Cheukting/mathqa huggingface dataset:
Question (physics): jonathan can type a 20 page document in 50 minutes , susan can type it in 30 minutes , and jack can type it in 24 minutes . working together , how much time will it take them to type the same document ?
Options: a ) 5 minutes , b ) 11 minutes , c ) 15 minutes , d ) 18 minutes , e ) 20 minutes
Rationale: you may set up common equation like this : job / a + job / b + job / c = job / x memorize this universal formula , you will need it definitely for gmat . and find x from this equation in this specific case , the equation will look like this : 20 / 50 + 20 / 30 + 20 / 24 = 20 / x if you solve this equation , you get the same answer b ( 11 )
Answer: b
Question (gain): in a certain village , 150 litres of water are required per household per month . at this rate , if there are 10 households in the village , how long ( in months ) will 6000 litres of water last ?
Options: a ) 8 , b ) 10 , c ) 6 , d ) 2 , e ) 4
Rationale: "i find it much easier to understand with real numbers , so choose ( almost ) any numbers to replace m , n and p : in a certain village , m 150 litres of water are required per household per month . at this rate , if there aren 10 households in the village , how long ( in months ) willp 2000 litres of water last ? water required is 150 * 10 = 1500 ( m * n ) water available is 6000 ( p ) it will last 4 months ( p / m * n ) ans : e"
Answer: e
Question (geometry): one side of a rectangle is 3 cm shorter than the other side . if we increase the length of each side by 1 cm , then the area of the rectangle will increase by 20 cm 2 . find the lengths of all sides .
Options: a ) 10 and 3 , b ) 7 and 10 , c ) 11 and 8 , d ) 3 and 10 , e ) 10 and 10
Rationale: "let x be the length of the longer side x > 3 , then the other side ' s length is x − 3 cm . then the area is s 1 = x ( x - 3 ) cm 2 . after we increase the lengths of the sides they will become ( x + 1 ) and ( x − 3 + 1 ) = ( x − 2 ) cm long . hence the area of the new rectangle will be a 2 = ( x + 1 ) ⋅ ( x − 2 ) cm 2 , which is 20 cm 2 more than the first area . therefore a 1 + 20 = a 2 x ( x − 3 ) + 20 = ( x + 1 ) ( x − 2 ) x 2 − 3 x + 20 = x 2 + x − 2 x − 2 2 x = 22 x = 11 . so , the sides of the rectangle are 11 cm and ( 11 − 3 ) = 8 cm long . so answer is c ."
Answer: c
Question (general): a rope of which a calf is tied is increased from 12 m to 18 m , how much additional grassy ground shall it graze ?
Options: a ) 1217 , b ) 1219 , c ) 1210 , d ) 565.7 , e ) 1312
Rationale: "π ( 182 – 122 ) = 565.7 answer : d"
Answer: d
Question (general): find a two digit number , given that the sum of the digits is 12 and the difference of the digits is 2 . ?
Options: a ) 66 , b ) 87 , c ) 75 , d ) 88 , e ) 90
Rationale: "using elimination method find which of the options fit the description of the number . . . from the option only 75 meets this description sum of digits - - - 7 + 5 = 12 difference of digits - - - 7 - 5 = 2 answer c ."
Answer: c
Question (general): lisa and robert have taken the same number of photos on their school trip . lisa has taken 3 times as many photos as claire and robert has taken 24 more photos than claire . how many photos has claire taken ?
Options: a ) 6 , b ) 8 , c ) 10 , d ) 12 , e ) 14
Rationale: l = r l = 3 c r = c + 24 3 c = c + 24 c = 12 the answer is d .
Answer: d
Question (gain): what is 25 % of 4 / 12 of 520 ?
Options: a ) 49 , b ) 56 , c ) 60 , d ) 43 , e ) 70
Rationale: 25 % = 25 / 100 = 1 / 4 of 4 / 12 = 1 / 4 * 4 / 12 = 1 / 12 of 520 = 1 / 12 * 520 = 43.33 = = 43 ans - d
Answer: d
Question (physics): 42 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 ) 16 , c ) 13 , d ) 14 , e ) 19
Rationale: "let the required number of days be x . less persons , more days ( indirect proportion ) more working hours per day , less days ( indirect proportion ) persons 30 : 42 : : 12 : x working hours / day 6 : 5 30 x 6 x x = 42 x 5 x 12 x = ( 42 x 5 x 12 ) / ( 30 x 6 ) x = 14 answer d"
Answer: d
Question (physics): calculate the circumference of a circular field whose radius is 6 centimeters .
Options: a ) 2 π cm , b ) 1 π cm , c ) 15 π cm , d ) 12 π cm , e ) 19 π cm
Rationale: "circumference c is given by c = 2 π r = 2 π * 6 = 12 π cm answer : d"
Answer: d
Question (general): for an agricultural experiment , 300 seeds were planted in one plot and 200 were planted in a second plot . if exactly 25 percent of the seeds in the first plot germinated and exactly 30 percent of the seeds in the second plot germinated , what percent of the total number of seeds germinated ?
Options: a ) 27 % , b ) 26 % , c ) 29 % , d ) 30 % , e ) 60 %
Rationale: "in the first plot 25 % of 300 seeds germinated , so 0.25 x 300 = 75 seeds germinated . in the second plot , 30 % of 200 seeds germinated , so 0.30 x 200 = 60 seeds germinated . since 75 + 60 = 135 seeds germinated out of a total of 300 + 200 = 500 seeds , the percent of seeds that germinated is ( 135 / 500 ) x 100 % , or 27 % . answer : a ."
Answer: a
Question (general): if x : y = 1 : 4 , then find the value of ( 7 x + 3 y ) : ( 2 x + y )
Options: a ) 14 : 5 , b ) 15 : 5 , c ) 16 : 5 , d ) 19 : 6 , e ) none of these
Rationale: explanation : let x = 1 k and y = 4 k , so = 7 ( k ) + 3 ( 4 k ) / 2 ( k ) + 1 ( 4 k ) = 19 k / 6 k = 19 : 6 option d
Answer: d
Question (general): ages of two persons differ by 24 years . if 6 year ago , the elder one be 3 times as old the younger one , find their present age
Options: a ) 12,28 , b ) 14,30 , c ) 16,32 , d ) 18,42 , e ) 19,34
Rationale: "explanation : let the age of younger person is x , then elder person age is ( x + 24 ) = > 3 ( x - 6 ) = ( x + 24 - 6 ) [ 6 years before ] = > 3 x - 18 = x + 18 = > x = 18 . so other person age is x + 24 = 42 answer : option d"
Answer: d
Question (general): john want to buy a $ 100 trouser at the store , but he think it â € ™ s too expensive . finally , it goes on sale for $ 55 . what is the percent decrease ?
Options: a ) 20 % , b ) 30 % , c ) 40 % , d ) 50 % , e ) 45 %
Rationale: "the is always the difference between our starting and ending points . in this case , it â € ™ s 100 â € “ 55 = 45 . the â € œ original â €  is our starting point ; in this case , it â € ™ s 100 . ( 45 / 100 ) * 100 = ( 0.45 ) * 100 = 45 % . e"
Answer: e
Question (physics): in a garden , 26 trees are planted at equal distances along a yard 800 metres long , one tree being at each end of the yard . what is the distance between two consecutive trees ?
Options: a ) 10 , b ) 8 , c ) 32 , d ) 14 , e ) 16
Rationale: "26 trees have 25 gaps between them . length of each gap = 800 / 25 = 32 i . e . , distance between two consecutive trees = 32 answer is c ."
Answer: c
Question (general): the average age of a , b and c is 28 years . if the average age of a and c is 29 years , what is the age of b in years ?
Options: a ) 19 , b ) 26 , c ) 20 , d ) 32 , e ) 21
Rationale: "age of b = age of ( a + b + c ) â € “ age of ( a + c ) = 28 ã — 3 â € “ 29 ã — 2 = 84 â € “ 58 = 26 years b"
Answer: b
Question (general): evaluate : 986 x 237 + 986 x 863
Options: a ) 986000 , b ) 968000 , c ) 978000 , d ) 987000 , e ) none of them
Rationale: "986 x 137 + 986 x 863 = 986 x ( 137 + 863 ) = 986 x 1000 = 986000 . answer is a ."
Answer: a
Question (gain): a reduction of 30 % in the price of oil enables a house wife to obtain 3 kgs more for rs . 700 , what is the reduced price for kg ?
Options: a ) 70 , b ) 50 , c ) 60 , d ) 80 , e ) 65
Rationale: "700 * ( 30 / 100 ) = 210 - - - - 3 ? - - - - 1 = > rs . 70 answer : a"
Answer: a
Question (general): a multiple choice test consists of 4 questions , and each question has 5 answer choices . in how many f ways can the test be completed if every question is unanswered ?
Options: a ) 24 , b ) 120 , c ) 625 , d ) 720 , e ) 1024
Rationale: "5 choices for each of the 4 questions , thus total f of 5 * 5 * 5 * 5 = 5 ^ 4 = 625 ways to answer all of them . answer : c ."
Answer: c
Question (other): two vessels p and q contain 62.5 % and 87.5 % of alcohol respectively . if 8 litres from vessel p is mixed with 4 litres from vessel q , the ratio of alcohol and water in the resulting mixture is ?
Options: a ) 17 : 7 , b ) 18 : 8 , c ) 19 : 9 , d ) 19 : 5 , e ) 19 : 4
Rationale: "quantity of alcohol in vessel p = 62.5 / 100 * 8 = 5 litres quantity of alcohol in vessel q = 87.5 / 100 * 4 = 7 / 2 litres quantity of alcohol in the mixture formed = 5 + 7 / 2 = 17 / 2 = 8.5 litres as 12 litres of mixture is formed , ratio of alcohol and water in the mixture formed = 8.5 : 3.5 = 17 : 7 . answer : a"
Answer: a
Question (physics): mariah has decided to hire three workers . to determine whom she will hire , she has selected a group of 10 candidates . she plans to have one working interview with 3 of the 10 candidates every day to see how well they work together . how many days will it take her to have working interviews with all the different combinations of job candidates ?
Options: a ) 720 , b ) 120 , c ) 300 , d ) 30 , e ) 333
Rationale: "there are c 310 = 120 different groups of three possible out of 10 candidates and since each of these groups is interviewed every day then total of 120 days are needed . answer : b"
Answer: b
Question (other): ratio between rahul and deepak is 4 : 3 , after 6 years rahul age will be 34 years . what is deepak present age ?
Options: a ) 22 , b ) 15 , c ) 77 , d ) 21 , e ) 182
Rationale: "present age is 4 x and 3 x , = > 4 x + 6 = 34 = > x = 7 so deepak age is = 3 ( 7 ) = 21 answer : d"
Answer: d
Question (gain): a retailer bought a machine at a wholesale price of $ 99 and later on sold it after a 10 % discount of the retail price . if the retailer made a profit equivalent to 20 % of the whole price , what is the retail price of the machine ?
Options: a ) 81 , b ) 100 , c ) 120 , d ) 132 , e ) 160
Rationale: "my solution : wholesale price = 99 retail price , be = x he provides 10 % discount on retail price = x - 10 x / 100 this retail price = 20 % profit on wholesale price x - 10 x / 100 = 99 + 1 / 5 ( 99 ) x = 132 ; answer : d"
Answer: d
Question (general): a store reported total sales of $ 480 million for february of this year . if the total sales for the same month last year was $ 320 million , approximately what was the percent increase in sales ?
Options: a ) 2 % , b ) 17 % , c ) 50 % , d ) 65 % , e ) 83 %
Rationale: "new value – old value ) / old value x 100 we are given : february sales this year = 480 million february sales last year = 320 million we need to determine the percent increase between sales from last year to sales this year . thus , the new value = 480 million and the old value = 320 million . let ’ s plug them into our percent change formula . ( new value – old value ) / old value x 100 [ ( 480 – 320 ) / 320 ] x 100 = 50 % . the answer is c ."
Answer: c
Question (gain): a cricket bat is sold for $ 850 , making a profit of $ 215 . the profit percentage would be
Options: a ) 24 % , b ) 25 % , c ) 34 % , d ) 36 % , e ) 40 %
Rationale: "215 / ( 850 - 215 ) = 215 / 635 = 43 / 127 = 34 % . answer : c ."
Answer: c
Question (gain): arun purchased 30 kg of wheat at the rate of rs . 11.50 per kg and 20 kg of wheat at the rate of 14.25 per kg . he mixed the two and sold the mixture . approximately what price per kg should be sell the mixture to make 35 % profit ?
Options: a ) 16.39 , b ) 16.33 , c ) 16.35 , d ) 17.01 , e ) 16.32
Rationale: c . p . of 50 kg wheat = ( 30 * 11.50 + 20 * 14.25 ) = rs . 630 . s . p . of 50 kg wheat = 135 % of rs . 630 = 135 / 100 * 630 = rs . 850.50 . s . p . per kg = 850.50 / 50 = rs . 16.38 = 16.30 . answer : d
Answer: d
Question (physics): how many times are the hands of a clock at right angle in 2 days ?
Options: a ) 80 , b ) 82 , c ) 84 , d ) 86 , e ) 88
Rationale: "in 1 day , they are at right angles 44 times . in 2 days , they are at right angles 88 times . answer : option e"
Answer: e
Question (general): a cyclist rides a bicycle 8 km at an average speed of 10 km / hr and again travels 10 km at an average speed of 8 km / hr . what is the average speed for the entire trip ?
Options: a ) 9.28 , b ) 8.48 , c ) 8.78 , d ) 8.98 , e ) 9.18
Rationale: "distance = 18 km time = 8 / 10 + 10 / 8 = ( 64 + 100 ) / 80 = 164 / 80 = 41 / 20 hours average speed = ( 18 * 20 ) / 41 = 8.78 km / h the answer is c ."
Answer: c
Question (general): find the value of 72516 x 9999 = m ?
Options: a ) 456578972 , b ) 436567874 , c ) 725087484 , d ) 725117481 , e ) 357889964
Rationale: "72516 x 9999 = 72516 x ( 10000 - 1 ) = 72516 x 10000 - 72516 x 1 = 725160000 - 72516 = 725087484 c"
Answer: c
Question (general): what is the tens digit of 7 ^ 1001 ?
Options: a ) 0 , b ) 0 , c ) 2 , d ) 3 , e ) 4
Rationale: "7 ^ 1 = 7 7 ^ 2 = 49 7 ^ 3 = 343 7 ^ 4 = 2401 7 ^ 5 = 16807 7 ^ 6 = 117649 we should see this as pattern recognition . we have a cycle of 4 . ( we can multiply the last 2 digits only as we care about ten ' s digit ) 0 , 4 , 4 , 0 . 1001 = 4 * 250 + 1 the ten ' s digit will be 1 . answer b"
Answer: b
Question (gain): suresh started a business , investing rs . 18000 . after 3 months and 4 months respectively , rohan and sudhir joined him with capitals of 12000 and 9000 . at the end of the year the total profit was rs . 3872 . what is the difference between rohan ’ s and sudhir ’ s share in the profit ?
Options: a ) s . 345 , b ) s . 350 , c ) s . 352 , d ) s . 362 , e ) s . 368
Rationale: "suresh : rohan : sudhir ratio of their investments = 18000 × 12 : 12000 × 9 : 9000 × 8 = 6 : 3 : 2 the difference between rohan ’ s and sudhir ’ s share = 1 share : . i . e . = rs . 3872 × 1 / 11 = rs . 352 . c"
Answer: c
Question (gain): john invests $ x at the semi - annual constant compounded rate of 2 percent and also does $ 5,000 at the quarterly constant compounded rate of 4 percent . if the interests are the same after 1 year , what is the value of x ? ?
Options: a ) 10000 , b ) 10100.5 , c ) 20000 , d ) 15000 , e ) 19000
Rationale: "a = p ( 1 + r / n ) ^ nt a = total amount accrued p = principal deposited r = rate of interest in decimal form n = number of times per year , interest compounded t = time in number of years . . x ( 1 + 0.02 / 2 ) ^ 2 - x = 5,000 ( 1 + 0.04 / 4 ) ^ 4 - 5,000 [ when the principal is subtracted from the total amount accrued , the resulting difference is the interest portion and question states interests are equal ) = > x [ ( 1.01 ) ^ 2 - 1 ] = 5,000 [ ( 1.01 ) ^ 4 - 1 ] = > x [ ( 1.01 ) ^ 2 - 1 ] = 5,000 [ ( 1.01 ) ^ 2 + 1 ] [ ( 1.01 ) ^ 2 - 1 ] - - > using a ^ 2 - b ^ 2 = a + b x a - b formula and cancel common expression on both sides = > x = 5,000 ( 1.0201 + 1 ) = 10 , 100.5 hence answer is b ."
Answer: b
Question (general): what number is obtained by adding the units digits of 734 ^ 98 and 347 ^ 82 ?
Options: a ) 11 , b ) 12 , c ) 13 , d ) 14 , e ) 15
Rationale: "the units digit of 734 ^ 98 is 6 because 4 raised to the power of an even integer ends in 6 . the units digit of 347 ^ 82 is 9 because powers of 7 end in 7 , 9 , 3 , or 1 cyclically . since 82 is in the form 4 n + 2 , the units digit is 9 . then 6 + 9 = 15 . the answer is e ."
Answer: e
Question (other): in a certain alphabet , 20 letters contain a dot and a straight line . 36 letters contain a straight line but do not contain a dot . if that alphabet has 60 letters , all of which contain either a dot or a straight line or both , how many letters contain a dot but do not contain a straight line ?
Options: a ) 4 , b ) 3 , c ) 14 , d ) 20 , e ) 28
Rationale: "we are told that all of the letters contain either a dot or a straight line or both , which implies that there are no letters without a dot and a line ( no line / no dot box = 0 ) . first we find the total # of letters with lines : 20 + 36 = 56 ; next , we find the total # of letters without line : 60 - 56 = 4 ; finally , we find the # of letters that contain a dot but do not contain a straight line : 4 - 0 = 4 ."
Answer: a
Question (general): an auction house charges a commission of 25 % on the first $ 50,000 of the sale price of an item , plus 10 % on the amount of of the sale price in excess of $ 50,000 . what was the price of a painting for which the house charged a total commission of $ 24,000 ?
Options: a ) $ 115,000 , b ) $ 165,000 , c ) $ 215,000 , d ) $ 240,000 , e ) $ 365,000
Rationale: "say the price of the house was $ x , then 0.25 * 50,000 + 0.1 * ( x - 50,000 ) = 24,000 - - > x = $ 165,000 ( 25 % of $ 50,000 plus 10 % of the amount in excess of $ 50,000 , which is x - 50,000 , should equal to total commission of $ 24,000 ) . answer : b ."
Answer: b
Question (general): a meal cost $ 35.50 adn there was no tax . if the tip was more than 15 pc but less than 25 pc of the price , then the total amount paid should be :
Options: a ) 41 - 44 , b ) 39 - 41 , c ) 38 - 40 , d ) 37 - 39 , e ) 36 - 37
Rationale: "15 % ( 35.5 ) = 5.325 25 % ( 35.5 ) = 8.875 total amount could have been 35.5 + 5.325 and 35.5 + 8.875 = > could have been between 40.825 and 44.375 = > approximately between 41 and 44 answer is a ."
Answer: a
Question (general): the sum of the even numbers between 1 and n is 95 * 96 , where n is an odd number , then n = ?
Options: a ) 167 , b ) 175 , c ) 183 , d ) 191 , e ) 199
Rationale: "let n - 1 = 2 a . 2 + 4 + . . . + 2 a = 2 * ( 1 + 2 + . . . + a ) = 2 * ( a ) ( a + 1 ) / 2 = ( a ) ( a + 1 ) = 95 * 96 then a = 95 and n = 191 . the answer is d ."
Answer: d
Question (other): the present ratio of students to teachers at a certain school is 50 to 1 . if the student enrollment were to increase by 50 students and the number of teachers were to increase by 5 , the ratio of students to teachers would then be 25 to 1 . what is the present number of teachers ?
Options: a ) 3 , b ) 8 , c ) 10 , d ) 12 , e ) 15
Rationale: we are given that the ratio of students to teacher is 50 to 1 . we can rewrite this using variable multipliers . students : teachers = 50 x : x we are next given that student enrollment increases by 50 and the number of teachers increases by 5 . with this change the new ratio becomes 25 to 1 . we can put all this into an equation : students / teachers  25 / 1 = ( 30 x + 50 ) / ( x + 5 ) if we cross multiply we have : 25 ( x + 5 ) = 50 x + 50 25 x + 125 = 50 x + 50 3 = x since x is the present number of teachers , currently there are 3 teachers . answer a .
Answer: a
Question (general): julie decided to save a certain amount of her monthly salary each month and her salary was unchanged from month to month . if julie ' s savings by the end of the year from these monthly savings were 4 times the amount she spent per month , what should be the fraction of her salary that she spent each month ?
Options: a ) 5 / 3 , b ) 3 / 9 , c ) 3 / 2 , d ) 3 / 5 , e ) 3 / 4
Rationale: let julie ' s monthly savings = s julie ' s monthly pay = p julie ' s monthly expenditure = p - s julie ' s savings by the end of the year from these monthly savings were four times the amount she spent per month 12 s = 4 * ( p - s ) = > 3 s = p - s = > p = 4 s julie ' s monthly expenditure = p - s = 4 s - s = 3 s fraction of her salary that julie spent each month = 3 s / 4 s = p - s / p = 3 / 4 . answer is e
Answer: e
Question (general): the function f ( n ) is defined as the product of all the consecutive positive integers between 2 and n ^ 2 , inclusive , whereas the function g ( n ) is defined as the product of the squares of all the consecutive positive integers between 1 and n , inclusive . the exponent on 2 in the prime factorization of f ( 3 ) / g ( 3 ) is
Options: a ) 1 , b ) 2 , c ) 3 , d ) 4 , e ) 5
Rationale: "f ( 3 ) / g ( 3 ) = product ( 1 to 3 ^ 2 ) / 1.2 ^ 2.3 ^ 2 = 1 . 2.3 . 4.5 . 6.7 . 8.9 / 1 . 4.9 = 1 . 2.3 . ( 2 ^ 2 ) . 5 . ( 2.3 ) . 7 . ( 2 ^ 3 ) . 9 / 1 . ( 2 ^ 2 ) . 9 = 1 . ( 2 ^ 7 ) . 3.5 . 7.9 / 1 . ( 2 ^ 2 ) . 9 loof for 2 ^ 7 / 2 ^ 2 = 2 ^ 5 - - - - exponent 3 answer : c"
Answer: c
Question (gain): calculate the amount that an investor needs to be invest to earn $ 441 in interest in 12 months if the investor plans to invest x dollars in a savings account that pays interest at an annual rate of 7 % compounded semi - annually ?
Options: a ) 6209 , b ) 6200 , c ) 6799 , d ) 6199 , e ) 6685
Rationale: the approach is substitution , our interest requirement is $ 441 after 12 months , 2 compounding period . calculate the compound interest on each option and find out the one that yields $ 441 in 12 months 6200 yielded $ 441 using the formula a = p ( 1 + r / n ) nt hence answer is b
Answer: b
Question (general): how many positive integers less than 6,000 are there in which the sum of the digits equals 5 ?
Options: a ) 65 , b ) 62 , c ) 61 , d ) 56 , e ) 58
Rationale: "basically , the question asks how many 4 digit numbers ( including those in the form 0 xxx , 00 xx , and 000 x ) have digits which add up to 5 . think about the question this way : we know that there is a total of 5 to be spread among the 4 digits , we just have to determine the number of ways it can be spread . let x represent a sum of 1 , and | represent a seperator between two digits . as a result , we will have 5 x ' s ( digits add up to the 5 ) , and 3 | ' s ( 3 digit seperators ) . so , for example : xx | x | x | x = 2111 | | xxx | xx = 0032 etc . there are 8 c 3 ways to determine where to place the separators . hence , the answer is 8 c 3 = 56 . d"
Answer: d
Question (physics): the ratio between the length and the breadth of a rectangular park is 3 : 1 . if a man cycling along the boundary of the park at the speed of 12 km / hr completes one round in 8 min , then the area of the park ( in sq . m ) is ?
Options: a ) 124545 m , b ) 134561 m , c ) 156787 m , d ) 15450 m , e ) 120000 m
Rationale: "perimeter = distance covered in 8 min . = 12000 x 8 m = 1600 m . 60 let length = 3 x metres and breadth = 1 x metres . then , 2 ( 3 x + 1 x ) = 1600 or x = 200 . length = 600 m and breadth = 200 m . area = ( 600 x 200 ) m 2 = 120000 m e"
Answer: e
Question (general): the average ( arithmetic mean ) of 8 numbers is 8 . if 4 is added from each of 5 of the numbers , what is the new average ?
Options: a ) 4.5 , b ) 8.9 , c ) 10.5 , d ) 4.5 , e ) 5.6
Rationale: sum of 8 numbers = 8 * 8 = 64 if 4 is added from each of five of the numbers , we added 4 * 5 = 20 from the total sum sum of 8 number after adding 4 from each of five of the numbers = 64 + 20 = 84 new average = 84 / 8 = 10.5 answer c
Answer: c
Question (general): list k consists of 10 consecutive integers . if - 3 is the least integer in list k , what is the range of the positive integers in list k ?
Options: a ) 5 , b ) 6 , c ) 7 , d ) 11 , e ) 12
Rationale: "answer = a = 5 if least = - 3 , then largest = 6 range = 6 - 1 = 5"
Answer: a
Question (gain): a shopkeeper has 280 kg of apples . he sells 40 % of these at 20 % profit and remaining 60 % at 30 % profit . find his % profit on total .
Options: a ) 24 % , b ) 25 % , c ) 26 % , d ) 28 % , e ) 35 %
Rationale: "total number of apples = 280 let the cost price be x selling price at 20 % profit = 1.2 x selling price at 30 % profit = 1.3 x profit % = ( ( sp - cp ) / cp ) * 100 profit % = ( ( 2 / 5 ) * 280 * 1.2 x + ( 3 / 5 ) * 280 * 1.3 x - 280 x ) / 280 x * 100 = ( 1 / 5 * ( 2.4 + 3.9 ) - 1 ) * 100 = ( 6.3 - 5 ) * 20 = 26 % answer : c"
Answer: c
Question (general): we run a business that rents out canoes and kayaks . a canoe rental costs $ 14 per day , and a kayak rental costs $ 15 dollars per day . one day , our business rents out 3 canoes for every 2 kayaks and receives a total of $ 288 in revenue . how many more canoes than kayaks were rented out ?
Options: a ) 3 , b ) 4 , c ) 5 , d ) 6 , e ) 7
Rationale: let x be the number of canoes . then 2 x / 3 is the number of kayaks . 14 x + ( 2 x / 3 ) * 15 = 288 14 x + 10 x = 288 24 x = 288 x = 12 ( canoes ) 2 x / 3 = 8 ( kayaks ) there were 12 - 8 = 4 more canoes rented out . the answer is b .
Answer: b