Cheukting/mathqa huggingface dataset:
Question (physics): walking with 4 / 5 of my usual speed , i miss the bus by 7 minutes . what is my usual time ?
Options: a ) 16 min , b ) 26 min , c ) 28 min , d ) 20 min , e ) 12 min
Rationale: "speed ratio = 1 : 4 / 5 = 5 : 4 time ratio = 4 : 51 - - - - - - - - 7 4 - - - - - - - - - ? è 28 answer : c"
Answer: c
Question (gain): if difference between compound interest and simple interest on a sum at 10 % p . a . for 2 years is rs . 150 then sum is
Options: a ) s . 15000 , b ) s . 15100 , c ) s . 15800 , d ) s . 16000 , e ) s . 16200
Rationale: "p ( r / 100 ) ^ 2 = c . i - s . i p ( 10 / 100 ) ^ 2 = 150 15000 answer : a"
Answer: a
Question (gain): in one hour , a boat goes 8 km along the stream and 2 km against the stream . the sped of the boat in still water ( in km / hr ) is :
Options: a ) 3 , b ) 5 , c ) 8 , d ) 9 , e ) 10
Rationale: "solution speed in still water = 1 / 2 ( 8 + 2 ) km / hr = 5 kmph . answer b"
Answer: b
Question (gain): coconuts were purchased at 150 per 100 and sold at 2 per coconut . if 2000 coconuts were sold , what was the total profit made ?
Options: a ) 500 , b ) 1000 , c ) 1500 , d ) 2000 , e ) none of these
Rationale: c . p . for one coconut = 150 ⁄ 100 = 3 ⁄ 2 s . p . for one coconut = 2 profit on one coconut = 2 - 3 ⁄ 2 = 1 ⁄ 2 ∴ profit on 2000 coconut = 1 ⁄ 2 × 2000 = 1000 answer b
Answer: b
Question (other): what is the factorial of 5 ?
Options: a ) 1 , b ) 60 , c ) 120 , d ) 130 , e ) 180
Rationale: "c 120 120 ( 5 x 4 x 3 x 2 x 1 ) ."
Answer: c
Question (physics): when working alone , painter w can paint a room in 2 hours , and working alone , painter x can paint the same room in e hours . when the two painters work together and independently , they can paint the room in 3 / 4 of an hour . what is the value of e ?
Options: a ) 3 / 4 , b ) 1 [ 1 / 5 ] , c ) 1 [ 2 / 5 ] , d ) 1 [ 3 / 4 ] , e ) 2
Rationale: "rate * time = work let painter w ' s rate be w and painter x ' s rate be x r * t = work w * 2 = 1 ( if the work done is same throughout the question then the work done can be taken as 1 ) = > w = 1 / 2 x * e = 1 = > x = 1 / e when they both work together then their rates get added up combined rate = ( w + x ) r * t = work ( w + x ) * 3 / 4 = 1 = > w + x = 4 / 3 = > 1 / 2 + 1 / e = 4 / 3 = > 1 / e = ( 8 - 3 ) / 6 = 5 / 6 = > e = 6 / 5 = 1 [ 1 / 5 ] answer b"
Answer: b
Question (physics): a train is 435 meter long is running at a speed of 45 km / hour . in what time will it pass a bridge of 140 meter length
Options: a ) 20 seconds , b ) 30 seconds , c ) 46 seconds , d ) 50 seconds , e ) none of these
Rationale: "explanation : speed = 45 km / hr = 45 * ( 5 / 18 ) m / sec = 25 / 2 m / sec total distance = 435 + 140 = 575 meter time = distance / speed = 575 ∗ 2 / 25 = 46 seconds option c"
Answer: c
Question (physics): if the l . c . m of two numbers is 450 and their product is 22500 , find the h . c . f of the numbers .
Options: a ) 50 , b ) 30 , c ) 125 , d ) 25 , e ) none of these
Rationale: "h . c . f = ( product of the numbers ) / ( their l . c . m ) = 22500 / 450 = 50 . answer : a"
Answer: a
Question (geometry): the area of a parallelogram is 72 cm ^ 2 and its altitude is twice the corresponding base . what is the length of the base ?
Options: a ) 1 cm
b ) 3 cm
c ) 6 cm
d ) 4 cm
e ) 2 cm
Rationale: let base = x cm height = 2 x cm area = x ã — 2 x = 2 x ^ 2 area = x ã — 2 x = 2 x ^ 2 area is given as 72 cm ^ 2 2 x ^ 2 = 72 x ^ 2 = 36 x = 6 cm answer : c
Answer: c
Question (gain): martin buys a pencil and a notebook for 80 cents . at the same store , gloria buys a notebook and an eraser for $ 1.15 cents , and zachary buys a pencil and an eraser for 75 cents . how many cents would it cost to buy 3 pencils , 3 notebooks , and 3 erasers ? ( assume that there is no volume discount . )
Options: a ) 325 , b ) 345 , c ) 365 , d ) 385 , e ) 405
Rationale: pencil + notebook = 80 notebook + eraser = 115 pencil + eraser = 75 let ' s add all three equations . 2 pencils + 2 notebooks + 2 erasers = 270 cents the cost to buy 3 of each would be ( 3 / 2 ) ( 270 ) = 405 the answer is e .
Answer: e
Question (general): when 200 is divided by positive integer x , the remainder is 3 . what is the remainder when 297 is divided by x ?
Options: a ) 2 , b ) 3 , c ) 4 , d ) 6 , e ) 8
Rationale: "f 200 / x leaves a reminder 3 then ( 200 - 3 ) i . e . 197 is divisible by x so ( 200 + 197 ) / x leaves a reminder rem ( 200 / x ) + rem ( 197 / x ) = > 3 + 0 = 3 answer : b"
Answer: b
Question (physics): if a fast song has 160 beats per minute , and a slow song has 90 beats per minute , how many minutes total would you play a fast and a slow song to have a stream of music that had a total of 1020 beats ?
Options: a ) 6 , b ) 7 , c ) 8 , d ) 9 , e ) 10
Rationale: we can determine quickly that total number should range between 1020 / 160 < = n < = 1020 / 90 , so ans should be between 6 and 12 . now solving the expression 160 a + 90 b = 1020 decreasing 1020 by multiples of 160 and checking divisibility of that number by 9 , we get fast song plays for 3 minutes and slow somg plays for 6 minutes , 3 * 160 + 6 * 90 = 1020 hence total number of minutes stream of music plays is 3 + 6 = 9 minutes ans d
Answer: d
Question (general): in a party every person shakes hands with every other person . if there were a total of 190 handshakes in the party then what is the number of persons present in the party ?
Options: a ) 15 , b ) 16 , c ) 17 , d ) 18 , e ) 20
Rationale: "explanation : let the number of persons be n â ˆ ´ total handshakes = nc 2 = 190 n ( n - 1 ) / 2 = 190 â ˆ ´ n = 20 answer : option e"
Answer: e
Question (geometry): a cube of edge 7 cm is cut into cubes each of edge 1 cm . the ratio of the total surface area of one of the small cubes to that of the large cube is equal to :
Options: a ) 1 : 25 , b ) 1 : 49 , c ) 1 : 52 , d ) 1 : 522 , e ) none
Rationale: "sol . required ratio = 6 * 1 * 1 / 6 * 7 * 7 = 1 / 49 = 1 : 49 . answer b"
Answer: b
Question (other): ratio between rahul and deepak is 4 : 3 , after 6 years rahul age will be 30 years . what is deepak present age ?
Options: a ) 18 , b ) 15 , c ) 77 , d ) 266 , e ) 182
Rationale: "present age is 4 x and 3 x , = > 4 x + 6 = 30 = > x = 6 so deepak age is = 3 ( 6 ) = 18 answer : a"
Answer: a
Question (general): a , b and c rents a pasture for rs . 480 . a put in 12 horses for 8 months , b 16 horses for 9 months and 18 horses for 6 months . how much should c pay ?
Options: a ) 270 , b ) 199 , c ) 676 , d ) 149 , e ) 122
Rationale: "12 * 8 : 16 * 9 = 18 * 6 8 : 12 : 9 9 / 29 * 480 = 149 answer : d"
Answer: d
Question (general): what is remainder of the division ( 1525 * 1527 * 1529 ) / 12 ?
Options: a ) 0 , b ) 1 , c ) 2 , d ) 3 , e ) 4
Rationale: "remainder will be number / 100 here as the divisor is two digit number = 12 . hence checking for the last two digits = 5 * 7 * 9 = 15 thus remainder = 3 . answer : d"
Answer: d
Question (general): a pharmaceutical company received $ 5 million in royalties on the first $ 20 million in sales of the generic equivalent of one of its products and then $ 9 million in royalties on the next $ 108 million in sales . by approximately what percent did the ratio of royalties to sales decrease from the first $ 20 million in sales to the next $ 108 million in sales ?
Options: a ) 8 % , b ) 15 % , c ) 45 % , d ) 52 % , e ) 67 %
Rationale: solution : this is a percent decrease problem . we will use the formula : percent change = ( new – old ) / old x 100 to calculate the final answer . we first set up the ratios of royalties to sales . the first ratio will be for the first 20 million in sales , and the second ratio will be for the next 108 million in sales . because all of the sales are in millions , we do not have to express all the trailing zeros in our ratios . first 20 million royalties / sales = 5 / 20 = 1 / 4 next 108 million royalties / sales = 9 / 108 = 1 / 12 because each ratio is not an easy number to use , we can simplify each one by multiplying each by the lcm of the two denominators , which is 60 . keep in mind that we are able to do this only because our answer choices are expressed in percents . first 20 million royalties / sales = ( 5 / 20 ) x 12 = 3 next 108 million royalties / sales = 9 / 108 = ( 1 / 12 ) x 12 = 1 we can plug 15 and 5 into our percent change formula : ( new – old ) / old x 100 [ ( 1 – 3 ) / 3 ] x 100 - 200 / 3 x 100 at this point we can stop and consider the answer choices . since we know that 200 / 3 is just a bit less than ½ , we know that - 200 / 3 x 100 is about a 67 % decrease . answer e .
Answer: e
Question (gain): in the first 10 overs of a cricket game , the run rate was only 5.2 . what should be the run rate in the remaining 40 overs to reach the target of 282 runs ?
Options: a ) 6.25 , b ) 6.5 , c ) 6.75 , d ) 5.75 , e ) 8
Rationale: "10 overs - run rate = 5.2 runs scored in first 10 overs = 52 remaining overs 40 total runs to be scored = 282 52 runs already scored 282 - 52 = 230 230 runs to be scored in 40 overs let required runrate be x 40 * x = 230 x = 230 / 40 x = 5.75 the required runrate is 5.75 answer : d"
Answer: d
Question (other): of the diplomats attending a summit conference , 30 speak french , 32 do not speak russian , and 20 % of the diplomats speak neither french nor russian . if 10 % of the diplomats speak both languages , then how many diplomats attended the conference ?
Options: a ) 20 , b ) 96 , c ) 108 , d ) 120 , e ) 150
Rationale: "{ total } = { french } + { russian } - { both } + { neither } { total } = 30 + ( { total } - 32 ) - ( 0.1 * { total } ) + 0.2 * { total } solving gives { total } = 20 . answer : a ."
Answer: a
Question (gain): during the second quarter of 1984 , a total of 3 , 976000 domestic cars were sold . if this was 32 % greater than the number sold during the first quarter of 1984 , how many were sold during the first quarter ?
Options: a ) 714,240 , b ) 2 , 261,760 , c ) 2 , 400,000 , d ) 3 , 012,121 , e ) 3 , 915,790
Rationale: let number of cars sold in 1 st quarter = x number of cars sold in 2 nd quarter = 32 % greater than the number sold during the first quarter = ( 1 + 32 / 100 ) x = 1.32 x 1.32 x = 3 , 976,000 = > x = 3 , 012,121 so , answer will be d
Answer: d
Question (other): if 0.2 of a number is equal to 0.08 of another number , the ratio of the numbers is :
Options: a ) 2 : 3 , b ) 3 : 4 , c ) 2 : 5 , d ) 20 : 3 , e ) 30 : 7
Rationale: "0.2 a = 0.08 b - > a / b = 0.08 / 0.20 = 8 / 20 = 2 / 5 : . a : b = 2 : 5 answer : c"
Answer: c
Question (physics): a man covered a certain distance at some speed . had he moved 3 kmph faster , he would have taken 40 minutes less . if he had moved 2 kmph slower , he would have taken 40 minutes more . the distance ( in km ) is
Options: a ) 27 , b ) 87 , c ) 40 , d ) 18 , e ) 17
Rationale: explanation : let distance = x km and usual rate = y kmph . then , x / y - x / ( y + 3 ) = 40 / 60 - - > 2 y ( y + 3 ) = 9 x - - - - - ( i ) also , x / ( y - 2 ) - x / y = 40 / 60 - - > y ( y - 2 ) = 3 x - - - - - - - - ( ii ) on dividing ( i ) by ( ii ) , we get : x = 40 km . answer : c
Answer: c
Question (general): if the average of w , b , c , 14 and 15 is 12 . what is the average value of w , b , c and 29
Options: a ) 12 , b ) 13 , c ) 14 , d ) 15 , e ) 16
Rationale: w + b + c + 14 + 15 = 12 * 5 = 60 = > w + b + c = 60 - 29 = 31 w + b + c + 29 = 31 + 29 = 60 average = 60 / 4 = 15 answer d
Answer: d
Question (general): set a of 8 positive integers may have the same element and have 40 . and set b of 8 positive integers must have different elements and have 40 . when m and n are the greatest possible differences between 40 and other elements ’ sums in set a and set b , respectively , m - n = ?
Options: a ) 21 , b ) 29 , c ) 23 , d ) 25 , e ) 26
Rationale: this is maximum - minimum . hence , 40 - ( 1 + 1 + 1 + 1 + 1 + 1 + 1 ) = 32 and 40 - ( 1 + 2 + 3 + 4 + 5 + 6 + 7 ) = 11 . so , 32 - 11 = 21 . the correct answer is a .
Answer: a
Question (general): after 6 games , team b had an average of 65 points per game . if it got only 47 points in game 7 , how many more points does it need to score to get its total above 500 ?
Options: a ) 85 , b ) 74 , c ) 67 , d ) 63 , e ) 28
Rationale: "( 6 * 65 ) + 47 + x > 500 390 + 47 + x > 500 437 + x > 500 = > x > 63 option d"
Answer: d
Question (general): on thursday mabel handled 90 transactions . anthony handled 10 % more transactions than mabel , cal handled 2 / 3 rds of the transactions that anthony handled , and jade handled 16 more transactions than cal . how much transactions did jade handled ?
Options: a ) 80 , b ) 81 , c ) 82 , d ) 83 , e ) 84
Rationale: "solution : mabel handled 90 transactions anthony handled 10 % more transactions than mabel anthony = 90 + 90 × 10 % = 90 + 90 × 0.10 = 90 + 9 = 99 cal handled 2 / 3 rds of the transactions than anthony handled cal = 2 / 3 × 99 = 66 jade handled 16 more transactions than cal . jade = 66 + 16 = 82 jade handled = 82 transactions . answer : c"
Answer: c
Question (gain): a man buys an article for $ 100 . and sells it for $ 125 . find the gain percent ?
Options: a ) 10 % , b ) 15 % , c ) 25 % , d ) 20 % , e ) 30 %
Rationale: "c . p . = $ 100 s . p . = $ 125 gain = $ 25 gain % = 25 / 100 * 100 = 25 % answer is c"
Answer: c
Question (gain): what is 35 % of 4 / 13 of 780 ?
Options: a ) 62 , b ) 73 , c ) 84 , d ) 95 , e ) 106
Rationale: "this problem can be solved easily if we just use approximation : 35 % is a little over 1 / 3 , while 4 / 13 is a little less than 4 / 12 , which is 1 / 3 . thus , the answer is about 1 / 3 of 1 / 3 of 780 , or 1 / 9 of 780 . since the first 1 / 3 is a slight underestimate and the second 1 / 3 is a slight overestimate , the errors will partially cancel each other out . our estimate will be relatively accurate . the number 780 is between 720 and 810 , so ( 1 / 9 ) * 780 will be between 80 and 90 . keeping track not only of your current estimate , but also of the degree to which you have overestimated or underestimated , can help you pinpoint the correct answer more confidently . the closest answer is 84 , so this is the answer to choose . the answer is c ."
Answer: c
Question (physics): two pipes can fill a tank in 20 minutes and 12 minutes . an outlet pipe can empty the tank in 10 minutes . if all the pipes are opened when the tank is empty , then how many minutes will it take to fill the tank ?
Options: a ) 24 , b ) 26 , c ) 28 , d ) 30 , e ) 32
Rationale: "let v be the volume of the tank . the rate per minute at which the tank is filled is : v / 20 + v / 12 - v / 10 = v / 30 per minute the tank will be filled in 30 minutes . the answer is d ."
Answer: d
Question (physics): the radius of a wheel is 20 cm . what is the distance covered by the wheel in making 500 resolutions ?
Options: a ) 708 m , b ) 704 m , c ) 314.3 m , d ) 714 m , e ) 744 m
Rationale: "in one resolution , the distance covered by the wheel is its own circumference . distance covered in 500 resolutions . = 500 * 2 * 22 / 7 * 20 = 31428.5 cm = 314.3 m answer : c"
Answer: c
Question (general): list a consists of 12 consecutive integers . if - 4 is the least integer in list a , what is the range of positive integers in list a ?
Options: a ) 5 , b ) 6 , c ) 7 , d ) 11 , e ) 12
Rationale: since - 4 is the least integer in list a , then 7 is the largest integer in that list . thus the range of the positive integers in the list is 7 - 1 = 6 . answer : b .
Answer: b
Question (physics): joe needs to paint all the airplane hangars at the airport , so he buys 360 gallons of paint to do the job . during the first week , he uses 1 / 2 of all the paint . during the second week , he uses 1 / 5 of the remaining paint . how many gallons of paint has joe used ?
Options: a ) 18 , b ) 144 , c ) 175 , d ) 216 , e ) 250
Rationale: "total paint initially = 360 gallons paint used in the first week = ( 1 / 2 ) * 360 = 180 gallons . remaning paint = 180 gallons paint used in the second week = ( 1 / 5 ) * 180 = 36 gallons total paint used = 216 gallons . option d"
Answer: d
Question (physics): convert 100 miles into inches ?
Options: a ) 6336000 , b ) 6542000 , c ) 5462300 , d ) 6213000 , e ) 6120330
Rationale: "1 feet = 12 inches 1 mile = 5280 feet 100 mile = 5280 * 12 * 100 = 6336000 ans : a"
Answer: a
Question (general): how many digits will be there to the right of the decimal point in the product of 95.75 and . 02554 ?
Options: a ) 2 , b ) 3 , c ) 4 , d ) 5 , e ) 6
Rationale: "sum of decimal places = 7 . since the last digit to the extreme right will be zero ( since 5 x 4 = 20 ) so there will be 6 significant digits to the right of the decimal point . answer is e ."
Answer: e
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 4 ?
Options: a ) 1 / 4 , b ) 3 / 8 , c ) 1 / 2 , d ) 5 / 8 , e ) 3 / 4
Rationale: "i get 5 / 8 as well 1 to 96 inclusive means we have 48 odd and 48 even integers e o e / 4 = integer , therefore we have 48 / 96 numbers divisible by 8 o e o / 4 = not integer we can not forget multiples of 8 from 1 to 96 we have 24 numbers that are multiple of 4 therefore , 48 / 96 + 24 / 96 = 72 / 96 = 3 / 4 answer : e"
Answer: e
Question (general): in township k each property is taxed at 12 percent of its assessed value . if the assessed value of a property in township k is increased from $ 20,000 to $ 24,000 , by how much will the property tax increase ?
Options: a ) $ 32 , b ) $ 50 , c ) $ 320 , d ) $ 400 , e ) $ 480
Rationale: "increase in house value = $ 24,000 - $ 20,000 = $ 4000 so , tax increase = 12 % of $ 4000 = $ 480 answer : e"
Answer: e
Question (general): when y is divided by 288 , the remainder is 44 . what is the remainder when the same y is divided by 24 ?
Options: a ) 20 , b ) 21 , c ) 23 , d ) 25 , e ) 26
Rationale: y = 288 * a + 44 = ( 24 * 12 ) * a + 24 + 20 the answer is a .
Answer: a
Question (other): a certain university will select 1 of 5 candidates eligible to fill a position in the mathematics department and 2 of 10 candidates eligible to fill 2 identical positions in the computer science department . if none of the candidates is eligible for a position in both departments , how many different sets of 3 candidates are there to fill the 3 positions ?
Options: a ) 42 , b ) 70 , c ) 140 , d ) 165 , e ) 225
Rationale: "1 of 5 will be chosen for the math 2 of 10 will be chosen for the computer none of the 3 chosen people can be in more than one departments . we can choose any of the 5 candidates for the math dep . , which gives as 5 selections . we can choose 2 of the 10 candidates for the computer dep . , which gives us 2 selections and 8 rejections . so , the way to find how many different selections of 2 candidates we can have for the computer dep . , we do : 10 ! / 2 ! * 8 ! = ( 9 * 10 ) / 2 = 90 / 2 = 45 . we are multiplying our individual selections : 5 * 45 = 225 in the bolded part , we do n ' t have to multiply all of the numbers , as those in 8 ! are included in 10 ! , so we simplify instead . ans e"
Answer: e
Question (physics): the cross - section of a cannel is a trapezium in shape . if the cannel is 14 m wide at the top and 4 m wide at the bottom and the area of cross - section is 380 sq m , the depth of cannel is ?
Options: a ) 39 , b ) 28 , c ) 27 , d ) 42 , e ) 71
Rationale: "1 / 2 * d ( 14 + 4 ) = 380 d = 42 answer : d"
Answer: d
Question (gain): after decreasing 24 % in the price of an article costs rs . 1140 . find the actual cost of an article ?
Options: a ) 1500 , b ) 6789 , c ) 1200 , d ) 6151 , e ) 1421
Rationale: "cp * ( 76 / 100 ) = 1140 cp = 15 * 100 = > cp = 1500 answer : a"
Answer: a
Question (other): in a class of 60 students , 20 did not opt for math . 15 did not opt for science and 5 did not opt for either . how many students of the class opted for both math and science ?
Options: a ) 23 , b ) 25 , c ) 27 , d ) 30 , e ) 48
Rationale: "60 students total 20 did not opt for math 15 did not opt for science 5 did not opt for either total of 40 students in math and 10 did not opt for sci but did for math 40 - 10 = 30 30 students of the class opted for both math and science answer : d . 30"
Answer: d
Question (physics): a jeep takes 6 hours to cover a distance of 540 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 ) 48 kmph , b ) 52 kmph , c ) 6 o kmph , d ) 63 kmph , e ) 65 kmph
Rationale: "time = 6 distance = 540 3 / 2 of 6 hours = 6 * 3 / 2 = 9 hours required speed = 540 / 9 = 60 kmph c )"
Answer: c
Question (physics): a room 5 m 44 cm long and 3 m 74 cm broad needs to be paved with square tiles . what will be the least number of square tiles required to cover the floor ?
Options: a ) 176 , b ) 124 , c ) 224 , d ) 186 , e ) 190
Rationale: "length = 5 m 44 cm = 544 cm breadth = 3 m 74 cm = 374 cm area = 544 * 374 hcf = 34 area of square = 34 * 34 cm 2 no of tiles req = 544 * 374 / 34 * 34 = 16 * 11 = 176 answer a"
Answer: a
Question (other): the ratio of 2 numbers is 2 : 3 and their h . c . f . is 10 . their l . c . m . is ?
Options: a ) 30 , b ) 60 , c ) 20 , d ) 10 , e ) 40
Rationale: "let the numbers be 2 x and 3 x their h . c . f . = 10 so the numbers are 2 * 10 , 3 * 10 = 20,30 l . c . m . = 60 answer is b"
Answer: b
Question (general): what is the remainder when 1250 * 1090 * 1045 * 1055 is divided by 18 ?
Options: a ) 34 , b ) 19 , c ) 16 , d ) 14 , e ) 10
Rationale: "oa is ' c ' . oe : take the remainder from each of 1250 / 18 , 1090 / 18 and so on . . 1250 / 18 gives remainder = 8 1090 / 18 gives remainder = 10 1045 / 18 gives remainder = 1 1055 / 18 gives remainder = 11 the net remainder is the product of above individual remainders . i . e = 8 * 10 * 1 * 11 break them into pairs 8 * 10 / 18 gives remainder 8 and 1 * 11 / 18 gives remainder 11 so 8 * 11 / 18 gives remainder 16 . answer : c"
Answer: c
Question (general): the least number , which when divided by 12 , 15 , 20 and 54 leaves in each case a remainder of 8 , is :
Options: a ) 504 , b ) 536 , c ) 544 , d ) 548 , e ) none of these
Rationale: "explanation : required number = ( l . c . m . of 12 , 15 , 20 , 54 ) + 8 = 540 + 8 = 548 . answer : option d"
Answer: d
Question (general): if 7 a - 3 b = 10 b + 50 = - 12 b - 2 a , what is the value of 9 a + 9 b ?
Options: a ) - 9 , b ) - 6 , c ) 0 , d ) 6 , e ) 9
Rationale: "( i ) 7 a - 13 b = 50 ( ii ) 2 a + 22 b = - 50 adding ( i ) and ( ii ) : 9 a + 9 b = 0 the answer is c ."
Answer: c
Question (physics): suppose 10 monkeys take 20 minutes to eat 10 bananas . how many monkeys would it take to eat 80 bananas in 80 minutes ?
Options: a ) 9 , b ) 10 , c ) 11 , d ) 20 , e ) 13
Rationale: "one monkey takes 20 min to eat 1 banana , so in 80 mins 1 monkey will eat 4 bananas , so for 80 bananas in 80 min we need 80 / 4 = 20 monkeys answer : d"
Answer: d
Question (general): if x + | x | + y = 4 and x + | y | - y = 6 what is x + y = ?
Options: a ) 11 , b ) - 1 , c ) 3 , d ) 5 , e ) 13
Rationale: "if x < 0 and y < 0 , then we ' ll have x - x + y = 7 and x - y - y = 6 . from the first equation y = 7 , so we can discard this case since y is not less than 0 . if x > = 0 and y < 0 , then we ' ll have x + x + y = 7 and x - y - y = 6 . solving gives x = 4 > 0 and y = - 1 < 0 - - > x + y = 3 . since in ps questions only one answer choice can be correct , then the answer is c ( so , we can stop here and not even consider other two cases ) . answer : c . adding both eqn we get 2 x + ixi + iyi = 13 now considering x < 0 and y > 0 2 x - x + y = 13 we get x + y = 11 hence answer should be a"
Answer: a
Question (general): if 3 x + y = 40 , 2 x - y = 20 , for integers of x and y , 4 y ^ 2 = ?
Options: a ) 2 , b ) 4 , c ) 0 , d ) 10 , e ) 64
Rationale: "3 x + y = 40 2 x - y = 20 5 x = 60 x = 12 y = 4 4 y ^ 2 = 4 * 16 = 64 answer is e"
Answer: e