Cheukting/mathqa huggingface dataset:
Question (physics): a and b complete a work in 80 days . a alone can do it in 40 days . if both together can do the work in how many days ?
Options: a ) 1.0875 days , b ) 0.1875 days , c ) 0.0675 days , d ) 0.0375 days , e ) 0.0775 days
Rationale: "1 / 80 + 1 / 40 = 0.0375 days answer : d"
Answer: d
Question (general): a customer purchased a package of ground beef at a cost of $ 1.80 per pound . for the same amount of money , the customer could have purchased a piece of steak that weighed 20 percent less than the package of ground beef . what was the cost per pound of the steak ?
Options: a ) $ 2.05 , b ) $ 2.15 , c ) $ 2.25 , d ) $ 2.35 , e ) $ 2.45
Rationale: for simplicity , let ' s assume the customer bought 1 pound of ground beef for $ 1.80 . let x be the price per pound for the steak . then 0.8 x = 180 x = 180 / 0.8 = $ 2.25 the answer is c .
Answer: c
Question (other): if two dice are thrown together , the probability of getting prime number on both dice is
Options: a ) 5 / 9 , b ) 1 / 9 , c ) 2 / 9 , d ) 4 / 9 , e ) 7 / 9
Rationale: "the number of exhaustive outcomes is 36 . let e be the event of getting a prime number on both the dice . p ( e ) = 8 / 36 = 2 / 9 . c )"
Answer: c
Question (other): at a wedding reception , 125 guests ate chicken and 75 guests ate beef . if exactly 100 guests ate only one of the two types of meat , how many guests ate both types of meat ?
Options: a ) 5 , b ) 100 , c ) 7 , d ) 4 , e ) 50
Rationale: say x guests ate both types of meat . ( 125 - x ) + ( 75 - x ) = 100 - - > x = 50 . answer : e .
Answer: e
Question (general): the average temperature for monday , tuesday and wednsday is 36.3 degrees c . the average temperature for tuesday , wednesday and thursday is 36.7 degrees c . if monday ’ s temperature recorded as 39 degrees c , find the thursday ’ s temperature ?
Options: a ) 60.2 degrees c , b ) 50.2 degrees c , c ) 40.2 degrees c , d ) 70.2 degrees c , e ) none of these
Rationale: explanation : mon + tue + wed temperature = 3 x 36.3 = 108.9 tue + wed temperature = 108.9 – 39 = 69.9 tue + wed + thu temperature = 3 x 36.7 = 110.1 so , thursday ’ s temperature = 110.1 – 69.9 = 40.2 degrees c answer : c
Answer: c
Question (other): a farmer with 1,350 acres of land had planted his fields with corn , sugar cane , and tobacco in the ratio of 4 : 2 : 3 , respectively , but he wanted to make more money , so he shifted the ratio to 2 : 2 : 5 , respectively . how many more acres of land were planted with tobacco under the new system ?
Options: a ) 90 , b ) 150 , c ) 270 , d ) 300 , e ) 450
Rationale: "originally ( 3 / 9 ) * 1350 = 450 acres were planted with tobacco . in the new system ( 5 / 9 ) * 1350 = 750 acres were planted with tobacco . thus 750 - 450 = 300 more acres were planted with tobacco . the answer is d ."
Answer: d
Question (general): a palindrome is a number that reads the same forward and backward , such as 343 . how many odd , 6 - digit numbers are palindromes ?
Options: a ) 400 , b ) 450 , c ) 500 , d ) 900 , e ) 2500
Rationale: "first recognize you only need to consider the first three digits ( because the second three are just the first three flipped ) there are 900 possibilities for the first three digits of a 6 digit number , 100 - 999 inclusive . everything starting with a 1 , 3,5 , 7,9 will be odd , which is 5 / 9 ths of the combinations . 5 / 9 * 900 = 500 answer : c"
Answer: c
Question (general): p , q and r have $ 6000 among themselves . r has two - thirds of the total amount with p and q . find the amount with r ?
Options: a ) 2400 , b ) 2403 , c ) 3998 , d ) 2539 , e ) 1930
Rationale: "a 2400 let the amount with r be $ r r = 2 / 3 ( total amount with p and q ) r = 2 / 3 ( 6000 - r ) = > 3 r = 12000 - 2 r = > 5 r = 12000 = > r = 2400 ."
Answer: a
Question (general): light glows for every 15 seconds . how many max . times did it glow between 1 : 57 : 58 and 3 : 20 : 47 am .
Options: a ) 380 times , b ) 381 times , c ) 382 times , d ) 392 times , e ) 331 times
Rationale: "time difference is 1 hr , 22 min , 49 sec = 4969 sec . so , light glows floor ( 4969 / 15 ) = 331 times . answer : e"
Answer: e
Question (physics): a boy goes to his school from his house at a speed of 3 km / hr and returns at a speed of 2 km / hr . if he takes 5 hours in going and coming . the distance between his house and school is :
Options: a ) 4.5 km , b ) 5.5 km , c ) 6 km , d ) 7 km , e ) none
Rationale: "sol . average speed = [ 2 * 3 * 2 / 3 + 2 ] km / hr = 12 / 5 km / hr . distance travelled = [ 12 / 5 * 5 ] km = 12 km . ∴ distance between house and school = [ 12 / 2 ] km = 6 km . answer c"
Answer: c
Question (gain): of the 120 passengers on flight 750 , 60 % are female . 10 % of the passengers sit in first class , and the rest of the passengers sit in coach class . if 1 / 3 of the passengers in first class are male , how many females are there in coach class ?
Options: a ) 44 , b ) 48 , c ) 50 , d ) 64 , e ) 56
Rationale: "number of passengers on flight = 120 number of female passengers = . 6 * 120 = 72 number of passengers in first class = ( 10 / 100 ) * 120 = 12 number of passengers in coach class = ( 90 / 100 ) * 120 = 108 number of male passengers in first class = 1 / 3 * 12 = 4 number of female passengers in first class = 12 - 4 = 8 number of female passengers in coach class = 72 - 8 = 64 answer d"
Answer: d
Question (geometry): the ratio of radius of a circle and the side of a square is 2 : 7 . find the ratio of their areas :
Options: a ) 2 : 1 , b ) 4 : 7 , c ) 8 : 77 , d ) 4 : 49 , e ) none
Rationale: "radius / side = 2 / 7 â ‡ ’ area of circle / area of square = 4 / 49 answer : d"
Answer: d
Question (gain): how many kilograms of sugar costing rs . 9 per kg must be mixed with 27 kg of sugar costing rs . 7 per kg so that there may be a gain of 10 % by selling the mixture at rs . 9.24 per kg ?
Options: a ) 33 , b ) 39 , c ) 38 , d ) 63 , e ) 01
Rationale: by the rule of alligation : c . p . of 1 kg sugar of 1 st kind c . p . of 1 kg sugar of 2 nd kind { \ color { blue } \ therefore } ratio of quantities of 1 st and 2 nd kind = 14 : 6 = 7 : 3 . let x kg of sugar of 1 st kind be mixed with 27 kg of 2 nd kind . then , 7 : 3 = x : 27 or x = ( 7 x 27 / 3 ) = 63 kg . answer : d ) 63 kg
Answer: d
Question (general): a sum of money lent out at s . i . amounts to rs . 820 after 2 years and to rs . 1020 after a further period of 5 years . the sum is ?
Options: a ) rs . 440 , b ) rs . 500 , c ) rs . 540 , d ) rs . 740 , e ) rs . 840
Rationale: "s . i for 5 years = ( 1020 - 820 ) = rs . 200 . s . i . for 2 years = 200 / 5 * 2 = rs . 80 . principal = ( 820 - 80 ) = rs . 740 . answer : d"
Answer: d
Question (general): a business executive and his client are charging their dinner tab on the executive ' s expense account . the company will only allow them to spend a total of 60 $ for the meal . assuming that they will pay 7 % in sales tax for the meal and leave a 15 % tip , what is the most their food can cost ?
Options: a ) 39.55 $ , b ) 40.63 $ , c ) 41.63 $ , d ) 42.15 $ , e ) 48.7 $
Rationale: "let x is the cost of the food 1.07 x is the gross bill after including sales tax 1.15 * 1.07 x = 60 x = 48.7 hence , the correct option is e"
Answer: e
Question (general): for 2 consecutive yrs , my incomes are in the ratio of 4 : 7 and expenses in the ratio of 3 : 5 . if my income in the 2 nd yr is rs . 42000 & my expenses in the first yr in rs . 21000 , my total savings for the two - year is
Options: a ) rs . 8000 , b ) rs . 9000 , c ) rs . 9800 , d ) rs . 9900 , e ) rs . 10000
Rationale: sol . income in first year = * x 42000 = rs . 24000 expenses in second year = \ x 21000 = rs . 35000 total savings = total income - total expenses = ( 42000 + 24000 ) - ( 21000 + 35000 ) = 66000 - s 6000 = rs . 10000 e
Answer: e
Question (general): how many three - digit numbers are divisible by 6 in all ?
Options: a ) 149 , b ) 150 , c ) 151 , d ) 166 , e ) none
Rationale: "solution required numbers are 102 , 018,114 , . . . . 996 . this is an a . p with a = 102 , d = 6 . let the number of its terms be n . then a + ( n - 1 ) d ‹ = › 102 + ( n - 1 ) × 6 = 996 ‹ = › n = 150 . answer b"
Answer: b
Question (physics): a boat can travel with a speed of 12 km / hr in still water . if the speed of the stream is 4 km / hr , find the time taken by the boat to go 68 km downstream .
Options: a ) 4.25 hr , b ) 5.25 hr , c ) 8.25 hr , d ) 2.25 hr , e ) 2.50 hr
Rationale: "speed of boat in still water = 12 km / hr speed of the stream = 4 km / hr speed downstream = ( 12 + 4 ) = 16 km / hr time taken to travel 68 km downstream = 68 ⁄ 16 = 17 ⁄ 4 = 4.25 hours answer is a"
Answer: a
Question (gain): the cost of one photocopy is $ 0.02 . however , a 25 % discount is offered on orders of more than 100 photocopies . if saran and david have to make 80 copies each , how much will each of them save if they submit a single order of 160 copies ?
Options: a ) $ 0.32 , b ) $ 0.40 , c ) $ 0.45 , d ) $ 0.48 , e ) $ 0.54
Rationale: if saran and david submit separate orders , each would be smaller than 100 photocopies , so no discount . each would pay ( 80 ) * ( $ 0.02 ) = $ 1.60 , or together , a cost of $ 3.20 - - - that ' s the combinedno discount cost . if they submit things together as one big order , they get a discount off of that $ 3.20 price - - - - 25 % or 1 / 4 of that is $ 0.80 , the discount on the combined sale . they each effective save half that amount , or $ 0.40 . answer = ( b ) .
Answer: b
Question (physics): jane makes toy bears . when she works with an assistant , she makes 100 percent more bears per week and works 10 percent fewer hours each week . having an assistant increases jane ’ s output of toy bears per hour by what percent ?
Options: a ) 20 % , b ) 80 % , c ) 100 % , d ) 180 % , e ) 200 %
Rationale: "we can use fractional equivalents here to solve the problem 80 % = 4 / 5 ; this means that in 1 st case if she prepares 5 bears , in 2 nd case she prepares 9 bears 10 % = 1 / 10 ; this means that in 1 st case if she needs 10 hours , in 2 nd case she needs 9 hours now we come to productivity based on above fractional values the productivity in 1 st case is 0.5 bears / hour and in the 2 nd case it is 1 bear / hour hence the productivity is double with the assistant i . e . the increase in productivity is 200 % e"
Answer: e
Question (physics): p is able to do a piece of work in 10 days and q can do the same work in 12 days . if they can work together for 5 days , what is the fraction of work left ?
Options: a ) 7 / 12 , b ) 5 / 12 , c ) 1 / 12 , d ) 3 / 12 , e ) 1 / 2
Rationale: "explanation : amount of work p can do in 1 day = 1 / 10 amount of work q can do in 1 day = 1 / 12 amount of work p and q can do in 1 day = 1 / 10 + 1 / 12 = 11 / 60 amount of work p and q can together do in 5 days = 5 × ( 11 / 60 ) = 11 / 12 fraction of work left = 1 – 11 / 12 = 1 / 12 answer : option c"
Answer: c
Question (physics): the ratio between the length and the breadth of a rectangular park is 3 : 2 . if a man cycling along the boundary of the park at the speed of 12 km / hr completes one round in 6 minutes , then the area of the park ( in sq . m ) is :
Options: a ) 153601 , b ) 153600 , c ) 86400 , d ) 153603 , e ) 153604
Rationale: "perimeter = distance covered in 6 min . = ( 12000 / 60 ) x 6 m = 1200 m . let length = 3 x metres and breadth = 2 x metres . then , 2 ( 3 x + 2 x ) = 1200 or x = 120 . length = 360 m and breadth = 240 m . area = ( 360 x 240 ) m 2 = 86400 m 2 . answer : c"
Answer: c
Question (geometry): find the area of a parallelogram with base 24 cm and height 12 cm ?
Options: a ) 297 cm 2 , b ) 384 cm 2 , c ) 672 cm 2 , d ) 267 cm 2 , e ) 288 cm 2
Rationale: "area of a parallelogram = base * height = 24 * 12 = 288 cm 2 answer : e"
Answer: e
Question (general): for each 6 - month period during a light bulb ' s life span , the odds of it not burning out from over - use are half what they were in the previous 6 - month period . if the odds of a light bulb burning out during the first 6 - month period following its purchase are 2 / 3 , what are the odds of it burning out during the period from 6 months to 1 year following its purchase ?
Options: a ) 5 / 27 , b ) 2 / 9 , c ) 1 / 3 , d ) 4 / 9 , e ) 2 / 7
Rationale: p ( of not burning out in a six mnth period ) = 1 / 2 of p ( of not burning out in prev 6 mnth period ) p ( of burning out in 1 st 6 mnth ) = 2 / 3 - - - > p ( of not burning out in 1 st 6 mnth ) = 1 - 2 / 3 = 1 / 3 - - - - > p ( of not burning out in a six mnth period ) = 1 / 2 * 1 / 3 = 1 / 6 - - - > p ( of burning out in a six mnth period ) = 1 - 1 / 3 = 2 / 3 now p ( of burning out in 2 nd six mnth period ) = p ( of not burning out in 1 st six mnth ) * p ( of burning out in a six mnth ) = 2 / 3 * 1 / 6 = 2 / 7 ans e
Answer: e
Question (gain): a glass was filled with 10 ounces of water , and 0.05 ounce of the water evaporated each day during a 20 - day period . what percent of the original amount of water evaporated during this period ?
Options: a ) 0.002 % , b ) 0.02 % , c ) 0.2 % , d ) 2 % , e ) 10 %
Rationale: "we are given that 0.05 ounces of water evaporated each day . furthermore , we know that this process happened over a 20 - day period . to calculate the total amount of water that evaporated during this time frame we need to multiply 0.05 by 20 . this gives us : 0.05 x 20 = 1 ounces finally , we are asked for “ what percent ” of the original amount of water evaporated during this period . to determine this percentage , we have to make sure we translate the expression correctly . we can translate it to : ( amount evaporated / original amount ) x 100 % ( 1 / 10 ) x 100 % ( 10 / 100 ) x 100 % = 10 % answer e"
Answer: e
Question (other): a starts business with rs . 3500 and after 5 months , b joins with a as his partner . after a year , the profit is divided in the ratio 2 : 3 . what is b ' s contribution in the capital
Options: a ) rs 9000 , b ) rs 7000 , c ) rs 5000 , d ) rs 4000 , e ) none of these
Rationale: "explanation : let b contribution is x . 3500 * 12 / 7 x = 2 / 3 = > 14 x = 126000 = > x = rs 9000 option a"
Answer: a
Question (gain): what percent of 5.2 kg is 16 gms ?
Options: a ) 30 , b ) 66 , c ) 58 , d ) 29 , e ) 17
Rationale: "explanation : required percentage = ( 16 / 5200 * 100 ) % = 3 / 10 % = 0.30 % answer : a ) . 30 %"
Answer: a
Question (gain): the true discount on a bill due 9 months hence at 16 % per annum is rs . 162 . the amount of the bill is
Options: a ) rs . 1386 , b ) rs . 1350 , c ) rs . 1575 , d ) rs . 2268 , e ) none of these
Rationale: "solution 32.5 let p . w . be rs . x . then , s . i . on rs . x at 16 % for 9 months = rs . 162 . ∴ x 16 x 9 / 12 x 1 / 100 } = 162 or x = 1350 . ∴ p . w . = rs . 1350 . answer b"
Answer: b
Question (physics): a cistern can be filled by a tap in 5 hours while it can be emptied by another tap in 10 hours . if both the taps are opened simultaneously then after how much time will the cistern get filled ?
Options: a ) 20 hr , b ) 10 hr , c ) 5 hr , d ) 4 hr , e ) 15 hr
Rationale: "net part filled in 1 hour 1 / 5 - 1 / 10 = 1 / 10 the cistern will be filled in 10 hr answer is b"
Answer: b
Question (physics): the mall charges 50 cents for the first hour of parking and $ 3 for each additional hour until the customer reaches 4 hours , after that the parking fee is $ 1 per hour . if a certain customer parked his in the mall for 7 hours and 30 minutes , how much is he going to pay ?
Options: a ) $ 11.5 . , b ) $ 12 . , c ) $ 13 . , d ) $ 14.5 , e ) $ 15 .
Rationale: charges for 7 hours = ( first hour @ $ 0.50 ) + ( 3 hours @ $ 3 ) + ( 3.5 hours @ $ 1 ) charges for 7 hours = ( 1 @ $ 0.50 ) + ( 3 hours @ $ 3 ) + ( 3.5 hours @ $ 1 ) charges for 7 hours = ( $ 0.50 ) + ( $ 9 ) + ( $ 3.5 ) charges for 7 hours = ( $ 0.50 ) + ( $ 9 ) + ( $ 3.50 ) charges for 7 hours = $ 13 hence correct answer must be ( c )
Answer: c
Question (gain): x and y invested in a business . they earned some profit which they divided in the ratio of 2 : 3 . if x invested rs . 40000 , the amount invested by y is
Options: a ) 33488 , b ) 63809 , c ) 60000 , d ) 37887 , e ) 77824
Rationale: explanation : suppose y invested rs . y . then 40000 / y = 2 / 3 or y = 60000 . answer : c ) 60000
Answer: c
Question (geometry): a 12 meter long wire is cut into two pieces . if the longer piece is then used to form a perimeter of a square , what is the probability that the area of the square will be more than 4 if the original wire was cut at an arbitrary point ?
Options: a ) 1 / 6 , b ) 2 / 3 , c ) 3 / 10 , d ) 1 / 3 , e ) 2 / 5
Rationale: "a square with an area of 4 has a perimeter of 8 . for the area to be > 4 , the longer piece must be > 8 . the wire must be cut within 4 meters from either end . the probability of this is 8 / 12 = 2 / 3 . the answer is b ."
Answer: b
Question (gain): an article with cost price of 245 is sold at 34 % profit . what is the selling price ?
Options: a ) 328 , b ) 320 , c ) 300 , d ) 207 , e ) 310
Rationale: sp = 1.34 * 245 = 328 answer : a
Answer: a
Question (physics): two stations p and q are 155 km apart on a straight track . one train starts from p at 7 a . m . and travels towards q at 20 kmph . another train starts from q at 8 a . m . and travels towards p at a speed of 25 kmph . at what time will they meet ?
Options: a ) 10 am , b ) 12 am , c ) 10.30 am , d ) 12.30 am , e ) 11 am
Rationale: "assume both trains meet after x hours after 7 am distance covered by train starting from p in x hours = 20 x km distance covered by train starting from q in ( x - 1 ) hours = 25 ( x - 1 ) total distance = 155 = > 20 x + 25 ( x - 1 ) = 155 = > 45 x = 180 = > x = 4 means , they meet after 3 hours after 7 am , ie , they meet at 11 am answer is e ."
Answer: e
Question (general): the captain of a cricket team of 11 members is 26 years old and the wicket keeper is 3 years older . if the ages of these two are excluded , the average age of the remaining players is one year less than the average age of the whole team . what is the average age of the team ?
Options: a ) 23 years , b ) 20 years , c ) 25 years , d ) 22 years , e ) 28 years
Rationale: "a 23 years let the average age of the whole team by x years . 11 x - ( 26 + 29 ) = 9 ( x - 1 ) 11 x - 9 x = 46 2 x = 46 x = 23 . so , average age of the team is 23 years"
Answer: a
Question (physics): the number of students in each section of a school is 24 . after admitting new students , 3 new sections were started . now , the total number of sections is 16 and there are 21 students in each section . the number of new students admitted is :
Options: a ) 12 , b ) 42 , c ) 24 , d ) 28 , e ) 26
Rationale: original number of sections = 16 - 3 = 13 original number of students = 24 x 13 = 312 present number of students = 21 x 16 = 336 number of new students admitted = 336 - 312 = 24 so the answer is option c ) 24 .
Answer: c
Question (general): simplify : 81 x 81 + 68 x 68 - 2 x 81 x 68 .
Options: a ) 169 , b ) 159 , c ) 189 , d ) 179 , e ) 219
Rationale: = ( 81 ) ^ 2 + ( 68 ) ^ 2 – 2 x 81 x 68 = a ^ 2 + b ^ 2 – 2 ab , where a = 81 , b = 68 = ( a - b ) ^ 2 = ( 81 – 68 ) ^ 2 = ( 13 ) ^ 2 = 169 . answer is a .
Answer: a
Question (general): - 24 * 29 + 1240 = ?
Options: a ) - 544 , b ) 584 , c ) 544 , d ) 345 , e ) none of these
Rationale: "= > - 24 * ( 30 - 1 ) + 1240 ; = > - ( 24 * 30 ) + 24 + 1240 ; = > - 720 + 1264 = 544 . correct option : c"
Answer: c
Question (general): 4 liters of a 25 percent solution of alcohol in water are mixed with 3 liters of a 11 percent alcohol in water solution . what is the percentage of alcohol in the new solution ?
Options: a ) 18.2 % , b ) 18.6 % , c ) 19.0 % , d ) 19.4 % , e ) 19.8 %
Rationale: "the total amount of alcohol is 0.25 ( 4 ) + 0.11 ( 3 ) = 1.33 liters . the percentage is 1.33 / 7 = 133 / 700 = 19 / 100 which is 19 % the answer is c ."
Answer: c
Question (gain): x and y started a business by investing rs . 36000 and rs . 42000 respectively after 4 months z joined in the business with an investment of rs . 48000 , then find share of z in the profit of rs . 13750 ?
Options: a ) 3200 , b ) 4000 , c ) 3250 , d ) 3825 , e ) 3985
Rationale: ratio of investment , as investments is for different time . investment x number of units of time . ratio of investments x : y : z = 36000 : 42000 : 48000 = > 6 : 7 : 8 . x = 6 x 12 months = 72 , y = 7 x 12 = 84 , z = 8 x 8 = 64 = > 18 : 21 : 16 . ratio of investments = > x : y : z = 18 : 21 : 16 . investment ratio = profit sharing ratio . z = 13750 × 16 / 55 = rs . 4000 . share of z in the profit is rs . 4000 . option b
Answer: b
Question (gain): machine a and machine b are each used to manufacture 550 sprockets . it takes machine a 10 hours longer to produce 550 sprockets than machine b . machine b produces 10 percent more sprockets per hour than machine a . how many sprockets per hour does machine a produces ?
Options: a ) 6 , b ) 5 , c ) 7 , d ) 8 , e ) 9
Rationale: "machine b : takes x hours to produce 550 sprockets machine a : takes ( x + 10 ) hours to produce 550 sprockets machine b : in 1 hour , b makes 550 / x sprockets machine a : in 1 hour , a makes 550 / ( x + 10 ) sprockets equating : 1.1 ( 550 / ( x + 10 ) ) = 550 / x 605 / ( x + 10 ) = 550 / x 605 x = 550 x + 5500 55 x = 5500 x = 100 a makes 550 / ( 110 ) = 5 sprockets per hour answer : b"
Answer: b
Question (physics): how long does a train 100 m long travelling at 60 kmph takes to cross a bridge of 120 m in length ?
Options: a ) 15.8 sec , b ) 13.2 sec , c ) 12.4 sec , d ) 16.8 sec , e ) 11.8 sec
Rationale: "b 13.2 sec d = 100 + 120 = 220 m s = 60 * 5 / 18 = 50 / 3 t = 220 * 3 / 50 = 13.2 sec answer is b"
Answer: b
Question (general): a rainstorm increased the amount of water stored in state j reservoirs from 5 billion gallons to 7.5 billion gallons . if the storm increased the amount of water in the reservoirs to 55 percent of total capacity , approximately how many billion gallons of water were the reservoirs short of total capacity prior to the storm ?
Options: a ) 6.9 , b ) 1.4 , c ) 2.5 , d ) 3.0 , e ) 4.4
Rationale: after the reservoir is filled to 7.5 gallons the amount of water is at 55 % - which means that 45 % of the reservoir is empty . to figure out what that 45 % is approximate : 7.5 gallons / 55 percent = x gallons / 45 percent , therefore , x = 6.136 gallons , answer choices e , b , c , d are below 6.136 . we know that the reservoir must be short more than 6.136 gallons , therefore , the only possible choice is a .
Answer: a
Question (gain): the total cost of 100 paper plates and 200 paper cups is $ 4.50 at the same rates what is the total cost of 20 of the plates and 40 of the cups ?
Options: a ) $ . 90 , b ) $ 1.00 , c ) $ 1.20 , d ) $ 1.50 , e ) $ 1.60
Rationale: "u dont need to go through all this what u have with u is 100 p + 200 c = $ 4.50 just divide the equation by 5 and you will get what u are looking for 20 p + 40 c = $ 0.90 therefore oa is a"
Answer: a
Question (physics): kathleen can paint a room in 2 hours , and anthony can paint an identical room in 3 hours . how many hours would it take kathleen and anthony to paint both rooms if they work together at their respective rates ?
Options: a ) 8 / 15 , b ) 4 / 3 , c ) 12 / 5 , d ) 9 / 4 , e ) 15 / 4
Rationale: "( 1 / 2 + 1 / 3 ) t = 2 t = 12 / 5 answer : c"
Answer: c
Question (physics): a can run 2.7 km distance in 1 min 20 seconds , while b can run this distance in 1 min 30 sec . by how much distance can a beat b ?
Options: a ) 90 m , b ) 30 m , c ) 120 m , d ) 300 m , e ) 190 m
Rationale: "a takes time 1.20 minutes = 80 sec b takes time 1.30 minutes = 90 sec diffrence = 90 - 80 = 10 sec now we are to find distance covered in 10 sec by b 90 sec = 30 m 1 sec = 30 m 10 sec = 10 x 30 = 300 m answer : d"
Answer: d
Question (other): how many different positive integers are factors of 25 ?
Options: a ) 1 , b ) 5 , c ) 4 , d ) 6 , e ) 8
Rationale: "5 * 5 answer : a"
Answer: a
Question (geometry): a parallelogram has a base that is four time the size of it ' s height . the total area of this parallelogram is 2,304 sq ft . what is the height of the parallelogram ?
Options: a ) 19
b ) 23
c ) 24
d ) 16
e ) 17
Rationale: 4 x * x = 2304 = > x = 24 answer : c
Answer: c