Cheukting/mathqa huggingface dataset:
Question (geometry): the number 46 can be written as the sum of the squares of 3 different positive integers . what is the sum of these 3 integers ?
Options: a ) 17 , b ) 16 , c ) 15 , d ) 10 , e ) 13
Rationale: "i think brute force with some common sense should be used to solve this problem . write down all perfect squares less than 46 : 1 , 4 , 9 , 16 , 25 , 36 . now , 46 should be the sum of 3 of those 8 numbers . also to simplify a little bit trial and error , we can notice that as 46 is an odd numbers then either all three numbers must be odd ( odd + odd + odd = odd ) or two must be even and one odd ( even + even + odd = odd ) . we can find that 46 equals to 1 + 9 + 36 = 1 ^ 2 + 3 ^ 2 + 6 ^ 2 = 46 - - > 1 + 3 + 6 = 10 . answer : d ."
Answer: d
Question (geometry): in a certain circle there are 9 points . what is the number of the triangles connecting 4 points of the 9 points ?
Options: a ) 80
b ) 96
c ) 108
d ) 126
e ) 132
Rationale: imo : d here we have to select 4 points out of 9 points . order is not important so the answer will be 9 c 4 = 126 answer d
Answer: d
Question (gain): find the amount on rs . 5000 in 2 years , the rate of interest being 5 % per first year and 6 % for the second year ?
Options: a ) 3377 , b ) 2678 , c ) 5565 , d ) 1976 , e ) 1671
Rationale: "5000 * 105 / 100 * 106 / 100 = > 5565 answer : c"
Answer: c
Question (other): how many trailing zeroes does 49 ! + 50 ! have ?
Options: a ) 9 , b ) 10 , c ) 11 , d ) 12 , e ) 22
Rationale: "49 ! + 50 ! = 51 * 49 ! no of trailing 0 ' s = no of 5 * 2 no of 2 ' s = 49 / 2 + 49 / 4 + 49 / 8 + 49 / 16 + 49 / 32 = d no of 5 ' s = 49 / 5 + 49 / 25 = 10 = p now since p < d no of trailing 0 ' s = 10 answer : b"
Answer: b
Question (general): a club wants to mix 30 pounds of candy worth $ 8.00 per pound with candy worth $ 5.00 per pound to reduce the cost of the mixture to $ 6.00 per pound . how many pounds of the $ 5.00 per pound candy should be used ?
Options: a ) 30 , b ) 40 , c ) 50 , d ) 60 , e ) 70
Rationale: "let number of pounds of 5 $ candy to be used be w 6 = ( 30 * 8 + 5 * w ) / ( 30 + w ) = > 180 + 6 w = 240 + 5 w = > w = 60 answer d"
Answer: d
Question (general): the sum of the ages of 5 children born at the intervals of 3 years each is 70 years . what is the age of the youngest child ?
Options: a ) 2 years , b ) 4 years , c ) 6 years , d ) 8 years , e ) 10 years
Rationale: "let the ages of the children be x , ( x + 3 ) , ( x + 6 ) , ( x + 9 ) and ( x + 12 ) years . then , x + ( x + 3 ) + ( x + 6 ) + ( x + 9 ) + ( x + 12 ) = 70 5 x = 40 = > x = 8 . age of youngest child = x = 8 years . answer : d"
Answer: d
Question (general): rs . 1070 is divided so that 4 times the first share , thrice the 2 nd share and twice the third share amount to the same . what is the value of the third share ?
Options: a ) rs . 190 , b ) rs . 260 , c ) rs . 493 , d ) rs . 393 , e ) rs . 593
Rationale: "a + b + c = 1070 4 a = 3 b = 2 c = x a : b : c = 1 / 4 : 1 / 3 : 1 / 2 = 3 : 4 : 6 6 / 13 * 1070 = rs . 493 answer : c"
Answer: c
Question (general): nancy obtained 66 , 75 , 52 , 68 and 89 marks ( out of 100 ) in american literature , history , home economics , physical education and art . calculate her average marks ?
Options: a ) 50 , b ) 80 , c ) 70 , d ) 60 , e ) 71
Rationale: explanation : average = ( 66 + 75 + 52 + 68 + 89 ) / 5 = 70 . answer : c ) 70
Answer: c
Question (general): the difference between the local value and the face value of 7 in the numerical 32675149 is
Options: a ) 75142 , b ) 64851 , c ) 5149 , d ) 69993 , e ) none of them
Rationale: "= ( local value of 7 ) - ( face value of 7 ) = ( 70000 - 7 ) = 69993 answer is d"
Answer: d
Question (general): the average of numbers 0.64206 , 0.64207 , 0.64208 and 0.64209 is ?
Options: a ) 0.64202 , b ) 0.64204 , c ) 0.642022 , d ) 0.642075 , e ) none
Rationale: "answer average = ( 0.64206 + 0.64207 + 0.64208 + 0.64209 ) / 4 = 2.5683 / 4 = 0.642075 correct option : d"
Answer: d
Question (general): a textile manufacturing firm employees 80 looms . it makes fabrics for a branded company . the aggregate sales value of the output of the 80 looms is rs 5 , 00,000 and the monthly manufacturing expenses is rs 1 , 50,000 . assume that each loom contributes equally to the sales and manufacturing expenses are evenly spread over the number of looms . monthly establishment charges are rs 75000 . if one loom breaks down and remains idle for one month , the decrease in profit is :
Options: a ) 13000 , b ) 7000 , c ) 10000 , d ) 4375 , e ) none of these
Rationale: "explanation : profit = 5 , 00,000 â ˆ ’ ( 1 , 50,000 + 75,000 ) = rs . 2 , 75,000 . since , such loom contributes equally to sales and manufacturing expenses . but the monthly charges are fixed at rs 75,000 . if one loan breaks down sales and expenses will decrease . new profit : - = > 500000 ã — ( 79 / 80 ) â ˆ ’ 150000 ã — ( 79 / 80 ) â ˆ ’ 75000 . = > rs 2 , 70,625 . decrease in profit = > 2 , 75,000 â ˆ ’ 2 , 70,625 = > rs . 4,375 answer : d"
Answer: d
Question (physics): a hiker walking at a constant rate of 4 kilometers per hour is passed by a cyclist travelling in the same direction along the same path at a constant rate of 12 kilometers per hour . the cyclist stops and waits 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 ) 25 , e ) 30
Rationale: "in 5 minutes , the cyclist travels a distance of ( 5 / 60 ) * 12 = 1 km . the time it takes the hiker to complete this distance is 1 / 4 hours = 15 minutes the cyclist needs to wait 15 - 5 = 10 minutes the answer is a ."
Answer: a
Question (gain): a milk man has 30 liters of milk . if he mixes 5 liters of water , which is freely available , in 20 liters of pure milk . if the cost of pure milk is rs . 18 per liter , then the profit of the milkman , when he sells all the mixture at cost price is :
Options: a ) 20 % , b ) 25 % , c ) 33.33 % , d ) 35 % , e ) none of these
Rationale: explanation : when the water is freely available and all the water is sold at the price of the milk , then the water gives the profit on the cost of 30 liters of milk . therefore , profit percentage = 35 % . answer : d
Answer: d
Question (general): of the goose eggs laid at a certain pond , 2 / 3 hatched and 3 / 4 of the geese that hatched from those eggs survived the first month . of the geese that survived the first month , 3 / 5 did not survive the first year . if 180 geese survived the first year and if no more than one goose hatched from each egg , how many goose eggs were laid at the pond ?
Options: a ) 280 , b ) 400 , c ) 540 , d ) 900 , e ) 840
Rationale: "of the goose eggs laid at a certain pond , 2 / 3 hatched and 3 / 4 of the geese that hatched from those eggs survived the first month : 2 / 3 * 3 / 4 = 1 / 2 survived the first month . of the geese that survived the first month , 3 / 5 did not survive the first year : ( 1 - 3 / 5 ) * 1 / 2 = 1 / 5 survived the first year . 180 geese survived the first year : 1 / 5 * ( total ) = 180 - - > ( total ) = 900 . answer : d ."
Answer: d
Question (general): 20 litres of mixture of acid and water contain 10 % water . how much water should be added so that percentage of water becomes 20 % in this mixture ?
Options: a ) 2 l , b ) 3 l , c ) 2.5 l , d ) 4 l , e ) 5 l
Rationale: total mixture = 20 ltr water contain = 10 % of 20 ltr = > 2 ltr water it means 18 ltr is acid in that mixture we have to make 20 % water so . . 20 % of 20 = 4 ltr water must be there in the new mixture we have already 2 ltr water so we have to add 2 ltr more answer : a
Answer: a
Question (general): what will be the remainder when 8 - 3 + 3 ^ 5 + 2 ^ 10 is divided by 4 ?
Options: a ) 12 , b ) 3 , c ) 16 , d ) 0 , e ) 9
Rationale: "the multiplication ( e . g . 2 ^ 10 ) is done first and then the sum ( e . g . 15 + 20 ) and subtraction ( e . g . 8 - 3 ) , and after all this expression it should be divided by 4 and the answer is 0 , option d ."
Answer: d
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 9 hours and 64 hours respectively . the ratio of their speeds is ?
Options: a ) 4 : 5 , b ) 8 : 3 , c ) 8 : 4 , d ) 4 : 8 , e ) 4 : 1
Rationale: let us name the trains a and b . then , ( a ' s speed ) : ( b ' s speed ) = √ b : √ a = √ 64 : √ 9 = 8 : 3 answer : b
Answer: b
Question (gain): a trader bought a car at 15 % discount on its original price . he sold it at a 40 % increase on the price he bought it . what percent of profit did he make on the original price ?
Options: a ) 119 , b ) 110 , c ) 112 , d ) 113 , e ) 115
Rationale: "original price = 100 cp = 85 s = 85 * ( 140 / 100 ) = 119 100 - 119 = 19 % answer : a"
Answer: a
Question (other): the ratio between the present ages of a and b is 6 : 3 respectively . the ratio between a ' s age 4 years ago and b ' s age 4 years hence is 1 : 1 . what is the ratio between a ' s age 4 years hence and b ' s age 4 years ago ?
Options: a ) 5 : 4 , b ) 3 : 0 , c ) 5 : 1 , d ) 3 : 2 , e ) 3 : 7
Rationale: "let the present ages of a and b be 6 x and 3 x years respectively . then , ( 6 x - 4 ) / ( 3 x + 4 ) = 1 / 1 3 x = 8 = > x = 2.67 required ratio = ( 5 x + 4 ) : ( 3 x - 4 ) = 20 : 4 = 5 : 1 . answer : c"
Answer: c
Question (geometry): if the height of a cone is increased by 100 % then its volume is increased by ?
Options: a ) 200 % , b ) 300 % , c ) 100 % , d ) 500 % , e ) 350 %
Rationale: "height of = > 100 % so increased by 100 % answer c"
Answer: c
Question (gain): a watch was sold at a loss of 10 % . if it was sold for rs . 225 more , there would have been a gain of 5 % . what is the cost price ?
Options: a ) 1000 , b ) 1500 , c ) 2778 , d ) 2788 , e ) 2991
Rationale: "90 % 105 % - - - - - - - - 15 % - - - - 225 100 % - - - - ? = > rs . 1500 answer : b"
Answer: b
Question (physics): in what time will a train 60 m long cross an electric pole , it its speed be 144 km / hr ?
Options: a ) 2.5 sec , b ) 2.8 sec , c ) 7.5 sec , d ) 2.3 sec , e ) 1.5 sec
Rationale: "speed = 144 * 5 / 18 = 40 m / sec time taken = 60 / 40 = 1.5 sec . answer : e"
Answer: e
Question (general): how much is 50 % of 40 is greater than 4 / 5 of 25 ?
Options: a ) 0 , b ) 67 , c ) 88 , d ) 12 , e ) 66
Rationale: "( 50 / 100 ) * 40 – ( 4 / 5 ) * 25 = 0 answer : a"
Answer: a
Question (general): a certain telescope increases the visual range at a particular location from 80 kilometers to 150 kilometers . by what percent is the visual range increased by using the telescope ?
Options: a ) 30 % , b ) 33 1 / 2 % , c ) 40 % , d ) 60 % , e ) 87.5 %
Rationale: "original visual range = 80 km new visual range = 150 km percent increase in the visual range by using the telescope = ( 150 - 80 ) / 80 * 100 % = 7 / 8 * 100 % = 87.5 % answer e"
Answer: e
Question (geometry): 34 . the side surface of a cylinder is rolled with a rectangle . if the height of a cylinder is 16 feet and the perimeter of the circular base . is 12 feet , what is the diagonal of the rectangle ?
Options: a ) 16
b ) 20
c ) 18
d ) 22
e ) 21
Rationale: think of an aluminum can can . if you took off the bottom and top and cut a slit down the length , it would flatten to a rectangle . the dimensions of the rectangle are the height of the can and the circumference of the circle . since you know both , use pythagoreans theorem or properties of 3 - 4 - 5 triangles to solve for the hypothenuse , 20 . ( correct answer b )
Answer: b
Question (general): if ( x + yi ) / i = ( 7 + 9 i ) , where x and y are real , what is the value of ( x + yi ) ( x - yi ) ?
Options: a ) 110 , b ) 120 , c ) 130 , d ) 140 , e ) 150
Rationale: ( x + yi ) / i = ( 7 + 9 i ) ( x + yi ) = i ( 7 + 9 i ) = - 9 + 7 i ( x + yi ) ( x - yi ) = ( - 9 + 7 i ) ( - 9 - 7 i ) = 81 + 49 = 130 correct answer is c 0130
Answer: c
Question (physics): how long does a train 110 m long traveling at 60 kmph takes to cross a bridge of 240 m in length ?
Options: a ) 18.9 sec , b ) 88.9 sec , c ) 22.9 sec , d ) 21.00 sec , e ) 72.0 sec
Rationale: "d = 110 + 240 = 350 m s = 60 * 5 / 18 = 50 / 3 t = 350 * 3 / 50 = 21.00 sec answer : d"
Answer: d
Question (physics): convert 250 inches into centimeter ?
Options: a ) 635 cm , b ) 620 cm , c ) 650 cm , d ) 610 cm , e ) 654 cm
Rationale: "1 inch = 2.54 cm 250 inches = 250 * 2.54 = 635 cm answer is a"
Answer: a
Question (physics): it takes 40 identical printing presses 12 hours to print 500,000 papers . how many hours would it take 30 of these printing presses to print 500,000 papers ?
Options: a ) 14 , b ) 15 , c ) 16 , d ) 18 , e ) 20
Rationale: "40 printing presses can do 1 / 12 of the job each hour . 30 printing presses can do 3 / 4 * 1 / 12 = 1 / 16 of the job each hour . the answer is c ."
Answer: c
Question (gain): a certain company reported that the revenue on sales increased 60 % from 2000 to 2003 , and increased 80 % from 2000 to 2005 . what was the approximate percent increase in revenue for this store from 2003 to 2005 ?
Options: a ) 50 % , b ) 40 % , c ) 35 % , d ) 32 % , e ) 13 %
Rationale: "assume the revenue in 2000 to be 100 . then in 2003 it would be 160 and and in 2005 180 , so from 2003 to 2005 it increased by ( 180 - 160 ) / 160 = 20 / 160 = 13 % answer : e ."
Answer: e
Question (general): if the price of a book is first decreased by 25 % and then increased by 20 % , then the net change in the price will be :
Options: a ) 10 , b ) 388 , c ) 37 , d ) 29 , e ) 22
Rationale: "explanation : let the original price be rs . 100 . new final price = 120 % of ( 75 % of rs . 100 ) = rs . ( 120 / 100 * 75 / 100 * 100 ) = rs . 90 . decrease = 10 % answer : a ) 10"
Answer: a
Question (gain): p runs 20 % faster than q so p gives q a 300 meter head start . if the race ends in a tie , how far ( in meters ) did p run in the race ?
Options: a ) 1500 , b ) 1600 , c ) 1700 , d ) 1800 , e ) 1900
Rationale: "let d be the race distance that p ran . let t be the time it took to complete the race . let v be q ' s speed . t = d / 1.2 v = ( d - 300 ) / v d = 1.2 d - 360 0.2 d = 360 d = 1800 meters . the answer is d ."
Answer: d
Question (general): if a certain number is divided by 11 , the quotient , dividend , and divisor , added together , will amount to 71 . what is the number ?
Options: a ) 18 , b ) 28 , c ) 48 , d ) 38 , e ) 55
Rationale: "let x = the number sought . then x / 11 + x + 11 = 71 and x = 55 . e"
Answer: e
Question (gain): the population of a town increases 25 % and 30 % respectively in two consecutive years . after the growth the present population of the town is 1950 . then what is the population of the town 2 years ago ?
Options: a ) a ) 800 , b ) b ) 900 , c ) c ) 1000 , d ) d ) 1100 , e ) e ) 1200
Rationale: "explanation : formula : ( after = 100 denominator ago = 100 numerator ) 1950 * 100 / 125 * 100 / 130 = 1200 answer : option e"
Answer: e
Question (general): the number 0.127 is how much greater than 1 / 8 ?
Options: a ) 1 / 100 , b ) 1 / 1500 , c ) 1 / 2 , d ) 1 / 500 , e ) 1 / 600
Rationale: "explanation : 0.127 expressed as a fraction = 127 / 1000 1 / 8 can also be expressed as ( 1 x 125 ) / ( 8 x 125 ) = 125 / 1000 the difference is 2 / 1000 , which is 1 / 500 answer is d"
Answer: d
Question (gain): a retailer purchases shirts from a wholesaler and then sells the shirts in her store at a retail price that is 80 percent greater than the wholesale price . if the retailer decreases the retail price by 25 percent this will have the same effect as increasing the wholesale price by what percent ?
Options: a ) 26 , b ) 37.5 , c ) 35 , d ) 44 , e ) 50
Rationale: "answer : c = 35 . assume rs . 100 to be the price at which the retailer buys from wholesaler . 80 % increase makes retail price = 180 . now 25 % decrease - > ( 1 - 25 / 100 ) * 180 = 135 . now compared to the wholesale price of 100 , 35 % increase is what will have the same effect as increasing the wholesale price ."
Answer: c
Question (physics): a cistern which could be filled in 4 hours takes one hour more to be filled owing to a leak in its bottom . if the cistern is full in what time will the leak empty it ?
Options: a ) 76 hrs , b ) 99 hrs , c ) 55 hrs , d ) 20 / 3 hrs , e ) 11 hrs
Rationale: "1 / 4 - 1 / x = 1 / 10 = > 20 / 3 hrs answer : d"
Answer: d
Question (general): let p be a prime number . if n = 7 p , how many divisors does n have ?
Options: a ) 1 , b ) 2 , c ) 3 , d ) 4 , e ) 5
Rationale: two . n = 7 * p , and both 7 and p are prime . so the answer is b .
Answer: b
Question (general): in a factory there are 3 types of machine m 1 , m 2 and m which produces 25 % , 35 % and 40 % of the total products respectively . m 1 , m 2 and m 3 produces 2 % , 4 % and 5 % defective products , respectively . what is the percentage of non - defective products ?
Options: a ) 89 % , b ) 97.1 % , c ) 96.1 % , d ) 86.1 % , e ) none of these
Rationale: solution : non - defective products , { [ ( 25 * 0.98 ) + ( 35 * 0.96 ) + ( 40 * 0.95 ) ] / 100 } * 100 = 96.1 % . answer : option c
Answer: c
Question (general): if a = - 1 , what is the value of – ( a ^ 2 + a ^ 3 + a ^ 4 + a ^ 5 + a ^ 6 ) ?
Options: a ) - 14 , b ) - 4 , c ) - 1 , d ) 4 , e ) 14
Rationale: if a = - 1 , then putting values in equation = - [ ( - 1 ) ^ 2 + ( - 1 ) ^ 3 + ( - 1 ^ 4 ) + ( - 1 ^ 5 ) + ( - 1 ^ 6 ) ] = - [ 1 - 1 + 1 - 1 + 1 ] = - 1 answer = c = - 1
Answer: c
Question (probability): 6 animals of a circus has to be placed inside in 6 cages one in each cage . if 4 of the cage are too small for 6 of the animal then find the number of ways of caging the animal .
Options: a ) a . 240 , b ) b . 808250 , c ) c . 502450 , d ) d . 784200 , e ) e . 302400
Rationale: ways for cages that are too small = 5 * 4 * 3 * 2 = 120 since we have 2 cages and 2 animal left therefore ways for 2 cages = 2 ! total ways = 120 * 2 ! = 604800 answer a
Answer: a
Question (physics): a goods train runs at the speed of 72 kmph and crosses a 250 m long platform in 30 seconds . what is the length of the goods train ?
Options: a ) 230 m , b ) 350 m , c ) 260 m , d ) 270 m , e ) none of these
Rationale: "explanation : speed = [ 72 x ( 5 / 18 ) ] m / sec = 20 m / sec . time = 30 sec . let the length of the train be x metres . then , [ ( x + 250 ) / 30 ] = 20 = > x + 250 = 600 = > x = 350 . answer : b"
Answer: b
Question (general): in a class of 20 students , 3 students did not borrow any books from the library , 9 students each borrowed 1 book , 4 students each borrowed 2 books , and the rest borrowed at least 3 books . if the average number of books per student was 2 , what is the maximum number of books any single student could have borrowed ?
Options: a ) 13 , b ) 14 , c ) 15 , d ) 16 , e ) 17
Rationale: "the total number of books the students borrowed is 20 * 2 = 40 . the students who borrowed zero , one , or two books borrowed 9 * 1 + 4 * 2 = 17 books . the 4 students who borrowed at least three books borrowed 40 - 17 = 23 books . if 3 of these students borrowed exactly 3 books , then the maximum that one student could have borrowed is 23 - 9 = 14 books . the answer is b ."
Answer: b
Question (physics): the speed at which a man can row a boat in still water is 6 km / hr . if he rows downstream , where the speed of current is 3 km / hr , how many seconds will he take to cover 80 meters ?
Options: a ) 28 , b ) 32 , c ) 36 , d ) 40 , e ) 44
Rationale: "the speed of the boat downstream = 6 + 3 = 9 km / hr 9 km / hr * 5 / 18 = 2.5 m / s the time taken to cover 80 meters = 80 / 2.5 = 32 seconds . the answer is b ."
Answer: b
Question (physics): a prison of 10,000 inmates has enough food to feed them all for 50 days . after 10 days some of the inmates leave and the food is now enough for the same period of 50 days as before . how many of them left ?
Options: a ) 3,000 , b ) 2,200 , c ) 2,000 , d ) 1,000 , e ) 200
Rationale: 10,000 - - - 50 10,000 - - - 40 x - - - 50 x * 50 = 10,000 * 40 x = 8,000 10,000 - - - - - - - - 2,000 answer = c
Answer: c
Question (gain): a retailer buys a radio for rs 225 . his overhead expenses are rs 15 . he sellis the radio for rs 300 . the profit percent of the retailer is
Options: a ) 10 % , b ) 50 % , c ) 25 % , d ) 52 % , e ) none of these
Rationale: "explanation : cost price = ( 225 + 15 ) = 240 sell price = 300 gain = ( 60 / 240 ) * 100 = 25 % . answer : c"
Answer: c
Question (physics): if teena is driving at 55 miles per hour and is currently 7.5 miles behind joe , who is driving at 40 miles per hour in the same direction then in how many minutes will teena be 52.5 miles ahead of joe ?
Options: a ) 15 , b ) 240 , c ) 75 , d ) 90 , e ) 105
Rationale: "this type of questions should be solved without any complex calculations as these questions become imperative in gaining that extra 30 - 40 seconds for a difficult one . teena covers 55 miles in 60 mins . joe covers 40 miles in 60 mins so teena gains 15 miles every 60 mins teena need to cover 7.5 + 52.5 miles . teena can cover 7.5 miles in 30 mins teena will cover 52.5 miles in 210 mins so answer 30 + 210 = 240 mins . ( answer b )"
Answer: b
Question (general): on a partly cloudy day , derek decides to walk back from work . when it is sunny , he walks at a speed of s miles / hr ( s is an integer ) and when it gets cloudy , he increases his speed to ( s + 1 ) miles / hr . if his average speed for the entire distance is 2.8 miles / hr , what fraction r of the total distance did he cover while the sun was shining on him ?
Options: a ) 1 / 4 , b ) 4 / 5 , c ) 1 / 5 , d ) 1 / 6 , e ) 1 / 7
Rationale: if s is an integer and we know that the average speed is 2.8 , s must be = 2 . that meanss + 1 = 3 . this implies that the ratio of time for s = 2 is 1 / 4 of the total time . the formula for distance / rate is d = rt . . . so the distance travelled when s = 2 is 2 t . the distance travelled for s + 1 = 3 is 3 * 4 t or 12 t . therefore , total distance covered while the sun was shining over him is r = 2 / 14 = 1 / 7 . answer : e
Answer: e
Question (gain): fresh grapes contain 90 % by weight while dried grapes contain 20 % water by weight . what is the weight of dry grapes available from 5 kg of fresh grapes ?
Options: a ) 2 kg , b ) 2.4 kg , c ) 2.5 kg , d ) 10 kg , e ) 0.625
Rationale: "the weight of non - water in 5 kg of fresh grapes ( which is 100 - 90 = 10 % of whole weight ) will be the same as the weight of non - water in x kg of dried grapes ( which is 100 - 20 = 80 % of whole weight ) , so 5 â ˆ — 0.1 = x â ˆ — 0.8 - - > x = 0.625 answer : e ."
Answer: e
Question (physics): steve traveled the first 2 hours of his journey at 50 mph and the last 3 hours of his journey at 80 mph . what is his average speed of travel for the entire journey ?
Options: a ) 68 mph , b ) 56.67 mph , c ) 60 mph , d ) 64 mph , e ) 66.67 mph
Rationale: "average speed = total distance / total time = ( 50 * 2 + 80 * 3 ) / ( 2 + 3 ) = 68 ans : a"
Answer: a
Question (other): in a certain state , the ratio of registered republicans to registered democrats is 3 to 2 , and every registered voter is either a republican or a democrat . if 80 percent of the republicans and 25 percent of the democrats are expected to vote for candidate x , and everyone else is expected to vote for candidate y , by what percent is candidate x expected to win the election ?
Options: a ) 2 % , b ) 5 % , c ) 16 % , d ) 20 % , e ) 25 %
Rationale: "since we were expected to find a percentage figure - it thought that it might be easier to pick a ' smart number ' to represent the total number of voters ( republicans and democrats ) . therefore , i picked 100 ( as the total number of voters ) and thus 30 : 20 represents the number ratio of republicans : democrats . if 80 % of republicans ( which is ( 60 * 0.8 ) = 48 ) and 25 % of democrats ( 40 * 0.25 = 10 ) voted for candidate x , means that out of total of 100 voters ; 58 ( 48 + 10 ) voters voted for candidate x and 42 voted for candidate y . thus we can infer that candidate x is expected to win the election by 16 ( 58 - 42 ) votes . therefore candidate x is expected to win the election by ( 16 / 100 ) votes which is equivalent to 16 % . i think the answer is c ."
Answer: c