Cheukting/mathqa huggingface dataset:
Question (general): at a restaurant , glasses are stored in two different - sized boxes . one box contains 12 glasses , and the other contains 16 glasses . if the average number of glasses per box is 15 , and there are 16 more of the larger boxes , what is the total number of glasses r at the restaurant ? ( assume that all boxes are filled to capacity . )
Options: a ) 96 , b ) 240 , c ) r = 256 , d ) r = 384 , e ) r = 480
Rationale: most test takers would recognize thesystemof equations in this prompt and just do algebra to get to the solution ( and that ' s fine ) . the wording of the prompt and the ' spread ' of the answer choices actually provide an interesting ' brute force ' shortcut that you can take advantage of to eliminate the 4 wrong answers . . . . we ' re told that there are 2 types of boxes : those that hold 12 glasses and those that hold 16 glasses . since the average number of boxes is 15 , we know that there must be at least some of each . we ' re also told that that there are 16 more of the larger boxes . this means , at the minimum , we have . . . 1 small box and 17 large boxes = 1 ( 12 ) + 17 ( 16 ) = 12 + 272 = 284 glasses at the minimum since the question asks for the total number of glasses , we can now eliminate answers a , b and c . . . . the difference in the number of boxes must be 16 though , so we could have . . . . 2 small boxes and 18 large boxes 3 small boxes and 19 large boxes etc . with every additional small box + large box that we add , we add 12 + 16 = 28 more glasses . thus , we can justadd 28 suntil we hit the correct answer . . . . 284 + 28 = 312 312 + 28 = 340 340 + 28 = 368 368 + 28 = 396 at this point , we ' ve ' gone past ' answer d , so the correct answer must be answer e . . . . . but here ' s the proof . . . . 396 + 28 = 424 424 + 28 = 452 452 + 28 = 480 final answer : e
Answer: e
Question (physics): a factory has three types of machines , each of which works at its own constant rate . if 7 machine as and 11 machine bs can produce 360 widgets per hour , and if 8 machine as and 22 machine cs can produce 600 widgets per hour , how many widgets could one machine a , one machine b , and one machine c produce in one 8 - hour day ?
Options: a ) 400 , b ) 475 , c ) 480 , d ) 625 , e ) 700
Rationale: "let machine a produce a widgets per hour . b produce b widgets per hour and c produce c widgets per hour . 7 a + 11 b = 360 - - - ( 1 ) 8 a + 22 c = 600 - - - ( 2 ) dividing ( 2 ) by 2 4 a + 11 c = 300 . . . . . ( 3 ) adding ( 1 ) ( 3 ) 11 a + 11 b + 11 c = 660 a + b + c = 60 per hour so for eight hrs = 60 * 8 = 480 = answer = c"
Answer: c
Question (general): on increasing the number of lines in a page by 60 , they become 240 . what is the % of increase in the no . of lines in the page ?
Options: a ) 33.3 % , b ) 305 , c ) 50 % , d ) 55 % , e ) 60 %
Rationale: "explanation : number of pages increased = 60 now , the number of pages of book = 240 number of pages of the books before increase = 240 – 60 = 180 % increase in the number of pages in the book = 60 / 180 x 100 % = 33.3 % a"
Answer: a
Question (general): if ( 2 ^ 14 ) ( 25 ^ s ) = 5 ( 10 ^ m ) what is the value of m ?
Options: a ) 7 , b ) 8 , c ) 15 , d ) 16 , e ) 14
Rationale: "given 2 ^ 14 * 25 ^ s = 5 * 10 ^ 2 = > 2 ^ 14 * 5 ^ ( 2 s ) = 2 ^ m * 5 ^ ( m + 1 ) ans e on comparing the power of 2 = > m = 14"
Answer: e
Question (general): in a box carrying one dozen of oranges , one - third have become bad . if 3 oranges are taken out from the box at random , what is the probability that at least one orange out of the 3 oranges picked up is good ?
Options: a ) 1 ⁄ 55 , b ) 54 ⁄ 55 , c ) 45 ⁄ 55 , d ) 3 ⁄ 55 , e ) none of these
Rationale: n ( s ) = 12 c 3 = 12 × 11 × 10 / 3 × 2 = 2 × 11 × 10 = 220 no . of selection of 3 oranges out of the total 12 oranges = 12 c 3 = 2 × 11 × 10 = 220 no . of selection of 3 bad oranges out of the total 4 bad oranges = 4 c 3 = 4 \ n ( e ) = no . of desired selection of oranges = 220 – 4 = 216 \ p ( e ) = n ( e ) / n ( s ) = 216 / 220 = 54 / 55 answer b
Answer: b
Question (physics): a goods train runs at the speed of 72 km / hr and crosses a 220 m long platform in 26 sec . what is the length of the goods train ?
Options: a ) 382 , b ) 782 , c ) 300 , d ) 270 , e ) 881
Rationale: "speed = 72 * 5 / 18 = 20 m / sec . time = 26 sec . let the length of the train be x meters . then , ( x + 220 ) / 26 = 20 x = 300 m . answer : c"
Answer: c
Question (general): a and b are two partially filled buckets of water . if 5 liters are transferred from a to b , then a would contain one - third of the amount of water in b . alternatively , if 3 liters are transferred from b to a , b would contain one - half of the amount of water in a . bucket a contains how many liters of water ?
Options: a ) 11 , b ) 13 , c ) 17 , d ) 49 / 5 , e ) 23
Rationale: "let a contains a , b contains b liters so , ( a - 5 ) / ( b + 5 ) = 1 / 3 . . . . . . . ( 1 ) again , ( b - 3 ) / ( a + 3 ) = 1 / 2 . . . . . . . . . . ( 2 ) from ( 1 ) ( 2 ) we find a = 49 / 5 ans : ( d )"
Answer: d
Question (general): two kinds of vodka are mixed in the ratio 1 : 2 and 2 : 1 and they are sold fetching the profit 10 % and 35 % respectively . if the vodkas are mixed in equal ratio and the individual profit percent on them are increased by 4 / 3 and 5 / 3 times respectively , then the mixture will fetch the profit of
Options: a ) 18 % , b ) 20 % , c ) 21 % , d ) 35 % , e ) can not be determined
Rationale: answer : d .
Answer: d
Question (other): of 60 children , 30 are happy , 10 are sad , and 20 are neither happy nor sad . there are 18 boys and 42 girls . if there are 6 happy boys and 4 sad girls , how many boys are neither happy nor sad ?
Options: a ) 2 , b ) 4 , c ) 6 , d ) 8 , e ) 10
Rationale: "venn diagrams are useful for multiple values of a single variable e . g . state of mind - happy / sad / neither . when you have two or more variables such as here where you have gender - boy / girl too , it becomes unwieldy . in this case , either use the table or logic . table method is shown above ; here is how you will use logic : there are 6 happy boys . there are 4 sad girls but total 10 sad children . so rest 6 sad children must be sad boys . we have 6 happy boys and 6 sad boys . total we have 18 boys . so 18 - 6 - 6 = 6 boys must be neither happy nor sad . answer ( c )"
Answer: c
Question (general): the sum of all the integers k such that − 26 < k < 24 is
Options: a ) 0 , b ) − 2 , c ) − 25 , d ) − 49 , e ) − 51
Rationale: "since k defines a range between − 26 < k < 24 we can set 0 as the reference point for the negative values and positive values . the negative values will range from - 25 to 0 whereas the positive values will range from 0 - 23 . we can conclude that for all but - 25 and - 24 the number pairs will add to 0 . so we have left - 25 - 24 = - 49 . answer d ."
Answer: d
Question (general): evaluate 75 / . 05
Options: a ) 1400 , b ) 1500 , c ) 1505 , d ) none of these , e ) 1506
Rationale: "explanation : 75 / . 05 = 7500 / 5 = 1500 option b"
Answer: b
Question (geometry): the length of a rectangle is three times of its width . if the length of the diagonal is 8 √ 10 then find the perimeter of the rectangle .
Options: a ) 77 cm
b ) 88 cm
c ) 64 cm
d ) 11 cm
e ) 18 cm
Rationale: let breadth = x cm , then , length = 3 x cm x 2 + ( 3 x ) 2 = ( 810 − − √ ) 2 = > 10 x 2 = 640 = > x = 8 x 2 + ( 3 x ) 2 = ( 810 ) 2 = > 10 x 2 = 640 = > x = 8 so , length = 24 cm and breadth = 8 cm perimeter = 2 ( l + b ) = 2 ( 24 + 8 ) = 64 cm answer : c
Answer: c
Question (physics): 225 metres long yard , 26 trees are palnted at equal distances , one tree being at each end of the yard . what is the distance between 2 consecutive trees
Options: a ) 10 , b ) 12 , c ) 14 , d ) 16 , e ) 17
Rationale: "26 trees have 25 gaps between them , required distance ( 225 / 25 ) = 10 a"
Answer: a
Question (physics): car a runs at the speed of 60 km / hr and reaches its destination in 8 hours . car b runs at the speed of 70 km / h and reaches its destination in 4 hours . what is the ratio of distances covered by car a and car b ?
Options: a ) 3 : 7 , b ) 4 : 9 , c ) 12 : 7 , d ) 5 : 7 , e ) 6 : 11
Rationale: car a travels 60 × 8 = 480 km car b travels 70 × 4 = 280 km the ratio is 480 : 280 = 48 : 28 = 12 : 7 the answer is c .
Answer: c
Question (physics): if an object travels at five feet per second , how many feet does it travel in one hour ?
Options: a ) 3488 , b ) 3778 , c ) 12788 , d ) 1800 , e ) 2881
Rationale: "explanation : if an object travels at 5 feet per second it covers 5 x 60 feet in one minute , and 5 x 60 x 60 feet in one hour . answer = 1800 answer : d ) 1800"
Answer: d
Question (general): a house wife saved $ 4 in buying an item on sale . if she spent $ 29 for the item , approximately how much percent she saved in the transaction ?
Options: a ) 8 % , b ) 9 % , c ) 10 % , d ) 11 % , e ) 12 %
Rationale: "actual price = 29 + 4 = $ 33 saving = 4 / 33 * 100 = 12 % approximately answer is e"
Answer: e
Question (general): tough and tricky questions : exponents . if 2 ^ ( 3 x + 2 ) * 3 ^ ( 2 y - 3 ) = 32 ^ x * 9 ^ y , then x + y =
Options: a ) - 3 , b ) - 1 , c ) 0 , d ) - 5 , e ) - 2
Rationale: here is my solution . 2 ^ ( 3 x + 2 ) * 3 ^ ( y - 3 ) = 32 ^ x * 9 ^ y here rhs 32 ^ x * 9 ^ y = 2 ^ ( 5 x ) * 3 ^ ( 2 y ) equating powers on both sides - - > 3 x + 2 = 5 x , thus x = 1 and y - 3 = 2 y giving y = - 3 so , x + y = - 2 option : e
Answer: e
Question (general): what is the units digit of ( 147 ^ 25 ) ^ 49 ?
Options: a ) 1 , b ) 3 , c ) 5 , d ) 7 , e ) 9
Rationale: the units digit of the exponents of 7 repeat in a cycle of four , which is { 7,9 , 3,1 } . the number 25 has the form 4 n + 1 so the units digit is 7 inside the bracket . the exponent 49 has the form 4 n + 1 , so the units digit is 7 . the answer is d .
Answer: d
Question (gain): simple interest on a certain sum of money for 3 years at 8 % per annum is half the compound interest on $ 4000 for 2 years at 10 % per annum . the sum placed on simple interest is :
Options: a ) $ 1750 , b ) $ 2250 , c ) $ 1250 , d ) $ 1500 , e ) $ 2000
Rationale: "compound interest = ( 4000 x ( 1 + 10 / 100 ) ^ 2 - 4000 ) = 4000 x 11 / 10 x 11 / 10 - 4000 = 840 therefore the sum is 420 x 100 / ( 3 x 8 ) = 1750 . answer a ) $ 1750"
Answer: a
Question (gain): in one hour , a boat goes 11 km along the stream and 3 km against the stream . the sped of the boat in still water ( in km / hr ) is :
Options: a ) 3 , b ) 5 , c ) 7 , d ) 9 , e ) 10
Rationale: "solution speed in still water = 1 / 2 ( 11 + 3 ) km / hr = 7 kmph . answer c"
Answer: c
Question (general): if a + b = − 6 , and a = 10 / b , what is the value of a ^ 2 + b ^ 2 ?
Options: a ) 22 , b ) 24 , c ) 16 , d ) 18 , e ) 20
Rationale: a ^ 2 + b ^ 2 should make you think of these formulas : ( a + b ) ( a + b ) = a ^ 2 + b ^ 2 + 2 ab we already know ( a + b ) = - 6 and a * b = 10 ( a + b ) ( a + b ) = ( - 6 ) ( - 6 ) = a ^ 2 + b ^ 2 + 2 * ( 10 ) a ^ 2 + b ^ 2 = 36 - 20 = 16 answer : c
Answer: c
Question (general): a professional basketball player just signed a contract that has a 10 % raise in base salary from last year to this year . the contract also has provisions for a performance bonus of up to $ 10000 . if he earns the maximum performance bonus , his new effective salary will be a 10.5 % raise over last year ' s total salary , when he received no performance bonus . assuming he earns the full performance bonus , what will be his new salary ?
Options: a ) 2010000 , b ) 2110000 , c ) 2150000 , d ) 2200000 , e ) 2210000
Rationale: let x = old salary then ( 1 + . 10 ) * x + 10000 = ( 1 + . 105 ) * x i . e . new base salary + 10000 = effective new salary thus 1.1 * x + 10000 = 1.105 * x 10000 = . 005 * x 2000000 = x thus the new effective salary is 1.105 * 2000000 = 2210000 e
Answer: e
Question (physics): how long does a train 110 m long running at the speed of 72 km / hr takes to cross a bridge 175 m length ?
Options: a ) 12.9 sec , b ) 12.1 sec , c ) 17.9 sec , d ) 16.8 sec , e ) 14.25 sec
Rationale: "speed = 72 * 5 / 18 = 20 m / sec total distance covered = 110 + 175 = 285 m . required time = 285 / 20 = 14.25 sec . answer : e"
Answer: e
Question (physics): find the length of the wire required to go 15 times round a square field containing 69696 m 2 .
Options: a ) 15840 , b ) 15848 , c ) 15828 , d ) 27892 , e ) 22892
Rationale: "a 2 = 69696 = > a = 264 4 a = 1056 1056 * 15 = 15840 answer : a"
Answer: a
Question (general): 5 n + 2 > 17 and 7 n - 5 < 44 ; n must be between which numbers ?
Options: a ) 1 and 8 , b ) 2 and 6 , c ) 0 and 9 , d ) 3 and 7 , e ) 2 and 9
Rationale: "5 n > 15 - - > n > 3 7 n < 49 - - > n < 7 3 < n < 7 answer : d"
Answer: d
Question (general): find the average of first 6 multiples of 5 ?
Options: a ) 10 , b ) 15 , c ) 12.5 , d ) 13 , e ) 17.5
Rationale: "average = ( 5 + 10 + 15 + 20 + 25 + 30 ) / 6 = 17.5 answer is e"
Answer: e
Question (general): a large box contains 15 small boxes and each small box contains 20 chocolate bars . how many chocolate bars are in the large box ?
Options: a ) a ) 220 , b ) b ) 490 , c ) c ) 380 , d ) d ) 300 , e ) e ) 690
Rationale: "the only thing you have to do is a simple multiply we have : 15 * 20 = 300 correct answer is : d ) 300"
Answer: d
Question (physics): the current of a stream runs at the rate of 4 kmph . a boat goes 10 km and back to the starting point in 2 hours , then find the speed of the boat in still water ?
Options: a ) a ) 7 , b ) b ) 2 , c ) c ) 8.9 , d ) d ) 11.4 , e ) e ) 3
Rationale: "s = 4 m = x ds = x + 4 us = x - 4 10 / ( x + 4 ) + 10 / ( x - 4 ) = 2 x = 11.4 answer : d"
Answer: d
Question (physics): the length of the bridge , which a train 170 metres long and travelling at 45 km / hr can cross in 30 seconds , is ?
Options: a ) 245 , b ) 777 , c ) 282 , d ) 266 , e ) 205
Rationale: "speed = [ 45 x 5 / 18 ] m / sec = [ 25 / 2 ] m / sec time = 30 sec let the length of bridge be x metres . then , ( 170 + x ) / 30 = 25 / 2 = > 2 ( 170 + x ) = 750 = > x = 205 m . answer : e"
Answer: e
Question (gain): a retail appliance store priced a video recorder at 20 percent above the wholesale cost of $ 200 . if a store employee applied the 5 percent employee discount to the retail price to buy the recorder , how much did the employee pay for the recorder ?
Options: a ) $ 198 , b ) $ 228 , c ) $ 220 , d ) $ 230 , e ) $ 240
Rationale: "wholesale cost of video recorder = 200 $ video recorder was priced at 20 percent above 200 = 240 $ % discount given by store employee = 5 emlpoyee paid = . 95 * 240 = 228 $ answer b"
Answer: b
Question (general): if a # b = ab – b + b ^ 2 , then 3 # 6 =
Options: a ) 2 , b ) 8 , c ) 15 , d ) 21 , e ) 48
Rationale: "solution - simply substitute 3 and 6 in equation in the place of a and b respectively . 3 # 6 = 3 * 6 - 6 + 6 ^ 2 = 18 - 6 + 36 = 48 . ans e"
Answer: e
Question (general): a man engaged a servant on a condition that he ' ll pay rs 90 and also give him a bag at the end of the yr . he served for 9 months and was given a turban and rs 65 . so the price of turban is
Options: a ) rs 10 , b ) rs 9 , c ) rs 0 , d ) rs 55 , e ) rs 8
Rationale: let the value of turban = rs x for 1 year = 90 + x for 9 months ( i , e 3 / 4 year ) = 65 + x i , e 1 : ( 90 + x ) : : 3 / 4 : ( 65 + x ) i , e ( 90 + x ) / ( 65 + x ) = 1 / ( 3 / 4 ) 270 + 3 x = 260 + 4 x thus x = 10 answer : a
Answer: a
Question (other): if w is the set of all the integers between 29 and 99 , inclusive , that are either multiples of 3 or multiples of 2 or multiples of both , then w contains how many numbers ?
Options: a ) 26 , b ) 32 , c ) 33 , d ) 34 , e ) 47
Rationale: "multiples of 2 from 29 to 99 = multiples of 2 from 1 to 99 - multiples of 2 from 1 to 28 = [ 99 / 2 ] - [ 28 / 2 ] = 49 - 14 = 35 multiples of 3 from 29 to 99 = multiples of 3 from 1 to 99 - multiples of 3 from 1 to 28 = [ 99 / 3 ] - [ 28 / 3 ] = 33 - 9 = 24 multiples of 2 and 3 bothi . e . 6 from 29 to 99 = multiples of 6 from 1 to 99 - multiples of 6 from 1 to 28 = [ 99 / 6 ] - [ 28 / 6 ] = 16 - 4 = 12 these 8 numbers have been counted twice in both the above calculation while calculating multiples of 2 and 3 i . e . total numbers in w = 35 + 24 - 12 = 47 answer option e"
Answer: e
Question (general): for a certain exam , a score of 86 was 7 standard deviations below mean and a score of 90 was 3 standard deviations above mean . what was the mean score for the exam ?
Options: a ) 86.25 , b ) 84 , c ) 85 , d ) 88.8 , e ) 80
Rationale: "mean - 7 sd = 86 mean + 3 sd = 90 by solving above equations we get , sd ( absolute value ) = 0.4 mean = 88.8 ans . d"
Answer: d
Question (geometry): the area of a square is equal to three times the area of a rectangle of dimensions 49 cm * 27 cm . what is the perimeter of the square ?
Options: a ) 380 cm , b ) 264 cm , c ) 252 cm , d ) 324 cm , e ) 296 cm
Rationale: "area of the square = s * s = 3 ( 49 * 27 ) = > s = 7 * 3 * 3 = 63 cm perimeter of the square = 4 * 63 = 252 cm . answer : c"
Answer: c
Question (general): in a division , a student took 72 as divisor instead of 36 . his answer was 24 . the correct answer is -
Options: a ) 42 , b ) 32 , c ) 48 , d ) 28 , e ) 38
Rationale: "x / 72 = 24 . x = 24 * 72 . so correct answer would be , ( 24 * 72 ) / 36 = 48 . answer : c"
Answer: c
Question (general): a scientist used a unique two - color code to identify each of the test subjects involved in a certain study . if the scientist found that choosing from among 5 colors produced enough color codes to identify all but 6 of the test subjects , how many test subjects were in the study ? ( assume that the order of the colors in the codes does not matter . )
Options: a ) 14 , b ) 15 , c ) 16 , d ) 17 , e ) 18
Rationale: 5 c 2 = 10 the number of test subjects is 10 + 6 = 16 the answer is c .
Answer: c
Question (general): enrollment in city college in 1980 was 85 / 3 percent of enrollment in 1990 . what was the percent increase in the college ’ s enrollment from 1980 to 1990 ?
Options: a ) 100 % , b ) 16 2 / 3 % , c ) 200 % , d ) 253 % , e ) 183 1 / 3 %
Rationale: assume 100 enrollments present in 1990 85 / 3 % of 1990 = enrollments on 1980 enrollments on 1980 = 28.33 % change = ( enrollment in 1990 - enrollment in 1980 ) * 100 / ( enrollment in 1980 ) = ( 100 - 28.33 ) * 100 / 28.333 = 7166.67 / 28.333 = 253 % ans - d
Answer: d
Question (gain): there were two candidates in an election . winner candidate received 54 % of votes and won the election by 288 votes . find the number of votes casted to the winning candidate ?
Options: a ) 776 , b ) 1944 , c ) 2199 , d ) 2157 , e ) 2125
Rationale: "w = 54 % l = 46 % 54 % - 46 % = 8 % 8 % - - - - - - - - 288 54 % - - - - - - - - ? = > 1944 answer : b"
Answer: b
Question (gain): a person bought 115 glass bowls at a rate of rs . 18 per bowl . he sold 104 of them at rs . 20 and the remaining broke . what is the percentage gain for a ?
Options: a ) 40 , b ) 300 / 11 , c ) 243 / 7 , d ) 279 / 11 , e ) 100 / 207
Rationale: "cp = 115 * 18 = 2070 and sp = 104 * 20 = 2080 gain % = 100 * ( 2080 - 2070 ) / 2070 = 100 / 207 answer : e"
Answer: e
Question (general): lisa and robert have taken the same number of photos on their school trip . lisa has taken 3 times as many photos as claire and robert has taken 10 more photos than claire . how many photos has claire taken ?
Options: a ) 5 , b ) 8 , c ) 11 , d ) 12 , e ) 14
Rationale: "l = r l = 3 c r = c + 10 3 c = c + 10 c = 5 the answer is a ."
Answer: a
Question (general): how many even multiples of 45 are there between 449 and 901 ?
Options: a ) 5 , b ) 6 , c ) 9 , d ) 10 , e ) 11
Rationale: 450 = 10 * 45 900 = 20 * 45 the even multiples are 45 multiplied by 10 , 12 , 14 , 16 , 18 , and 20 for a total of 6 . the answer is b .
Answer: b
Question (general): 19 chess players take part in a tournament . every player plays twice with each of his opponents . how many games are to be played ?
Options: a ) 286 , b ) 342 , c ) 422 , d ) 540 , e ) 618
Rationale: "2 * 19 c 2 = 2 * 171 = 342 the answer is b ."
Answer: b
Question (general): rs . 585 is divided amongst a , b , c so that 4 times a ' s share , 6 times b ' s share and 3 times c ' s share are all equal . find c ' s share ?
Options: a ) 260 , b ) 150 , c ) 817 , d ) 716 , e ) 616
Rationale: a + b + c = 585 4 a = 6 b = 3 c = x a : b : c = 1 / 4 : 1 / 6 : 1 / 3 = 3 : 2 : 4 4 / 9 * 585 = rs . 260 answer : a
Answer: a
Question (general): in 10 years , a will be twice as old as b was 10 years ago . if a is now 8 years older than b the present age of b is
Options: a ) 37 , b ) 38 , c ) 39 , d ) 40 , e ) 41
Rationale: "let present age of a be a and b be b a + 10 = 2 * ( b - 10 ) = > 2 b - a = 30 . . . . . . ( i ) a = b + 8 = > 2 b - b - 8 = 30 b = 38 so the present age of b is 38 years answer : b"
Answer: b
Question (general): a die is rolled twice . what is the probability of getting a sum equal to 12 ?
Options: a ) 1 / 36 , b ) 1 / 9 , c ) 1 / 7 , d ) 1 / 24 , e ) 2 / 36
Rationale: "total number of outcomes possible when a die is rolled = 6 ( ∵ any one face out of the 6 faces ) hence , total number of outcomes possible when a die is rolled twice , n ( s ) = 6 × 6 = 36 e = getting a sum of 12 when the two dice fall = { ( 6 , 6 ) } hence , n ( e ) = 1 p ( e ) = n ( e ) / n ( s ) = 1 / 36 = 1 / 36 answer : option a"
Answer: a
Question (gain): a man can row his boat with the stream at 14 km / h and against the stream in 4 km / h . the man ' s rate is ?
Options: a ) 1 kmph , b ) 3 kmph , c ) 8 kmph , d ) 7 kmph , e ) 5 kmph
Rationale: "ds = 14 us = 4 s = ? s = ( 14 - 4 ) / 2 = 5 kmph answer : e"
Answer: e
Question (general): cost is expressed by the formula tb ^ 4 . if b is doubled , the new cost is what percent t of the original cost ?
Options: a ) t = 200 , b ) t = 600 , c ) t = 800 , d ) t = 1600 , e ) t = 50
Rationale: "original cost c 1 = t 1 * b 1 ^ 4 new cost c 2 = t 2 * b 2 ^ 4 . . . . only b is doubled so t 2 = t 1 and b 2 = 2 b 1 c 2 = t 2 * ( 2 b 1 ) ^ 4 = 16 ( t 1 * b 1 ^ 4 ) = 16 c 1 16 times c 1 = > 1600 % of c 1 ans d = 1600"
Answer: d
Question (general): in a certain egg - processing plant , every egg must be inspected , and is either accepted for processing or rejected . for every 96 eggs accepted for processing , 4 eggs are rejected . if , on a particular day , 12 additional eggs were accepted , but the overall number of eggs inspected remained the same , the ratio of those accepted to those rejected would be 99 to 1 . how many q eggs does the plant process per day ?
Options: a ) 100 , b ) 300 , c ) 400 , d ) 3000 , e ) 4000
Rationale: straight pluggin in for me . as usual , i started with c and got the answer . lets ' back calculate and see what we get let us consider eggs processed each day to be 400 so initial ratio of eggs processed and rejected is 96 : 4 or 24 : 1 so out of 400 eggs , there will be 384 eggs processed and 16 rejected . now if the no . of eggs inspected remain and 12 more eggs get accepted that means there q = 384 + 12 = 396 eggs accepted and 4 rejected . . . and the ratio will be 99 : 1 bingo . . . this is what the questions says . . . . its always a good idea to start with c .
Answer: c
Question (physics): on her annual road trip to visit her family in seal beach , california , traci stopped to rest after she traveled 1 ⁄ 2 of the total distance and again after she traveled 1 ⁄ 4 of the distance remaining between her first stop and her destination . she then drove the remaining 400 miles and arrived safely at her destination . what was the total distance , in miles , from traci ’ s starting point to seal beach ?
Options: a ) 250 , b ) 3200 / 3 , c ) 3150 / 3 , d ) 4002 / 3 , e ) 550
Rationale: "let d = total distance traci traveled 1 / 2 = d / 2 i . e . remaining distance = d / 2 she traveled 1 / 4 th of d / 2 = d / 8 thus : d = ( d / 2 ) + ( d / 8 ) + 400 d = 3200 / 3 answer : b"
Answer: b
Question (general): a certain country had a total annual expenditure of $ 1.2 x 10 ^ 11 last year . if the population of the country was 240 million last year , what was the per capita expenditure ?
Options: a ) $ 500 , b ) $ 1,000 , c ) $ 2,000 , d ) $ 3,000 , e ) $ 5,000
Rationale: "total expenditure / population = per capita expenditure hence , ( 1,2 x 10 ^ 11 ) / 240 000 000 = ( 12 x 10 ^ 10 ) / ( 2,4 x 10 ^ 8 ) = 5 x 10 ^ ( 10 - 8 ) = 5 x 10 ^ 2 = 500 . answer is a ."
Answer: a