Cheukting/mathqa huggingface dataset:
Question (general): of the final grades received by the students in a certain math course , 1 / 5 are a ' s , 1 / 4 are b ' s , 1 / 2 are c ' s , and the remaining 40 grades are d ' s . what is the number of students in the course ?
Options: a ) 80 , b ) 110 , c ) 160 , d ) 800 , e ) 400
Rationale: we start by creating a variable for the total number of students in the math course . we can say : t = total number of students in the math course next , we can use variable t in an equation that we translate from the given information . we are given that , of the final grades received by the students in a certain math course , 1 / 5 are a ' s , 1 / 4 are b ' s , 1 / 2 are c ' s , and the remaining 40 grades are d ' s . since this represents all the grades in the class , it represents all the students in the class . thus we know : # a ’ s + # b ’ s + # c ’ s + # d ’ s = total number of students in the class 1 / 5 ( t ) + ¼ ( t ) + ½ ( t ) + 40 = t we can multiply the entire equation by 20 to cancel out the denominators of the fractions and we have : 4 t + 5 t + 10 t + 800 = 20 t 19 t + 800 = 20 t 800 = t there are a total of 800 students in the math class . answer is d .
Answer: d
Question (general): the scoring system in a certain football competition goes as follows : 3 points for victory , 1 point for a draw , and 0 points for defeat . each team plays 20 matches . if a team scored 8 points after 5 games , what is the least number of the remaining matches it has to win to reach the 40 - point mark by the end of the tournament ?
Options: a ) 6 , b ) 7 , c ) 8 , d ) 9 , e ) 10
Rationale: to get 40 points as end of season we need another 32 points or more from remaining 15 matches : option a = 6 * 3 + 9 * 1 = 27 option b = 7 * 3 + 8 * 1 = 29 option c = 8 * 3 + 7 * 1 = 31 option d = 9 * 3 + 6 * 1 = 33 hence option d - 9
Answer: d
Question (general): what least number must be subtracted from 427398 so that remaining no . is divisible by 12
Options: a ) 3 , b ) 5 , c ) 6 , d ) 7 , e ) 8
Rationale: explanation : on dividing 427398 by 12 we get the remainder 6 , so 6 should be subtracted answer : option c
Answer: c
Question (general): charges made by two companies for the same a / c company xcompany y price $ 575 $ 530 surcharge as a percent of price 4 % 3 % installation charge $ 82.50 $ 93.00 the table above shows the various charges made by two companies for the same air conditioner . what is the total amount that can be saved on the purchase and installation of the air conditioner by dealing with the company that offers the lower total charge ?
Options: a ) $ 41.60 , b ) $ 45.00 , c ) $ 50.75 , d ) $ 55.75 , e ) $ 61.25
Rationale: looking at the values / percentage , its clear that company x costlier than company y just observed the oa ; they have 4 distinct numbers after decimal point total calculation of company x gives . 00 + . 00 + . 50 = . 50 at the decimal total calculation of company y gives . 00 + . 90 + . 00 = . 90 at the decimal there difference provides . 60 at the decimal ; only 41.60 fits in answer = a
Answer: a
Question (physics): two trains , one from howrah to patna and the other from patna to howrah , start simultaneously . after they meet , the trains reach their destinations after 49 hours and 25 hours respectively . the ratio of their speeds is ?
Options: a ) 4 : 9 , b ) 5 : 7 , c ) 4 : 5 , d ) 4 : 1 , e ) 4 : 2
Rationale: "let us name the trains a and b . then , ( a ' s speed ) : ( b ' s speed ) = √ b : √ a = √ 25 : √ 49 = 5 : 7 answer : b"
Answer: b
Question (geometry): the area of a square is equal to 2 times the area of a rectangle of dimensions 8 cm * 64 cm . what is the perimeter of the square ?
Options: a ) 482 , b ) 268 , c ) 800 , d ) 128 , e ) 632
Rationale: "area of the square = s * s = 2 ( 8 * 64 ) = > s = 4 * 8 = 32 cm perimeter of the square = 4 * 32 = 128 cm . answer : d"
Answer: d
Question (general): total dinning bill for 6 people was $ 211.00 . if they add 15 % tip and divided the bill evenly , approximate . what was each persons find share
Options: a ) $ 30.14 , b ) 40.44 , c ) 34.66 , d ) 32.29 , e ) 33.16
Rationale: "211 * 15 = 3165 / 100 = 31.65 211 + 31.65 = 242.65 242.65 / 6 = 40.44 answer : b"
Answer: b
Question (general): there are 7 baskets numbered from 1 to 7 and filled with apples . 10 children are asked to pick apples one by one from each basket such that the number of apples picked by each child from each basket is equal to the number marked on the basket . if there were 1000 apples in total and the baskets were filled in such a way that none of the basket became empty in the process , how many apples were left in the end ?
Options: a ) 90 , b ) 120 , c ) 250 , d ) 720 , e ) 910
Rationale: "each child takes a total of 1 + 2 + 3 + 4 + 5 + 6 + 7 = 7 * 8 / 2 = 28 apples . the total number of apples taken by 10 children is 10 * 28 = 280 the number of apples left in the end is 1000 - 280 = 720 apples . the answer is d ."
Answer: d
Question (general): there are 400 female managers in a certain company . find the total number of female employees in the company , if 2 / 5 of all the employees are managers and 2 / 5 of all male employees are managers .
Options: a ) 800 , b ) 900 , c ) 1000 , d ) 1100 , e ) none of these
Rationale: as per question stem 2 / 5 m ( portion of men employees who are managers ) + 400 ( portion of female employees who are managers ) = 2 / 5 t ( portion of total number of employees who are managers ) , thus we get that 2 / 5 m + 400 = 2 / 5 t , or 2 / 5 ( t - m ) = 400 , from here we get that t - m = 1000 , that would be total number of female employees and the answer ( c )
Answer: c
Question (physics): a and b together can do a work in 6 days . if a alone can do it in 42 days . in how many days can b alone do it ?
Options: a ) 11 , b ) 7 , c ) 8 , d ) 20 , e ) 25
Rationale: "b 7 1 / 6 â € “ 1 / 42 = 1 / 7 = > 7"
Answer: b
Question (general): a bucket full of nuts was discovered by the crow living in the basement . the crow eats a fifth of the total number of nuts in 8 hours . how many hours in total will it take the crow to finish a quarter of the nuts ?
Options: a ) 9 , b ) 10 , c ) 11 , d ) 12 , e ) 14
Rationale: in one hour , the crow eats 1 / 40 of the nuts . ( 1 / 4 ) / ( 1 / 40 ) = 10 hours the answer is b .
Answer: b
Question (general): if all the numbers between 11 and 100 are written on a piece of paper . how many times will the number 4 be used ?
Options: a ) 87 , b ) 267 , c ) 68 , d ) 26 , e ) 21
Rationale: we have to consider the number of 4 ' s in two digit numbers . _ _ if we fix 4 in the 10 th place , unit place be filled with 10 ways . if we fix 4 in units place , 10 th place be filled with 9 ways ( 0 is not allowed ) so total 19 ways . alternatively : answer : a
Answer: a
Question (geometry): the length and breadth of a square are increased by 40 % and 30 % respectively . the area of the rectangle so formed exceeds the area of the square by ?
Options: a ) 82 %
b ) 78 %
c ) 80 %
d ) 90 %
e ) none of these
Rationale: since side 1 x side 2 = area therefore , net % change in area = ( x + y + xy / 100 ) % = [ 40 + 30 + ( 40 x 30 ) / 100 ] % or 82 % . therefore , area is increased by 82 % . answer : a
Answer: a
Question (general): when asked what the time is , a person answered that the amount of time left is 2 / 6 of the time already completed . what is the time .
Options: a ) 2 pm , b ) 9 pm , c ) 3 pm , d ) 6 pm , e ) 7 pm
Rationale: a day has 24 hrs . assume x hours have passed . remaining time is ( 24 - x ) 24 − x = 2 / 6 x ⇒ x = 18 time is 6 pm answer : d
Answer: d
Question (physics): a walks at 10 kmph and 7 hours after his start , b cycles after him at 20 kmph . how far from the start does b catch up with a ?
Options: a ) 100 km , b ) 140 km , c ) 50 km , d ) 120 km , e ) 200 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 7 hours . x / 10 - x / 20 = 7 x = 140 km answer is b"
Answer: b
Question (geometry): the length of a rectangualr hll is 5 m more than its breadth . the area of the hall is 750 m . the length of the hall is
Options: a ) 15 m
b ) 22.5 m
c ) 25 m
d ) 30 m
e ) none
Rationale: solution let the length = xmetres . then length = ( x + 5 ) metres . then , x ( x + 5 ) = 750 = x ² + 5 x - 750 = 0 ( x + 30 ) ( x - 25 ) = 0 x = 25 . answer c
Answer: c
Question (general): how many distinct integer values of n satisfy the inequality | | n - 3 | + 2 | ≤ 12 ?
Options: a ) 15 , b ) 16 , c ) 12 , d ) 18 , e ) 19
Rationale: "so i can write this as in - 3 i + 2 < = 12 or in - 3 i < = 10 so n can have - 7 to 13 = 12 true values . . . . c"
Answer: c
Question (general): if a = 105 and a ^ 3 = 21 * 35 * 45 * b , what is the value of b ?
Options: a ) 35 , b ) 42 , c ) 45 , d ) 49 , e ) 54
Rationale: "first step will be to break down all the numbers into their prime factors . 105 = 3 * 5 * 7 21 = 7 * 3 35 = 7 * 5 45 = 3 * 3 * 5 so , ( 105 ) ^ 3 = 3 * 7 * 7 * 5 * 3 * 3 * 5 * b therefore ( 3 * 5 * 7 ) ^ 3 = 3 ^ 3 * 5 ^ 2 * 7 ^ 2 * b therefore , b = 3 ^ 3 * 5 ^ 3 * 7 ^ 3 / 3 ^ 3 * 5 ^ 2 * 7 ^ 2 b = 5 * 7 = 35 correct answer a ."
Answer: a
Question (physics): a thief is spotted by a policeman from a distance of 175 meters . when the policeman starts the chase , the thief also starts running . if the speed of the thief be 8 km / hr and that of the policeman 10 km / hr , how far the thief will have run before he is overtaken ?
Options: a ) 350 m , b ) 200 m , c ) 400 m , d ) 700 m , e ) none of them
Rationale: relative speed of the policeman = ( 10 - 8 ) km / hr = 2 km / hr . time taken by police man to cover ( 175 m / 1000 ) x 1 / 2 hr = 7 / 80 hr . in 7 / 80 hrs , the thief covers a distance of 8 x 7 / 80 km = 7 / 10 km = 700 m answer is d .
Answer: d
Question (gain): in an election between two candidates , one got 60 % of the total valid votes , 20 % of the votes were invalid . if the total number of votes was 2000 , the number of valid votes that the other candidate got , was :
Options: a ) 1200 , b ) 750 , c ) 800 , d ) 600 , e ) 900
Rationale: "number of valid votes = 80 % of 2000 = 1600 . valid votes polled by other candidate = 40 % of 2000 = ( 40 / 100 ) x 2000 = 800 answer = c"
Answer: c
Question (geometry): a semicircle has a radius of 20 . what is the approximate perimeter of the semicircle ?
Options: a ) 50 , b ) 25 , c ) 86 , d ) 75 , e ) 102
Rationale: "circumference of a circle = 2 pi * r perimeter of a semicircle = pi * r + 2 r aprox perimiter = 3.14 * 20 + 2 * 20 = 102.8 approximately 102 answer e"
Answer: e
Question (physics): amar takes as much time in running 18 meters as a car takes in covering 48 meters . what will be the distance covered by amar during the time the car covers 1.5 km ?
Options: a ) 375 m , b ) 200 m , c ) 300 m , d ) 400 m , e ) 100 m
Rationale: "a 375 m distance covered by amar = 18 / 4.8 ( 1.5 km ) = 3 / 8 ( 1500 ) = 375 m"
Answer: a
Question (general): a prize of $ 400 is to be distributed among 20 winners , each of whom must be awarded at least $ 20 . if 2 / 5 of the prize will be distributed to 3 / 5 of the winners , what is the greatest possible individual award ?
Options: a ) $ 100 , b ) $ 220 , c ) $ 280 , d ) $ 300 , e ) $ 360
Rationale: "total value of the prize = $ 400 number of people = 20 2 / 5 of 400 ( = $ 160 ) should be distributed among 3 / 5 of 20 ( = 12 people ) with each getting $ 20 each . remaining money = 400 - 160 = $ 240 . now in order to ' maximize ' 1 prize , we need to minimise the others and we have been given that each should get $ 20 . thus , minimising the remaining 7 people ( = 20 - 12 - 1 . ' - 1 ' to exclude 1 that needs to be maximised ) = 7 * 20 = 140 . thus the maximum award can be = 240 - 140 = $ 100 , hence a is the correct answer ."
Answer: a
Question (general): the average height of 35 boys in a class was calculated as 181 cm . it has later found that the height of one of the boys in the class was wrongly written as 166 cm whereas his actual height was 106 cm . find the actual average height of the boys in the class ( round off your answer to two decimal places ) . ?
Options: a ) 178.27 cm , b ) 179.29 cm , c ) 978.29 cm , d ) 178.89 cm , e ) 176.29 cm
Rationale: "calculated average height of 35 boys = 181 cm . wrong total height of 35 boys = 181 * 35 cm . this was as a result of an actual height of 106 cm being wrongly written as 166 cm . correct total height of 35 boys = 181 cm - ( 166 cm - 106 cm ) / 35 = 181 cm - 60 / 35 cm = 181 cm - 1.71 cm = 179.29 cm . answer : b"
Answer: b
Question (physics): if 10 typists can type 20 letters in 20 minutes , then how many letters will 40 typists working at the same rate complete in 1 hour ?
Options: a ) 220 , b ) 210 , c ) 200 , d ) 240 , e ) 260
Rationale: "no . of letters typing by 10 typists in 20 minutes = 20 no . of letters typing by 10 typists in 60 minutes = 20 * 3 = 60 no . of letters typing by 40 typists in 60 minutes = 60 / 10 * 40 = 240 answer : d"
Answer: d
Question (physics): john and steve are speed walkers in a race . john is 16 meters behind steve when he begins his final push . john blazes to the finish at a pace of 4.2 m / s , while steve maintains a blistering 3.7 m / s speed . if john finishes the race 2 meters ahead of steve , how long was john ’ s final push ?
Options: a ) 13 seconds , b ) 17 seconds , c ) 36 seconds , d ) 34 seconds , e ) 51 seconds
Rationale: "let t be the time that john spent for his final push . thus , per the question , 4.2 t = 3.7 t + 16 + 2 - - - > 0.5 t = 18 - - - > t = 36 seconds . c is the correct answer ."
Answer: c
Question (geometry): a lady builds 9 cm length , 12 cm width , and 3 cm height box using 3 cubic cm cubes . what is the minimum number of cubes required to build the box ?
Options: a ) 107 , b ) 108 , c ) 109 , d ) 110 , e ) 111
Rationale: "number of cubes required = volume of box / volume of cube = 9 * 12 * 3 / 3 = 108 cubes answer : b"
Answer: b
Question (physics): dan ’ s car gets 32 miles per gallon . if gas costs $ 4 / gallon , then how many miles can dan ’ s car go on $ 58 of gas ?
Options: a ) 242 , b ) 353 , c ) 464 , d ) 575 , e ) 686
Rationale: "58 / 4 = 14.5 gallons 14.5 * 32 = 464 miles the answer is c ."
Answer: c
Question (general): of the two - digit positive integers that have no digits equal to zero , how many have two digits that are equal to each other and the remaining digit different from the other two ?
Options: a ) 24 , b ) 9 , c ) 72 , d ) 144 , e ) 216
Rationale: of the two - digit positive integers that have no digits equal to zero , how many have two digits that are equal to each other and the remaining digit different from the other two ? a . 24 b . 36 c . 72 d . 144 e . 216 choosing the digit for x - 9 ways ; # of permutations of 3 digits in xx - 2 ! / 2 ! total : 9 * 2 ! / 2 ! = 9 . answer : b .
Answer: b
Question (general): . 3 + 33 + 333 + 33.3 = ?
Options: a ) 362.33 , b ) 399.6 , c ) 702.33 , d ) 702 , e ) none of them
Rationale: ". 3 33 333 33.3 - - - - - - - - - - 399.6 - - - - - - - - - - answer is b"
Answer: b
Question (general): if a certain number x is divided by 82 , the reminder is 5 . what is the reminder when x + 17 is divided by 41 ?
Options: a ) 3 , b ) 5 , c ) 6 , d ) 22 , e ) 18
Rationale: "x can be written as 82 k + 5 or x = 5 , 87,169 , etc . x + 17 = 82 k + 5 + 17 = 82 k + 22 or x + 17 = 22,104 , 186 etc . when divided by 41 , we will get the remainder 22 . d"
Answer: d
Question (general): at a certain fruit stand , the price of each apple is 40 cents and the price of each orange is 60 cents . mary selects a total of 15 apples and oranges from the fruit stand , and the average ( arithmetic mean ) price of the 15 pieces of fruit is 48 cents . how many oranges must mary put back so that the average price of the pieces of fruit that she keeps is 45 cents ?
Options: a ) 1 , b ) 2 , c ) 3 , d ) 8 , e ) 9
Rationale: let number of apples = a number of oranges = b a + b = 15 - - - 1 . 48 = ( . 4 a + . 6 b ) / 15 = > 48 = 4 a + 6 b - - - - 2 solving 1 and 2 , we get a = 9 b = 6 let the number of oranges put back = c 45 * ( 15 - c ) = 40 * 9 + 60 ( 6 - c ) = > c = 3 answer c
Answer: c
Question (general): on the richter scale , which measures the total amount of energy released during an earthquake , a reading of x - 1 indicates one - tenth the released energy as is indicated by a reading of x . on that scale , the frequency corresponding to a reading of 5 is how many times as great as the frequency corresponding to a reading of 3 ?
Options: a ) 100 , b ) 200 , c ) 10 ^ 4 , d ) 10 ^ 5 , e ) 10 ^ 6
Rationale: if richter scale reading goes from x - 1 to x it will be 10 if richter scale reading goes from 3 to 4 it will be 10 if richter scale reading goes from 4 to 5 it will be 10 so it will from 3 to 5 i . e 4,5 = 10 * 10 = 10 ^ 2 answer is a
Answer: a
Question (gain): the balance of a trader weighs 8 % less than it should . still the trader marks up his goods to get an overall profit of 30 % . what is the mark up on the cost price ?
Options: a ) 40 % , b ) 19 % , c ) 25 % , d ) 16.66 % , e ) 9 %
Rationale: "the most natural way to deal with ' weights ' questions is by assuming values . say the trader ' s balance shows 100 gms . it is actually 92 gms because it weighs 8 % less . say , the cost price is $ 92 ( $ 1 / gm ) . since he gets a profit of 30 % , the selling price must be 92 + ( 30 / 100 ) * 90 = $ 119 since the cost price is actually supposed to be $ 100 ( for 100 gms ) and the selling price is $ 119 , the mark up is simply 19 % ans : b ."
Answer: b
Question (general): 115 liters of a mixture of milk and water contains in the ratio 3 : 2 . how much water should now be added so that the ratio of milk and water becomes 3 : 4 ?
Options: a ) 12 liters , b ) 32 liters , c ) 46 liters , d ) 50 liters , e ) 34 liters
Rationale: "milk = 3 / 5 * 115 = 69 liters water = 46 liters 69 : ( 46 + p ) = 3 : 4 138 + 3 p = 276 = > p = 46 46 liters of water are to be added for the ratio become 3 : 4 . answer : c"
Answer: c
Question (physics): a , b and c completed a piece of work , a worked for 6 days , b for 9 days and c for 4 days . their daily wages were in the ratio of 3 : 4 : 5 . find the daily wages of c , if their total earning was rs . 1406 ?
Options: a ) s . 109 , b ) s . 108 , c ) s . 100 , d ) s . 95 , e ) s . 102
Rationale: "3 x 4 x 5 x 6 9 4 18 x + 36 x + 20 x = 1406 74 x = 1406 = > x = 19 5 x = 95 rs . answer : d"
Answer: d
Question (physics): efrida and frazer who live 10 miles apart , meet at a restaurant that is directly north of efrida ' s home and directly east of frazer ' s home . if the restaurant is four miles closer to efrida ' s home , than to frazer ' s home , how many miles is the restaurant from frazer ' s home ?
Options: a ) 6 , b ) 7 , c ) 8 , d ) 10 , e ) 11
Rationale: "it ' s a simple geometry problem . look at the diagram below : answer : a ."
Answer: a
Question (general): 2 / [ ( 1 / 0.03 ) + ( 1 / 0.37 ) ] = ?
Options: a ) 0.004 , b ) 0.05555 , c ) 2.775 , d ) 3.6036 , e ) 36.036
Rationale: "approximate . 1 / . 03 = 100 / 3 = 33 1 / . 37 = 100 / 37 = 3 denominator becomes 33 + 3 = 36 2 / 36 = . 05 something answer ( b )"
Answer: b
Question (general): if p ( a ) = 4 / 7 and p ( b ) = 2 / 5 , find p ( a n b ) if a and b are independent events .
Options: a ) 7 / 25 , b ) 3 / 25 , c ) 8 / 35 , d ) 2 / 13 , e ) 3 / 17
Rationale: p ( a n b ) = p ( a ) . p ( b ) p ( a n b ) = 4 / 7 . 2 / 5 p ( a n b ) = 8 / 35 . c
Answer: c
Question (general): bottle r contains 250 capsules and costs $ 6.25 . bottle t contains 100 capsules and costs $ 3.0 . what is the difference between the cost per capsule for bottle r and the cost per capsule for bottle t ?
Options: a ) $ 0.25 , b ) $ 0.12 , c ) $ 0.05 , d ) $ 0.003 , e ) $ 0.005
Rationale: "cost per capsule in r is 6.25 / 250 = 0.625 / 25 = 0.025 cost per capsule in t is 3.00 / 100 = 0.03 the difference is 0.005 the answer is e"
Answer: e
Question (general): for what value of “ k ” will the equation ( 2 kx 2 + 5 kx + 2 ) = 0 have equal roots ?
Options: a ) 2 / 7 , b ) 9 / 4 , c ) 16 / 25 , d ) 7 / 1 , e ) 7 / 2
Rationale: for a 2 nd degree equation ax 2 + bx _ c = 0 has equal roots the condition is b 2 - 4 ac = 0 in the given equation ( 5 k ) ^ 2 - 4 * 2 k * 2 = 0 by solving this equation we get k = 0 , k = 16 / 25 answer : c
Answer: c
Question (geometry): the weight of a hollow sphere is directly dependent on its surface area . the surface area of a sphere is 4 π · r ^ 2 , where r is the radius of the sphere . if a hollow sphere of radius 0.15 cm made of a certain metal weighs 8 grams , a hollow sphere of radius 0.3 cm made of the same metal would weigh how many grams w ?
Options: a ) w = 16 , b ) w = 32 , c ) 64 , d ) 128 , e ) 512
Rationale: "weight directly proportional to 4 pi r ^ 2 now , 4 pi is constant , so , weight is directly proportional to r ^ 2 . when radius = 0.15 , weight = 8 , so ( 0.15 ) ^ 2 proportional to 8 ; ( 0.15 ) ^ 2 * 4 proportional to 8 * 4 , solving further ( 0.15 ) ^ 2 * 2 ^ 2 = ( 0.15 * 2 ) ^ 2 = 0.3 ^ 2 ; so answer = 32 ( b )"
Answer: b
Question (general): it takes 30 days to fill a laboratory dish with bacteria . if the size of the bacteria doubles each day , how long did it take for the bacteria to fill one sixteenth of the dish ?
Options: a ) 16 days , b ) 26 days , c ) 27 days , d ) 28 days , e ) 29 days
Rationale: the bacteria doubles each day , so after 29 days , the dish was half full . after 28 days , the dish was one quarter full . after 27 days , the dish was one eighth full . after 26 days , the dish was one sixteenth full . the answer is b .
Answer: b
Question (physics): some persons can do a piece of work in 8 days . two times the number of these people will do half of that work in ?
Options: a ) 2 , b ) 4 , c ) 5 , d ) 6 , e ) 8
Rationale: "8 / ( 2 * 2 ) = 2 days answer : a"
Answer: a
Question (geometry): rectangular tile each of size 35 cm by 30 cm must be laid horizontally on a rectangular floor of size 1000 cm by 210 cm , such that the tiles do not overlap and they are placed with edges jutting against each other on all edges . a tile can be placed in any orientation so long as its edges are parallel to the edges of floor . no tile should overshoot any edge of the floor . the maximum number of tiles that can be accommodated on the floor is :
Options: a ) 600
b ) 400
c ) 200
d ) 500
e ) 100
Rationale: area of tile = 35 * 30 = 1050 area of floor = 1000 * 210 = 210000 no of tiles = 210000 / 1050 = 200 so , the no of tile = 200 answer : c
Answer: c
Question (general): ( 1000 ) 7 ÷ ( 10 ) 18 = ?
Options: a ) 10 , b ) 100 , c ) 1000 , d ) 10000 , e ) none of these
Rationale: "explanation : = ( 103 ) 7 / ( 10 ) 18 = ( 10 ) 21 / ( 10 ) 18 = 10 ( 3 ) = 1000 option c"
Answer: c
Question (geometry): the length of a rectangular garden is 2 feet longer than 3 times its width . if the perimeter of the garden is 100 feet , find the width and the length of the garden .
Options: a ) 80 , b ) 90 , c ) 100 , d ) 70 , e ) 110
Rationale: "let l and w be the length and width of the garden . the statement ` ` the length of a rectangular garden is 2 feet longer than 3 times its width ' ' may be formulated by l = 2 + 3 w the formula for the perimeter is given by p = 2 l + 2 w substitute p and l in the above equation by 100 and 2 + 3 w respectively to obtain 100 = 2 ( 2 + 3 w ) + 2 w solve for w and l w = 12 and l = 2 + 3 w = 38 . check that the perimeter of the rectangular garden is 100 p = 2 l + 2 w = 76 + 24 = 100 answer c"
Answer: c
Question (general): if a certain toy store ' s revenue in november was 3 / 5 of its revenue in december and its revenue in january was 1 / 6 of its revenue in november , then the store ' s revenue in december was how many times the average ( arithmetic mean ) of its revenues in november and january ?
Options: a ) 3 / 2 , b ) 5 / 4 , c ) 10 / 3 , d ) 20 / 7 , e ) 25 / 9
Rationale: n = 3 d / 5 j = n / 6 = d / 10 the average of november and january is ( n + j ) / 2 = 7 d / 10 / 2 = 7 d / 20 d is 20 / 7 times the average of november and january . the answer is d .
Answer: d