Cheukting/mathqa huggingface dataset:
Question (general): a sum is divided among w , x and y in such a way that for each rupee w gets , x gets 30 paisa and y gets 20 paisa . if the share of w is rs . 10 , what is the total amount ?
Options: a ) 12 , b ) 13 , c ) 14 , d ) 15 , e ) 16
Rationale: w : x : y = 100 : 30 : 20 20 : 6 : 4 20 - - - 10 30 - - - ? = > 15 answer : d
Answer: d
Question (physics): a plant manager must assign 12 new workers to one of five shifts . she needs a first , second , and third shift , and two alternate shifts . each of the shifts will receive 4 new workers . how many different ways can she assign the new workers ?
Options: a ) 1485 , b ) 2700 , c ) 3300 , d ) 4860 , e ) 5400
Rationale: whatever : my take selecting team of 4 out of 12 to assign to the shifts = 12 c 4 = 495 ways . now 4 out of 12 means total of 3 group possible . so putting them in shifts = counting methode : first , second , third , = 3 * 2 * 1 = 6 here alt and alt are the same : so 6 / 2 = 3 ways . total ways of selecting = ( selecting 4 out of 12 ) * arranging those teams in shifts = 495 * 3 = 1485 ans : a
Answer: a
Question (general): a car was driving at 66 km / h for 30 minutes , and then at 100 km / h for another 45 minutes . what was its average speed ?
Options: a ) 84 . , b ) 75 . , c ) 70 . , d ) 65 . , e ) 54 .
Rationale: "driving at 66 km / h for 30 minutes , distance covered = 60 * 1 / 2 = 30 km driving at 100 km / h for 45 minutes , distance covered = 100 * 3 / 4 = 75 km average speed = total distance / total time = 105 / 1.25 = 84 km / h answer : a"
Answer: a
Question (general): if the price of a book is first decreased by 30 % and then increased by 20 % , then the net change in the price will be :
Options: a ) 10 , b ) 16 , c ) 37 , d ) 29 , e ) 22
Rationale: "explanation : let the original price be rs . 100 . decreased by 30 % = 70 then increased 20 % on rs 70 = 70 + 14 = 84 net change in price = 100 - 84 = 16 answer : b"
Answer: b
Question (general): what is theleast number should be added to 519 , so the sum of the number is completely divisible by 25 ?
Options: a ) 1 , b ) 2 , c ) 5 , d ) 6 , e ) 8
Rationale: "( 519 / 25 ) gives remainder 19 19 + 6 = 25 , so we need to add 6 answer : d"
Answer: d
Question (physics): a man can do a piece of work in 10 days , but with the help of his son , he can do it in 4 days . in what time can the son do it alone ?
Options: a ) 13 / 2 , b ) 17 / 3 , c ) 15 / 2 , d ) 20 / 3 , e ) 9
Rationale: "son ' s 1 day ' s work = ( 1 / 4 ) - ( 1 / 10 ) = 3 / 20 the son alone can do the work in 20 / 3 days answer is d"
Answer: d
Question (general): find the next term 88 , 62 , . . ?
Options: a ) - 2 , b ) - 4 , c ) - 6 , d ) - 8 , e ) - 9
Rationale: 8 , 8 , 6 , 2 , x i guess each differ in d range of 2 8 - 8 = 0 8 - 6 = 2 6 - 2 = 4 2 - x should be ` ` 6 ' ' 2 - x = 6 x = - 4 answer : b
Answer: b
Question (gain): the cash difference between the selling prices of an book at a profit of 2 % and 4 % is $ 3 . the ratio of the two selling prices is :
Options: a ) 55 : 23 , b ) 52 : 33 , c ) 51 : 52 , d ) 45 : 53 , e ) 51 : 34
Rationale: "let c . p . of the book be $ x . then , required ratio = 102 % of x / 104 % of x = 102 / 104 = 51 / 52 = 51 : 52 c"
Answer: c
Question (physics): how long does a train 100 m long running at the speed of 75 km / hr takes to cross a bridge 135 m length ?
Options: a ) 11.3 sec , b ) 12.1 sec , c ) 13.1 sec , d ) 16.5 sec , e ) 12.7 sec
Rationale: "speed = 75 * 5 / 18 = 20.8 m / sec total distance covered = 100 + 135 = 235 m . required time = 235 / 20.8 ' = 11.3 sec . answer : a"
Answer: a
Question (geometry): what is the smallest positive integer x , such that 7000 x is a perfect cube ?
Options: a ) 4 , b ) 6 , c ) 8 , d ) 12 , e ) 18
Rationale: "take out the factors of 7000 x that will come 10 ^ 3 * 7 . for perfect cube you need every no . raise to the power 3 . for 7000 x to be a perfect cube , need two 7 that means 49 . e is the answer ."
Answer: d
Question (general): if x = 1 - 5 t and y = 2 t - 1 , then for what value of t does x = y ?
Options: a ) 5 / 2 , b ) 3 / 2 , c ) 2 / 3 , d ) 2 / 7 , e ) 0
Rationale: "we are given x = 1 – 5 t and y = 2 t – 1 , and we need to determine the value for t when x = y . we should notice that both x and y are already in terms of t . thus , we can substitute 1 – 5 t for x and 2 t – 1 for y in the equation x = y . this gives us : 1 – 5 t = 2 t – 1 2 = 7 t 2 / 7 = t the answer is d ."
Answer: d
Question (gain): a person buys an article at $ 1200 . at what price should he sell the article so as to make a profit of 40 % ?
Options: a ) 1670 , b ) 1600 , c ) 1680 , d ) 1900 , e ) 1230
Rationale: c 1680 cost price = $ 1200 profit = 40 % of 1200 = $ 480 selling price = cost price + profit = 1200 + 480 = 1680
Answer: c
Question (probability): there is a 75 % chance that tigers will not win at all during the whole season . there is a 25 % chance that germany will not play at all in the whole season . what is the greatest possible probability that the tigers will win and germany will play during the season ?
Options: a ) 55 % , b ) 60 % , c ) 70 % , d ) 75 % , e ) 80 %
Rationale: there is a 75 % chance that tigers will not win at all during the whole season we can infer that there is 25 % chance tigers will win . similarly there is a 25 % chance that germany will not play at all in the whole season we can also infer that there is 75 % chance that germany will play . answer d
Answer: d
Question (general): in the coordinate plane , points ( x , 8 ) and ( 20 , y ) are on line k . if line k passes through the origin and has slope 1 / 4 , then x * y =
Options: a ) 120 , b ) 100 , c ) 135 , d ) 140 , e ) 160
Rationale: line k passes through the origin and has slope 1 / 4 means that its equation is y = 1 / 4 * x . thus : ( x , 8 ) = ( 32 , 8 ) and ( 20 , y ) = ( 20,5 ) - - > x * y = 32 * 5 = 160 . answer : e
Answer: e
Question (general): find the sum of first 35 odd numbers
Options: a ) 4900 , b ) 3000 , c ) 1250 , d ) 1200 , e ) 1225
Rationale: "explanation : n 2 = 352 = 1225 answer : option e"
Answer: e
Question (general): bill is golfing with 3 friends and can either buy generic golf tees that are packaged by the dozen or the higher quality aero flight tees that come by the pair . what is the minimum number of packages of aero flight tees bill must purchase to ensure that he has at least 20 golf tees for each member of his foursome , if he will buy no more than 2 packages of the generic golf tees ?
Options: a ) 16 , b ) 10 , c ) 28 , d ) 4 , e ) 2
Rationale: at least 20 golf tees for each member of his foursome = total of at least 4 * 20 = 80 tees . 2 packages of the generic golf tees , that are packaged by the dozen = 2 * 12 = 24 tees . so , bill must by at least 16 aero tees . they come by the pair , hence he must by at least 56 / 2 = 28 packages of aero flight tees . answer : c .
Answer: c
Question (physics): a man ' s speed with the current is 20 kmph and speed of the current is 3 kmph . the man ' s speed against the current will be
Options: a ) 11 kmph , b ) 12 kmph , c ) 14 kmph , d ) 17 kmph , e ) none of these
Rationale: "explanation : if you solved this question yourself , then trust me you have a all very clear with the basics of this chapter . if not then lets solve this together . speed with current is 20 , speed of the man + it is speed of the current speed in still water = 20 - 3 = 17 now speed against the current will be speed of the man - speed of the current = 17 - 3 = 14 kmph option c"
Answer: c
Question (general): country x imported approximately $ 1.44 billion of goods in 1996 . if country x imported $ 388 million of goods in the first two months of 1997 and continued to import goods at the same rate for the rest of the year , by how much would country xs 1997 imports exceed those of 1996 ?
Options: a ) $ 24 million , b ) $ 120 million , c ) $ 144 million , d ) $ 240 million , e ) $ 888 million
Rationale: "convert units to millions as answer is in millions 1996 imports = $ 1.44 bill = $ 1440 mill i . e . 1440 / 12 = $ 120 mill / month 1997 imports = $ 388 mill / 2 month i . e . $ 194 mill / month difference / month = 194 - 120 = 74 difference / year = $ 74 mill * 12 = $ 988 mill answer : e"
Answer: e
Question (gain): 90 students represent x percent of the boys at jones elementary school . if the boys at jones elementary make up 70 % of the total school population of x students , what is x ?
Options: a ) 113 , b ) 150 , c ) 225 , d ) 250 , e ) 500
Rationale: "90 = x / 100 * 70 / 100 * x = > x ^ 2 = 9 * 10000 / 7 = > x = 113 a"
Answer: a
Question (general): what is the remainder when 43 ^ 88 is divided by 5 ?
Options: a ) 0 , b ) 1 , c ) 2 , d ) 3 , e ) 4
Rationale: "the units digit of the exponents of 3 cycle in a group of 4 : { 3 , 9 , 7 , 1 } 88 has the form 4 k so the units digit of 43 ^ 88 is 1 . the remainder when dividing by 5 is 1 . the answer is b ."
Answer: b
Question (other): how many factors of 990 are odd numbers greater than 1 ?
Options: a ) 13 , b ) 14 , c ) 15 , d ) 16 , e ) 17
Rationale: when factorized , 990 has 5 prime factors . of these prime factors 4 are odd and 1 is even . hence total number of odd factors is 2 * 2 * 2 * 2 ( 16 ) , which includes 1 . the total number of odd factors greater than 1 are 15 . ( option c )
Answer: c
Question (geometry): square a has an area of 25 square centimeters . square b has a perimeter of 12 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 ) 9 / 25 , b ) 1 / 5 , c ) 16 / 25 , d ) 3 / 5 , e ) 6 / 25
Rationale: "i guess it ' s mean that square b is placed within square aentirely . since , the perimeter of b is 12 , then its side is 12 / 4 = 3 and the area is 3 ^ 2 = 9 empty space between the squares is 25 - 9 = 16 square centimeters , so if a random point is in this area then it wo n ' t be within square b : p = favorable / total = 16 / 25 . answer : c"
Answer: c
Question (physics): the length of a rectangular plot is 20 metres more than its breadth . if the cost of fencing the plot @ 26.50 per metre is rs . 5300 , what is the length of the plot in metres ?
Options: a ) 40
b ) 50
c ) 60
d ) 70
e ) 80
Rationale: let breadth = x metres . then , length = ( x + 20 ) metres . perimeter = 5300 / 26.50 m = 200 m . 2 [ ( x + 20 ) + x ] = 200 2 x + 20 = 100 2 x = 80 x = 40 . hence , length = x + 20 = 60 m . answer : c
Answer: c
Question (physics): two trains 150 meters and 165 meters in length respectively are running in opposite directions , one at the rate of 80 km and the other at the rate of 65 kmph . in what time will they be completely clear of each other from the moment they meet ?
Options: a ) 7.18 , b ) 7.12 , c ) 7.16 , d ) 7.55 , e ) 7.82
Rationale: "t = ( 150 + 165 ) / ( 80 + 65 ) * 18 / 5 t = 7.82 answer : e"
Answer: e
Question (physics): a train running at the speed of 50 km / hr crosses a pole in 9 sec . what is the length of the train ?
Options: a ) 125 m , b ) 150 m , c ) 187 m , d ) 167 m , e ) 197 m
Rationale: "speed = 50 * 5 / 18 = 125 / 9 m / sec length of the train = speed * time = 125 / 9 * 9 = 125 m answer : a"
Answer: a
Question (general): two - third of a positive number and 25 / 216 of its reciprocal are equal . the number is :
Options: a ) 5 / 12 , b ) 12 / 5 , c ) 25 / 144 , d ) 144 / 25 , e ) 146 / 25
Rationale: "let the number be x . then , 2 / 3 x = 25 / 216 * 1 / x x 2 = 25 / 216 * 3 / 2 = 25 / 144 x = 5 / 12 answer : a"
Answer: a
Question (general): if 50 % of ( x - y ) = 40 % of ( x + y ) then what percent of x is y ?
Options: a ) 2.5 % , b ) 11 % , c ) 5 % , d ) 15 % , e ) 25 %
Rationale: "50 % of ( x - y ) = 40 % of ( x + y ) ( 50 / 100 ) ( x - y ) = ( 40 / 100 ) ( x + y ) 5 ( x - y ) = 4 ( x + y ) x = 9 y x = 9 y therefore required percentage = ( ( y / x ) x 100 ) % = ( ( y / 9 y ) x 100 ) = 11 % answer is b ."
Answer: b
Question (other): a certain quantity of 60 % solution is replaced with 25 % solution such that the new concentration is 35 % . what is the fraction of the solution that was replaced ?
Options: a ) 1 / 4 , b ) 1 / 3 , c ) 1 / 2 , d ) 2 / 3 , e ) 5 / 7
Rationale: "let ' s say that the total original mixture a is 100 ml the original mixture a thus has 60 ml of alcohol out of 100 ml of solution you want to replace some of that original mixture a with another mixture b that contains 25 ml of alcohol per 100 ml . thus , the difference between 60 ml and 25 ml is 35 ml per 100 ml of mixture . this means that every time you replace 100 ml of the original mixture a by 100 ml of mixture b , the original alcohol concentration will decrease by 35 % . the question says that the new mixture , let ' s call it c , must be 35 % alcohol , a decrease of only 25 % . therefore , 25 out of 35 is 5 / 7 and e is the answer ."
Answer: e
Question (physics): two dogsled teams raced across a 300 mile course in wyoming . team a finished the course in 3 fewer hours than team t . if team a ' s average speed was 5 mph greater than team t ' s , what was team t ' s average mph ?
Options: a ) 12 , b ) 15 , c ) 18 , d ) 20 , e ) 25
Rationale: "this is a very specific format that has appeared in a handful of real gmat questions , and you may wish to learn to recognize it : here we have a * fixed * distance , and we are given the difference between the times and speeds of two things that have traveled that distance . this is one of the very small number of question formats where backsolving is typically easier than solving directly , since the direct approach normally produces a quadratic equation . say team t ' s speed was s . then team t ' s time is 300 / s . team a ' s speed was then s + 5 , and team a ' s time was then 300 / ( s + 5 ) . we need to find an answer choice for s so that the time of team a is 3 less than the time of team t . that is , we need an answer choice so that 300 / ( s + 5 ) = ( 300 / s ) - 3 . you can now immediately use number properties to zero in on promising answer choices : the times in these questions will always work out to be integers , and we need to divide 300 by s , and by s + 5 . so we want an answer choice s which is a factor of 300 , and for which s + 5 is also a factor of 300 . so you can rule out answers a and c immediately , since s + 5 wo n ' t be a divisor of 300 in those cases ( sometimes using number properties you get to the correct answer without doing any other work , but unfortunately that ' s not the case here ) . testing the other answer choices , if you try answer d , you find the time for team t is 15 hours , and for team a is 12 hours , and since these differ by 3 , as desired , d is correct ."
Answer: d
Question (physics): a boat takes 90 minutes less to travel 36 miles downstream than to travel the same distance upstream . if the speed of the boat in still water is 10 mph , the speed of the stream is :
Options: a ) 4 mph , b ) 2.5 mph , c ) 3 mph , d ) 2 mph , e ) none of these
Rationale: explanation : speed of the boat in still water = 10 mph let speed of the stream be x mph then , speed downstream = ( 10 + x ) mph speed upstream = ( 10 - x ) mph time taken to travel 36 miles upstream - time taken to travel 36 miles downstream = 90 / 60 hours = > 36 / ( 10 − x ) − 36 / ( 10 + x ) = 3 / 2 = > 12 / ( 10 − x ) − 12 / ( 10 + x ) = 1 / 2 = > 24 ( 10 + x ) − 24 ( 10 − x ) = ( 10 + x ) ( 10 − x ) = > 240 + 24 x − 240 + 24 x = ( 100 − x 2 ) = > 48 x = 100 − x 2 = > x 2 + 48 x − 100 = 0 = > ( x + 50 ) ( x − 2 ) = 0 = > x = - 50 or 2 . answer : option d
Answer: d
Question (geometry): ) a cube is painted blue on all of its surfaces . it is then cut in to 27 smaller cubes of equal size . find how many smaller cubes have no color ?
Options: a ) 1
b ) 3
c ) 8
d ) 5
e ) 7
Rationale: if the cube is cut in to 27 smaller cubes , then number of separations made = n = 3 ( since 3 × 3 × 3 = 27 ) . number of smaller cubes with no color = ( n – 2 ) 3 = ( 3 – 2 ) 3 = 13 = 1 answer : a
Answer: a
Question (geometry): a rectangular field has to be fenced on three sides leaving a side of 25 feet uncovered . if the area of the field is 880 sq . feet , how many feet of fencing will be required ?
Options: a ) 75.4 feet , b ) 98.4 feet , c ) 95.4 feet , d ) 85.4 feet , e ) 92.4 feet
Rationale: "area of the field = 880 sq . feet . length of the adjacent sides are 25 feet and 880 / 25 = 35.2 feet . required length of the fencing = 25 + 35.2 + 35.2 = 95.4 feet answer : c"
Answer: c
Question (general): x + ( 1 / x ) = 2.5 find x ^ 2 + ( 1 / x ^ 2 )
Options: a ) 2.25 , b ) 3.25 , c ) 4.25 , d ) 5.25 , e ) 6.25
Rationale: "squaring on both sides ( x + 1 / x ) ^ 2 = 2.5 ^ 2 x ^ 2 + 1 / x ^ 2 = 6.25 - 2 x ^ 2 + 1 / x ^ 2 = 4.25 answer : c"
Answer: c
Question (general): a = { 0 , 1 , - 3 , 6 , - 8 , - 10 } b = { - 1 , 2 , - 4 , 7 , 6 , - 9 } if a is a number that is randomly selected from set a , and b is a number that is randomly selected from set b , what is the probability that ab < 0 ?
Options: a ) 1 / 4 , b ) 1 / 3 , c ) 5 / 13 , d ) 5 / 12 , e ) 1 / 2
Rationale: for the product of 2 numbers to be negative either of them must be positive or negative : p ( positive , negative ) = 2 / 6 * 3 / 6 = 6 / 36 ; p ( negative , positive ) = 3 / 6 * 3 / 6 = 9 / 36 p = 6 / 36 + 9 / 36 p = 15 / 36 p = 5 / 12 answer : d
Answer: d
Question (general): which number need to add to 172835 to get a number exactly divisible by 136 ?
Options: a ) 27 , b ) 25 , c ) 26 , d ) 21 , e ) 24
Rationale: "172835 / 136 = 1270 and reminder = 115 . 136 - 115 = 21 so , the next number divisible by 115 is 21 places in front of 172835 which means 21 + 172835 = 172856 21 should be added to 172835 d"
Answer: d
Question (general): simplify : 99 ^ 48 / 49 * 245 .
Options: a ) 23345 , b ) 26695 , c ) 24495 , d ) 25575 , e ) none of them
Rationale: "given expression = ( 100 - 1 / 49 ) * 245 = ( 4899 / 49 ) * 245 = 4899 * 5 = 24495 . answer is c ."
Answer: c
Question (physics): a boy swims downstream 91 km and upstream 21 km taking 7 hours each time , what is the speed of the boy in still water ?
Options: a ) 6 , b ) 7 , c ) 8 , d ) 9 , e ) 10
Rationale: 91 - - - 7 ds = 13 ? - - - - 1 21 - - - - 7 us = 3 ? - - - - 1 m = ? m = ( 13 + 3 ) / 2 = 8 answer : c
Answer: c
Question (physics): speed of a boat in standing water is 14 kmph and the speed of the stream is 1.2 kmph . a man rows to a place at a distance of 4664 km and comes back to the starting point . the total time taken by him is :
Options: a ) 784 hours , b ) 794 hours , c ) 780 hours , d ) 684 hours , e ) 884 hours
Rationale: "speed downstream = ( 12 + 1.2 ) = 13.2 kmph speed upstream = ( 12 - 1.2 ) = 10.8 kmph total time taken = 4664 / 13.2 + 4664 / 10.8 = 353 + 431 = 784 hours answer : a"
Answer: a
Question (physics): the hiker walking at a constant rate of 4 miles per hour is passed by a cyclist traveling in the same direction along the same path at 10 miles per hour . the cyclist stops to wait for the hiker 5 minutes after passing her , while the hiker continues to walk at her constant rate , how many minutes must the cyclist wait until the hiker catches up ?
Options: a ) 10 , b ) 15 , c ) 20 , d ) 15 / 2 , e ) 24
Rationale: after passing the hiker the cyclist travels for 5 minutes at a rate of 10 miles / hour . in those 5 mins the cyclist travels a distance of 5 / 6 miles . in those 5 mins the hiker travels a distance of 1 / 2 miles . so the hiker still has to cover 1 / 2 miles to meet the waiting cyclist . the hiker will need 15 / 2 mins to cover the remaining 1 / 2 miles . so the answer is d .
Answer: d
Question (general): the average of first five multiples of 2 is :
Options: a ) 3 , b ) 9 , c ) 12 , d ) 15 , e ) e
Rationale: "solution average = 2 ( 1 + 2 + 3 + 4 + 5 ) / 5 = 30 / 5 = 6 answer e"
Answer: e
Question (gain): find the amount on rs . 9000 in 2 years , the rate of interest being 4 % per first year and 5 % for the second year ?
Options: a ) 5568 , b ) 9828 , c ) 5460 , d ) 5635 , e ) 6734
Rationale: "9000 * 104 / 100 * 105 / 100 = > 9828 answer : b"
Answer: b
Question (physics): what decimal fraction is 40 ml of a litre ?
Options: a ) . 4 , b ) . 04 , c ) . 05 , d ) 0.04 , e ) none of these
Rationale: "answer required fraction = 40 / 1000 = 4 / 100 = . 04 correct option : b"
Answer: b
Question (general): how many even integers n , such that 20 < = n < = 180 are of the form 3 k + 4 , where k is any natural number ?
Options: a ) 24 , b ) 27 , c ) 30 , d ) 33 , e ) 36
Rationale: the first number is 22 = 16 + 6 ( 1 ) . we can continue adding 6 to make a list : 22 , 28 , 34 , . . . the last number is 278 = 16 + 6 ( 27 ) there are 27 numbers in the list . the answer is b .
Answer: b
Question (physics): two numbers n and 12 have lcm = 48 and gcf = 8 . find n .
Options: a ) 24 , b ) 34 , c ) 44 , d ) 54 , e ) 32
Rationale: "the product of two integers is equal to the product of their lcm and gcf . hence . 12 × n = 48 × 8 n = 48 × 8 / 12 = 32 correct answer e"
Answer: e
Question (general): in a hostel , the number of students decreased by 9 % and the price of food increased by 20 % over the previous year . if each student consumes the same amount of food then by how much should the consumption of food be cut short by every student , so that the total cost of the food remains the same as that of the previous year ?
Options: a ) 19 % , b ) 15 % , c ) 25 % , d ) 40 % , e ) 8.4 %
Rationale: "cost of food ( c ) = food consumed per student ( f ) * number of students ( n ) * price of food ( p ) originally , c = fnp when number of students decrease by 8 % , and the price of food increases by 20 % , c = f ( new ) * ( 0.91 n ) * ( 1.2 p ) = > f ( new ) = f / ( 0.91 * 1.2 ) = > f ( new ) = 0.915 f therefore the new cost of food must be 91.5 % of the old cost , or the cost of food must decrease by 8.4 % ( option e )"
Answer: e
Question (general): a company produces on an average 4000 items per month for the first 3 months . how many items it must produce on an average per month over the next 9 months , to average of 4375 items per month over the whole ?
Options: a ) 4500 , b ) 4600 , c ) 4680 , d ) 4710 , e ) none
Rationale: sol . required average = ( 4375 x 12 ) - ( 4000 x 3 ) / 9 ⇔ 52500 - 12000 / 9 ⇔ 40500 / 9 = 4500 . answer a
Answer: a
Question (general): pat , kate and mark charged a total of 144 hours to a certain project . if pat charged twice as much time to the project as kate and 1 / 3 as much times as mark , how many more hours did mark charge to the project than kate .
Options: a ) 18 , b ) 36 , c ) 80 , d ) 90 , e ) 108
Rationale: "let kate charge for x hours , then pat charged for 2 x and mat - for 6 x . so , 2 x + 6 x + x = 144 - total hours charged for , x = 16 . mat charged 6 x - x or 5 x for more hours than kate , or for 80 hours . c is correct"
Answer: c
Question (general): 69 laboratories raise the bacterium , the laboratory have 48 culture dishes on average , which has about 25,075 bacteria each . how many bacteria are there approximately ?
Options: a ) 10 ^ 7 , b ) 10 ^ 8 , c ) 10 ^ 9 , d ) 10 ^ 10 , e ) 10 ^ 11
Rationale: "69 laboratories raise the bacterium , the laboratory have 48 culture dishes on average , which has about 25,075 bacteria each . how many bacteria are there approximately ? a . 10 ^ 7 b . 10 ^ 8 c . 10 ^ 9 d . 10 ^ 10 e . 10 ^ 11 - > due to approximately , 69 = 70 , 48 = 50 , 25,075 = 25,000 are derived , which makes ( 69 ) ( 48 ) ( 25,075 ) = ( 70 ) ( 50 ) ( 25,000 ) = 10 ^ 7 . the answer is a ."
Answer: a
Question (general): divide $ 5000 among x , y in the ratio 2 : 8 . how many $ that x get ?
Options: a ) $ 1000 , b ) $ 1050 , c ) $ 1100 , d ) $ 1150 , e ) $ 1200
Rationale: sum of ratio terms = 2 + 8 = 10 x = 5000 * 2 / 10 = $ 1000 answer is a
Answer: a