Cheukting/mathqa huggingface dataset:
Question (physics): in an intercollegiate competition that lasted for 3 days , 150 students took part on day 1 , 110 on day 2 and 140 on day 3 . if 75 took part on day 1 and day 2 and 25 took part on day 2 and day 3 and 15 took part on all three days , how many students took part only on day 2 ?
Options: a ) 50 , b ) 35 , c ) 45 , d ) 25 , e ) 60
Rationale: "day 1 & 2 = 75 ; only day 1 & 2 ( 75 - 15 ) = 60 , day 2 & 3 = 25 ; only day 2 & 3 ( 25 - 15 ) = 10 , only day 2 = 110 - ( 60 + 10 + 15 ) = 25 answer : d"
Answer: d
Question (general): what is the remainder when you divide 2 ^ 200 + 2 by 7 ?
Options: a ) 1 , b ) 2 , c ) 3 , d ) 6 , e ) 5
Rationale: answer is d . this is very similar to the 32 ^ 32 ^ 32 + 2 divided by 7 question .
Answer: d
Question (physics): jim drove 923 miles of a 1200 miles journey . how many more miles does he need to drive to finish his journey ?
Options: a ) 113 miles , b ) 277 miles , c ) 456 miles , d ) 887 miles , e ) 767 miles
Rationale: the number of miles to drive to finish his journey is given by 1200 - 923 = 277 miles correct answer b
Answer: b
Question (gain): on increasing the price of t . v . sets by 70 % , their sale decreases by 20 % . what is the effect on the revenue receipts of the shop ?
Options: a ) 4 , b ) 5 , c ) 36 , d ) 2 , e ) 7
Rationale: "explanation : let the price be = rs . 100 , and number of units sold = 100 then , sale value = rs . ( 100 × 100 ) = rs . 10000 new sale value = rs . ( 170 × 80 ) = rs . 13600 increase % = 3600 / 10000 × 100 = 36 % answer : c"
Answer: c
Question (physics): how many cubes of 10 cm edge can be put in a cubic box of 1 m edge ?
Options: a ) 4000 , b ) 2000 , c ) 3000 , d ) 5000 , e ) 1000
Rationale: "( 110 × 100 × 100 ) / 10 × 10 × 10 = 1000 answer is e ."
Answer: e
Question (general): what is the remainder when you divide 2 ^ 200 + 1 by 7 ?
Options: a ) 1 , b ) 2 , c ) 3 , d ) 4 , e ) 5
Rationale: answer is e . this is very similar to the 32 ^ 32 ^ 32 + 1 divided by 7 question .
Answer: e
Question (physics): a train running at the speed of 60 km / hr crosses a pole in 36 seconds . find the length of the train ?
Options: a ) 150 meter , b ) 600 meter , c ) 167 meter , d ) 719 meter , e ) 169 meter
Rationale: "speed = 60 * ( 5 / 18 ) m / sec = 50 / 3 m / sec length of train ( distance ) = speed * time ( 50 / 3 ) * 36 = 600 meter answer : b"
Answer: b
Question (geometry): the area of a parallelogram is 128 sq m and its altitude is twice the corresponding base . then the length of the base is ?
Options: a ) 8
b ) 7
c ) 6
d ) 5
e ) 2
Rationale: 2 x * x = 128 = > x = 8 answer : a
Answer: a
Question (general): the total marks obtained by a student in mathematics and physics is 60 and his score in chemistry is 20 marks more than that in physics . find the average marks scored in mathamatics and chemistry together ?
Options: a ) 40 , b ) 99 , c ) 88 , d ) 77 , e ) 66
Rationale: "let the marks obtained by the student in mathematics , physics and chemistry be m , p and c respectively . given , m + c = 60 and c - p = 20 m + c / 2 = [ ( m + p ) + ( c - p ) ] / 2 = ( 60 + 20 ) / 2 = 40 . answer : a"
Answer: a
Question (gain): a , b , and c were started a business , the total profit for one year is $ 56700 . the profit sharing ratio is 8 : 9 : 10 ( according to their investment they divide their profit ) . what is the profit of c ?
Options: a ) $ 5670 , b ) $ 18900 , c ) $ 21000 , d ) $ 13500 , e ) $ 27000
Rationale: a : b : c = 8 + 9 + 10 = 27 ; c ' share = 10 / 27 of the total profit . c will get = 10 / 27 * $ 56700 = $ 21000 . answer : c
Answer: c
Question (general): if the product of the integers from 1 to n is divisible by 1029 , what is the least possible value of n ?
Options: a ) 7 , b ) 14 , c ) 21 , d ) 28 , e ) 35
Rationale: 1029 = 7 x 7 x 7 x 3 n must include at least 7 , 2 * 7 , and 3 * 7 . the answer is c .
Answer: c
Question (general): average families of 4 pay $ 3000 for their health insurance deductibles annually . there will be a 2 / 3 increase in the deductibles for next year . how much more will the average family pay in deductibles next year ?
Options: a ) $ 1000 , b ) $ 2000 , c ) $ 3000 , d ) $ 4000 , e ) $ 5000
Rationale: a certain percentage of questions in the quant section of the gmat are just ' math questions ' - you ' ll use a formula , do some calculations and you ' ll have the answer . this is one of those types of questions . you still have to write everything down and stay organized , but the work involved is relatively straight - forward . here , we ' re told that the current annual deductible is $ 3000 and that the deductible is to be increased by 2 / 3 . we ' re asked how much more will the deductible cost a family next year . original deductible = $ 3000 increase in deductible = 2 / 3 the answer is calculated by the equation : $ 3000 × 2 / 3 = $ 2000 . b
Answer: b
Question (other): a certain university will select 1 of 3 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 ) 135 , e ) 315
Rationale: "1 of 3 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 3 candidates for the math dep . , which gives as 3 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 : 3 * 45 = 135 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 d"
Answer: d
Question (general): at the end of the month , a certain ocean desalination plant ’ s reservoir contained 6 million gallons of water . this amount is twice the normal level . if this amount represents 60 % of the reservoir ’ s total capacity , how many million gallons short of total capacity is the normal level ?
Options: a ) 15 , b ) 10 , c ) 5 , d ) 20 , e ) 25
Rationale: "the q talks of total capacity , normal level , present level , shortage etc . . so it is all about not going wrong in these terms 6 mg = 60 % of total . . total = 6 / . 6 = 10 mg . . normal level = 1 / 2 of 10 = 5 mg . . shortage of normal level = 10 - 5 = 5 mg . . c"
Answer: c
Question (physics): two interconnected , circular gears travel at the same circumferential rate . if gear a has a diameter of 60 centimeters and gear b has a diameter of 50 centimeters , what is the ratio of the number of revolutions that gear a makes per minute to the number of revolutions that gear b makes per minute ?
Options: a ) 6 : 5 , b ) 9 : 25 , c ) 5 : 6 , d ) 25 : 9 , e ) can not be determined from the information provided
Rationale: "same circumferential rate means that a point on both the gears would take same time to come back to the same position again . hence in other words , time taken by the point to cover the circumference of gear a = time take by point to cover the circumference of gear b time a = 2 * pi * 25 / speed a time b = 2 * pi * 30 / speed b since the times are same , 50 pi / speed a = 60 pi / speed b speeda / speed b = 50 pi / 60 pi = 5 / 6 correct option : c"
Answer: c
Question (general): a sum of money lent out at s . i . amounts to a total of $ 600 after 2 years and to $ 850 after a further period of 5 years . what was the initial sum of money that was invested ?
Options: a ) $ 500 , b ) $ 520 , c ) $ 540 , d ) $ 560 , e ) $ 580
Rationale: s . i for 5 years = $ 850 - $ 600 = $ 250 the s . i . is $ 50 / year s . i . for 2 years = $ 100 principal = $ 600 - $ 100 = $ 500 the answer is a .
Answer: a
Question (physics): a train passes a station platform in 46 sec and a man standing on the platform in 16 sec . if the speed of the train is 54 km / hr . what is the length of the platform ?
Options: a ) 227 , b ) 240 , c ) 460 , d ) 450 , e ) 455
Rationale: "speed = 54 * 5 / 18 = 15 m / sec . length of the train = 15 * 16 = 240 m . let the length of the platform be x m . then , ( x + 240 ) / 46 = 15 = > x = 450 m . answer : d"
Answer: d
Question (geometry): if the area of a square with sides of length 5 centimeters is equal to the area of a rectangle with a width of 4 centimeters , what is the length of the rectangle , in centimeters ?
Options: a ) 4 , b ) 8 , c ) 12 , d ) 7 , e ) 18
Rationale: "let length of rectangle = l 5 ^ 2 = l * 4 = > l = 25 / 4 = 7 answer d"
Answer: d
Question (physics): a rectangular grassy plot 110 m . by 65 m has a gravel path 2.5 m wide all round it on the inside . find the cost of gravelling the path at 80 paise per sq . metre
Options: a ) rs 680 , b ) rs 780 , c ) rs 880 , d ) rs 480 , e ) rs 980
Rationale: "area of the plot = 110 m * 65 m = 7150 sq . m area of plot excluding gravel = 105 m * 60 m = 6300 sq . m area of gravel = 7150 sq . m - 6300 sq . m = 850 sq . m cost of building it = 850 sq . m * 80 = 68000 p in rs = 68000 / 100 = rs 680 answer : a"
Answer: a
Question (general): a certain board game is played by rolling a pair of fair 6 - sided dice and then moving one ' s piece forward the number of spaces indicated by the sum showing on the dice . a player is frozen if her opponent ' s piece comes to rest in the space already occupied by her piece . if player a is about to roll and is currently 8 spaces behind player b , what is the probability that player b will be frozen after player a rolls ?
Options: a ) 1 / 12 , b ) 5 / 36 , c ) 1 / 6 , d ) 1 / 3 , e ) 17 / 36
Rationale: no . of possible outcomes = 6 * 6 = 36 no . of outcomes that result a total of 8 ( as a is 8 spaces behind b ) = 5 ( ( 2,6 ) , ( 3,5 ) , ( 4,4 ) , ( 5,3 ) , ( 6,2 ) ) so , the probability = 5 / 36 ( option b )
Answer: b
Question (general): we bought 85 hats at the store . blue hats cost $ 6 and green hats cost $ 7 . the total price was $ 548 . how many green hats did we buy ?
Options: a ) 36 , b ) 38 , c ) 40 , d ) 42 , e ) 44
Rationale: "let b be the number of blue hats and let g be the number of green hats . b + g = 85 . b = 85 - g . 6 b + 7 g = 548 . 6 ( 85 - g ) + 7 g = 548 . 510 - 6 g + 7 g = 548 . g = 548 - 510 = 38 . the answer is b ."
Answer: b
Question (physics): in a 100 m race , sam beats john by 5 seconds . on the contrary , if sam allowed john to start 35 m ahead of sam , then sam and john reach the finishing point at the same time . how long does sam take to run the 100 m race ?
Options: a ) 13 seconds , b ) 25 seconds , c ) 29 seconds , d ) 21 seconds , e ) 6.25 seconds
Rationale: "their difference is 5 second but this difference is 0 if john allows sam to start the race from 35 m ahead . that means jhon was 35 m away from finishing line when they started together . so he will cover 35 m in 5 seconds . so his speed = 35 / 5 = 7 metre / second . so time taken = 100 / 5 = 20 seconds . so sam took = 13 seconds . correct answer = a"
Answer: a
Question (physics): when a train travels at a speed of 110 kmph , it reaches the destination on time . when the same train travels at a speed of 50 kmph , it reaches its destination 15 min late . what is the length of journey ?
Options: a ) 12.5 km , b ) 50 km , c ) 60 km , d ) 8.5 km , e ) 9.5 km
Rationale: "let x be the time reached with the speed 110 km / h 50 km / h - - - - > x + 15 distance is equal so 110 ( km / h ) × xhr = 50 ( km / h ) × ( x + 15 ) hr so 110 x = 50 x + 750 so the would be in km and x = 12.5 answer : a"
Answer: a
Question (geometry): three runners running around a circular track can complete one revolution in 2 , 4 and 5.5 respectively . when will they meet at starting point ?
Options: a ) 40 h
b ) 44 h
c ) 38 h
d ) 20 h
e ) 22 h
Rationale: time at which they meet at starting point = lcm of 2 , 4 and 5.5 = 44 h answer : b
Answer: b
Question (general): 3 bottles contain equal mixtures of spirit and water in the ratio 6 : 1 , 5 : 2 and 3 : 1 respectively . if all the solutions are mixed together , the ratio of spirit to water in the final mixture will be
Options: a ) 64 : 65 , b ) 65 : 64 , c ) 19 : 65 , d ) 65 : 19 , e ) none of these
Rationale: given that all bottles contain equal amount of mixture say v . so in the first vessel - > water : spirit = 1 / 7 : 6 / 7 in the second bottle - > 2 / 7 : 5 / 7 in the third bottle - > l / 4 : 3 / 4 . hence , the final ratio is = ( ( 6 / 7 ) + ( 5 / 7 ) + ( 3 / 4 ) ) / ( ( 1 / 7 ) + ( 2 / 7 ) + ( 1 / 4 ) ) = 65 / 19 answer : d
Answer: d
Question (physics): 12 machines can do a work in 10 days . how many machines are needed to complete the work in 40 days ?
Options: a ) 10 , b ) 3 , c ) 4 , d ) 7 , e ) 5
Rationale: required number of machines = 12 * 10 / 40 = 3 answer is b
Answer: b
Question (general): the age of somu is one - third his father ' s . 10 years back he was one - fifth of his father ' s age . what is his persent age ?
Options: a ) 11 , b ) 13 , c ) 14 , d ) 12 , e ) 20
Rationale: "explanation : let somu ' s age be x and that of his father be 3 x . so , x - 10 = 3 x - 10 / 5 = x = 20 answer : option e"
Answer: e
Question (gain): from january 1 , 2015 , to january 1 , 2017 , the number of people enrolled in health maintenance organizations increased by 8 percent . the enrollment on january 1 , 2017 , was 45 million . how many million people , to the nearest million , were enrolled in health maintenance organizations on january 1 , 2015 ?
Options: a ) 38 , b ) 39 , c ) 40 , d ) 41 , e ) 42
Rationale: "soln : - 8 x = 45 - - > 27 / 25 * x = 45 - - > x = 45 * 25 / 27 = 125 / 3 = ~ 42 . answer : e ."
Answer: e
Question (general): a group of students decided to collect as many paise from each member of group as is the number of members . if the total collection amounts to rs . 92.16 , the number of the member is the group is :
Options: a ) 57 , b ) 67 , c ) 77 , d ) 87 , e ) 96
Rationale: "explanation : money collected = ( 92.16 x 100 ) paise = 9216 paise . ∴ number of members = √ ( 9216 ) = 96 . answer : e"
Answer: e
Question (general): if a person walks at 10 km / hr instead of 5 km / hr , he would have walked 20 km more . the actual distance traveled by him is ?
Options: a ) 50 km , b ) 76 km , c ) 20 km , d ) 16 km , e ) 97 km
Rationale: "let the actual distance traveled be x km . then , x / 5 = ( x + 20 ) / 10 5 x - 100 = > x = 20 km . answer : c"
Answer: c
Question (gain): in a public show 75 % of the seats were filled . if there were 700 seats in the hall , how many seats were vacant ?
Options: a ) 100 , b ) 110 , c ) 120 , d ) 175 , e ) 150
Rationale: "75 % of 600 = 75 / 100 × 700 = 450 therefore , the number of vacant seats = 700 - 450 = 175 . answer : d"
Answer: d
Question (general): find the value of m 82519 x 9999 = m ?
Options: a ) 724533811 , b ) 353654655 , c ) 825107481 , d ) 725117481 , e ) 477899932
Rationale: "82519 x 9999 = 82519 x ( 10000 - 1 ) = 82519 x 10000 - 82519 x 1 = 825190000 - 82519 = 825107481 c"
Answer: c
Question (probability): on a ranch , a rancher can place a loop of rope , called a lasso , once in every 3 throws around a cow ’ s neck . what is the probability that the rancher will be able to place a lasso around a cow ’ s neck at least once in 4 attempts ?
Options: a ) 4 / 9 , b ) 5 / 9 , c ) 17 / 27 , d ) 23 / 27 , e ) 65 / 81
Rationale: "p ( missing all 3 ) = ( 2 / 3 ) ^ 4 = 16 / 81 p ( success on at least one attempt ) = 1 - 16 / 81 = 65 / 81 the answer is e ."
Answer: e
Question (general): if one root of the equation 2 x ^ 2 + 3 x – k = 0 is 4 , what is the value of k ?
Options: a ) 35 , b ) 40 , c ) 44 , d ) 45 , e ) 56
Rationale: "we just enter this root into the equation in order to recieve an equation to find the answer ! 2 * 4 ^ 2 + 3 * 4 - k = 0 k = 32 + 12 = 44 the answer is c"
Answer: c
Question (physics): 4 different airplanes owned by a rock band will be refueling today at the same airport . there are 2 larger planes carrying people and 2 smaller planes carrying equipment . all tanks are empty and will need to be filled completely . the 2 smaller tanks hold 60 liters each and the larger tanks are 50 % bigger . fuel is . 50 cents a liter and there is a charge of $ 100 service for each plane . how much will it cost to fill all 4 planes ?
Options: a ) $ 475 , b ) $ 500 , c ) $ 525 , d ) $ 550 , e ) $ 575
Rationale: lots of calculations . 100 * 4 + 2 * 60 * . 50 + 60 * ( 3 / 2 ) * 2 * . 50 answer = $ 550 the correct option is d
Answer: d
Question (gain): how many litres of pure acid are there in 12 litres of a 40 % solution
Options: a ) 3.6 , b ) 4.8 , c ) 3.5 , d ) 2.3 , e ) 4.4
Rationale: explanation : question of this type looks a bit typical , but it is too simple , as below . . . it will be 12 * 40 / 100 = 4.8 answer : option b
Answer: b
Question (physics): a train 100 meters long takes 6 seconds to cross a man walking at 5 kmph in the direction opposite to that of the train . find the speed of the train .
Options: a ) 45 kmph , b ) 50 kmph , c ) 55 kmph , d ) 60 kmph , e ) 70 kmph
Rationale: "explanation : let the speed of the train be x kmph . speed of the train relative to man = ( x + 5 ) kmph = ( x + 5 ) × 5 / 18 m / sec . therefore 100 / ( ( x + 5 ) × 5 / 18 ) = 6 < = > 30 ( x + 5 ) = 1800 < = > x = 55 speed of the train is 55 kmph . answer : option c"
Answer: c
Question (geometry): if the length of the diagonal of a square is 20 cm , then its perimeter must be
Options: a ) 40
b ) 38
c ) 27
d ) 29
e ) 11
Rationale: explanation : d = √ 2 l answer : a ) 40
Answer: a
Question (general): line m lies in the xy - plane . the y - intercept of line m is - 4 , and line m passes through the midpoint of the line segment whose endpoints are ( 2 , 4 ) and ( 6 , - 8 ) . what is the slope of line m ?
Options: a ) - 2 , b ) - 1 , c ) - 1 / 3 , d ) 0 , e ) undefined
Rationale: "ans : a solution : line m goes through midpoint of ( 2 , 4 ) and ( 6 , - 8 ) . midpoint is ( 4 , - 2 ) as we can see that the y axis of intercept point is ( 0 , - 4 ) means line m is parallel to x axis slope m = - 2 ans : a"
Answer: a
Question (physics): two pipes a and b can fill a tank in 6 hours and 4 hours respectively . if they are opened on alternate hours and if pipe a is opened first , in how many hours , the tank shall be full ?
Options: a ) 2 hrs , b ) 4 hrs , c ) 5 hrs , d ) 6 hrs , e ) 7 hrs
Rationale: "a ' s work in 1 hour = 1 / 6 b ' s work in 1 hour = 1 / 4 a + b 2 hour ' s work when opened alternately = 1 / 6 + 1 / 4 = 5 / 12 a + b 4 hour ' s work when opened alternately = 10 / 12 = 5 / 6 remaining part = 1 - 5 / 6 = 1 / 6 it is a ' s turn and 1 / 6 part is filled by a in 1 hour . total time taken to fill the tank = 4 + 1 = 5 hrs answer is c"
Answer: c
Question (physics): two trains of equal length are running on parallel lines in the same direction at 46 km / hr and 36 km / hr . the faster train catches and completely passes the slower train in 45 seconds . what is the length of each train ( in meters ) ?
Options: a ) 48.5 , b ) 62.5 , c ) 73.5 , d ) 87.5 , e ) 96.5
Rationale: the relative speed = 46 - 36 = 10 km / hr = 10 * 5 / 18 = 25 / 9 m / s in 45 seconds , the relative difference in distance traveled is 45 * 25 / 9 = 125 meters this distance is twice the length of each train . the length of each train is 125 / 2 = 62.5 meters the answer is b .
Answer: b
Question (general): a certain lab experiments with white and brown mice only . in one experiment , 4 / 9 of the mice are brown . if there are 20 brown mice in the experiment , how many mice in total are in the experiment ?
Options: a ) 32 , b ) 26 , c ) 36 , d ) 28 , e ) 24
Rationale: "let total number of mice = m number of brown mice = 4 / 9 m number of white mice = 5 / 9 m = 20 = > m = 36 answer c"
Answer: c
Question (general): if a + b + c = 21 , what is the total number of non - negative integral solutions ?
Options: a ) 223 , b ) 233 , c ) 240 , d ) 243 , e ) 253
Rationale: think of it is a problem of diving 21 items to three people a , b & c which may or may not receive an item . so simply use combination here as ( n - r + 1 ) c ( r - 1 ) i . e . ( 21 + 3 - 1 ) c ( 3 - 1 ) = > 23 c 2 = = > 253 solutions . answer : e
Answer: e
Question (physics): a driver goes on a trip of 60 kilometers , the first 30 kilometers at 48 kilometers per hour and the remaining distance at 24 kilometers per hour . what is the average speed of the entire trip in kilometers per hour ?
Options: a ) 30 , b ) 32 , c ) 36 , d ) 40 , e ) 42
Rationale: "the time for the first part of the trip was 30 / 48 = 5 / 8 hours . the time for the second part of the trip was 30 / 24 = 5 / 4 hours . the total time fro the trip was 5 / 8 + 5 / 4 = 15 / 8 hours . the average speed for the trip was 60 / ( 15 / 8 ) = 32 kph the answer is b ."
Answer: b
Question (physics): a train travelled from point a to point b at 160 km / h . on its way back the train travelled at 120 km / h and therefore the trip back lasted one hour longer . what is the distance ( in km ) between a and b ?
Options: a ) 480 . , b ) 500 . , c ) 510 . , d ) 600 . , e ) 800 .
Rationale: distance = speed * time d 1 = s 1 t 1 d 2 = s 2 t 2 the distance from point a to point b is the same for each trip so , d 1 = d 2 and t 2 = t 1 + 1 thus , s 1 t 1 = s 2 ( t 1 + 1 ) 160 t 1 = 120 ( t 1 + 1 ) t 1 = 3 160 * 3 = 480 answer : a
Answer: a
Question (physics): the length of the bridge , which a train 120 meters long and travelling at 45 km / hr can cross in 30 seconds , is ?
Options: a ) 328 , b ) 279 , c ) 255 , d ) 288 , e ) 211
Rationale: speed = ( 45 * 5 / 18 ) m / sec = ( 25 / 2 ) m / sec . time = 30 sec . let the length of bridge be x meters . then , ( 120 + x ) / 30 = 25 / 2 = = > 2 ( 120 + x ) = 750 = = > x = 255 m . answer : c
Answer: c
Question (general): if a is an integer greater than 8 but less than 15 and b is an integer greater than 6 but less than 21 , what is the range of a / b ?
Options: a ) 140 / 217 , b ) 156 / 185 , c ) 217 / 140 , d ) 263 / 149 , e ) 241 / 163
Rationale: the way to approach this problem is 8 < a < 15 and 6 < b < 21 minimum possible value of a is 9 and maximum is 14 minimum possible value of b is 7 and maximum is 20 range = max a / min b - min a / max b ( highest - lowest ) 14 / 7 - 9 / 20 = 217 / 140 hence c
Answer: c
Question (general): the average ( arithmetic mean ) of the integers from 25 to 225 , inclusive , is how much lower than the average of the integers from 50 to 1050 inclusive ?
Options: a ) 450 , b ) 375 , c ) 500 , d ) 425 , e ) 400
Rationale: "for an ap the mean or average of series is average of first and last term . so , average of numbers between 50 to 1050 , inclusive = ( 50 + 1050 ) / 2 = 550 average of numbers between 25 to 225 , inclusive = ( 25 + 225 ) / 2 = 125 difference = 550 - 125 = 425 answer is d"
Answer: d
Question (physics): 8 identical machines , working alone and at their constant rates , take 6 hours to complete a job lot . how long would it take for 5 such machines to perform the same job ?
Options: a ) 2.25 hours , b ) 8.75 hours , c ) 12 hours , d ) 14.25 hours , e ) 9.6 hours
Rationale: "let each machine do 1 unit of work for 1 hour 8 machines - - > 8 units of work in 1 hour for 6 hours = 8 * 6 = 48 units of total work is done . now this 48 units of total work must be done by 5 machines 5 units of work ( 5 machines ) - - - > 1 hour for 48 units of work 5 * 9.6 - - - > 1 * 9.6 hours e 9.6 hours"
Answer: e
Question (geometry): the length and breadth of a rectangle is increased by 10 % and 25 % respectively . what is the increase in the area ?. a . 27.5 %
Options: a ) 37.2 %
b ) 37.5 %
c ) 30.2 %
d ) 37.7 %
e ) 33.2 %
Rationale: explanation : 100 * 100 = 10000 110 * 125 = 13750 - - - - - - - - - - - 3750 10000 - - - - - - 3750 100 - - - - - - - ? = > 37.5 % answer : option b
Answer: b