Cheukting/mathqa huggingface dataset:
Question (geometry): if a square mirror has a 20 - inch diagonal , what is the approximate perimeter q of the mirror , in inches ?
Options: a ) 40 , b ) 60 , c ) 80 , d ) 100 , e ) 120
Rationale: "if you draw the square and diagonal inside the square . u can see square becomes part of two triangles opposite to each other . and we know the property of the triangle , addition of two sides of triangle must be greater than its diagonal in order to complete the triangle . and each side must be less than 20 and perimeter q must be less than 80 , so we can eliminate answer choice c , d and e . so side 1 + side 2 > 20 , that means side 1 or side 2 must be > 10 . so we can eliminate the answer choice a . now we are left with is b"
Answer: b
Question (physics): pipes a and b can fill a tank in 3 and 4 hours . pipe c can empty it in 4 hours . if all pipes are opened together , then the tank will be filled in ?
Options: a ) 3 hr , b ) 1 / 2 hr , c ) 1 hr , d ) 9 / 7 hr , e ) 5 / 3 hr
Rationale: "net part filled in 1 hour = 1 / 3 + 1 / 4 - 1 / 4 = 1 / 3 the tank will be full in 3 hr answer is a"
Answer: a
Question (other): a certain car dealership sells economy cars , luxury cars , and sport utility vehicles . the ratio of economy to luxury cars is 3 : 5 . the ratio of economy cars to sport utility vehicles is 4 : 3 . what is the ratio of luxury cars to sport utility vehicles ?
Options: a ) 9 : 8 , b ) 8 : 9 , c ) 3 : 2 , d ) 20 : 9 , e ) 1 : 2
Rationale: "the ratio of economy to luxury cars is 3 : 5 - - > e : l = 3 : 5 = 12 : 20 . the ratio of economy cars to sport utility vehicles is 4 : 3 - - > e : s = 4 : 3 = 12 : 9 . thus , l : s = 20 : 9 . answer : d ."
Answer: d
Question (general): in a graduating class , the difference between the highest and lowest salaries is $ 100000 . the median salary is $ 50000 higher than the lowest salary and the average salary is $ 20000 higher than the median . what is the minimum number of students r in the class ?
Options: a ) a ) 10 , b ) b ) 12 , c ) c ) 15 , d ) d ) 20 , e ) e ) 25
Rationale: the difference between the highest and lowest salaries is $ 100000 . so there are at least 2 people - say one with salary 0 and the other with 100 k . no salary will be outside this range . median = 50 k more than lowest . so median is right in the center of lowest and highest since lowest and highest differ by 100 k . in our example , median = 50 k . since there are more than 2 people , there would probably be a person at 50 k . mean = 20 k more than median so in our example , mean salary = 70 k on the number line , 0 . . . . . . . . 50 k ( median ) . . . . . . . . 100 k mean = 70 k so there must be people more toward 100 k to bring the mean up to 70 k . since we want to add minimum people , we will add people at 100 k to quickly make up the right side deficit . 0 and 50 k are ( 70 k + 20 k ) = 90 k away from 70 k . 100 k is 30 k away from 70 k . to bring the mean to 70 k , we will add two people at 100 k each to get : 0 . . . . 50 k . . . . . 100 k , 100 k , 100 k but when we add more people to the right of 70 k , the median will shift to the right . we need to keep the median at 50 k . so every time we add people to the right of 70 k , we need to add people at 50 k too to balance the median . 50 k is 20 k less than 70 k while 100 k is 30 k more than 70 k . to keep the mean same , we need to add 2 people at 100 k for every 3 people we add at 50 k . so if we add 3 people at 50 k and 2 people at 100 k , we get : 0 , . . . 50 k , 50 k , 50 k , 50 k , . . . 100 k , 100 k , 100 k , 100 k , 100 k the median is not at 50 k yet . add another 3 people at 50 k and another 2 at 100 k to get 0 , 50 k , 50 k , 50 k , 50 k , 50 k , 50 k , 50 k , 100 k , 100 k , 100 k , 100 k , 100 k , 100 k , 100 k now the median is 50 k and mean is 70 k . total number of people is 15 . answer ( c )
Answer: c
Question (general): if 10 people contributed a total of $ 20.00 toward a gift and each of them contributed at least $ 1.00 , then the maximum possible amount any one person could have contributed is
Options: a ) $ 11.00 , b ) $ 1.25 , c ) $ 5.00 , d ) $ 6.00 , e ) $ 20.00
Rationale: "a for me 9 people with 1 $ each - > maximum = 11"
Answer: a
Question (general): the average salary of workers in an industry is rs . 200 the average salary of technicians being rs . 400 and that of non - technicians being rs . 125 . what is the total number of workers ?
Options: a ) 277 , b ) 665 , c ) 662 , d ) 552 , e ) 281
Rationale: "8 * 84 = 672 – 7 = 665 answer : b"
Answer: b
Question (physics): two trains of equal lengths take 10 sec and 8 sec respectively to cross a telegraph post . if the length of each train be 120 m , in what time will they cross other travelling in opposite direction ?
Options: a ) 22 , b ) 12 , c ) 9 , d ) 99 , e ) 21
Rationale: speed of the first train = 120 / 10 = 12 m / sec . speed of the second train = 120 / 8 = 15 m / sec . relative speed = 12 + 15 = 27 m / sec . required time = ( 120 + 120 ) / 27 = 9 sec . answer : c
Answer: c
Question (gain): reema took a loan of rs 1200 with simple interest for as many years as the rate of interest . if she paid rs . 432 as interest at the end of the loan period , what was the rate of interest .
Options: a ) 5 % , b ) 6 % , c ) 7 % , d ) 8 % , e ) 9 %
Rationale: "explanation : let rate = r % then time = r years . = > 1200 ∗ r ∗ r / 100 = 432 = > r 2 = 36 = > r = 6 % option b"
Answer: b
Question (other): each of the dogs in a certain kennel is a single color . each of the dogs in the kennel either has long fur or does not . of the 45 dogs in the kennel , 26 have long fur , 22 are brown , and 8 are neither long - furred nor brown . how many long - furred dogs are brown ?
Options: a ) 26 , b ) 19 , c ) 11 , d ) 8 , e ) 6
Rationale: "no of dogs = 45 long fur = 26 brown = 22 neither long fur nor brown = 8 therefore , either long fur or brown = 45 - 8 = 37 37 = 26 + 22 - both both = 11 answer c"
Answer: c
Question (general): evaluate : 6202.5 + 620.25 + 62.025 + 6.2025 + 0.62025
Options: a ) 6819.59775 , b ) 6981.59775 , c ) 6918.59775 , d ) 6198.59775 , e ) 6891.59775
Rationale: "6202.5 620.25 62.025 6.2025 + 0.62025 - - - - - - - - - - - - - - - 6891.59775 answer is e ."
Answer: e
Question (physics): a van takes 5 hours to cover a distance of 465 km . what speed in kph should the van maintain to cover the same distance in 3 / 2 of the previous time ?
Options: a ) 56 , b ) 58 , c ) 60 , d ) 62 , e ) 64
Rationale: "( 3 / 2 ) * 5 = 7.5 hours 465 / 7.5 = 62 kph the answer is d ."
Answer: d
Question (general): the product of two numbers is 120 and the sum of their squares is 289 . the sum is :
Options: a ) 23 , b ) 21 , c ) 43 , d ) 56 , e ) 30
Rationale: "xy = 120 and x 2 + y 2 = 289 . ( x + y ) 2 = x 2 + y 2 + 2 xy = 289 + ( 2 x 120 ) = 529 x + y = 529 = 23 . answer a"
Answer: a
Question (physics): in what time will a railway train 60 m long moving at the rate of 54 kmph pass a telegraph post on its way ?
Options: a ) 4 sec , b ) 7 sec , c ) 2 sec , d ) 6 sec , e ) 9 sec
Rationale: "t = 60 / 54 * 18 / 5 = 4 sec answer : a"
Answer: a
Question (physics): a person walks at a speed of 4 km / hr and runs at a speed of 8 km / hr . how many hours will the person require to cover a distance of 4 km , if the person completes half of the distance by walking and the other half by running ?
Options: a ) 0.25 , b ) 0.5 , c ) 0.75 , d ) 1 , e ) 1.25
Rationale: "time = 2 / 4 + 2 / 8 = 6 / 8 = 0.75 hours the answer is c ."
Answer: c
Question (physics): mary passed a certain gas station on a highway while traveling west at a constant speed of 50 miles per hour . then , 15 minutes later , paul passed the same gas station while traveling west at a constant speed of 60 miles per hour . if both drivers maintained their speeds and both remained on the highway for at least 4 hours , how long after he passed the gas station did paul catch up with mary ?
Options: a ) 2 , b ) 1.5 , c ) 1.6 , d ) 1.7 , e ) 1.25
Rationale: "d = rt m : r = 50 mph , t = t + 1 / 4 hr d = 50 ( t + 1 / 4 ) p : r = 60 , t = t d = 60 t since they went the same distance : 50 t + 50 / 4 = 60 t 10 t = 50 / 4 t = 1.25 or 1 hr , 15 min e"
Answer: e
Question (physics): the sum of three consecutive even numbers is 36 . find the middle number of the three ?
Options: a ) 14 , b ) 16 , c ) 18 , d ) 24 , e ) 36
Rationale: "three consecutive even numbers ( 2 p - 2 ) , 2 p , ( 2 p + 2 ) . ( 2 p - 2 ) + 2 p + ( 2 p + 2 ) = 36 6 p = 36 = > p = 6 . the middle number is : 6 p = 36 . answer : e"
Answer: e
Question (general): the average of runs of a cricket player of 10 innings was 32 . how many runs must he make in his next innings so as to increase his average of runs by 4 ?
Options: a ) 87 , b ) 16 , c ) 10 , d ) 76 , e ) 17
Rationale: "average after 11 innings = 36 required number of runs = ( 36 * 11 ) - ( 32 * 10 ) = 396 - 320 = 76 . answer : d"
Answer: d
Question (general): the guests at a football banquet consumed a total of 323 pounds of food . if no individual guest consumed more than 2 pounds of food , what is the minimum number of guests that could have attended the banquet ?
Options: a ) 160 , b ) 161 , c ) 162 , d ) 163 , e ) 164
Rationale: "to minimize one quantity maximize other . 161 * 2 ( max possible amount of food a guest could consume ) = 322 pounds , so there must be more than 161 guests , next integer is 162 . answer : c ."
Answer: c
Question (physics): a person can swim in still water at 10 km / h . if the speed of water 4 km / h , how many hours will the man take to swim back against the current for 12 km ?
Options: a ) 2 , b ) 7 , c ) 5 , d ) 9 , e ) 6
Rationale: "m = 10 s = 4 us = 10 - 4 = 6 d = 12 t = 12 / 6 = 2 answer : a"
Answer: a
Question (general): in plutarch enterprises , 70 % of the employees are marketers , 20 % are engineers , and the rest are managers . marketers make an average salary of $ 70,000 a year , and engineers make an average of $ 80,000 . what is the average salary for managers if the average for all employees is also $ 80,000 ?
Options: a ) $ 80,000 , b ) $ 150,000 , c ) $ 240,000 , d ) $ 290,000 , e ) $ 320,000
Rationale: "for sake of ease , let ' s say there are 10 employees : 7 marketers , 2 engineers , and 1 manager . average company salary * number of employees = total company salary > > > $ 80,000 * 10 = $ 800,000 subtract the combined salaries for the marketers ( 7 * $ 70,000 ) and the engineers ( 2 * $ 80,000 ) > > > $ 800,000 - $ 490,000 - $ 160,000 = $ 150,000 . the correct answer is b ."
Answer: b
Question (general): 2525 * 9
Options: a ) 22725 , b ) 25675 , c ) 22655 , d ) 27575 , e ) none of these
Rationale: "explanation : 2525 * ( 10 - 1 ) = 25250 - 2525 = 22725 option a"
Answer: a
Question (geometry): the diagonals of a rhombus are 15 cm and 21 cm . find its area ?
Options: a ) 277 , b ) 266 , c ) 150 , d ) 288 , e ) 157.5
Rationale: "1 / 2 * 15 * 21 = 157.5 answer : e"
Answer: e
Question (gain): rs . 500 amounts to rs . 620 in 2 years at simple interest . if the interest is increased by 2 % , it would amount to how much ?
Options: a ) 120 , b ) 25 , c ) 614 , d ) 530 , e ) 210
Rationale: "( 500 * 3 * 2 ) / 100 = 30 500 + 30 = 530 answer : d"
Answer: d
Question (general): if the sales tax be reduced from 3 ( 1 / 5 ) % to 2 ( 1 / 2 ) % , then what difference does it make to a person who purchases a bag with marked price of rs . 6400 ?
Options: a ) rs . 150.40 , b ) rs . 44.80 , c ) rs . 140.40 , d ) rs . 50.48 , e ) none of these
Rationale: "explanation : required difference = ( 3 ( 1 / 5 ) of rs . 6400 ) - ( 2 ( 1 / 2 ) of rs . 6400 ) = ( 16 / 5 – 5 / 2 ) % of rs . 6400 = ( 7 / 10 ) x ( 1 / 100 ) x 6400 = rs . 44.80 answer b"
Answer: b
Question (general): circles x and y are concentric . if the radius of circle x is 6 times that of circle y , what is the probability that a point selected inside circle x at random will be outside circle y ?
Options: a ) 13 , b ) pi / 3 , c ) pi / 2 , d ) 35 / 36 , e ) 8 / 9
Rationale: small circle radius = a , so area = pi a ^ 2 large circle radius = 6 a , so area = 9 . pi a ^ 2 area of shaded region = 36 pi a ^ 2 - pi a ^ 2 = 35 pi a ^ 2 so , probability = ( 35 pi a ^ 2 ) / ( 36 pi a ^ 2 ) = 35 / 36 = answer = d
Answer: d
Question (general): if x + y = 8 and y − 3 x = 7 , then what is the value of y - x ?
Options: a ) 1 / 7 , b ) 3 , c ) 15 , d ) 15 / 2 , e ) 60 / 7
Rationale: x + y = 8 . . . equation 1 - 3 x + y = 7 . . . equation 2 adding both the equations - 2 x + 2 y = 15 = > y - x = 15 / 2 correct answer option d
Answer: d
Question (general): if 6 / w + 6 / x = 6 / y and wx = y , then the average ( arithmetic mean ) of w and x is
Options: a ) 1 / 2 , b ) 1 , c ) 2 , d ) 4 , e ) 8
Rationale: "given : 6 / w + 6 / x = 6 / ywx = y find : ( w + x ) / 2 = ? 6 ( 1 / w + 1 / x ) = 6 ( 1 / y ) - divide both sides by 6 ( 1 / w + 1 / x ) = 1 / y ( x + w ) / wx = 1 / wx - sub ' d in y = wx x + w - 1 = 0 x + w = 1 therefore ( w + x ) / 2 = 1 / 2 ans : a"
Answer: a
Question (gain): a cycle is bought for rs . 900 and sold for rs . 1350 , find the gain percent ?
Options: a ) 39 % , b ) 20 % , c ) 23 % , d ) 50 % , e ) 83 %
Rationale: "900 - - - - 450 100 - - - - ? = > 50 % answer : d"
Answer: d
Question (physics): some persons can do a piece of work in 24 days . two times the number of these people will do half of that work in ?
Options: a ) 3 , b ) 4 , c ) 5 , d ) 6 , e ) 8
Rationale: "24 / ( 2 * 2 ) = 6 days answer : d"
Answer: d
Question (general): if 1 / 12 of the passengers on a ship are from north america , 1 / 4 are europeans , 2 / 9 are from africa , 1 / 6 are from asia and the remaining 50 people are citizens of other continents , then how many passengers are on board the ship ?
Options: a ) 120 , b ) 140 , c ) 150 , d ) 160 , e ) 180
Rationale: "1 / 12 + 1 / 4 + 2 / 9 + 1 / 6 = ( 3 + 9 + 8 + 6 ) / 36 = 13 / 18 let x be the number of passengers on the ship . 50 = ( 5 / 18 ) x x = 180 the answer is e ."
Answer: e
Question (general): what is the sum of all 3 digit numbers that leave a remainder of ' 2 ' when divided by 3 ?
Options: a ) 897 , b ) 164,850 , c ) 164,749 , d ) 149,700 , e ) 156,720
Rationale: "explanatory answer step 1 : identify the series the smallest 3 digit number that will leave a remainder of 2 when divided by 3 is 101 . the next couple of numbers that will leave a remainder of 2 when divided by 3 are 104 and 107 . the largest 3 digit number that will leave a remainder of 2 when divided by 3 is 998 . it is evident that any number in the sequence will be a 3 digit positive integer of the form ( 3 n + 2 ) . so , the given numbers are in an arithmetic sequence with the first term being 101 and the last term being 998 and the common difference being 3 . step 2 : compute the sum sum of an arithmetic progression ( ap ) = [ first term + last term / 2 ] n we know the first term : 101 we know the last term : 998 . the only unknown is the number of terms , n . in an a . p . , the nth term an = a 1 + ( n - 1 ) * d in this case , therefore , 998 = 101 + ( n - 1 ) * 3 or 897 = ( n - 1 ) * 3 ( n - 1 ) = 299 or n = 300 . sum of the ap will therefore , be [ 101 + 998 / 2 ] ∗ 300 = 164,850 choice b is the correct answer ."
Answer: b
Question (physics): if it takes 4 movers 40 minutes to unpack their van , how long would 5 movers take ?
Options: a ) 38 minutes , b ) 35 minutes , c ) 32 minutes , d ) 29 minutes , e ) 26 minutes
Rationale: 4 * 40 = 5 * x x = 32 answer : c
Answer: c
Question (physics): a person can row at 9 kmph and still water . he takes 5 1 / 2 hours to row from a to b and back . what is the distance between a and b if the speed of the stream is 1 kmph ?
Options: a ) 32 , b ) 28 , c ) 29 , d ) 24 , e ) 20
Rationale: "let the distance between a and b be x km . total time = x / ( 9 + 1 ) + x / ( 9 - 1 ) = 5.5 = > x / 10 + x / 8 = 11 / 2 = > ( 4 x + 5 x ) / 40 = 11 / 2 = > x = 24 km . answer : d"
Answer: d
Question (general): a grocer has a sale of rs . 5420 , rs . 5660 , rs . 6200 , rs . 6350 and rs . 6500 for 5 consecutive months . find the sale he should have in the sixth month , so that he gets an average sale of rs . 6300 ?
Options: a ) rs . 5870 , b ) rs . 5991 , c ) rs . 6020 , d ) rs . 7670 , e ) none of these
Rationale: "explanation : total sale for 5 months = rs . ( 5420 + 5660 + 6200 + 6350 + 6500 ) = rs . 30,130 therefore , required sale = rs . [ ( 6300 * 6 ) – 30,130 ] = rs . ( 37800 – 30,130 ) = rs . 7670 answer d"
Answer: d
Question (physics): a train moves with a speed of 189 kmph . its speed in metres per second is
Options: a ) 60.8 , b ) 18 , c ) 30 , d ) 52.5 , e ) none
Rationale: "solution speed = 189 kmph = ( 189 x 5 / 18 ) m / sec = 52.5 m / sec . answer d"
Answer: d
Question (general): a man has some hens and cows . if the number of heads be 100 and the number of feet equals 180 , then the number of hens will be :
Options: a ) 22 , b ) 23 , c ) 80 , d ) 90 , e ) 28
Rationale: "explanation : let the number of hens be x and the number of cows be y . then , x + y = 100 . . . . ( i ) and 2 x + 4 y = 220 x + 2 y = 110 . . . . ( ii ) solving ( i ) and ( ii ) we get : x = 90 , y = 10 . the required answer = 90 . answer : d"
Answer: d
Question (general): if 5 x = 6 y and xy ≠ 0 , what is the ratio of 1 / 3 * x to 1 / 5 * y ?
Options: a ) 25 / 6 , b ) 36 / 25 , c ) 2 , d ) 5 / 6 , e ) 25 / 36
Rationale: 5 x = 6 y = > x / y = 6 / 5 1 / 3 * x to 1 / 5 * y = x / y * 5 / 3 = ( 6 / 5 ) * ( 5 / 3 ) = 2 ans : c
Answer: c
Question (physics): john and jacob set out together on bicycle traveling at 12 and 9 miles per hour , respectively . after 40 minutes , john stops to fix a flat tire . if it takes john one hour to fix the flat tire and jacob continues to ride during this time , how many hours will it take john to catch up to jacob assuming he resumes his ride at 12 miles per hour ? ( consider john ' s deceleration / acceleration before / after the flat to be negligible )
Options: a ) 3 , b ) 2 1 / 3 , c ) 3 1 / 2 , d ) 4 , e ) 4 1 / 2
Rationale: "john ' s speed - 12 miles / hr jacob ' s speed - 9 miles / hr after 40 min ( i . e 2 / 3 hr ) , distance covered by john = 12 x 2 / 3 = 8 miles . jacob continues to ride for a total of 1 hour and 40 min ( until john ' s bike is repaired ) . distance covered in 1 hour 40 min ( i . e 5 / 3 hr ) = 9 x 5 / 3 = 15 miles . now , when john starts riding back , the distance between them is 7 miles . jacob and john are moving in the same direction . for john to catch jacob , the effective relative speed will be 12 - 9 = 3 miles / hr . thus , to cover 7 miles at 3 miles / hr , john will take 7 / 3 = 2 1 / 3 hours answer b"
Answer: b
Question (general): the proportion of water to alcohol in solution a is 5 : 1 and the proportion of water to alcohol in solution b is 2 : 3 . if an equal amount of each solution is mixed together , what is the concentration of alcohol in the new solution ?
Options: a ) 36.7 % , b ) 37.6 % , c ) 38.3 % , d ) 39.8 % , e ) 40.5 %
Rationale: "let v be the total volume of the new solution . then a volume of v / 2 was added from each solution a and b . the amount of alcohol added to the new solution was : ( 1 / 6 ) ( v / 2 ) + ( 3 / 5 ) ( v / 2 ) = v / 12 + 3 v / 10 = 23 v / 60 . the concentration of alcohol is 23 / 60 = 38.3 % the answer is c ."
Answer: c
Question (physics): 51 persons can repair a road in 12 days , working 5 hours a day . in how many days will 30 persons , working 6 hours a day , complete the work ?
Options: a ) 10 , b ) 13 , c ) 14 , d ) 15 , e ) 17
Rationale: "according to the chain rule , m 1 x t 1 = m 2 x t 2 therefore , 51 x 12 x 5 = 30 x 6 x x x = 17 hence , the number of days = 17 . answer : e"
Answer: e
Question (general): a palindrome is a word or a number that reads the same forward and backward . for example , 2442 and 111 are palindromes . if 5 - digit palindromes are formed using one or more of the digits 1 , 2 , 3 , 4 , 5 , and 6 , how many palindromes are possible ?
Options: a ) 36 , b ) 96 , c ) 132 , d ) 216 , e ) 256
Rationale: "there are 6 choices for each of the first three digits . the number of possible palindromes is 6 ^ 3 = 216 . the answer is d ."
Answer: d
Question (gain): a sells a bicycle to b at a profit of 20 % . b sells it to c at a profit of 25 % . if c pays rs . 225 for it , the cost price of the bicycle for a is ?
Options: a ) 277 , b ) 268 , c ) 270 , d ) 150 , e ) 282
Rationale: "125 % of 120 % of a = 225 125 / 100 * 120 / 100 * a = 225 a = 225 * 2 / 3 = 150 . answer : d"
Answer: d
Question (general): the average marks of a class of 30 students is 50 and that of another class of 50 students is 60 . find the average marks of all the students ?
Options: a ) 56.25 , b ) 52.9 , c ) 52.1 , d ) 52.3 , e ) 42.5
Rationale: "sum of the marks for the class of 30 students = 30 * 50 = 1500 sum of the marks for the class of 50 students = 50 * 60 = 3000 sum of the marks for the class of 80 students = 1500 + 3000 = 4500 average marks of all the students = 4500 / 80 = 56.25 answer : a"
Answer: a
Question (general): if equation | x / 2 | + | y / 2 | = 1 encloses a certain region on the coordinate plane , what is the area of this region ?
Options: a ) 8 , b ) 50 , c ) 100 , d ) 200 , e ) 400
Rationale: the equation can be reduced to intercept form as | x / 2 | + | y / 2 | = 1 , so these are lines in four quadrants with x and y intercept as 2 , so it is a rhombus with diagonals of 4 each and hence area = 1 / 2 * d 1 * d 2 = 1 / 2 * 4 * 4 = 8 . answer a .
Answer: a
Question (general): andrea wants to fill in two sections of her backyard with sod that must be purchased in 2 - x - 2 - foot squares . if the two sections measure 30 x 40 feet and 60 x 80 feet , how many squares of sod does she need to buy ?
Options: a ) 1000 , b ) 1250 , c ) 1500 , d ) 1600 , e ) 2000
Rationale: to begin , find the area of each of the two sections by multiplying the lengths of the sides : 30 feet × 40 feet = 1200 square feet 60 feet × 80 feet = 4800 square feet the total area that needs sod has an area of 1200 + 4800 = 6000 square feet . each individual square is 2 feet by 2 feet , so each has an area of 4 square feet . because all the numbers are even , there will be no waste when the squares of sod are placed . therefore , you just have to find the number of squares needed by dividing : 6000 ÷ 4 = 1500 correct answer c ) 1500
Answer: c
Question (geometry): carol and jordan draw rectangles of equal area . if carol ' s rectangle measures 5 inches by 24 inches and jordan ' s rectangle is 4 inches long , how wide is jordan ' s rectangle , in inches ?
Options: a ) 25 , b ) 23 , c ) 32 , d ) 30 , e ) 18
Rationale: "area of carol ' s rectangle = 24 * 5 = 120 let width of jordan ' s rectangle = w since , the areas are equal 4 w = 120 = > w = 30 answer d"
Answer: d
Question (general): this year , mbb consulting fired 7 % of its employees and left remaining employee salaries unchanged . sally , a first - year post - mba consultant , noticed that that the average ( arithmetic mean ) of employee salaries at mbb was 10 % more after the employee headcount reduction than before . the total salary pool allocated to employees after headcount reduction is what percent of that before the headcount reduction ?
Options: a ) 98.5 % , b ) 100.0 % , c ) 102.3 % , d ) 104.5 % , e ) 105.0 %
Rationale: "100 employees getting 1000 $ avg , so total salary for 100 ppl = 100000 7 % reduction in employees lead to 93 employees and a salary increase of 10 % of previous avg salary thus the new avg salary is = 10 % ( 1000 ) + 1000 = 1100 so total salary of 93 employees is 93 * 1100 = 102300 now the new salary is more than previous salary by x % . x = ( 102300 / 100000 ) * 100 = 102.3 % so the answer is c"
Answer: c
Question (general): at a certain company , each employee has a salary grade s that is at least 1 and at most 6 . each employee receives an hourly wage p , in dollars , determined by the formula p = 9.50 + 0.25 ( s – 1 ) . an employee with a salary grade of 6 receives how many more dollars per hour than an employee with a salary grade of 1 ?
Options: a ) $ 0.50 , b ) $ 1.00 , c ) $ 1.25 , d ) $ 1.50 , e ) $ 1.75
Rationale: "salary grade of 6 is p ( 6 ) = 9.50 + 0.25 ( 6 – 1 ) = 9.50 + 0.25 * 5 ; salary grade of 1 is p ( 1 ) = 9.50 + 0.25 ( 1 – 1 ) = 9.50 ; p ( 6 ) - p ( 1 ) = 9.50 + 0.25 * 5 - 9.50 = 1.25 . answer : c ."
Answer: c