Cheukting/mathqa huggingface dataset:
Question (physics): the average wages of a worker during a fortnight comprising 15 consecutive working days was $ 90 per day . during the first 7 days , his average wages was $ 87 per day and the average wages during the last 7 days was $ 91 per day . what was his wage on the 8 th day ?
Options: a ) $ 83 , b ) $ 90 , c ) $ 92 , d ) $ 97 , e ) $ 104
Rationale: "average daily wage of a worker for 15 consecutive working days = 90 $ during the first 7 days , the daily average daily wage = 87 $ during the last 7 days , the daily average daily wage = 91 $ wage on 8 th day = 90 * 15 - ( 87 * 7 + 91 * 7 ) = 1350 - ( 609 + 637 ) = 1350 - 1246 = 104 answer e"
Answer: e
Question (geometry): it is decided to construct a 2 metre broad pathway around a rectangular plot on the inside . if the area of the plots is 96 sq . m . and the rate of construction is rs . 50 per square metre . , what will be the total cost of the construction ?
Options: a ) rs . 3500
b ) rs . 4200
c ) insufficient data
d ) rs . 4400
e ) none of these
Rationale: explanation : let length and width of the rectangular plot be l and b respectively total area of the rectangular plot = 96 sq . m . = > lb = 96 width of the pathway = 2 m length of the remaining area in the plot = ( l - 4 ) breadth of the remaining area in the plot = ( b - 4 ) area of the remaining area in the plot = ( l - 4 ) ( b - 4 ) area of the pathway = total area of the rectangular plot - remaining area in the plot = 96 - [ ( l - 4 ) ( b - 4 ) ] = 96 - [ lb - 4 l - 4 b + 16 ] = 96 - [ 96 - 4 l - 4 b + 16 ] = 96 - 96 + 4 l + 4 b - 16 = 4 l + 4 b - 16 = 4 ( l + b ) - 16 we do not know the values of l and b and hence area of the pathway can not be found out . so we can not determine total cost of the construction . answer : option c
Answer: c
Question (general): in a class , there are 18 boys who are over 160 cm tall . if these constitute 3 - fourths of the boys and the total number of boys is two - thirds of the total number of students in the class , what is the number of girls in the class ?
Options: a ) 11 , b ) 12 , c ) 28 , d ) 27 , e ) 19
Rationale: let the number of boys be x . then , ( 3 / 4 ) x = 18 or x = 18 x ( 4 / 3 ) = 24 . if total number of students is y , then ( 2 / 3 ) y = 24 or y = 24 x ( 3 / 2 ) = 36 . therefore number of girls in the class = ( 36 - 24 ) = 12 . answer : b
Answer: b
Question (gain): a and b invests rs . 10000 each , a investing for 6 months and b investing for all the 12 months in the year . if the total profit at the end of the year is rs . 24000 , find their shares ?
Options: a ) 8000 , 16000 , b ) 1599,2000 , c ) 7290,3000 , d ) 15000,4000 , e ) 72821,5000
Rationale: "the ratio of their profits a : b = 6 : 12 = 1 : 2 share of a = 1 * 24000 / 3 = 8000 share of b = 2 * 24000 / 3 = 16000 answer : a"
Answer: a
Question (geometry): the perimeter of a triangle is 40 cm and the inradius of the triangle is 2.5 cm . what is the area of the triangle ?
Options: a ) 87 cm 2 , b ) 28 cm 2 , c ) 98 cm 2 , d ) 26 cm 2 , e ) 50 cm 2
Rationale: "area of a triangle = r * s where r is the inradius and s is the semi perimeter of the triangle . area of triangle = 2.5 * 40 / 2 = 50 cm 2 answer : e"
Answer: e
Question (other): if 75 percent of a class answered the first question on a certain test correctly , 70 percent answered the second question on the test correctly , and 20 percent answered neither of the questions correctly , what percent answered both correctly ?
Options: a ) 10 % , b ) ( 8 ) 20 % , c ) 30 % , d ) 50 % , e ) 65 %
Rationale: { total } = { first } + { second } - { both } + { neither } 100 % = 75 % + 70 % - { both } + 20 % - - > { both } = 65 % . answer : e .
Answer: e
Question (gain): if a man lost 4 % by selling oranges at the rate of 72 a rupee at how many a rupee must he sell them to gain 44 % ?
Options: a ) 41 , b ) 48 , c ) 49 , d ) 44 , e ) 43
Rationale: "96 % - - - - 72 144 % - - - - ? 96 / 144 * 72 = 48 answer : b"
Answer: b
Question (physics): a man swims downstream 40 km and upstream 16 km taking 4 hours each time , what is the speed of the man in still water ?
Options: a ) 7 , b ) 7.5 , c ) 6.8 , d ) 7.8 , e ) 8.0
Rationale: "40 - - - 4 ds = 10 ? - - - - 1 20 - - - - 4 us = 5 ? - - - - 1 m = ? m = ( 10 + 5 ) / 2 = 7.5 answer : b"
Answer: b
Question (general): | 5 - 2 | - | 6 - 9 | = ?
Options: a ) 3 , b ) 2 , c ) 1 , d ) 0 , e ) 4
Rationale: "| 5 - 2 | - | 6 - 9 | = | 3 | - | - 3 | = 3 - 3 = 0 correct answer d"
Answer: d
Question (general): find value of x : 121 × 54 = x
Options: a ) 34545 , b ) 46576 , c ) 67887 , d ) 57687 , e ) 75625
Rationale: 121 × 54 = 121 × ( 102 ) 4 = 121 × 1000016 = 7.5625 × 10000 = 75625 e
Answer: e
Question (physics): two pipes a and b can fill a tank in 20 and 30 minutes respectively . if both the pipes are used together , then how long it will take to fill the tank ?
Options: a ) 10 mins , b ) 12 mins , c ) 15 mins , d ) 20 mins , e ) 30 mins
Rationale: "explanation : in this type of questions we first get the filling in 1 minute for both pipes then we will add them to get the result , as part filled by a in 1 min = 1 / 20 part filled by b in 1 min = 1 / 30 part filled by ( a + b ) in 1 min = 1 / 20 + 1 / 30 = 1 / 12 so both pipes can fill the tank in 12 mins . answer : option b"
Answer: b
Question (general): how many integers are between 4 and 87 / 8 , inclusive ?
Options: a ) 4 , b ) 5 , c ) 7 , d ) 9 , e ) 10
Rationale: "87 / 8 = 10 . xx we are not concerned about the exact value of 87 / 8 as we just need the integers . since the values are small , we can write down the integers . the different integers between 4 and 87 / 8 would be 4 , 5 , 6 , 7 , 8 , 9 , 10 total number of integers = 7 option c"
Answer: c
Question (general): aishwarya rai walks into a bank to cash out her check . by mistake the bank teller gives her dollar amount in change , and her cent amount in dollars . on the way home she spends 5 cent , and then suddenly she notices that she has twice the amount of her check . how much was her check amount ?
Options: a ) 21.55 , b ) 25.89 , c ) 30.56 , d ) 31.55 , e ) 31.63
Rationale: e the check was for dollars 31.63 . the bank teller gave her dollars 63.31 she spent . 05 , and then she had dollars 63.26 , which is twice the check . let x be the dollars of the check , and y be the cent . the check was for 100 x + y cent he was given 100 y + x cent also 100 y + x - 5 = 2 ( 100 x + y ) expanding this out and rearranging , we find : 98 y = 199 x + 5 or 199 x ≡ - 5 ( mod 98 ) or 98 * 2 * x + 3 x ≡ - 5 ( mod 98 ) 3 x ≡ - 5 ≡ 93 ( mod 98 ) this quickly leads to x = 31
Answer: e
Question (physics): the length of a room is 9 m and width is 4.75 m . what is the cost of paying the floor by slabs at the rate of rs . 900 per sq . metre .
Options: a ) 25650 , b ) 25750 , c ) 26550 , d ) 30750 , e ) 38475
Rationale: "area = 9 × 4.75 sq . metre . cost for 1 sq . metre . = rs . 900 hence total cost = 9 × 4.75 × 900 = 9 × 4275 = rs . 38475 answer is e ."
Answer: e
Question (general): if 2 ^ 5 , 3 ^ 3 , and 13 ^ 2 are all factors of the product of 936 and w where w is a positive integer , what is the smallest possible value of w ?
Options: a ) 26 , b ) 39 , c ) 42 , d ) 65 , e ) 156
Rationale: "here 156 has three two ' s two three ' s and one 13 rest of them must be in w so w = 13 * 3 * 4 = 156 answer : e"
Answer: e
Question (gain): a sum of money at simple interest amounts to rs . 815 in 2 years and to rs . 854 in 4 years . the sum is :
Options: a ) s . 650 , b ) s . 690 , c ) s . 698 , d ) s . 700 , e ) s . 737
Rationale: "s . i . for 1 year = rs . ( 854 - 815 ) = rs . 39 . s . i . for 2 years = rs . ( 39 x 2 ) = rs . 78 . principal = rs . ( 815 - 78 ) = rs . 737 . answer : option e"
Answer: e
Question (general): i chose a number and divide it by 12 . then i subtracted 240 from the result and got 8 . what was the number i chose ?
Options: a ) 2976 , b ) 2989 , c ) 2789 , d ) 2888 , e ) 2098
Rationale: "let x be the number i chose , then x / 12 − 240 = 8 x / 12 = 248 x = 2976 answer is a ."
Answer: a
Question (physics): at 1 : 00 pm , a truck left city p and headed toward city q at a constant speed of 36 km / h . one hour later , a car left city q and headed toward city p along the same road at a constant speed of 48 km / h . if the distance between city p and city q is 330 km , at what time will the truck and the car meet each other ?
Options: a ) 4 : 30 , b ) 4 : 45 , c ) 5 : 00 , d ) 5 : 15 , e ) 5 : 30
Rationale: at 2 : 00 pm , the truck and the car are 294 km apart . the truck and the car complete a distance of 84 km each hour . the time it takes to meet is 294 / 84 = 3.5 hours . they will meet at 5 : 30 pm . the answer is e .
Answer: e
Question (general): if x = 27 ^ 324 and y = 3 ^ 134 , what is the units digit of x / y ?
Options: a ) 1 , b ) 3 , c ) 5 , d ) 7 , e ) 9
Rationale: "basically it tests pattern : ( 3,9 , 7,1 ) if we take write 27 in terms of 3 and take the dr to the top , it will result in 3 ^ 838 since pattern = 4 divide 838 / 4 and reminder = 2 - - - - - - - this points to 9 in the pattern ( 3,9 , 7,1 ) answer : e"
Answer: e
Question (physics): in what time will a train 100 meters long cross an electric pole , if its speed is 72 km / hr
Options: a ) 5 seconds , b ) 2.8 seconds , c ) 3.5 seconds , d ) 2.5 seconds , e ) 2.6 seconds
Rationale: "first convert speed into m / sec speed = 72 * ( 5 / 18 ) = 20 m / sec time = distance / speed = 100 / 20 = 5 seconds answer : a"
Answer: a
Question (gain): at joel ’ s bookstore , the current inventory is 30 % historical fiction . of the historical fiction books , 40 % are new releases , while 50 % of the other books are new releases . what fraction of all new releases are the historical fiction new releases ?
Options: a ) 4 / 25 , b ) 12 / 47 , c ) 2 / 5 , d ) 8 / 15 , e ) 2 / 3
Rationale: let there be 100 books in all historic fiction books = 30 % of total = 30 other books = 70 new historic fiction = 40 % of 30 = 12 other new books = 50 % of 70 = 35 total new books = 35 + 12 = 47 fraction = 12 / 47 ans : b
Answer: b
Question (gain): if 45 % of a class averages 95 % on a test , 50 % of the class averages 78 % on the test , and the remainder of the class averages 60 % on the test , what is the overall class average ? ( round final answer to the nearest percent ) .
Options: a ) 83 % , b ) 84 % , c ) 85 % , d ) 86 % , e ) 87 %
Rationale: "this question is a weighted average question with a series of dependent variables . the remaining portion of the class represents 100 % - 45 % - 50 % = 5 % of the class converting the portions of the class population to decimal weights , we find : class average = 0.45 x 95 + 0.50 x 78 + 0.05 x 60 = 84.75 the class average ( rounded ) is 85 % final answer c ) 85 %"
Answer: c
Question (general): on a certain day , orangeade was made by mixing a certain amount of orange juice with an equal amount of water . on the next day , orangeade was made by mixing the same amount of orange juice with twice the amount of water . on both days , all the orangeade that was made was sold . if the revenue from selling the orangeade was the same for both days and if the orangeade was sold at $ 0.30 per glass on the first day , what was the price per glass on the second day ?
Options: a ) $ 0.15 , b ) $ 0.20 , c ) $ 0.30 , d ) $ 0.40 , e ) $ 0.45
Rationale: "on the first day 1 unit of orange juice and 1 unit of water was used to make 2 units of orangeade ; on the second day 1 unit of orange juice and 2 units of water was used to make 3 units of orangeade ; so , the ratio of the amount of orangeade made on the first day to the amount of orangeade made on the second day is 2 to 3 . naturally the ratio of the # of glasses of orangeade made on the first day to the # of glasses of orangeade made on the second day is 2 to 3 . we are told thatthe revenue from selling the orangeade was the same for both daysso the revenue from 2 glasses on the first day equals to the revenue from 3 glasses on the second day . say the price of the glass of the orangeade on the second day was $ x then 2 * 0.3 = 3 * x - - > x = $ 0.2 . answer : b ."
Answer: b
Question (geometry): calculate the effect changes in dimension of a rectangle will have on its area , if length is increased by 40 % and its breadth is decreased by 25 % ?
Options: a ) 5 % increase , b ) 7 % increase , c ) 6 % increase , d ) 4 % increase , e ) 3 % increase
Rationale: "let l and b be 100 each 100 * 100 = 10000 l increase by 40 % = 140 b decrease by 25 % = 75 140 * 75 = 10500 5 % increase answer : a"
Answer: a
Question (general): if 3 / w + 3 / x = 3 / y and wx = y , then the average ( arithmetic mean ) of w and x is
Options: a ) 1 / 2 , b ) 1 , c ) 2 , d ) 4 , e ) 8
Rationale: "given : 3 / w + 3 / x = 3 / ywx = y find : ( w + x ) / 2 = ? 3 ( 1 / w + 1 / x ) = 3 ( 1 / y ) - divide both sides by 3 ( 1 / w + 1 / x ) = 1 / y ( x + w ) / wx = 1 / wx - sub ' d in y = wx x + w - 1 = 0 x + w = 1 therefore ( w + x ) / 2 = 1 / 2 ans : a"
Answer: a
Question (general): - - - - - - - - - - - - - - - - yes - - - - - - - - - no - - - - unsure subject m - - - - 500 - - - - - - - - 200 - - - - - 100 subject r - - - - 400 - - - - - - - - 100 - - - - - 300 a total of 800 students were asked whether they found two subjects , m and r , interesting . each answer was either yes or no or unsure , and the numbers of students who gave these answers are listed in the table above . if 140 students answered yes only for subject m , how many of the students did not answer yes for either subject ?
Options: a ) 100 , b ) 260 , c ) 360 , d ) 400 , e ) 500
Rationale: "since 140 students answered yes only for subject m , then the remaining 360 students who answered yes for subject m , also answered yes for subject r . so , 360 students answered yes for both subjects . if 360 students answered yes for both subjects , then 400 - 360 = 40 students answered yes only for subject r . so , we have that : 200 students answered yes only for subject m ; 40 students answered yes only for subject r ; 300 students answered yes for both subjects ; therefore 800 - ( 200 + 40 + 300 ) = 260 students did not answer yes for either subject . answer : b ."
Answer: b
Question (geometry): the area of a square field is 7201 sq m . how long will a lady take to cross the field diagonally at the rate of 2.4 km / hr ?
Options: a ) 2 min
b ) 3 min
c ) 4 min
d ) 5 min
e ) 6 min
Rationale: area of a square field = 7201 sq m let the side of square = a a ^ 2 = 7201 = > a = 84.86 diagonal = ( 2 ) ^ ( 1 / 2 ) * a = 1.414 * 84.86 = 120 speed of lady = 2.4 km / hour = 2400 m / hour = 40 m / min time taken by lady to cross the field diagonally = 120 / 40 = 3 min answer b
Answer: b
Question (physics): a man can do a piece of work in 7 days , but with the help of his son , he can finish it in 3 days . in what time can the son do it alone ?
Options: a ) 5 , b ) 4 1 / 5 , c ) 7 1 / 2 , d ) 6 , e ) 9 1 / 2
Rationale: "son ' s 1 day work = 1 / 3 - 1 / 7 = 5 / 21 son alone can do the work in 21 / 5 days = 4 1 / 5 days answer is b"
Answer: b
Question (other): 30 liters of a mixture contains milk and water in the ratio 2 : 1 . if 5 liters of this mixture be replaced by 5 liters of milk , the ratio of milk to water in the new mixture would be ?
Options: a ) 3 : 2 , b ) 3 : 1 , c ) 4 : 1 , d ) 5 : 2 , e ) 2 : 1
Rationale: "quantity of milk in 30 liters if mix = 30 * 2 / 3 = 20 liters quantity of milk in 35 liters of new mix = 20 + 5 = 25 liters quantity of water in it = 35 - 25 = 10 liters ratio of milk and water in new mix = 25 : 10 = 5 : 2 answer is d"
Answer: d
Question (general): if | 5 x - 25 | = 100 , then find the sum of the values of x ?
Options: a ) 1 , b ) - 2 , c ) 10 , d ) - 3 , e ) 4
Rationale: "| 5 x - 25 | = 100 5 x - 25 = 100 or 5 x - 25 = - 100 5 x = 125 or 5 x = - 75 x = 25 or x = - 15 sum = 25 - 15 = 10 answer is c"
Answer: c
Question (gain): running at the same constant rate , 6 identical machines can produce a total of 270 bottles per minute . at this rate , how many bottles could 8 such machines produce in 4 minutes ?
Options: a ) 648 , b ) 1800 , c ) 2700 , d ) 1440 , e ) none of these
Rationale: "solution let the required number of bottles be x . more machines , more bottles ( direct proportion ) more minutes , more bottles ( direct proportion ) â ˆ ´ 6 ã — 1 ã — x = 8 ã — 4 ã — 270 â ‡ ” x = 8 x 4 x 270 / 6 = 1440 . answer d"
Answer: d
Question (general): how many zeroes are there at the end of the number n , if n = 100 ! + 200 ! ?
Options: a ) 73 , b ) 49 , c ) 20 , d ) 48 , e ) 24
Rationale: "the number of zeroes at the end of 100 ! will be less than the number of zeroes at the end of 200 ! hence it would be sufficient to calculate the number of zeroes at the end of 100 ! number of zeroes = [ 100 / 5 ] + [ 100 / 25 ] + [ 100 / 125 ] = 20 + 4 + 0 = 24 correct option : e"
Answer: e
Question (general): a number when divided b the sum of 555 and 445 gives two times their difference as quotient and 30 as the remainder . the number is :
Options: a ) 1220 , b ) 1250 , c ) 2030 , d ) 22030 , e ) 1350
Rationale: required number = ( 555 + 445 ) * 2 * 110 + 30 = 220000 + 30 = 220030 . answer : d
Answer: d
Question (probability): if two dice are thrown together , the probability of getting an even prime number on the dice is
Options: a ) 1 / 36 , b ) 1 / 18 , c ) 1 / 13 , d ) 1 / 9 , e ) 5 / 36
Rationale: "the number of exhaustive outcomes is 36 . let e be the event of getting an even number prime number on the dice . p ( e ) = 1 / 36 a )"
Answer: a
Question (other): compound x contains elements a and b at an approximate ratio , by weight , of 2 : 10 . approximately how many grams of element b are there in 108 grams of compound x ?
Options: a ) 90 , b ) 162 , c ) 250 , d ) 270 , e ) 322
Rationale: "total number of fractions = 2 + 10 = 12 element b constitutes = 10 out of 12 parts of x so in 108 gms of x have 108 * 10 / 12 = 90 gms of b and 108 - 90 = 18 gms of a . cross check : - a / b = 18 / 90 = 2 / 10 ( as given ) ans a"
Answer: a
Question (general): find the greatest number that will divide 205 , 626 and 588 leaving 5 , 6 and 8 as remainders respectively
Options: a ) 19 , b ) 17 , c ) 13 , d ) 9 , e ) 20
Rationale: "explanation : answer will be hcf of ( 205 - 5 , 626 - 6 , 588 - 8 ) hcf of ( 200 , 626 , 580 ) = 20 option e"
Answer: e
Question (other): tough and tricky questions : ratios 4 / 5 of a certain class left on a field trip . 1 / 3 of the students who stayed behind did not want to go on the field trip ( all the others did want to go ) . when another vehicle was located , 1 / 2 of the students who did want to go on the field trip but had been left behind were able to join . what fraction of the class ended up going on the field trip ?
Options: a ) 1 / 2 , b ) 2 / 3 , c ) 13 / 15 , d ) 23 / 30 , e ) 4 / 5
Rationale: let total no . of students be 30 students left on a field trip = 4 / 5 ( 30 ) = 24 thus 6 students left behind 1 / 3 ( 6 ) = 2 students did not want to go . thus 4 students want to go on the trip 1 / 2 ( 4 ) = 2 were able to join the other students on the field trip . thus total number of students that went on a field trip = 24 + 2 = 26 thus required fraction = 26 / 30 = 13 / 15 c
Answer: c
Question (general): if x ^ 2 + 9 / x ^ 2 = 10 , what is the value of x - 3 / x
Options: a ) 36 , b ) 25 , c ) 2 , d ) 5 , e ) 3
Rationale: to find : x - 3 / x . let it be t . = > x - 3 / x = t = > ( x ^ 2 + 9 / x ^ 2 ) - 2 * x * 3 / x = t ^ 2 ( squaring both sides ) . = > ( 10 ) - 2 * 3 = 4 = > t ^ 2 = 4 . thus t = 2 or t = - 2 . answer c
Answer: c
Question (general): the average salary / head of all the workers in a workshop is rs . 1100 , if the average salary / head of 9 technician is rs . 1300 and the average salary / head of the rest is rs . 880 , the total no . of workers in the work - shop is ?
Options: a ) 18 , b ) 20 , c ) 22 , d ) 17 , e ) 26
Rationale: let the total number of workers be y . so sum of salary for all workers = sum of salary of 9 technician + sum of salary for other y - 9 workers . 9 x 1300 + 880 ( y - 9 ) = 1100 y ⇒ 11700 + 880 y - 7920 = 1100 y ⇒ 220 y = 3780 ∴ y = 17 so total number of workers = 17 d
Answer: d
Question (physics): in traveling from a dormitory to a certain city , a student went 1 / 5 of the way by foot , 2 / 3 of the way by bus , and the remaining 10 kilometers by car . what is the distance , in kilometers , from the dormitory to the city ?
Options: a ) 30 , b ) 45 , c ) 62 , d ) 90 , e ) 120
Rationale: "i believe there is a better way to do it . basically one of the options should satisfy the given criteria . 60 did 1 / 5 * 60 = 12 2 / 3 * 60 = 40 so total distance 52 + remaining 10 = 62 answer c"
Answer: c
Question (gain): joe invested a certain sum of money in a simple interest bond whose value grew to $ 310 at the end of 3 years and to $ 410 at the end of another 5 years . what was the rate of interest in which he invested his sum ?
Options: a ) 6 % , b ) 7 % , c ) 8 % , d ) 9 % , e ) 10 %
Rationale: "in 5 years , the value grew $ 100 , so the simple interest was $ 20 per year . in 3 years , the total interest was 3 * $ 20 = $ 60 the principal is $ 310 - $ 60 = 250 . the interest rate is $ 20 / $ 250 = 8 % the answer is c ."
Answer: c
Question (physics): a rhombus has area 432 sq m , one diagonal is 36 cm . find other diagonal ?
Options: a ) 2400 m
b ) 2500 m
c ) 2600 m
d ) 2700 m
e ) 2900 m
Rationale: area of rhombus = 1 / 2 * d 1 * d 2 432 = 1 / 2 * d 1 * . 36 d 1 = 2400 m answer : a
Answer: a
Question (general): if { x } is the product of all even integers from 1 to x inclusive , what is the greatest prime factor of { 12 } + { 10 } ?
Options: a ) 23 , b ) 20 , c ) 13 , d ) 5 , e ) 2
Rationale: "soln : { 12 } + { 10 } = 12 * { 10 } + { 10 } = 13 * { 10 } answer : c"
Answer: c
Question (gain): a , b and c invested rs . 2400 , rs . 7200 and rs . 9600 respectively , in a partnership business . find the share of a in profit of rs . 9000 after a year ?
Options: a ) 1125 , b ) 2400 , c ) 7200 , d ) 2500 , e ) 2511
Rationale: "explanation : 2400 : 7200 : 9600 1 : 3 : 4 1 / 8 * 9000 = 1125 answer : a"
Answer: a
Question (general): a women purchased 3 towels @ rs . 100 each , 5 towels @ rs . 150 each and two towels at a certain rate which is now slipped off from his memory . but she remembers that the average price of the towels was rs . 165 . find the unknown rate of two towels ?
Options: a ) a ) 400 , b ) b ) 450 , c ) c ) 500 , d ) d ) 550 , e ) e ) 600
Rationale: "10 * 150 = 1650 3 * 100 + 5 * 150 = 1050 1650 – 1050 = 600 e"
Answer: e
Question (physics): aaron will jog from home at 2 miles per hour and then walk back home by the same route at 4 miles per hour . how many miles from home can aaron jog so that he spends a total of 3 hours jogging and walking ?
Options: a ) 5 , b ) 7 , c ) 3 , d ) 9 , e ) 10
Rationale: xyt / ( x + y ) x = 2 , y = 4 t = 3 2 * 4 * 3 / 2 + 4 = 18 / 6 = 3 answer : c
Answer: c
Question (general): every year an amount increases by 1 / 8 th of itself . how much will it be after two years if its present value is rs . 57600 ?
Options: a ) 81000 , b ) 81028 , c ) 27772 , d ) 72900 , e ) 22312
Rationale: 57600 * 9 / 8 * 9 / 8 = 72900 . answer : d
Answer: d
Question (general): for each of her sales , a saleswoman receives a commission equal to 20 percent of the first $ 500 of the total amount of the sale , plus 35 percent of the total amount in excess of $ 500 . if the total amount of one of her sales was $ 800 , the saleswoman ’ s commission was approximately what percent of the total amount of the sale ?
Options: a ) 22 % , b ) 24 % , c ) 25 % , d ) 26 % , e ) 28 %
Rationale: "total sales = 800 comission = ( 20 / 100 ) * 500 + ( 35 / 100 ) * 300 = 100 + 105 = 205 % comission = ( 205 / 800 ) * 100 = 25.6 ~ 26 % answer is d"
Answer: d
Question (physics): a boat can travel with a speed of 22 km / hr in still water . if the speed of the stream is 5 km / hr , find the time taken by the boat to go 135 km downstream
Options: a ) 5 hours , b ) 4 hours , c ) 3 hours , d ) 2 hours , e ) none of these
Rationale: "explanation : speed of the boat in still water = 22 km / hr speed of the stream = 5 km / hr speed downstream = ( 22 + 5 ) = 27 km / hr distance travelled downstream = 135 km time taken = distance / speed = 135 / 27 = 5 hours . answer : option a"
Answer: a