Cheukting/mathqa huggingface dataset:
Question (physics): 3 pumps , working 8 hours a day , can empty a tank in 2 days . how many hours a day must 4 pumps work to empty the tank in 1 day ?
Options: a ) 9 , b ) 10 , c ) 11 , d ) 12 , e ) 13
Rationale: the required number of working hours per day x , more pumps , less working hours per day ( indirect ) less days , more working hours per day ( indirect ) pumps 4 : 3 , days 1 : 2 } : : 8 : x therefore 4 * 1 * x = 3 * 2 * 8 , x = ( 3 * 2 * 8 ) / 4 x = 12 correct answer ( d )
Answer: d
Question (gain): peter invests a sum of money and gets back an amount of $ 810 in 3 years . david invests an equal amount of money and gets an amount of $ 854 in 4 years . if both amounts were invested at the same rate ( simple interest ) what was the sum of money invested ?
Options: a ) 670 , b ) 683 , c ) 698 , d ) 744 , e ) 700
Rationale: since both peter and david invested the same amount of money at the same rate , they would earn same interest per year . david invested for one year more than peter and hence he got interest amount for one more year . interest earned per year = amount received by david - amount received by peter = 854 - 810 = 44 interest earned for 3 years = 44 * 3 = 132 amount invested = 815 - 132 = 683 answer : b
Answer: b
Question (general): a envelop weight 9.2 gm , if 800 of these envelop are sent with an advertisement mail . how much wieght ?
Options: a ) 6.6 kg , b ) 6.8 kg , c ) 6.7 kg , d ) 6.9 kg , e ) 7.36 kg
Rationale: "800 * 9.2 7360.0 gm 7.36 kg answer : e"
Answer: e
Question (general): what least number should be added to 1022 , so that the sum is completely divisible by 25 ?
Options: a ) 4 , b ) 3 , c ) 2 , d ) 0 , e ) 5
Rationale: "1022 ã · 25 = 40 with remainder = 22 22 + 3 = 25 . hence 3 should be added to 1022 so that the sum will be divisible by 25 answer : option b"
Answer: b
Question (gain): a hostel had provisions for 250 men for 44 days . if 50 men left the hostel , how long will the food last at the same rate ?
Options: a ) 55 , b ) 40 , c ) 50 , d ) 60 , e ) 65
Rationale: "a hostel had provisions for 250 men for 44 days if 50 men leaves the hostel , remaining men = 250 - 50 = 200 we need to find out how long the food will last for these 200 men . let the required number of days = x days more men , less days ( indirect proportion ) ( men ) 250 : 200 : : x : 44 250 × 44 = 200 x 5 × 44 = 4 x x = 5 × 11 = 55 answer a"
Answer: a
Question (gain): the owner of a furniture shop charges his customer 24 % more than the cost price . if a customer paid rs . 8339 for a computer table , then what was the cost price of the computer table ?
Options: a ) rs . 6825 , b ) rs . 6721 , c ) rs . 6725 . , d ) rs . 4298 , e ) rs . 6729
Rationale: "cp = sp * ( 100 / ( 100 + profit % ) ) = 8339 ( 100 / 124 ) = rs . 6725 . answer : c"
Answer: c
Question (general): 63 + 5 * 12 / ( 180 / 3 ) = ?
Options: a ) 22 , b ) 77 , c ) 29 , d ) 64 , e ) 21
Rationale: "63 + 5 * 12 / ( 180 / 3 ) = 63 + 5 * 12 / ( 60 ) = 63 + ( 5 * 12 ) / 60 = 63 + 1 = 64 . answer : d"
Answer: d
Question (general): in a fuel station the service costs $ 1.75 per car , every liter of fuel costs 0.45 $ . assuming that a company owns 12 cars and that every fuel tank contains 55 liters and they are all empty , how much money total will it cost to fuel all cars ?
Options: a ) 318 $ , b ) 380 $ , c ) 420 $ , d ) 450 $ , e ) 480 $
Rationale: 12 * 1.75 + 0.45 * 12 * 55 = 318 hence - a
Answer: a
Question (general): if ( - 6 ) ^ ( 2 x ) = 6 ^ ( 7 + x ) and x is an integer , what is the value of x ?
Options: a ) 5 , b ) 4 , c ) 3 , d ) 8 , e ) 7
Rationale: "since x is an integer , ( - 6 ) ^ 2 x is always positive . so , 6 ^ 2 x = 6 ^ ( 7 + x ) 2 x = 7 + x x = 7 answer : e"
Answer: e
Question (other): a hen leaps 3 leaps for every 2 leaps of a duck , but 4 leaps of the duck are equal to 3 leaps of the hen . what is the ratio of the speed of the hen to that of the duck ?
Options: a ) 2 : 1 , b ) 3 : 4 , c ) 4 : 3 , d ) 1 : 4 , e ) 5 : 6
Rationale: "given ; 4 duck = 3 hen ; or , duck / hen = 3 / 4 ; let hen ' s 1 leap = 4 meter and ducks 1 leap = 3 meter . then , ratio of speed of hen and duck = 4 * 3 / 3 * 2 = 2 : 1 ' ' answer : 2 : 1 ;"
Answer: a
Question (other): praveen starts business with rs . 3640 and after 5 months , hari joins with praveen as his partner . after a year , the profit is divided in the ratio 2 : 3 . what is hari ’ s contribution in the capital ?
Options: a ) s . 7500 , b ) s . 8000 , c ) s . 8500 , d ) s . 9000 , e ) s . 9360
Rationale: "let hari ’ s capital be rs . x . then , 3640 * 12 / 7 x = 2 / 3 = > 14 x = 131040 = > x = 9360 . answer : e"
Answer: e
Question (gain): salad dressing p is made up of 30 % vinegar and 70 % oil , and salad dressing q contains 10 % vinegar and 90 % oil . if the two dressings are combined to produce a salad dressing that is 20 % vinegar , dressing p comprises what percentage of the new dressing ?
Options: a ) 60 % , b ) 50 % , c ) 40 % , d ) 30 % , e ) 20 %
Rationale: "let x be the percentage of dressing p in the new dressing . 0.3 x + 0.1 ( 1 - x ) = 0.20 0.2 x = 0.10 x = 0.5 = 50 % the answer is b ."
Answer: b
Question (other): how many positive integers q between 200 and 300 ( both inclusive ) are not divisible by 2 , 3 or 5 ?
Options: a ) 3 , b ) 16 , c ) 75 , d ) 24 , e ) 26
Rationale: 1 ) i figured there are 101 integers ( 300 - 200 + 1 = 101 ) . since the set begins with an even and ends with an even , there are 51 evens . 2 ) question says integers are not divisible by 2 , leaving all of the odds ( 101 - 51 = 50 integers ) . 3 ) question says integers are not divisible by 5 , removing all the integers ending in 5 ( already took out those ending in 0 ) . take out 10 integers ( 2 ? 5 , ? = 0 to 9 ) , leaving us with 40 integers . 4 ) now the painstaking part . we have to remove the remaining numbers that are multiples of 3 . those are 201 , 207 , 213 , 219 , 231 , 237 , 243 , 249 , 261 , 267 , 273 , 279 , 291 , and 297 . . . a total of 14 numbers . 26 numbers left ! 6 ) answer choice e .
Answer: e
Question (gain): rs . 850 becomes rs . 956 in 3 years at a certain rate of simple interest . if the rate of interest is increased by 4 % , what amount will rs . 850 become in 3 years ?
Options: a ) rs . 1020.80 , b ) rs . 1025 , c ) rs . 1058 , d ) data inadequate , e ) none of these
Rationale: "solution s . i . = rs . ( 956 - 850 ) = rs . 106 rate = ( 100 x 106 / 850 x 3 ) = 212 / 51 % new rate = ( 212 / 51 + 4 ) % = 416 / 51 % new s . i . = rs . ( 850 x 416 / 51 x 3 / 100 ) rs . 208 . ∴ new amount = rs . ( 850 + 208 ) = rs . 1058 . answer c"
Answer: c
Question (geometry): a specialized type of sand consists of 40 % mineral x by volume and 60 % mineral y by volume . if mineral x weighs 2.5 grams per cubic centimeter and mineral y weighs 4 grams per cubic centimeter , how many grams does a cubic meter of specialized sand combination weigh ? ( 1 meter = 100 centimeters )
Options: a ) 3 , 400,000 , b ) 2 , 800,000 , c ) 55,000 , d ) 28,000 , e ) 280
Rationale: "let the volume be 1 m ^ 3 = 1 m * 1 m * 1 m = 100 cm * 100 cm * 100 cm = 1 , 000,000 cm ^ 3 by volume 40 % is x = 400,000 cm ^ 3 60 % is y = 600,000 cm ^ 3 by weight , in 1 cm ^ 3 , x is 2.5 gms in 400,000 cm ^ 3 , x = 2.5 * 400,000 = 1 , 000,000 grams in 1 cm ^ 3 , y is 4 gms in 600,000 cm ^ 3 , y = 4 * 600,000 = 2 , 400,000 gms total gms in 1 m ^ 3 = 1 , 000,000 + 2 , 400,000 = 3 , 400,000 answer : a"
Answer: a
Question (physics): it takes ten minutes to load a certain video on a cellphone , and fifteen seconds to load that same video on a laptop . if the two devices were connected so that they operated in concert at their respective rates , how many seconds would it take them to load the video , rounded to the nearest hundredth ?
Options: a ) 13.42 , b ) 13.86 , c ) 14.25 , d ) 14.63 , e ) 14.88
Rationale: "the laptop can load the video at a rate of 1 / 15 of the video per second . the phone can load the video at a rate of 1 / ( 60 * 10 ) = 1 / 600 of the video per second . the combined rate is 1 / 15 + 1 / 600 = 41 / 600 of the video per second . the time required to load the video is 600 / 41 = 14.63 seconds . the answer is d ."
Answer: d
Question (general): a certain scholarship committee awarded scholarships in the amounts of $ 1250 , $ 2500 and $ 4000 . the committee awarded twice as many $ 2500 scholarships as $ 4000 and it awarded 3 times as many $ 1250 scholarships as $ 2500 scholarships . if the total of $ 75000 was awarded in $ 1250 scholarships , how many $ 4000 scholarships were awarded ?
Options: a ) 5 , b ) 6 , c ) 9 , d ) 10 , e ) 15
Rationale: since the starting point is given as the $ 4000 scholarship , assume $ 4000 scholarships to be x by the given information , $ 2500 scholarships = 2 x and $ 1250 scholarships = 6 x gievn : total $ 1250 scholarships = $ 75000 6 x * 1250 = 75000 solve for x = 10 option d
Answer: d
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 6 eggs . if the cost of each pound of rice is $ 0.33 , then how many cents does a liter of kerosene cost ? [ one dollar has 100 cents . ]
Options: a ) 0.33 , b ) 0.44 , c ) 33 , d ) 44 , e ) 55
Rationale: "a dozen eggs cost as much as a pound of rice - - > 12 eggs = 1 pound of rice = 33 cents ; a half - liter of kerosene costs as much as 6 eggs - - > 6 eggs = 1 / 2 liters of kerosene . how many cents does a liter of kerosene cost - - > 1 liter of kerosene = 12 eggs = 12 / 12 * 33 = 33 cents . answer : c ."
Answer: c
Question (general): a pupil ' s marks were wrongly entered as 73 instead of 40 . due to the average marks for the class got increased by half . the number of pupils in the class is ?
Options: a ) 18 , b ) 82 , c ) 66 , d ) 27 , e ) 77
Rationale: "let there be x pupils in the class . total increase in marks = ( x * 1 / 2 ) = x / 2 x / 2 = ( 73 - 40 ) = > x / 2 = 33 = > x = 66 . answer : c"
Answer: c
Question (gain): a baseball card decreased in value 25 % in its first year and 10 % in its second year . what was the total percent decrease of the card ' s value over the two years ?
Options: a ) 28 % , b ) 30 % , c ) 32.5 % , d ) 36 % , e ) 72 %
Rationale: "let the initial value of baseball card = 100 after first year , value of baseball card = ( 1 - 25 / 100 ) * 100 = 75 after second year , value of baseball card = ( 1 - 10 / 100 ) * 75 = 67.5 total percent decrease of the card ' s value over the two years = ( 100 - 67.5 ) / 100 * 100 % = 31.5 % answer c"
Answer: c
Question (general): if an integer n is to be chosen at random from the integers 1 to 96 , inclusive , what is the probability that n ( n + 1 ) ( n + 2 ) will be divisible by 8 ?
Options: a ) 1 / 4 , b ) 3 / 8 , c ) 1 / 2 , d ) 5 / 8 , e ) 3 / 4
Rationale: "total nos of ways in which we can choose n = 96 n ( n + 1 ) ( n + 2 ) will be divisible by 8 ? case 1 : n = odd then n + 2 = odd & n + 1 will be even i . e this needs get divided by 8 , hence is a multiple of 8 so we have 8 . . 96 = 12 multiples to fill the n + 1 pos hence 12 ways case 2 : n is even then n + 2 will be even & the product will be divisible by 24 & thus 8 so nos of values that can be used for n = 2 . . . . 96 ( all even nos ) i . e 48 nos total = 48 + 12 = 60 ways so reqd p = 60 / 96 = 5 / 8 ; answer : d"
Answer: d
Question (physics): a car going at 40 miles per hour set out on an 60 - mile trip at 9 : 00 a . m . exactly 10 minutes later , a second car left from the same place and followed the same route . how fast , in miles per hour , was the second car going if it caught up with the first car at 10 : 30 a . m . ?
Options: a ) 45 , b ) 60 , c ) 53 , d ) 55 , e ) 50
Rationale: "let car a = car that starts at 9 am car b = car that starts at 9 : 10 am time for which car a travels at speed of 40 m per hour = 1.5 hours distance travelled by car a = 40 * 1.5 = 60 miles since car b catches up car a at 10 : 30 , time = 60 mins = 1 hour speed of car b = 60 / ( 1 ) = 60 miles per hour answer b"
Answer: b
Question (general): 1 = 5,2 = 25,3 = 253,4 = 150,5 = 225 then 150 = ?
Options: a ) 1 , b ) 255 , c ) 4 , d ) 445 , e ) 235
Rationale: "1 = 5,2 = 25,3 = 253,4 = 150,5 = 225 then 150 = ? 150 = 4 check the fourth eqn . answer : c"
Answer: c
Question (gain): a dealer offers a cash discount of 16 % and still makes a profit of 25 % when he further allows 60 articles to be sold at the cost price of 50 articles to a particular sticky bargainer . how much percent above the cost price were his articles listed ?
Options: a ) 50 % , b ) 60 % , c ) 70 % , d ) 75 % , e ) 78 + ( 4 / 7 ) %
Rationale: "given cash discount - 16 % profit - 25 % items sold - 60 price sold at = list price of 50 assume list price = $ 10 total invoice = $ 500 - 16 % cash discount = $ 420 let cost price of 60 items be x so total cost = 60 * x given the shopkeeper had a profit of 25 % 60 * x * 125 / 100 = 420 or x = $ 7 * 4 / 5 = $ 28 / 5 which means his products were listed at $ 10 which is a 78 + ( 4 / 7 ) % markup over $ 28 / 5 answer e"
Answer: e
Question (general): if n divided by 8 has a remainder of 1 , what is the remainder when 3 times n is divided by 8 ?
Options: a ) 1 , b ) 3 , c ) 7 , d ) 5 , e ) 6
Rationale: as per question = > n = 8 p + 1 for some integer p hence 3 n = > 24 q + 3 = > remainder = > 3 for some integer q hence b
Answer: b
Question (geometry): the volume of a cube is 2197 cc . find its surface .
Options: a ) 864 , b ) 1014 , c ) 1299 , d ) 1268 , e ) 1191
Rationale: a 3 = 2197 = > a = 13 6 a 2 = 6 * 13 * 13 = 1014 answer : b
Answer: b
Question (geometry): 15 business executives and 3 chairmen meet at a conference . if each business executive shakes the hand of every other business executive and every chairman once , and each chairman shakes the hand of each of the business executives but not the other chairmen , how many handshakes would take place ?
Options: a ) 150 , b ) 131 , c ) 115 , d ) 90 , e ) 45
Rationale: "there are 15 business exec and in each handshake 2 business execs are involved . hence 15 c 2 = 105 also , each of 15 exec will shake hand with every 3 other chairmen for total of 45 handshake . total = 45 + 105 = 150 ans : a"
Answer: a
Question (general): if pintu is coded as 79523 in a certain code language , how would you code mumbo in the same language ?
Options: a ) 43426 , b ) 14236 , c ) 13436 , d ) 14263 , e ) 15263
Rationale: "1 2 3 4 5 6 7 8 9 a b c d e f g h i j k l m n o p q r s t u v w x y z sooo . . . mumbo is 43426 . . . answer : a"
Answer: a
Question (physics): a is twice as fast as b . if b alone can do a piece of work in 18 days , in what time can a and b together complete the work ?
Options: a ) 10 , b ) 16 , c ) 18 , d ) 6 , e ) 12
Rationale: "a can do the work in 18 / 2 i . e . , 9 days . a and b ' s one day ' s work = 1 / 9 + 1 / 18 = ( 2 + 1 ) / 18 = 1 / 6 so a and b together can do the work in 6 days . answer : d"
Answer: d
Question (geometry): the area of a triangle is with base 5.5 m and height 6 m ?
Options: a ) 11 m 2 , b ) 16.5 m 2 , c ) 18.5 m 2 , d ) 19.5 m 2 , e ) 12 m 2
Rationale: "1 / 2 * 5.5 * 6 = 16.5 m 2 answer : b"
Answer: b
Question (physics): working together , printer a and printer b would finish the task in 15 minutes . printer a alone would finish the task in 45 minutes . how many pages does the task contain if printer b prints 3 pages a minute more than printer a ?
Options: a ) 125 , b ) 135 , c ) 145 , d ) 155 , e ) 165
Rationale: "15 * a + 15 * b = x pages in 15 mins printer a will print = 15 / 45 * x pages = 1 / 3 * x pages thus in 15 mins printer printer b will print x - 1 / 3 * x = 2 / 3 * x pages also it is given that printer b prints 3 more pages per min that printer a . in 15 mins printer b will print 45 more pages than printer a thus 2 / 3 * x - 1 / 3 * x = 45 = > x = 135 pages answer : b"
Answer: b
Question (gain): the owner of a furniture shop charges his customer 25 % more than the cost price . if a customer paid rs . 8400 for a computer table , then what was the cost price of the computer table ?
Options: a ) rs . 5725 , b ) rs . 5275 , c ) rs . 6275 , d ) rs . 6720 , e ) none of these
Rationale: "cp = sp * ( 100 / ( 100 + profit % ) ) = 8400 ( 100 / 125 ) = rs . 6720 . answer : d"
Answer: d
Question (general): if you write down all the numbers from 1 to 100 , then how many times do you write 3 ?
Options: a ) 11 , b ) 18 , c ) 20 , d ) 21 , e ) 22
Rationale: "explanation : explanation : clearly , from 1 to 100 , there are ten numbers with 3 as the unit ' s digit - 3 , 13 , 23 , 33 , 43 , 53 , 63 , 73 , 83 , 93 ; and ten numbers with 3 as the ten ' s digit - 30 , 31 , 32 , 33 , 34 , 35 , 36 , 37 , 38 , 39 . so , required number = 10 + 10 = 20 . answer : c"
Answer: c
Question (other): the h . c . f . of two numbers is 23 and the other two factors of their l . c . m . are 10 and 11 . the larger of the two numbers is :
Options: a ) 276 , b ) 253 , c ) 322 , d ) 345 , e ) 395
Rationale: "clearly , the numbers are ( 23 x 10 ) and ( 23 x 11 ) . larger number = ( 23 x 11 ) = 253 . answer : option b"
Answer: b
Question (gain): at what rate percent on simple interest will rs . 1750 amount to rs . 2000 in 5 years ?
Options: a ) 4 % , b ) 3 6 / 7 % , c ) 2 6 / 7 % , d ) 5 % , e ) 6 %
Rationale: "explanation : 250 = ( 1750 x 5 xr ) / 100 250 = ( 175 xr ) / 2 500 = ( 175 xr ) r = 500 / 175 r = 2 6 / 7 % answer : option c"
Answer: c
Question (physics): tim and é lan are 60 miles away from one another . they are starting to move towards each other simultaneously , tim at a speed of 10 mph and é lan at a speed of 5 mph . if every hour they double their speeds , what is the distance that tim will pass until he meets é lan ?
Options: a ) 30 miles . , b ) 35 miles . , c ) 40 miles . , d ) 60 miles . , e ) 65 miles .
Rationale: tim and elan will meet at the same time while their ratio of speed is 2 : 1 respectively . so their individual distance traveled ratio will be same . plugging in the answer choice only answer choice c meet the 2 : 1 ( tim : elan = 40 : 20 ) ratio of maintaining total distance traveled 60 miles so correct answer c
Answer: c
Question (general): if y is 90 % greater than x , than x is what % less than y ?
Options: a ) 35.7 % , b ) 39.8 % , c ) 43.2 % , d ) 47.4 % , e ) 51.2 %
Rationale: "y = 1.9 x x = y / 1.9 = 10 y / 19 x is 9 / 19 less which is 47.4 % less than y . the answer is d ."
Answer: d
Question (physics): what is the length of a bridge ( in meters ) , which a train 166 meters long and travelling at 45 km / h can cross in 40 seconds ?
Options: a ) 310 , b ) 318 , c ) 326 , d ) 334 , e ) 342
Rationale: "speed = 45 km / h = 45000 m / 3600 s = 25 / 2 m / s in 40 seconds , the train can travel 25 / 2 * 40 = 500 meters 500 = length of train + length of bridge length of bridge = 500 - 166 = 334 meters the answer is d ."
Answer: d
Question (general): the average weight of 10 persons increases by 4.2 kg when a new person comes in place of one of them weighing 65 kg . what might be the weight of the new person ?
Options: a ) 107 kg , b ) 80 kg , c ) 120 kg , d ) 90 kg , e ) 100
Rationale: "solution total weight increased = ( 10 x 4.2 ) kg = 42 kg . weight of new person = ( 65 + 42 ) kg = 107 kg . answer a"
Answer: a
Question (general): if 5 < x < 9 and y = x + 3 , what is the greatest possible integer value of x + y ?
Options: a ) 19 , b ) 20 , c ) 21 , d ) 22 , e ) 23
Rationale: "x + y = x + x + 3 = 2 x + 3 we need to maximize this value and it needs to be an integer . 2 x is an integer when the decimal of x is . 0 or . 5 the largest such value is 8.5 then x + y = 8.5 + 11.5 = 20 . the answer is b ."
Answer: b
Question (general): a certain class of students is being divided into teams . the class can either be divided into 8 teams with an equal number of players on each team or 24 teams with an equal number of players on each team . what is the lowest possible number of students in the class ?
Options: a ) 6 , b ) 36 , c ) 48 , d ) 24 , e ) 72
Rationale: "let total no of students in the class be n so , we are told that n is divisible by both 8 24 so , lets find the least common multiple of 8 24 , ie 24 so our answer is ( d ) 24"
Answer: d
Question (geometry): a rectangular tiled patio is composed of 90 square tiles . the rectangular patio will be rearranged so that there will be 2 fewer columns of tiles and 4 more rows of tiles . after the change in layout , the patio will still have 90 tiles , and it will still be rectangular . how many rows are in the tile patio before the change in layout ?
Options: a ) 5 , b ) 6 , c ) 10 , d ) 11 , e ) 28
Rationale: "r * c = 90 and ( 11 + 4 ) ( c - 2 ) = 90 - - > r = 11 and c = 8 . answer : d ."
Answer: d
Question (general): what is the units digit of ( 3 ^ 5 ) ( 4 ^ 13 ) ?
Options: a ) 2 , b ) 4 , c ) 6 , d ) 7 , e ) 8
Rationale: "- > the ones place of ( ~ 3 ) ^ n repeats after 4 times like 3  9  7  1  3 . the ones place of ( ~ 4 ) ^ n repeats after 2 times like 4  6  4 . then , 3 ^ 5 = 3 ^ 4 * 1 + 1  3 ^ 1 . , 4 ^ 13 = 4 ^ 2 * 6 + 1 = 4 ^ 1 = ~ 4 which is ( 3 ^ 5 ) ( 4 ^ 13 )  ( 3 ^ 1 ) ( ~ 4 ) = ( ~ 3 ) ( ~ 4 ) = ~ 2 . therefore , the answer is a ."
Answer: a
Question (physics): the sum of three consecutive even numbers is 63 . find the middle number of the three ?
Options: a ) 14 , b ) 23 , c ) 25 , d ) 29 , e ) 21
Rationale: "middle no = 63 / 3 = 21 ans e"
Answer: e
Question (geometry): a cube is divided into 512 identical cubelets . each cut is made parallel to some surface of the cube . but before doing that , the cube is painted with green on one set of opposite faces , red on another set of opposite faces , and blue on the third set of opposite faces . how many cubelets are painted with exactly one colour ?
Options: a ) 216 , b ) 264 , c ) 296 , d ) 312 , e ) 324
Rationale: "each face of the cube has 8 x 8 = 64 cubelets . on each face , only the interior cubelets are painted one colour . on each side , 6 x 6 = 36 cubelets are painted one colour . since the cube has six sides , the number of cubes with one colour is 6 * 36 = 216 the answer is a ."
Answer: a
Question (general): of the 150 employees at company x , 70 are full - time , and 100 have worked at company x for at least a year . there are 20 employees at company x who aren ’ t full - time and haven ’ t worked at company x for at least a year . how many full - time employees of company x have worked at the company for at least a year ?
Options: a ) 20 , b ) 40 , c ) 50 , d ) 80 , e ) 100
Rationale: "150 employees 70 are full - time 100 have worked at company x for at least a year 20 employees at company x who aren ’ t full - time and haven ’ t worked at company x for at least a year . how many full - time employees of company x have worked at the company for at least a year ? 150 - 70 = 80 employees not full time 80 - 20 = 60 employees not full time who worked over a year 100 employees have worked at company x for at least a year - 60 employees not full time who worked over a year = 40 full - time employees of company x have worked at the company for at least a year ans b"
Answer: b
Question (general): paul ' s income is 40 % less than rex ' s income , quentin ' s income is 20 % less than paul ' s income , and sam ' s income is 40 % less than paul ' s income . if rex gave 60 % of his income to paul and 40 % of his income to quentin , paul ' s new income would be what fraction of quentin ' s new income ?
Options: a ) 11 / 12 , b ) 13 / 17 , c ) 13 / 19 , d ) 15 / 11 , e ) 11 / 19
Rationale: "make r = 10 p = 0.6 r = 6 q = 0.8 p = 4.8 s = 0.6 p = 3.6 for that we get p = 12 and q 8.8 so 12 / 8.8 = 3 / 2.2 ans : d"
Answer: d
Question (general): if 6 - 12 / x = 7 - 7 / x , then x =
Options: a ) - 5 , b ) 19 , c ) - 7 / 5 , d ) 1 , e ) 5 / 6
Rationale: "we ' re given the equation 6 - 12 / x = 7 - 7 / x . we ' re asked for the value of x . the common - denominator of these 4 numbers is x , so we need to multiply both sides of the equation by x , giving us . . . 6 x - 12 x / x = 7 x - 7 x / x we can then eliminate that denominator , which gives us . . . . 6 x - 12 = 7 x - 7 - 5 = x a"
Answer: a
Question (physics): the sector of a circle has radius of 14 cm and central angle 135 o . find its perimeter ?
Options: a ) 91.5 cm , b ) 61 cm , c ) 28.9 cm , d ) 29.2 cm , e ) 98.2 cm
Rationale: "perimeter of the sector = length of the arc + 2 ( radius ) = ( 135 / 360 * 2 * 22 / 7 * 14 ) + 2 ( 14 ) = 33 + 28 = 61 cm answer : b"
Answer: b