Cheukting/mathqa huggingface dataset:
Question (general): a sum of money is to be distributed among a , b , c , d in the proportion of 5 : 2 : 4 : 3 . if c gets rs . 900 more than d , what is b ' s share ?
Options: a ) rs . 500 , b ) rs . 1800 , c ) rs . 2000 , d ) rs . 2500 , e ) none of the above
Rationale: "let the shares of a , b , c and d be rs . 5 x , rs . 2 x , rs . 4 x and rs . 3 x respectively . then , 4 x - 3 x = 900 x = 900 . b ' s share = rs . 2 x = rs . ( 2 x 900 ) = rs . 1800 . answer = b"
Answer: b
Question (physics): the speed at which a man can row a boat in still water is 14 kmph . if he rows downstream , where the speed of current is 2 kmph , what time will he take to cover 40 metres ?
Options: a ) 16 seconds , b ) 34 seconds , c ) 9 seconds , d ) 12 seconds , e ) 15 seconds
Rationale: "speed of the boat downstream = 14 + 2 = 16 kmph = 16 * 5 / 18 = 40 / 9 m / s hence time taken to cover 40 m = 40 * 9 / 40 = 9 seconds . answer : c"
Answer: c
Question (general): a , b and c started a business with a total investment of rs . 90000 . a invests rs . 6000 more than b and b invests rs . 3000 less than c . if the total profit at the end of a year is rs . 8640 , find c ' s share .
Options: a ) rs . 3240 , b ) rs . 2520 , c ) rs . 2880 , d ) rs . 3360 , e ) none of these
Rationale: "explanation : let c ' s investment = rs . x b ' s investment = rs . ( x - 3000 ) a ' s investment = rs . ( x - 3000 + 6000 ) = rs . ( x + 3000 ) now , ( a + b + c ) ' s investment = rs . 90000 = > x + ( x - 3000 ) + ( x + 3000 ) = 90000 = > 3 x = 90000 = > x = 30000 hence , a ' s investment = rs . 33000 b ' s investment = rs . 27000 c ' s investment = rs . 30000 ratio of the capitals of a , b and c = 33000 : 27000 : 30000 = 11 : 9 : 10 a ' s share = rs . [ ( 10 / 30 ) ã — 8640 ] = rs . 2880 answer : option c"
Answer: c
Question (general): the ratio of the present age of sandy to that of molly is 9 : 2 . sixteen years from now , the ratio of the ages of sandy to molly will be 5 : 2 . what was sandy ' s age 6 years ago ?
Options: a ) 30 , b ) 36 , c ) 42 , d ) 48 , e ) 54
Rationale: "let the present age of sandy be 9 x years and that of molly be 2 x years . ( 9 x + 16 ) / ( 2 x + 16 ) = 5 / 2 8 x = 48 x = 6 six years ago , sandy ' s age was 9 ( 6 ) - 6 = 48 the answer is d ."
Answer: d
Question (general): how many 3 - digits number are palindromic numbers ? a palindromic number reads the same forward and backward , example 121 .
Options: a ) 90 , b ) 610 , c ) 729 , d ) 900 , e ) 1000
Rationale: "take the task of building palindromes and break it intostages . stage 1 : select the hundreds digit we can choose 1 , 2 , 3 , 4 , 5 , 6 , 7 , 8 , or 9 so , we can complete stage 1 in 9 ways stage 2 : select the tens digit we can choose 0 , 1 , 2 , 3 , 4 , 5 , 6 , 7 , 8 , or 9 so , we can complete stage 2 in 10 ways important : at this point , the remaining digits are alreadylocked in . stage 3 : select the units digit this digit must be the same as the thousands digit ( which we already chose in stage 2 ) so , we can complete this stage in 1 way . by thefundamental counting principle ( fcp ) , we can complete all 5 stages ( and thus build a 3 - digit palindrome ) in ( 9 ) ( 10 ) ( 1 ) ways ( = 900 ways ) answer : a"
Answer: a
Question (general): the average of the 5 numbers is 6.8 . if one of the numbers is multiplied by 3 , the average of the numbers increases to 9.2 . which of the 5 numbers is multiplied by 3 ?
Options: a ) 1.5 , b ) 3.0 , c ) 3.9 , d ) 4.0 , e ) 6.0
Rationale: initial avg is 6.8 so the summation of the nos is 6.8 * 5 = 34 now the new avg is 9.2 so summation will be 9.2 * 5 = 46 . so change in summation is 12 . this comes when a number is multiplied by 3 . in the original sum we already have that number added once . to bring additional 12 increment by multiplying by 3 , we get a total increase of 18 . thus , 6 is multiplied by 3 . answer : e
Answer: e
Question (general): ( 3192 + 6160 ) / 28
Options: a ) 380 , b ) 350 , c ) 334 , d ) 310 , e ) none of these
Rationale: "explanation : as per bodmas rule , first we will solve the equation in bracket then we will go for division = ( 9352 ) / 28 = 334 option c"
Answer: c
Question (general): a ferry can transport 100 tons of vehicles . automobiles range in weight from 1,800 to 3,200 pounds . what is the greatest number of automobiles that can be loaded onto the ferry ?
Options: a ) 115 , b ) 120 , c ) 110 , d ) 100 , e ) 90
Rationale: "to get maximum vehicles we must take into consideration the minimum weight i . e 1800 pounds here since , 1 ton = 2000 pounds 78 tons will be 200,000 pounds from the answer choices : let max number of vehicles be 110 total weight will be = 110 * 1800 = 198000 pounds , which is lesser than the maximum weight allowed . ans : c"
Answer: c
Question (general): when positive integer n is divided by positive integer j , the remainder is 25 . if n / j = 204.05 , what is value of j ?
Options: a ) 600 , b ) 500 , c ) 800 , d ) 200 , e ) 900
Rationale: "when a number is divided by another number , we can represent it as : dividend = quotient * divisor + remainder so , dividend / divisor = quotient + remainder / divisor given that n / j = 204.05 here 204 is the quotient . given that remainder = 25 so , 204.05 = 204 + 25 / j so , j = 500 answer : b"
Answer: b
Question (general): a , b , c subscribe rs . 50000 for a business . a subscribes rs . 4000 more than b and b rs . 5000 more than c . out of a total profit of rs . 30000 , b receives :
Options: a ) s . 10,000 , b ) s . 10,200 , c ) s . 10,400 , d ) s . 10,700 , e ) s . 10,800
Rationale: let c = x . then , b = x + 5000 and a = x + 5000 + 4000 = x + 9000 . so , x + x + 5000 + x + 9000 = 50000 3 x = 36000 x = 12000 a : b : c = 21000 : 17000 : 12000 = 21 : 17 : 12 . b ' s share = rs . ( 30000 x 17 / 50 ) = rs . 10,200 . b
Answer: b
Question (physics): a man swims downstream 48 km and upstream 18 km taking 3 hours each time , what is the speed of the man in still water ?
Options: a ) 2 , b ) 8 , c ) 9 , d ) 11 , e ) 14
Rationale: "48 - - - 3 ds = 16 ? - - - - 1 18 - - - - 3 us = 6 ? - - - - 1 m = ? m = ( 16 + 6 ) / 2 = 11 answer : d"
Answer: d
Question (physics): if the population of a certain country increases at the rate of one person every 30 seconds , by how many persons does the population increase in 10 minutes ?
Options: a ) 20 , b ) 30 , c ) 15 , d ) 10 , e ) 80
Rationale: "answer = 2 * 10 = 20 answer = a"
Answer: a
Question (physics): a can complete a project in 20 days and b can complete the same project in 30 days . if a and b start working on the project together and b quits 15 days before the project is completed , in how many days total will the project be completed ?
Options: a ) 12 , b ) 14 , c ) 16 , d ) 18 , e ) 20
Rationale: "a ' s rate is 1 / 20 of the project per day . b ' s rate is 1 / 30 of the project per day . the combined rate is 1 / 12 of the project per day . in the last 15 days , a can do 3 / 4 of the project . thus a and b must complete 1 / 4 of the project , which takes 3 days . the total number of days is 3 + 15 = 18 . the answer is d ."
Answer: d
Question (probability): a meeting has to be conducted with 4 managers . find the number of ways in which the managers be selected from among 7 managers , if 2 managers will not attend the meeting together ?
Options: a ) 25 , b ) 20 , c ) 35 , d ) 36 , e ) 38
Rationale: "we can either choose all 4 people from 5 manager who have no problems or choose 3 from the 5 and 1 from the 2 managers who have a problem sitting together so 5 c 4 + ( 5 c 3 * 2 c 1 ) this is 5 + 20 = 25 answer : a"
Answer: a
Question (physics): two trains each 150 m in length each , are running on two parallel lines in opposite directions . if one goes at the speed of 95 km / h while the other travels at 85 km / h . how long will it take for them to pass each other completely .
Options: a ) 25 sec , b ) 23 sec , c ) 34 sec , d ) 22 sec , e ) 6 sec
Rationale: "explanation : d = 150 m + 150 m = 300 m rs = 95 + 85 = 180 * 5 / 18 = 50 t = 300 * 1 / 50 = 6 sec answer : option e"
Answer: e
Question (physics): p is 10 % more efficient than q . p can complete a work in 21 days . if p and q work together , how many days will it take to complete the same work ?
Options: a ) 7 , b ) 9 , c ) 11 , d ) 13 , e ) 15
Rationale: "the work done by p in 1 day = 1 / 21 let work done by q in 1 day = q q × ( 110 / 100 ) = 1 / 21 q = 100 / ( 21 × 110 ) = 10 / ( 21 × 11 ) the work done by p and q in 1 day = 1 / 21 + 10 / ( 21 × 11 ) = 21 / ( 21 × 11 ) = 1 / 11 p and q together can do the work in 11 days . the answer is c ."
Answer: c
Question (general): the average weight of a , b and c is 44 kg . if the average weight of a and b be 40 kg and that of b and c be 43 kg , then the weight of b is :
Options: a ) 17 kg , b ) 28 kg , c ) 26 kg , d ) 31 kg , e ) 35 kg
Rationale: "let d sum of a , b , c is 3 * 44 = 132 and sum of a and b s 2 * 40 = 80 sum of b and c is 2 * 43 = 86 hence 80 + 86 - 132 = 28 ans = 28 answer : b"
Answer: b
Question (physics): a , b , k start from the same place and travel in the same direction at speeds of 30 km / hr , 40 km / hr , 100 km / hr respectively . b starts two hours after a . if b and k overtake a at the same instant , how many hours after a did k start ?
Options: a ) 4.2 , b ) 4.8 , c ) 5.6 , d ) 6.4 , e ) 7.2
Rationale: "in 2 hours , a travels 60 km . b can catch a at a rate of 10 km / hr , so b catches a 6 hours after b starts . so a and b both travel a distance of 240 km . c needs 2.4 hours to travel 240 km , so c leaves 5.6 hours after a . the answer is c ."
Answer: c
Question (gain): a shopkeeper bought 600 oranges and 400 bananas . he found 15 % of oranges and 4 % of bananas were rotten . find the percentage of fruits in good condition ?
Options: a ) 92.5 % , b ) 89.4 % , c ) 85.2 % , d ) 96.8 % , e ) 78.9 %
Rationale: "total number of fruits shopkeeper bought = 600 + 400 = 1000 number of rotten oranges = 15 % of 600 = 15 / 100 × 600 = 9000 / 100 = 90 number of rotten bananas = 4 % of 400 = 16 therefore , total number of rotten fruits = 90 + 16 = 106 therefore number of fruits in good condition = 1000 - 106 = 894 therefore percentage of fruits in good condition = ( 894 / 1000 × 100 ) % = ( 89400 / 1000 ) % = 89.4 % answer : b"
Answer: b
Question (physics): james took a 3 - hour bike ride . in the second hour he travlled 18 miles , which was 20 percent farther than he traveled the first hour . if he traveled 25 percent farther in the third hour than he did in the second hour , how many miles did jose travel during the entire ride ?
Options: a ) 54.0 , b ) 54.9 , c ) 55.5 , d ) 57.0 , e ) 63.0
Rationale: let the distance travelled in the first hour be x . thus , 1.2 x = 18 , x = 15 . now , the distance travelled in the 3 rd hour = 18 + 1 / 4 ∗ 18 = the only option ending with a 0.5 in the decimal place is c . answer : c
Answer: c
Question (gain): by weight , liquid x makes up 2 percent of solution p and 7.5 percent of solution q . if 400 grams of solution p are mixed with 600 grams of solution q , then liquid x accounts for what percent of the weight of the resulting solution ?
Options: a ) 4.5 % , b ) 4.7 % , c ) 4.9 % , d ) 5.1 % , e ) 5.3 %
Rationale: "the number of grams of liquid x is 2 ( 400 ) / 100 + 7.5 ( 600 ) / 100 = 8 + 45 = 53 grams . 53 / 1000 = 5.3 % the answer is e ."
Answer: e
Question (physics): a train traveling at 216 kmph crosses a platform in 30 seconds and a man standing on the platform in 12 seconds . what is the length of the platform in meters ?
Options: a ) 240 meters , b ) 360 meters , c ) 420 meters , d ) 720 meters , e ) can not be determined
Rationale: "answer distance covered by the train when crossing a man and when crossing a platform when a train crosses a man standing on a platform , the distance covered by the train is equal to the length of the train . however , when the same train crosses a platform , the distance covered by the train is equal to the length of the train plus the length of the platform . the extra time that the train takes when crossing the platform is on account of the extra distance that it has to cover . i . e . , length of the platform . compute length of platform length of the platform = speed of train * extra time taken to cross the platform . length of platform = 216 kmph * 12 seconds convert 216 kmph into m / sec 1 kmph = 5 / 18 m / s ( this can be easily derived . but if you can remember this conversion , it saves a good 30 seconds ) . ∴ 216 kmph = 5 / 18 ∗ 216 = 60 m / sec therefore , length of the platform = 60 m / s * 12 sec = 720 meters . choice d"
Answer: d
Question (physics): for my anniversary , i decided to surprise my wife . since she is a voracious reader , i decided to collect a lot of books for her . on the first day of the month , i bought one book , on the second , i bought two and on the third , i bought three . this process went on till the anniversary and on the day , i had 190 books with me to gift her . can you calculate , on which day is our anniversary ?
Options: a ) 31 , b ) 28 , c ) 19 , d ) 33 , e ) 25
Rationale: c 19 rd day 1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9 + 10 + 11 + 12 + 13 + 14 + 15 + 16 + 17 + 18 + 19 = 190 thus our anniversary falls on the 19 rd day of the month . you can apply other formulas to shorten the process but that is the simplest way to do it .
Answer: c
Question (physics): at a tanning salon , customers are charged $ 10 for their first visit in a calendar month and $ 3 for each visit after that in the same calendar month . in the last calendar month , 100 customers visited the salon , of which 30 made a second visit , and 10 made a third visit . all other customers made only one visit . if those visits were the only source of revenue for the salon , what was the revenue for the last calendar month at the salon ?
Options: a ) $ 1220 , b ) $ 1120 , c ) $ 1300 , d ) $ 1340 , e ) $ 1880
Rationale: "i get b . this question seems too straightforward for 600 + . am i missing something ? 100 first - time visits - - > 100 ( 10 ) = $ 1000 30 + 10 = 40 subsequent visits - - > 40 ( 3 ) = $ 120 total revenue : 1000 + 120 = $ 1120 the answer is b ."
Answer: b
Question (general): there are 7 players in a bowling team with an average weight of 94 kg . if two new players join the team , one weighs 110 kg and the second weighs 60 kg , what will be the new average weight ?
Options: a ) 75 kg . , b ) 80 kg . , c ) 86 kg . , d ) 90 kg . , e ) 92 kg .
Rationale: "the new average will be = ( 94 * 7 + 110 + 60 ) / 9 = 92 kgs e is the answer"
Answer: e
Question (general): the average weight of 12 person ' s increases by 4 kg when a new person comes in place of one of them weighing 58 kg . what is the weight of the new person ?
Options: a ) 85 , b ) 80 , c ) 95 , d ) 90 , e ) 106
Rationale: "total increase in weight = 12 × 4 = 48 if x is the weight of the new person , total increase in weight = x − 58 = > 48 = x - 58 = > x = 48 + 58 = 106 answer : e"
Answer: e
Question (geometry): a cube 125 mt is colored pink on two opposite surfaces and then cut in to 125 smaller cubes then find how many number of cubes have pink color ?
Options: a ) 3
b ) 4
c ) 5
d ) 6
e ) 7
Rationale: answer : b
Answer: b
Question (other): 6 ) a marketing firm determined that , of 180 households surveyed , 80 used neither brand a nor brand b soap . 60 used only brand a soap and for every household that used both brands of soap , 3 used only brand b soap . how many of the 200 household surveyed used both brands of soap ?
Options: a ) a ) 15 , b ) b ) 20 , c ) c ) 30 , d ) d ) 10 , e ) e ) 45
Rationale: 100 = at least one of soap a or b both brands = x brand b = 3 x = > 60 + x + 3 x = 100 = > 4 x = 40 = > x = 10 answer - d
Answer: d
Question (physics): one machine takes 3 minutes to check fault in 100 km fiber optic cable . another machine does the same job in 3 seconds . what time will it take to do the same job when both machines are put to work ?
Options: a ) 2.00 seconds , b ) 2.20 seconds , c ) 2.50 seconds , d ) 2.95 seconds , e ) 3.00 seconds
Rationale: by guess it is clear that the time taken will be less than 3 seconds and very near to it . therefore , answer 2.95 seconds will be correct . answer - d
Answer: d
Question (general): a certain telescope increases the visual range at a particular location from 60 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 ) 150 %
Rationale: "original visual range = 60 km new visual range = 150 km percent increase in the visual range by using the telescope = ( 150 - 60 ) / 60 * 100 % = 3 / 2 * 100 % = 150 % answer e"
Answer: e
Question (gain): a small company reduced its faculty by approximately 13 percent to 181 employees . what was the original number of employees ?
Options: a ) a ) 182 , b ) b ) 208 , c ) c ) 220 , d ) d ) 224 , e ) e ) 302
Rationale: "if x is the original number of employees , then after 13 % reduction in employees number is . 87 x but we are given . 87 x = 181 x = 208 so the original number of employees is 208 correct answer - b"
Answer: b
Question (geometry): 66 small identical cubes are used to form a large cube . how many more cubes are needed to add one top layer of small cube all over the surface of the large cube ?
Options: a ) 64 , b ) 150 , c ) 152 , d ) 216 , e ) 256
Rationale: "66 small cube will make a large cube with 4 cubes in each line i . e . adding one layer will require one cube at each end and hence new cube will have 6 cubes in each line . total number of small cubes in new cube = 6 ^ 3 = 216 extra cube required = 216 - 66 = 150 hence , b is the answer ."
Answer: b
Question (general): 0.9 * 0.007 = ­ ­ ­ ­ ­ ­ ­ ­ ­ ­ _________
Options: a ) 0.063 , b ) 0.0063 , c ) 0.63 , d ) 0.00063 , e ) 63
Rationale: 9 * 7 = 63 sum of decimal places = 4 so , 0.9 * 0.007 = 0.0063 answer : b
Answer: b
Question (physics): a train passes a station platform in 31 sec and a man standing on the platform in 20 sec . if the speed of the train is 54 km / hr . what is the length of the platform ?
Options: a ) 228 , b ) 240 , c ) 165 , d ) 166 , e ) 1811
Rationale: "speed = 54 * 5 / 18 = 15 m / sec . length of the train = 15 * 20 = 300 m . let the length of the platform be x m . then , ( x + 300 ) / 31 = 15 = > x = 165 m . answer : c"
Answer: c
Question (geometry): the length of a rectangular garden is three times its width . if the area of the rectangular garden is 768 square meters , then what is the width of the rectangular garden ?
Options: a ) 16 , b ) 17 , c ) 18 , d ) 19 , e ) 20
Rationale: "let x be the width of the garden . 3 x ^ 2 = 768 x ^ 2 = 256 x = 16 the answer is a ."
Answer: a
Question (gain): mr . hernandez , who was a resident of state x for only 9 months last year , had a taxable income of $ 42,500 for the year . if the state tax rate were 4 percent of the year ’ s taxable income prorated for the proportion of the year during which the taxpayer was a resident , what would be the amount of mr . hernandez ’ s state x tax for last year ?
Options: a ) $ 900 , b ) $ 1275 , c ) $ 1200 , d ) $ 1300 , e ) $ 1060
Rationale: total tax for the year = 42,500 x 4 % = 1700 as stated annual tax is prorated as per the duration of stay . prorated tax = 1700 ( 9 / 12 ) = 1275 answer b
Answer: b
Question (gain): if a man lost 10 % by selling oranges at the rate of 10 a rupee at how many a rupee must he sell them to gain 50 % ?
Options: a ) 6 , b ) 8 , c ) 7 , d ) 4 , e ) 2
Rationale: "90 % - - - - 10 150 % - - - - ? 90 / 150 * 10 = 6 answer : a"
Answer: a
Question (gain): a candidate appearing for an examination has to secure 42 % marks to pass paper i . but he secured only 42 marks and failed by 22 marks . what is the maximum mark for paper i ?
Options: a ) 110 , b ) 120 , c ) 130 , d ) 152 , e ) 150
Rationale: "he secured 42 marks nd fail by 22 marks so total marks for pass the examinatn = 64 let toal marks x x * 42 / 100 = 64 x = 152 answer : d"
Answer: d
Question (general): if ( - 3 ) ^ ( 2 x ) = 3 ^ ( 12 - x ) and x is an integer , what is the value of x ?
Options: a ) 5 , b ) 4 , c ) 3 , d ) 2 , e ) 1
Rationale: since x is an integer , ( - 3 ) ^ ( 2 x ) is always positive . so , 3 ^ 2 x = 3 ^ ( 12 - x ) 2 x = 12 - x 3 x = 12 x = 4 answer : b
Answer: b
Question (general): in a division sum , the divisor is 10 times the quotient and 5 times the remainder . if the remainder is 46 , what is the dividend ?
Options: a ) 5336 , b ) 5242 , c ) 6524 , d ) 3526 , e ) 4526
Rationale: "divisor = ( 5 * 46 ) = 230 10 * quotient = 230 quotient = 230 / 10 = 23 . dividend = ( divisor * quotient ) + remainder = ( 230 * 23 ) + 46 = ( 5290 + 46 ) = 5336 . answer is a"
Answer: a
Question (geometry): find the perimeter and area of a square of side 11 cm .
Options: a ) 11 cm ² , b ) 21 cm ² , c ) 22 cm ² , d ) 113 cm ² , e ) 121 cm ²
Rationale: "we know that the perimeter of square = 4 × side side = 11 cm therefore , perimeter = 4 × 11 cm = 44 cm now , area of the square = ( side × side ) sq . units = 11 × 11 cm ² = 121 cm ² answer : option e"
Answer: e
Question (gain): a company plans to gradually replace its fleet of 20 cars with newer models . at the end of every year starting with 2000 it retires 5 of its old cars and buys 6 new models . how many years did it take before the number of older cars left in the company ' s fleet was less than 50 percent of the fleet ?
Options: a ) 6 , b ) 3 , c ) 2 , d ) 4 , e ) 5
Rationale: total fleet - - 20 end of year 2000 - - ( retires 5 and buys 6 ) total fleet - - 21 ( 15 old 6 new ) . end of year 2001 - - ( retires 5 and buys 6 ) total fleet - - 22 ( 10 old 12 new ) . answer is c - - after 2 years the company has a total of 22 cars ( 10 old 12 new ) , the old cars are already less than 50 % of its fleet .
Answer: c
Question (geometry): the ratio of radius of a circle and the side of a square is 2 : 3 . find the ratio of their areas :
Options: a ) 2 : 1 , b ) 4 : 9 , c ) 8 : 77 , d ) 4 : 121 , e ) none
Rationale: "radius / side = 2 / 3 â ‡ ’ area of circle / area of square = 4 / 9 answer : b"
Answer: b
Question (gain): find the compound interest on $ 500 in 5 years at 5 % per annum , the interest being compounded yearly ?
Options: a ) $ 138.14 , b ) $ 150.12 , c ) $ 142.65 , d ) $ 152 , e ) $ 164.12
Rationale: "principle = $ 500 rate = 5 % yearly amount = 500 * ( 1 + 5 / 100 ) ^ 5 = 500 * 21 / 20 * 21 / 20 * 21 / 20 * 21 / 20 * 21 / 20 = $ 638.14 c . i . = 638.14 - 500 = $ 138.14 answer is a"
Answer: a
Question (general): during 2003 , a company produced an average of 1,000 products per month . how many products will the company need to produce from 2004 through 2007 in order to increase its monthly average for the period from 2003 through 2007 by 200 % over its 2003 average ?
Options: a ) 132,000 , b ) 235,000 , c ) 175,000 , d ) 200,000 , e ) 250,000
Rationale: "company produced 12 * 1000 = 12,000 products in 2003 . if company produces x products from 2004 to 2007 , then total amount of product produced in 4 years ( 2003 through 2007 ) is x + 12,000 . the gives the average of ( x + 12,000 ) / 4 . this average needs to be 200 % higher than that in 2003 . in math terms , 12,000 + 200 % ( 12,000 ) = 36,000 . so : ( x + 12,000 ) / 4 = 36,000 x + 12,000 = 144,000 x = 132,000 the answer is a ."
Answer: a
Question (general): the sum of two numbers is 45 . their difference is 5 . the bigger number is
Options: a ) 20 , b ) 25 , c ) 30 , d ) 35 , e ) 45
Rationale: x + y = 45 x - y = 5 adding 2 x = 50 = = > x = 25 and y = 45 - 25 = 20 bigger number is x = 25 answer b .
Answer: b
Question (gain): the present worth of rs . 338 due in 2 years at 4 % per annum compound interest is
Options: a ) rs . 312.5 , b ) rs . 154.75 , c ) rs . 156.25 , d ) rs . 158 , e ) none
Rationale: "solution present worth = rs . [ 338 / ( 1 + 4 / 100 ) ² ] = rs . ( 338 x 25 / 26 x 25 / 26 ) = rs . 312.5 answer a"
Answer: a
Question (general): the average of 6 observations is 11 . a new observation is included and the new average is decreased by 1 . the seventh observation is ?
Options: a ) 4 , b ) 3 , c ) 5 , d ) 6 , e ) 7
Rationale: "let seventh observation = x . then , according to the question we have = > ( 66 + x ) / 7 = 10 = > x = 4 . hence , the seventh observation is 4 . answer : a"
Answer: a