 : 00 clock a is at 4 : 40 ( 2 hours + gains 40 minutes ) in 4 hours the clock a gains 4 * 20 = 80 minutes or 1 hour 20 minutes if clock a is at 7 : 20 the clock b is at 6 : 00 answer is b
Answer: b
Question (gain): the sale price sarees listed for rs . 500 after successive discount is 10 % and 5 % is ?
Options: a ) 427.5 , b ) 277 , c ) 342 , d ) 882 , e ) 212
Rationale: "500 * ( 90 / 100 ) * ( 95 / 100 ) = 427.5 answer : a"
Answer: a
Question (general): the number of timeshare condos available at sunset beach is 2 / 5 the number of timeshare condos available at playa del mar . if the total number of timeshare condos available at the two beaches combined is 350 , what is the difference between the number of condos available at sunset beach and the number of condos available at playa del mar ?
Options: a ) 60 , b ) 90 , c ) 120 , d ) 150 , e ) 240
Rationale: let x be the number of timeshare condos available at playa del mar . then number of timeshare condos available at sunset beach = 3 / 5 x we know , x + 2 / 5 x = 350 hence , x = 250 . so , number of timeshare condos available at playa del mar = 250 the difference between the number of condos available at sunset beach and the number of condos available at playa del mar = x - 2 / 5 x = 3 / 5 x = 3 / 5 ( 250 ) = 150 the correct answer is d
Answer: d
Question (physics): a can do a piece of work in 8 days and b alone can do it in 12 days . how much time will both take to finish the work ?
Options: a ) a ) 4.8 , b ) b ) 6.333 , c ) c ) 7.333 , d ) d ) 8.5 , e ) e ) 9
Rationale: "this question can be solved by different methods . we need to conserve time in exams so solving this problem using equations is the good idea . time taken to finish the job = xy / ( x + y ) = 8 x 12 / ( 8 + 12 ) = 96 / 20 = 4.8 days answer : a"
Answer: a
Question (geometry): the measurement of a rectangular box with lid is 25 cmx 6 cmx 18 cm . find the volume of the largest sphere that can be inscribed in the box ( in terms of π cm 3 ) . ( hint : the lowest measure of rectangular box represents the diameter of the largest sphere )
Options: a ) 288
b ) 48
c ) 36
d ) 864
e ) 964
Rationale: d = 6 , r = 2 ; volume of the largest sphere = 4 / 3 π r 3 = 4 / 3 * π * 3 * 3 * 3 = 36 π cm 3 answer : c
Answer: c
Question (physics): a and b go around a circular track of length 150 m on a cycle at speeds of 36 kmph and 54 kmph . after how much time will they meet for the first time at the starting point ?
Options: a ) 30 sec , b ) 198 sec , c ) 178 sec , d ) 665 sec , e ) 276 sec
Rationale: "time taken to meet for the first time at the starting point = lcm { length of the track / speed of a , length of the track / speed of b } = lcm { 150 / ( 36 * 5 / 18 ) , 150 / ( 54 * 5 / 18 ) } = lcm ( 15 , 10 ) = 30 sec . answer : a"
Answer: a
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 50 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 ) 18 , c ) 20 , d ) 24 , e ) 30
Rationale: "time taken = total distance / relative speed total distance = 50 kms relative speed ( opposite side ) ( as they are moving towards each other speed would be added ) = 6 + 4 = 10 kms / hr time taken = 50 / 10 = 5 hrs distance traveled by brad = brad ' s speed * time taken = 6 * 5 = 30 kms . . . answer - e"
Answer: e
Question (physics): two trains of length 150 m and 280 m are running towards each other on parallel lines at 42 kmph and 30 kmph respectively . in what time will they be clear of each other from the moment they meet ?
Options: a ) 22 sec , b ) 77 sec , c ) 76 sec , d ) 21.5 sec , e ) 66 sec
Rationale: "relative speed = ( 42 + 30 ) * 5 / 18 = 4 * 5 = 20 mps . distance covered in passing each other = 150 + 280 = 430 m . the time required = d / s = 430 / 20 = 21.5 sec . answer : d"
Answer: d
Question (physics): source : knewton a cyclist ' s speed varies , depending on the terrain , between 6.0 miles per hour and 14.0 miles per hour , inclusive . what is the maximum distance , in miles , that the cyclist could travel in 5 hours ?
Options: a ) 42 , b ) 56 , c ) 70 , d ) 98 , e ) 140
Rationale: we are told that : generallya cyclist ' s speed varies , depending on the terrain , between 6.0 miles per hour and 14.0 miles per hour , inclusive . is it possible the cyclist to travel with maximum speed for some time ? why not , if there is right terrain for that . so , if there is long enough terrain for the maximum speed of 14 mph then the maximum distance , in miles , that the cyclist could travel in 5 hours would be 5 * 14 = 70 miles . answer : c .
Answer: c
Question (general): elena purchased brand x pens for $ 4.00 apiece and brand y for $ 2.40 apiece . if elena purchased a total of 12 of these pens for $ 42.00 , how many brand x pens did she purchase ?
Options: a ) 4 , b ) 5 , c ) 6 , d ) 7 , e ) 8
Rationale: "4 x + 2.8 y = 42 - - > multiply by 2.5 ( to get the integers ) - - > 10 x + 7 y = 105 - - > only one positive integers solutions x = 5 and y = 5 ( how to solve : 7 y must have the last digit of 5 in order the last digit of the sum to be 5 ) . answer : b ."
Answer: b
Question (geometry): the length of a rectangle is two - seventh of the radius of a circle . the radius of the circle is equal to the side of the square , whose area is 5929 sq . units . what is the area ( in sq . units ) of the rectangle if the rectangle if the breadth is 25 units ?
Options: a ) 660 sq . units
b ) 440 sq . units
c ) 770 sq . units
d ) 550 sq . units
e ) 220 sq . units
Rationale: given that the area of the square = 5929 sq . units = > side of square = â ˆ š 5929 = 77 units the radius of the circle = side of the square = 77 units length of the rectangle = 2 / 7 * 77 = 22 units given that breadth = 25 units area of the rectangle = lb = 22 * 25 = 550 sq . units answer : d
Answer: d
Question (physics): if 20 men take 15 days to to complete a job , in how many days can 25 men finish that work ?
Options: a ) 12 , b ) 66 , c ) 77 , d ) 8 , e ) 6
Rationale: ans . 12 days
Answer: a