Cheukting/mathqa huggingface dataset:
Question (general): a trained covered x km at 40 kmph and another 2 x km at 20 kmph . find the average speed of the train in covering the entire 3 x km .
Options: a ) 18 kmph , b ) 17 kmph , c ) 24 kmph , d ) 19 kmph , e ) 12 kmph
Rationale: "total time taken = x / 40 + 2 x / 20 hours = 5 x / 40 = x / 8 hours average speed = 3 x / ( x / 8 ) = 24 kmph answer : c"
Answer: c
Question (general): the avg weight of a , b & c is 70 kg . if d joins the group , the avg weight of the group becomes 70 kg . if another man e who weights is 3 kg more than d replaces a , then the avgof b , c , d & e becomes 68 kg . what is the weight of a ?
Options: a ) 81 , b ) 65 , c ) 75 , d ) 89 , e ) 90
Rationale: "a + b + c = 3 * 70 = 210 a + b + c + d = 4 * 70 = 280 - - - - ( i ) so , d = 70 & e = 70 + 3 = 73 b + c + d + e = 68 * 4 = 272 - - - ( ii ) from eq . ( i ) & ( ii ) a - e = 280 – 272 = 8 a = e + 8 = 73 + 8 = 81 answer : a"
Answer: a
Question (gain): john paid a sum of money for purchasing 30 pens , which he recovered in full when he sold 20 of them . what was his percentage of profit or loss per pen ?
Options: a ) 50 % , b ) 60 % , c ) 40 % , d ) 30 % , e ) 45 %
Rationale: "a 50 % if the sum he paid whilst purchasing 30 pens = a , then the cost price of each pen = a / 30 . since the amount he got whilst selling 20 pens is also = a then the selling price of each pen = a / 20 . since selling price > cost price , he made a profit . profit per pen = selling price - cost price = a / 20 - a / 30 = a / 60 . profit percentage per pen = profit per pen / cost per pen x 100 = ( a / 60 ) / ( a / 30 ) x 100 = 50 %"
Answer: a
Question (general): 1 / 0.025 is equal to
Options: a ) 25.5 , b ) 2.5 , c ) 40 , d ) . 25 , e ) none of these
Rationale: "explanation : 1 / 0.025 = ( 1 * 1000 ) / 25 = 1000 / 25 = 40 option c"
Answer: c
Question (geometry): find the circumference and area of radius 4 cm .
Options: a ) 24 cm ² , b ) 44 cm ² , c ) 50 cm ² , d ) 84 cm ² , e ) 94 cm ²
Rationale: "area of circle = π r ² = 22 / 7 × 4 × 4 cm ² = 50 cm ² answer : c"
Answer: c
Question (physics): a train covers a distance of 18 km in 3 min . if it takes 4 sec to pass a telegraph post , then the length of the train is ?
Options: a ) 370 , b ) 380 , c ) 390 , d ) 400 , e ) 410
Rationale: "speed = ( 18 / 3 * 60 ) km / hr = ( 360 * 5 / 18 ) m / sec = 100 m / sec . length of the train = 100 * 4 = 400 m . answer : option d"
Answer: d
Question (gain): a merchant sells an item at a 20 % discount , but still makes a gross profit of 25 percent of the cost . what percent of the cost would the gross profit on the item have been if it had been sold without the discount ?
Options: a ) 20 % , b ) 40 % , c ) 56.25 % , d ) 60 % , e ) 75 %
Rationale: "original sp = x cost = c current selling price = . 8 x ( 20 % discount ) . 8 x = 1.5 c ( 25 % profit ) x = 1.25 / . 8 * c x = 12.5 / 8 c original selling price is 1.5625 c which is 56.25 % profit answer c"
Answer: c
Question (general): evaluate : | 4 - 8 ( 3 - 12 ) | - | 5 - 11 | =
Options: a ) 49 , b ) 55 , c ) 69 , d ) 70 , e ) 82
Rationale: "according to order of operations , inner brackets first . hence | 4 - 8 ( 3 - 12 ) | - | 5 - 11 | = | 4 - 8 * ( - 9 ) | - | 5 - 11 | according to order of operations , multiplication within absolute value signs ( which may be considered as brackets when it comes to order of operations ) next . hence = | 4 + 72 | - | 5 - 11 | = | 76 | - | - 6 | = 76 - 6 = 70 correct answer d ) 70"
Answer: d
Question (physics): how much time will a train of length 200 m moving at a speed of 72 kmph take to cross another train of length 300 m , moving at 36 kmph in the same direction ?
Options: a ) 50 sec , b ) 26 sec , c ) 80 sec , d ) 82 sec , e ) 81 sec
Rationale: the distance to be covered = sum of their lengths = 200 + 300 = 500 m . relative speed = 72 - 36 = 36 kmph = 36 * 5 / 18 = 10 mps . time required = d / s = 500 / 10 = 50 sec . answer : a
Answer: a
Question (physics): a train covers a distance of 36 km in 12 min . if it takes 7 sec to pass a telegraph post , then the length of the train is ?
Options: a ) 330 , b ) 340 , c ) 350 , d ) 360 , e ) 370
Rationale: "speed = ( 36 / 12 * 60 ) km / hr = ( 180 * 5 / 18 ) m / sec = 50 m / sec . length of the train = 50 * 7 = 350 m . answer : option c"
Answer: c
Question (gain): a sum of money deposited at c . i . amounts to rs . 2420 in 2 years and to rs . 3146 in 3 years . find the rate percent ?
Options: a ) 11 , b ) 30 , c ) 28 , d ) 24 , e ) 82
Rationale: "explanation : 2420 - - - 726 100 - - - ? = > 30 % answer : option b"
Answer: b
Question (physics): the rate of spin of a certain gyroscope doubled every 10 seconds from the moment a particular stopwatch started . if after a minute and a half the gyroscope reached a speed of 800 meters per second , what was the speed , in meters per second , when the stopwatch was started ?
Options: a ) 25 / 3 , b ) 25 / 4 , c ) 25 / 8 , d ) 25 / 16 , e ) 25 / 32
Rationale: let x be the original speed when the stopwatch was started . in 90 seconds , the speed doubled 9 times . 2 ^ 9 * x = 800 x = ( 2 ^ 5 * 25 ) / 2 ^ 9 = 25 / 16 the answer is d .
Answer: d
Question (general): if i equals the sum of the even integers from 2 to 224 , inclusive , and k equals the sum of the even integers from 8 to 80 , inclusive , what is the value of i - k ?
Options: a ) 11028 , b ) 14172 , c ) 14284 , d ) 14015 , e ) 14397
Rationale: use following formulae for such problems : sum of evenly spaced integers = ( # of integers ) * ( mean of integers ) # of integers = [ ( last - first ) / 2 ] + 1 mean of integers = ( last + first ) / 2 in above problem : # of integers = [ ( 224 - 2 ) / 2 ] + 1 = 112 and [ ( 80 - 8 ) / 2 ] + 1 = 37 mean of integers = ( 224 + 2 ) / 2 = 113 and ( 80 + 8 ) / 2 = 44 sum of integers = ( 112 * 113 ) = 12656 and ( 37 * 44 ) = 1628 thus their difference ( i - k ) = 12656 - 1628 = 11028 answer : a
Answer: a
Question (general): if 25 % of x is 15 less than 12 % of 1500 , then x is ?
Options: a ) 660 , b ) 738 , c ) 837 , d ) 840 , e ) 83
Rationale: "25 % of x = x / 4 ; 12 % of 1500 = 12 / 100 * 1500 = 180 given that , x / 4 = 180 - 15 = > x / 4 = 165 = > x = 660 . answer : a"
Answer: a
Question (general): evaluate : 11 + sqrt ( - 4 + 6 × 4 ÷ 3 ) = . . . .
Options: a ) 3 , b ) 33 , c ) 43 , d ) 23 , e ) 13
Rationale: according to order of operations , inner brackets first where 6 × 4 ÷ 3 is first calculated since it has a multiplication and a division . 6 × 4 ÷ 3 = 24 ÷ 3 = 8 hence 11 + sqrt ( - 4 + 6 × 4 ÷ 3 ) = 11 + sqrt ( - 4 + 8 ) = 11 + sqrt ( 4 ) = 11 + 2 = 13 correct answer is e ) 13
Answer: e
Question (general): a “ palindromic integer ” is an integer that remains the same when its digits are reversed . so , for example , 43334 and 516615 are both examples of palindromic integers . how many 6 - digit palindromic integers are both even and greater than 800,000 ?
Options: a ) 60 , b ) 100 , c ) 160 , d ) 240 , e ) 300
Rationale: "the first digit and last digit are the same so the only possibility is 8 . the second and third digits can be any number from 0 to 9 . the total number of palindromic integers is 1 * 10 * 10 = 100 the answer is b ."
Answer: b
Question (gain): a trader sold an item at a loss of 18 % . if he had increased the price by $ 25 he would have made a gain of 5 % . what is the cost price of the item ?
Options: a ) $ 414.78 , b ) $ 424.78 , c ) $ 534.78 , d ) $ 434.78 , e ) $ 435.78
Rationale: let c . p . be $ x then 105 % of x - 82 % of x = 100 23 % of x = 100 23 / 100 * x = 100 23 x = 10000 x = 434.78 answer is d
Answer: d
Question (physics): if 3 women can color 180 m long cloth in 2 days , then 5 women can color 300 m long cloth in ?
Options: a ) 2 days , b ) 3 days , c ) 5 days , d ) 1 day , e ) 4 days
Rationale: "the length of cloth painted by one woman in one day = 180 / 3 × 2 = 30 m no . of days required to paint 300 m cloth by 5 women = 300 / 5 × 30 = 2 days answer : a"
Answer: a
Question (gain): if $ 5,000 is invested in an account that earns 6 % interest compounded semi - annually , then the interest earned after one year would be how much greater than if the $ 5,000 had been invested at 8 % simple yearly interest ?
Options: a ) $ 6 , b ) $ 8 , c ) $ 12 , d ) $ 16 , e ) $ 432
Rationale: "ans a solution amount ( ci ) = p + ( 1 + r / n ) ^ nt = 5000 + ( 1 + 0.06 / 2 ) ^ 2 = 5406 amount ( si ) = p + ptr / 100 = 5000 + ( 5000 * 1 * 8 / 100 ) = 5400 difference = 5406 - 5400 = 6 $ a"
Answer: a
Question (physics): a train with 1200 m crosses a tree in 120 sec , how much time will i take to pass a platform 700 m long ?
Options: a ) 150 sec , b ) 130 sec , c ) 190 sec , d ) 200 sec , e ) 100 sec
Rationale: s = 1200 / 120 s - 10 m / sec total length = 1900 m t = d / s t = 1900 / 10 t = 190 sec answer c
Answer: c
Question (geometry): the area of a circle is added to its diameter , and the circumference is then subtracted from this total , the result is 10 . what is the radius of the circle ?
Options: a ) 2 * pi
b ) pi
c ) 2
d ) 4 * pi
e ) 4
Rationale: the equation is ; diameter + area - circumference = d + a - c = d + pi * r ^ 2 - 2 * pi * r = 2 r + pi * r ( r - 2 ) . by plugging in the answers we can test the answers quickly ; then , 4 is the only possible answer . answer : e
Answer: e
Question (geometry): a circular well with a diameter of 2 metres , is dug to a depth of 8 metres . what is the volume of the earth dug out ?
Options: a ) 32 m 3 , b ) 25.1 m 3 , c ) 40 m 3 , d ) 44 m 3 , e ) none
Rationale: "solution volume = π r 2 h ‹ = › ( 22 / 7 × 1 × 1 × 8 ) m 3 ‹ = › 25.1 m 3 . answer b"
Answer: b
Question (physics): a man can row upstream at 5 kmph and downstream at 25 kmph , and then find the speed of the man in still water ?
Options: a ) 15 , b ) 77 , c ) 30 , d ) 88 , e ) 34
Rationale: "us = 5 ds = 25 m = ( 5 + 25 ) / 2 = 15 answer : a"
Answer: a
Question (general): sum of 49 odd numbers is ?
Options: a ) 2398 , b ) 2399 , c ) 2400 , d ) 2401 , e ) 2402
Rationale: sum of 1 st n odd no . s = 1 + 3 + 5 + 7 + . . . = n ^ 2 so , sum of 1 st 49 odd numbers = 49 ^ 2 = 2401 answer : d
Answer: d
Question (physics): a walks at 30 kmph and 30 hours after his start , b cycles after him at 40 kmph . how far from the start does b catch up with a ?
Options: a ) 1200 km , b ) 1500 km , c ) 2000 km , d ) 2500 km , e ) 3600 km
Rationale: "suppose after x km from the start b catches up with a . then , the difference in the time taken by a to cover x km and that taken by b to cover x km is 30 hours . x / 30 - x / 40 = 30 x = 3600 km answer is d"
Answer: d
Question (geometry): one side of a rectangular field is 16 m and one of its diagonal is 18 m . find the area of the field .
Options: a ) 100 , b ) 120 , c ) 150 , d ) 180 , e ) none
Rationale: "solution other side = √ ( 18 ) 2 - ( 16 ) 2 = √ 324 - 256 = √ 68 = 8.2 m . ∴ area = ( 16 x 8.2 ) m 2 = 131.2 m 2 . answer e"
Answer: e
Question (general): the product of x and y is a constant . if the value of x is increased by 20 % , by what percentage must the value of y be decreased ?
Options: a ) 16.66 % , b ) 33.33 % , c ) 44.44 % , d ) 55.55 % , e ) 19.92 %
Rationale: "x * y = constt . let x = y = 100 in beginning i . e . x * y = 100 * 100 = 10000 x ( 100 ) - - - becomes - - - > 1.2 x ( 120 ) i . e . 120 * new ' y ' = 10000 i . e . new ' y ' = 10000 / 120 = 83.33 i . e . y decreases from 100 to 83.33 i . e . decrease of 16.66 % answer : option a"
Answer: a
Question (physics): if 12 men or 20 women can do a piece of work in 27 days , then in how many days can 9 men and 12 women together do the work ?
Options: a ) 10 days , b ) 30 days , c ) 20 days , d ) 80 days , e ) 40 days
Rationale: "c 20 days given that 12 m = 20 w = > 3 m = 5 w 9 men + 12 women = 15 women + 12 women = 27 women 20 women can do the work in 27 days . so , 27 women can do it in ( 20 * 27 ) / 27 = 20 days ."
Answer: c
Question (general): how many trucks are there if each truck carrying 70 packages and total of 490 packages ?
Options: a ) a ) 7 , b ) b ) 6 , c ) c ) 9 , d ) d ) 11 , e ) e ) none of the above
Rationale: sol . total packages 490 each truck carries 70 packages = 490 / 70 = 7 answer : a
Answer: a
Question (general): calculate 42120 ÷ ? = 195
Options: a ) 212 , b ) 219 , c ) 217 , d ) 213 , e ) 216
Rationale: "answer let 42120 / x = 195 then x = 42120 / 195 = 216 option : e"
Answer: e
Question (general): the average of 6 observations is 14 . a new observation is included and the new average is decreased by 1 . the seventh observation is ?
Options: a ) 1 , b ) 3 , c ) 5 , d ) 6 , e ) 7
Rationale: "let seventh observation = x . then , according to the question we have = > ( 84 + x ) / 7 = 13 = > x = 7 . hence , the seventh observation is 7 . answer : e"
Answer: e
Question (general): find the value of ( 50 + 20 / 90 ) × 90
Options: a ) 2520 , b ) 3520 , c ) 4520 , d ) 1520 , e ) 1750
Rationale: "( 4500 + 20 ) / 90 * 90 = 4520 answer : c"
Answer: c
Question (general): if a and b are positive real numbers , and a ^ 3 + b ^ 3 = 20 , then the greatest possible value of a is between :
Options: a ) 0 and 3 , b ) 3 and 4 , c ) 4 and 5 , d ) 5 and 7 , e ) 7 and 9
Rationale: "if a > 3 , then a ^ 3 + b ^ 3 > 20 . the answer is a ."
Answer: a
Question (general): the ages of 2 persons differ by 32 years . if 9 years ago the elder one be 5 times as old as the younger one , find the present age of elder person .
Options: a ) 30 , b ) 42.5 , c ) 45 , d ) 49 , e ) 47.9
Rationale: "age of the younger person = x age of the elder person = x + 32 5 ( x - 9 ) = x + 32 - 9 x = 17 age of elder person = 17 + 32 = 49 answer is d"
Answer: d
Question (physics): what is the greatest possible length which can be used to measure exactly the lengths 18 m , 40 m and 6 m 50 cm ?
Options: a ) 20 cm , b ) 23 cm , c ) 25 cm , d ) 10 cm , e ) 28 cm
Rationale: "required length = hcf of 1800 cm , 4000 cm , 650 cm = 50 cm answer is d"
Answer: d
Question (gain): from january 1 , 2015 , to january 1 , 2017 , the number of people enrolled in health maintenance organizations increased by 5 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 ) 43
Rationale: "soln : - 5 x = 45 - - > 21 / 20 * x = 45 - - > x = 45 * 20 / 21 = 300 / 7 = ~ 43 . answer : e ."
Answer: e
Question (gain): the number which exceeds 16 % of it by 42 is :
Options: a ) 50 , b ) 52 , c ) 58 , d ) 60 , e ) 62
Rationale: "solution solution let the number be x . x - 16 % of x = 42 x - 16 / 100 x = 42 x - 4 / 25 x = 42 21 / 25 x = 42 x = ( 42 x 25 / 21 ) = 50 answer a"
Answer: a
Question (other): in assembling a bluetooth device , a factory uses one of two kinds of modules . one module costs $ 10 and the other one , that is cheaper , costs $ 2.5 . the factory holds a $ 62.50 worth stock of 22 modules . how many of the modules in the stock are of the cheaper kind ?
Options: a ) 31 , b ) 35 , c ) 21 , d ) 40 , e ) 45
Rationale: "so the number of $ 2.50 modules must be 21 so that the leftover 1 modules are of $ 10 which will give a total value $ 62.50 . 21 * 2.50 + 1 * 10 = 52.50 + 10 = 62.50 answer : c"
Answer: c
Question (physics): mary goes into labor at her local grocery store and is rushed to a hospital in an ambulance traveling 60 mph . her husband don drives after the ambulance at an average speed of 30 mph . mary reaches the hospital fifteen minutes later . how long does it take don to get there from the store ?
Options: a ) 25 minutes , b ) 30 minutes , c ) 10 minutes , d ) 15 minutes , e ) 7 minutes
Rationale: distance covered by the ambulance in 15 minutes = 15 miles 60 mph is one mile per minute , therefore 30 mph will be 1 / 2 a mile per minute . so , he reaches the hospital half an hour after leaving the store . correct answer : b
Answer: b
Question (geometry): what is the ratio between perimeters of two squares one having 7 times the diagonal then the other ?
Options: a ) 3 : 7 , b ) 3 : 5 , c ) 3 : 8 , d ) 7 : 1 , e ) 3 : 5
Rationale: "d = 7 d d = d a √ 2 = 7 d a √ 2 = d a = 7 d / √ 2 a = d / √ 2 = > 7 : 1 answer : d"
Answer: d
Question (geometry): square a has an area of 65 square centimeters . square b has a perimeter of 16 centimeters . if square b is placed within square a and a random point is chosen within square a , what is the probability the point is not within square b ?
Options: a ) 0.25 , b ) 0.5 , c ) 0.75 , d ) 0.1 , e ) 0.3
Rationale: "i guess it ' s mean that square b is placed within square aentirely . since , the perimeter of b is 16 , then its side is 16 / 4 = 4 and the area is 4 ^ 2 = 16 ; empty space between the squares is 65 - 16 = 48 square centimeters , so if a random point is in this area then it wo n ' t be within square b : p = favorable / total = 48 / 64 = 0.75 . answer : c"
Answer: c
Question (gain): in an election , candidate a got 80 % of the total valid votes . if 15 % of the total votes were declared invalid and the total numbers of votes is 560000 , find the number of valid vote polled in favor of candidate .
Options: a ) 330000 , b ) 340000 , c ) 380800 , d ) 356000 , e ) 357000
Rationale: "total number of invalid votes = 15 % of 560000 = 15 / 100 × 560000 = 8400000 / 100 = 84000 total number of valid votes 560000 – 84000 = 476000 percentage of votes polled in favour of candidate a = 80 % therefore , the number of valid votes polled in favour of candidate a = 80 % of 476000 = 80 / 100 × 476000 = 38080000 / 100 = 380800 c )"
Answer: c
Question (geometry): a rectangular field is to be fenced on three sides leaving a side of 20 feet uncovered . if the area of the field is 560 sq . feet , how many feet of fencing will be required ?
Options: a ) 34 , b ) 40 , c ) 68 , d ) 76 , e ) 92
Rationale: "given that length and area , so we can find the breadth . length x breadth = area 20 x breadth = 560 breadth = 28 feet area to be fenced = 2 b + l = 2 ( 28 ) + 20 = 76 feet answer : d"
Answer: d
Question (physics): if a man earns rs 20 on first day and spends rs 15 on second day , and earns rs 20 on third day and spends rs 15 on fourth day and goes on on which day he will be having rs 60 .
Options: a ) 40 rs , b ) 45 rs , c ) 50 rs , d ) 55 rs , e ) 60 rs
Rationale: earns rs 20 on first day and spends rs 15 on second day means , end of day 2 , he have 5 rs . therefore , in 16 days he have 40 rs 2 * 8 = 16 days 5 rs * 8 = 40 rs and on the 17 th day again he earn rs . 20 , 40 + 20 = 60 rs . answer : e
Answer: e
Question (gain): 4 mat - weaves can weaves 4 mats in 4 days . at the same rate , how many mats would be woven by 8 mat - weaves in 8 days ?
Options: a ) 4 , b ) 8 , c ) 12 , d ) 16 , e ) 17
Rationale: solution let the required number of mats be x . more weaves , more mats ( direct proportion ) more days , more mats ( direct proportion ) ∴ 4 × 4 × x = 8 × 8 × 4 ⇔ x = ( 8 x 8 x 4 ) / ( 4 x 4 ) = 16 . answer d
Answer: d
Question (general): the average age of 36 students in a group is 14 years . when teacher ’ s age is included to it , the average increases by one . what is the teacher ’ s age in years ?
Options: a ) 31 , b ) 36 , c ) 41 , d ) 51 , e ) none
Rationale: "sol . age of the teacher = ( 37 × 15 – 36 × 14 ) years = 51 years . answer d"
Answer: d
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 18 seconds . what is the length of each train ( in meters ) ?
Options: a ) 20 , b ) 25 , c ) 35 , d ) 50 , e ) 65
Rationale: "the relative speed = 46 - 36 = 10 km / hr = 10 * 5 / 18 = 25 / 9 m / s in 18 seconds , the relative difference in distance traveled is 18 * 25 / 9 = 50 meters this distance is twice the length of each train . the length of each train is 50 / 2 = 25 meters the answer is b ."
Answer: b
Question (general): the numbers 272738 and 232342 , when divided by n , a 2 digit number leave a remainder 13 and 17 respectively . find the sum of digits of n ?
Options: a ) 4 , b ) 5 , c ) 6 , d ) 7 , e ) 8
Rationale: "we have to find the h . c . f of both 1.272738 - 13 2.232325 - 17 h . c . f is 25 ans is 7 answer : d"
Answer: d
Question (physics): a train is 360 meter long is running at a speed of 90 km / hour . in what time will it pass a bridge of 140 meter length ?
Options: a ) 27 seconds , b ) 29 seconds , c ) 40 seconds , d ) 11 seconds , e ) 20 seconds
Rationale: "speed = 90 km / hr = 90 * ( 5 / 18 ) m / sec = 25 m / sec total distance = 360 + 140 = 500 meter time = distance / speed = 500 * ( 1 / 25 ) = 20 seconds answer : e"
Answer: e
Question (general): for each month of a given year except december , a worker earned the same monthly salary and donated one - tenth of that salary to charity . in december , the worker earned n times his usual monthly salary and donated one - fourth of his earnings to charity . if the worker ' s charitable contributions totaled one - eighth of his earnings for the entire year , what is the value of n ?
Options: a ) 8 / 5 , b ) 5 / 2 , c ) 3 , d ) 22 / 10 , e ) 4
Rationale: "let monthly salary for each of the 11 months except december was x , then 11 x * 1 / 10 + nx * 1 / 4 = 1 / 8 ( 11 x + nx ) ; 11 / 10 + n / 4 = 1 / 8 ( 11 + n ) = > 44 + 10 n / 40 = 11 + n / 8 352 + 80 n = 440 + 40 n = > 40 n = 88 n = 88 / 40 = 22 / 10 answer : d ."
Answer: d
Question (general): if sharon ' s weekly salary increased by 16 percent , she would earn $ 348 per week . if instead , her weekly salary were to increase by 20 percent , how much would she earn per week ?
Options: a ) $ 374 , b ) $ 382 , c ) $ 385 , d ) $ 360 , e ) $ 399
Rationale: "( 348 / 116 ) 120 = 360 in this case long division does not take much time . ( 348 / 116 ) = 3 3 * 120 = 360 ( 300 + 60 ) answer d"
Answer: d
Question (other): if the ratio of a to b is 11 to 3 and the ratio of b to c is 1 to 5 , what is the ratio of a to c ?
Options: a ) 4 / 15 , b ) 11 / 15 , c ) 2 / 5 , d ) 4 / 5 , e ) 7 / 6
Rationale: "a : b = 11 : 3 - - 1 b : c = 1 : 5 = > b : c = 3 : 15 - - 2 from 1 and 2 , we get a : c = 11 : 15 answer b"
Answer: b
Question (general): what should be the least number to be added to the 2496 number to make it divisible by 5 ?
Options: a ) 12 , b ) 17 , c ) 18 , d ) 4 , e ) 26
Rationale: "answer : 4 option : d"
Answer: d
Question (general): 1 ⁄ 5 of a number is equal to 5 ⁄ 8 of the second number . if 35 is added to the first number then it becomes 4 times of second number . what is the value of the second number ?
Options: a ) 125 , b ) 70 , c ) 40 , d ) 25 , e ) none of these
Rationale: let x be the first number and y be the second number . 1 ⁄ 5 x = 5 ⁄ 8 y \ x ⁄ y = 25 ⁄ 8 . . . . . . ( i ) x + 35 = 4 y or , 25 ⁄ 8 y + 35 = 4 y \ y = 40 answee c
Answer: c