Cheukting/mathqa huggingface dataset:
Question (general): 6 chess players take part in a tournament . every player plays twice with each of his opponents . how many games are to be played ?
Options: a ) 19 , b ) 20 , c ) 30 , d ) 33 , e ) 34
Rationale: "though 2 * ( 6 c 2 ) is the correct approcah to do this , but for people like me who find perm , comb n prob a nightmare , an easy approach can be used . the first guy has to play 2 matches with the rest of 5 , so he ' ll play 10 matches . similarly , second guy has to play with the rest of 4 as his 2 games with the first guy are already played . so he plays 8 matches . this continues like this and the total matches are 10 + 8 + 6 . . . + 2 10 + 8 + . . . + 2 = 2 ( 5 + 4 + . . . + 1 ) = 2 ( ( 5 * 6 ) / 2 ) = 5 * 6 = 30 . answer : c"
Answer: c
Question (physics): the time taken by a man to row his boat upstream is twice the time taken by him to row the same distance downstream . if the speed of the boat in still water is 51 kmph , find the speed of the stream ?
Options: a ) 12 kmph , b ) 13 kmph , c ) 14 kmph , d ) 15 kmph , e ) 17 kmph
Rationale: "the ratio of the times taken is 2 : 1 . the ratio of the speed of the boat in still water to the speed of the stream = ( 2 + 1 ) / ( 2 - 1 ) = 3 / 1 = 3 : 1 speed of the stream = 51 / 3 = 17 kmph answer : e"
Answer: e
Question (general): the average ( arithmetic man ) of 3 integers a , b , and c is exactly 4 times the median . if a < b < c and a = 0 , what is the value of c / b ?
Options: a ) 2 , b ) 3 , c ) 4 , d ) 11 , e ) can not be determined from the information given .
Rationale: the average of three integers a , b , and c is exactly twice the median - - > ( a + b + c ) / 3 = 4 b - - > since a = 0 , then ( 0 + b + c ) / 3 = 4 b - - > c = 11 b - - > c / b = 11 . answer : d .
Answer: d
Question (general): in 1950 , richard was 4 times as old as robert . in 1955 , richard was 3 times as old as robert . in which year was richard 1.75 times as old as robert ?
Options: a ) 1960 , b ) 1965 , c ) 1970 , d ) 1975 , e ) 1980
Rationale: "in 1950 : ri = 4 ro - - - - - - - - - - - - - - eq 1 in 1955 : ri + 5 = 3 ( ro + 5 ) - - - - - - - - - eq 2 thus in 1950 , solving eq 1 and eq 2 ro = 10 , ri = 40 now for each year we can calculate : 1960 : ri = 50 , ro = 20 1965 : ri = 55 , ro = 25 1980 : ri = 40 , ro = 70 thus 8 ans : e"
Answer: e
Question (gain): raman ' s salary was decreased by 50 % and subsequently increased by 50 % . how much percent does he loss
Options: a ) 75 , b ) 65 , c ) 45 , d ) 25 , e ) 35
Rationale: "explanation : let the origianl salary = rs . 100 it will be 150 % of ( 50 % of 100 ) = ( 150 / 100 ) * ( 50 / 100 ) * 100 = 75 so new salary is 75 , it means his loss is 25 % answer : option d"
Answer: d
Question (gain): a dishonest shopkeeper professes to sell pulses at the cost price , but he uses a false weight of 930 gm . for a kg . his gain is … % .
Options: a ) 5.26 % , b ) 5.36 % , c ) 4.26 % , d ) 6.26 % , e ) 7.53 %
Rationale: "his percentage gain is 100 * 7 / 930 as he is gaining 70 units for his purchase of 930 units . so 7.53 % . answer : e"
Answer: e
Question (gain): the majority owner of a business received 25 % of the profit , with each of 4 partners receiving 25 % of the remaining profit . if the majority owner and two of the owners combined to receive $ 62,500 , how much profit did the business make ?
Options: a ) $ 100,000 , b ) $ 125,000 , c ) $ 150,000 , d ) $ 200,000 , e ) $ 250,000
Rationale: "majority owner + two partners = 0.25 * p + 2 * ( 0.25 ) * ( 0.75 ) * p = 0.25 * p + ( 0.5 ) * ( 0.75 ) * p = 0.25 * p + ( 0.375 ) * p = ( 0.625 ) * p this equals $ 62,500 . ( 0.625 ) * p = 62,500 - - - - - divide both sides by 625 ( 0.001 ) * p = 100 - - - - - - multiply by 1000 p = 100,000 answer = a"
Answer: a
Question (general): when a random experiment is conducted , the probability that event a occurs is 1 / 5 . if the random experiment is conducted 4 independent times , what is the probability that event a occurs exactly twice ?
Options: a ) 16 / 625 , b ) 56 / 625 , c ) 96 / 625 , d ) 126 / 625 , e ) 156 / 625
Rationale: "one case is : 1 / 5 * 1 / 5 * 4 / 5 * 4 / 5 = 16 / 625 the total number of possible cases is 4 c 2 = 6 p ( event a occurs exactly twice ) = 6 * ( 16 / 625 ) = 96 / 625 the answer is c ."
Answer: c
Question (physics): two trains are moving in opposite directions at 60 km / hr and 90 km / hr . their lengths are 1.10 km and 0.9 km respectively . the time taken by the slower train to cross the faster train in seconds is :
Options: a ) 28 sec , b ) 36 sec , c ) 48 sec , d ) 52 sec , e ) 56 sec
Rationale: "relative speed = ( 60 + 90 ) km / hr = 150 x 5 / 18 = 120 / 3 m / sec distance covered = ( 1.10 + 0.9 ) km = 2 km = 2000 m . required time = 2000 x 3 / 125 = 48 sec . answer : c ."
Answer: c
Question (general): a 6 - liter solution is 30 % alcohol . how many liters of pure alcohol must be added to produce a solution that is 50 % alcohol ?
Options: a ) 1.8 , b ) 2.1 , c ) 2.4 , d ) 2.7 , e ) 3.0
Rationale: "let x be the amount of pure alcohol required . 0.3 ( 6 ) + x = 0.5 ( x + 6 ) 0.5 x = 3 - 1.8 x = 2.4 liters the answer is c ."
Answer: c
Question (general): find the average of all the numbers between 17 and 32 which are divisible by 3 .
Options: a ) 15 , b ) 18 , c ) 20 , d ) 26 , e ) none
Rationale: "sol . average = ( 21 + 24 + 27 + 30 / 4 ) = 102 / 4 = 25.5 answer d"
Answer: d
Question (physics): a boat can travel with a speed of 13 km / hr in still water . if the speed of the stream is 4 km / hr . find the time taken by the boat to go 72 km downstream ?
Options: a ) 2 hours , b ) 4 hours 12 minutes , c ) 4 hours , d ) 5 hours , e ) none
Rationale: "solution speed downstream = ( 13 + 4 ) km / hr = 17 km / hr . time taken to travel 72 km downstream = ( 72 / 17 ) hrs = 4 hrs 12 minutes . answer b"
Answer: b
Question (general): if you add all the numbers on your mobile phone , what is the answer ?
Options: a ) 45 , b ) 50 , c ) 55 , d ) 100 , e ) 60
Rationale: 0 , 1 , 2 , 3 , 4 , 5 , 6 , 7 , 8 , 9 are in your mobile phone . therefore 0 + 1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9 = 45 answer is a
Answer: a
Question (general): what is the sum of the integers from - 190 to 192 inclusive ?
Options: a ) 0 , b ) 5 , c ) 383 , d ) 875 , e ) 965
Rationale: "sum / n = average . sum = ( average ) ( n ) average = a + b / 2 = 190 + 192 / 2 = 1 number of items ( n ) = b - a + 1 = 192 - ( - 190 ) + 1 = 192 + 191 = 383 . sum = average * n = 1 * 383 = 383 . answer is c"
Answer: c
Question (gain): if $ 650 is deposited into a savings account at an annual interest rate of 5 % that compounds monthly , what is the value of the investment after 7 years ?
Options: a ) $ 750.00 , b ) $ 823.50 , c ) $ 973.25 , d ) $ 921.75 , e ) $ 110.00
Rationale: using ci formula : a = p ( 1 + r / n ) ^ n * t a = 650 ( 1 + 5 / 7 ) ^ 5 * 7 a = 921.75 option : d
Answer: d
Question (gain): in a certain candy store , 22 % of the customers are caught sampling the candy and are charged a small fine , but 15 % of the customers who sample the candy are not caught . what is the total percent of all customers who sample candy ?
Options: a ) 22 % , b ) 23 % , c ) 24 % , d ) 26 % , e ) 34 %
Rationale: since 15 % of the customers who sample the candyare notcaught , then 88 % of the customers who sample the candyarecaught : { % of customers who sample candy } * 0.85 = 0.22 ; { % of customers who sample candy } = 0.259 answer : d .
Answer: d
Question (general): the jogging track in a sports complex is 561 m in circumference . deepak and his wife start from the same point and walk in opposite directions at 4.5 km / hr and 3.75 km / hr respectively . they will meet for the first time in ?
Options: a ) 5.29 min , b ) 5.28 min , c ) 4.08 min , d ) 9.28 min , e ) 5.988 min
Rationale: clearly , the two will meet when they are 561 m apart . to be ( 4.5 + 3.75 ) = 8.25 km apart , they take 1 hour . to be 561 m apart , they take ( 100 / 825 * 561 / 1000 ) hrs = ( 561 / 8250 * 60 ) min = 4.08 min . answer : c
Answer: c
Question (gain): at a small company , 76 percent of the employees are women , and 60 percent of the employees are married . if 2 / 3 of the men are single , what fraction of the women are married ?
Options: a ) 13 / 19 , b ) 1 / 3 , c ) 9 / 20 , d ) 7 / 10 , e ) 5 / 7
Rationale: "lets take total employees are 100 . given that , total women = 76 and total married = 60 . total men = 100 - 76 = 24 and single men = 2 / 3 * 24 = 16 . married men = total men - single men = 24 - 16 = 8 . married women = total married - married men = 60 - 8 = 52 . fraction of women are married = married women / total women = 52 / 76 = 13 / 19 . ans a"
Answer: a
Question (gain): a shopkeeper sells 20 % of his stock at 25 % profit ans sells the remaining at a loss of 5 % . he incurred an overall profit of rs . 400 . find the total worth of the stock ?
Options: a ) 25500 , b ) 25000 , c ) 40500 , d ) 20000 , e ) 40000
Rationale: "let the total worth of the stock be rs . x . the sp of 20 % of the stock = 1 / 5 * x * 5 / 4 = 5 x / 20 the sp of 80 % of the stock = 4 / 5 * x * 0.95 = 152 x / 200 total sp = 50 x / 200 + 152 x / 200 = 202 x / 200 overall profit = 152 x / 200 - x = 2 x / 200 x / 50 = 400 = > x = 40000 answer : e"
Answer: e
Question (general): a store reported total sales of $ 385 million for february of this year . if the total sales for the same month last year was $ 340 million , approximately what was the percent increase in sales ?
Options: a ) 2 % , b ) 17 % , c ) 20 % , d ) 65 % , e ) 13 %
Rationale: "new value – old value ) / old value x 100 we are given : february sales this year = 385 million february sales last year = 340 million we need to determine the percent increase between sales from last year to sales this year . thus , the new value = 385 million and the old value = 340 million . let ’ s plug them into our percent change formula . ( new value – old value ) / old value x 100 [ ( 385 – 340 ) / 340 ] x 100 65 / 340 x 100 ≈ 13 % . the answer is e ."
Answer: e
Question (other): each of the dogs in a certain kennel is a single color . each of the dogs in the kennel either has long fur or does not . of the 45 dogs in the kennel , 36 have long fur , 27 are brown , and 8 are neither long - furred nor brown . how many long - furred dogs are brown ?
Options: a ) 26 , b ) 19 , c ) 11 , d ) 8 , e ) 6
Rationale: "no of dogs = 45 long fur = 36 brown = 27 neither long fur nor brown = 8 therefore , either long fur or brown = 45 - 8 = 37 37 = 36 + 27 - both both = 26 answer a"
Answer: a
Question (general): an army ’ s recruitment process included n rounds of selection tasks . for the first a rounds , the rejection percentage was 60 percent per round . for the next b rounds , the rejection percentage was 50 percent per round and for the remaining rounds , the selection percentage was 70 percent per round . if there were 10000 people who applied for the army and 98 were finally selected , what was the value of n ?
Options: a ) 4 , b ) 5 , c ) 6 , d ) 7 , e ) 10
Rationale: "step ( 1 ) 4000 accepted . step ( 2 ) another 40 % of 40000 = 1600 accepted . here it is quiet observable that if we further deduct candidate by 60 % it would change our probablity of easy going 2000 candidate . so i would get to second stage of recruitment where 50 % is accepted step ( 3 ) 50 % of 1600 = 800 step ( 4 ) 50 % of 800 = 400 step ( 5 ) 50 % of 400 = 200 . . . here we are done with total 5 steps 70 % of 200 = 140 and last step of accepting 70 % of 140 = 98 ( our target ) total 7 steps required . ans d"
Answer: d
Question (physics): a walks at 30 kmph and 30 hours after his start , b cycles after him at 55 kmph . how far from the start does b catch up with a ?
Options: a ) 1200 km , b ) 1980 km , c ) 2000 km , d ) 2500 km , e ) 3600 km
Rationale: "suppose after x km from the start b catches up with a . then , the difference in the time taken by a to cover x km and that taken by b to cover x km is 30 hours . x / 30 - x / 55 = 30 x = 1980 km answer is b"
Answer: b
Question (general): a certain protective additive increases from 20 days to 25 days the time between required maintenance checks on an industrial vehicle . by what percent is the time between maintenance checks increased by using the additive ?
Options: a ) 25 % , b ) 33 1 / 3 % , c ) 50 % , d ) 66 2 / 3 % , e ) 75 %
Rationale: "general formula for percent increase or decrease , ( percent change ) : percent = change / original ∗ 100 so , the time between maintenance checks increased by 25 − 20 / 20 ∗ 100 = 25 answer : a ."
Answer: a
Question (gain): a $ 500 investment and a $ 1,500 investment have a combined yearly return of 13 percent of the total of the two investments . if the $ 500 investment has a yearly return of 7 percent , what percent yearly return does the $ 1,500 investment have ?
Options: a ) 9 % , b ) 15 % , c ) 105 / 8 % , d ) 11 % , e ) 12 %
Rationale: "the equation we can form the question : return on total investment = sum of individual investments ( 500 + 1500 ) ( 13 ) = ( 500 â ˆ — 7 ) + ( 1500 x ) , where x is the return on investment of 1500 . solving the equation , we get x = 15 % ( option b ) answer : b"
Answer: b
Question (geometry): the monthly rent of a shop of dimension 20 feet × 15 feet is rs . 3600 . what is the annual rent per square foot of the shop ?
Options: a ) 43 , b ) 144 , c ) 68 , d ) 87 , e ) 92
Rationale: "sol . monthly rent per square feet = 3600 / ( 20 * 15 ) = 12 & annual rent per square feet = 12 * 12 = 144 answer : b"
Answer: b
Question (physics): liam is pulled over for speeding just as he is arriving at work . he explains to the police officer that he could not afford to be late today , and has arrived at work only four minutes before he is to start . the officer explains that if liam had driven 5 mph slower for his whole commute , he would have arrived at work exactly on time . if liam ' s commute is 40 miles long , how fast was he actually driving ? ( assume that liam drove at a constant speed for the duration of his commute . )
Options: a ) 50 mph , b ) 45 mph , c ) 48 mph , d ) 52 mph , e ) 60 mph
Rationale: let t be the number of hours he would need to reach office on time . when he is driving with over speed , he reached office 4 min earlier ! so the equation for this is s ( t - 4 / 60 ) = 40 where s is the speed and 30 is the distance . if he decreases his speed by 5 mph then he would have reached his office on time : ( s - 5 ) t = 40 if you solve above equations , you will arrive at t = 2 / 3 hr and s = 60 mph therefore answer is e
Answer: e
Question (gain): an article costing rs . 160 is sold at 20 % discount on a mark - up price . what is the selling price after discount ?
Options: a ) 106 , b ) 116 , c ) 128 , d ) 136 , e ) 146
Rationale: 160 * 80 / 100 = 128 answer : c
Answer: c
Question (general): 75 % of x is greater than 1 / 3 rd of x by 110 . what is x ?
Options: a ) 160 , b ) 264 , c ) 360 , d ) 354 , e ) 400
Rationale: 75 x / 100 - x / 3 = 110 5 x / 12 = 110 x = 264 answer : b
Answer: b
Question (general): there are 8 stores in town that had a total of 21 visitors on a particular day . however , only 12 people went shopping that day ; some people visited more than one store . if 8 people visited exactly two stores each , and everyone visited at least one store , what is the largest number of stores anyone could have visited ?
Options: a ) 2 , b ) 3 , c ) 4 , d ) 5 , e ) 6
Rationale: "8 people visited 2 stores each for 16 visits . to maximize the number of stores that one person visited , let ' s assume that 3 people visited 1 store each . the number of remaining visits is 21 - 16 - 3 = 2 , which is the maximum that one person could have visited . the answer is a ."
Answer: a
Question (gain): indu gave bindu rs . 2500 on compound interest for 2 years at 4 % per annum . how much loss would indu has suffered had she given it to bindu for 2 years at 4 % per annum simple interest ?
Options: a ) 1 , b ) 2 , c ) 3 , d ) 4 , e ) 5
Rationale: "2500 = d ( 100 / 4 ) 2 d = 4 answer : d"
Answer: d
Question (general): 7 people average age is 30 . youngest person age is 7 . find average of the people when youngest was born .
Options: a ) 23 , b ) 24 , c ) 25 , d ) 26 , e ) 27
Rationale: "average age of people = 30 so have total age = 210 before 7 years we have to deduct each person age by seven years 210 - 49 = 161 so average age would be 161 / 7 = 23 answer : a"
Answer: a
Question (gain): how many pounds of salt at 50 cents / lb must be mixed with 40 lbs of salt that costs 35 cents / lb so that a merchant will get 20 % profit by selling the mixture at 48 cents / lb ?
Options: a ) 20 , b ) 15 , c ) 40 , d ) 50 , e ) 25
Rationale: "selling price is 48 cents / lb for a 20 % profit , cost price should be 40 cents / lb ( cp * 6 / 5 = 48 ) basically , you need to mix 35 cents / lb ( salt 1 ) with 50 cents / lb ( salt 2 ) to get a mixture costing 40 cents / lb ( salt avg ) weight of salt 1 / weight of salt 2 = ( salt 2 - salt avg ) / ( salt avg - salt 1 ) = ( 50 - 40 ) / ( 40 - 35 ) = 2 / 1 we know that weight of salt 1 is 40 lbs . weight of salt 2 must be 20 lbs . answer ( a )"
Answer: a
Question (general): a factory that employs 1000 assembly line workers pays each of these workers $ 5 per hour for the first 40 hours worked during a week and 1 ½ times that rate for hours worked in excess of 40 . what was the total payroll for the assembly - line workers for a week in which 30 percent of them worked 10 hours , 50 percent worked 40 hours , and the rest worked 50 hours ?
Options: a ) $ 180,000 , b ) $ 185,000 , c ) $ 170,000 , d ) $ 200,000 , e ) $ 205,000
Rationale: 30 % of 1000 = 300 worked for 20 hours payment @ 5 / hr total payment = 300 * 10 * 5 = 15000 50 % of 1000 = 500 worked for 40 hours payment @ 5 / hr total payment = 500 * 40 * 5 = 100000 remaining 200 worked for 50 hours payment for first 40 hours @ 5 / hr payment = 200 * 40 * 5 = 40000 payment for next 10 hr @ 7.5 / hr payment = 200 * 10 * 7.5 = 15000 total payment = 15000 + 100000 + 40000 + 15000 = 170000 hence , answer is c
Answer: c
Question (physics): along a yard 273 metres long , 14 trees are palnted at equal distances , one tree being at each end of the yard . what is the distance between two consecutive trees
Options: a ) 18 , b ) 19 , c ) 10 , d ) 21 , e ) 12
Rationale: "explanation : 14 trees have 13 gaps between them , required distance ( 273 / 13 ) = 21 option d"
Answer: d
Question (gain): a sum of money deposited at c . i . amounts to rs . 2442 in 2 years and to rs . 2926 in 3 years . find the rate percent ?
Options: a ) 11 , b ) 20 , c ) 28 , d ) 24 , e ) 82
Rationale: "explanation : 2420 - - - 484 100 - - - ? = > 20 % answer : option b"
Answer: b
Question (other): a ratio between two numbers is 8 : 9 and their l . c . m . is 432 . the first number is
Options: a ) 60 , b ) 45 , c ) 50 , d ) 48 , e ) none
Rationale: sol . let the required numbers be 8 x and 9 x . then , their l . c . m . is 72 x . ∴ 72 x = 432 ⇔ x = 6 . hence , the first number is 48 . answer d
Answer: d
Question (general): jim needs $ 1000 to buy a new flat - screen tv . since he has only $ 7 , he borrows the remaining balance from his sister mary . the loan will be repaid in 3 annual installments at an interest rate of 10 % , compounded annually . the formula for calculating the monthly payment p is p = ( l x c x r ) / ( c – 1 ) where l = amount of the loan , r = annual interest rate , and c = compounding factor = ( 1 + r ) ^ n where n = number of annual payments . how much does jim have to pay mary at the end of each of the next 3 years ( rounded to the nearest penny ) ?
Options: a ) $ 357.67 , b ) $ 375.85 , c ) $ 387.40 , d ) $ 399.30 , e ) $ 433.33
Rationale: l = 993 r = 0.1 c = 1.1 ^ 3 = 1.331 insert all of these in the formula and we get p = 993 * 1.331 * 0.1 / 0.331 in order to resolve above without a calc , we need to find the approx value of 0.1331 / 0.331 ~ 0.4 ~ ~ 993 * 0.4 ~ 397 answer d
Answer: d
Question (physics): there is a 35 cm line marked at each centimeter and an insect is placed at every centimeter . 9 frogs are trained to jump a constant distance . the first one jumps 2 cm in every leap , the second one jumps 3 cm and so on until the 9 th one jumps 10 cm in every leap and they eat any insect that is available at that spot . if all of them start from start line and finish the entire 35 cm , how many insects were still left after the race was over ?
Options: a ) 0 , b ) 4 , c ) 6 , d ) 7 , e ) 10
Rationale: "only the prime numbers greater than 10 and less than 35 were left . that is 11 , 13 , 17 , 19 , 23 , 29 , and 31 . the total is 7 . the answer is d ."
Answer: d
Question (geometry): a circular well with a diameter of 2 metres , is dug to a depth of 14 metres . what is the volume of the earth dug out ?
Options: a ) 32 m 3 , b ) 36 m 3 , c ) 40 m 3 , d ) 44 m 3 , e ) none
Rationale: "sol . volume = π r 2 h = ( 22 / 7 x 1 x 1 x 14 ) m 3 = 44 m 3 . answer d"
Answer: d
Question (physics): a searchlight on top of the watchtower makes 4 revolutions per minute . what is the probability that a man appearing near the tower will stay in the dark for at least 5 seconds ?
Options: a ) 5 / 6 , b ) 4 / 5 , c ) 3 / 4 , d ) 2 / 3 , e ) 1 / 2
Rationale: the searchlight completes one revolution every 15 seconds . the probability that the man ' s area will be lit up is 5 / 15 = 1 / 3 . the probability that he will stay in the dark is 1 - 1 / 3 = 2 / 3 the answer is d .
Answer: d
Question (general): how many integers are between 7 and 120 / 9 , inclusive ?
Options: a ) 5 , b ) 6 , c ) 7 , d ) 9 , e ) 10
Rationale: "120 / 9 = 13 . xx we are not concerned about the exact value of 120 / 9 as we just need the integers . the different integers between 7 and 120 / 9 would be 7 , 8 , 9 , 10 , 11 , 12,13 total number of integers = 7 option c"
Answer: c
Question (general): the two lines y = x and x = - 5 intersect on the coordinate plane . what is the value of the area of the figure formed by the intersecting lines and the x - axis ?
Options: a ) 7.5 , b ) 10 , c ) 12.5 , d ) 15 , e ) 17.5
Rationale: "the point of intersection is ( - 5 , - 5 ) . the triangle has a base of length 5 and a height of 5 . area = ( 1 / 2 ) * base * height = ( 1 / 2 ) * 5 * 5 = 12.5 the answer is c ."
Answer: c
Question (general): in a 100 - mile trip , the first 30 miles were completed at 60 mph . if the average speed for the whole trip was 40 mph , what was the average speed in the last 70 miles ?
Options: a ) 30 mph , b ) 32 mph , c ) 35 mph , d ) 37 mph , e ) 38 mph
Rationale: the time to complete the first 30 miles was ( 30 miles / 60 mph ) = ( 1 / 2 ) hours . the time to complete the whole trip was ( 100 miles / 40 mph ) = ( 5 / 2 ) hours . the time to complete the last 70 miles was ( 5 / 2 ) - ( 1 / 2 ) = ( 2 ) hours . the average speed in the last 70 miles was ( 70 miles / 2 hours ) = 35 mph . the answer is c .
Answer: c
Question (general): diana took out a charge account at the general store and agreed to pay 6 % simple annual interest . if she charges $ 60 on her account in january , how much will she owe a year later , assuming she does not make any additional charges or payments ?
Options: a ) $ 62.40 , b ) $ 62.80 , c ) $ 63.20 , d ) $ 63.60 , e ) $ 64.00
Rationale: "1.06 * $ 60 = $ 63.60 the answer is d ."
Answer: d
Question (gain): a started a business with an investment of rs . 70000 and after 6 months b joined him investing rs . 120000 . if the profit at the end of a year is rs . 13000 , then the share of b is ?
Options: a ) 6000 , b ) 12000 , c ) 18000 , d ) 24009 , e ) 24002
Rationale: "ratio of investments of a and b is ( 70000 * 12 ) : ( 120000 * 6 ) = 7 : 6 total profit = rs . 13000 share of b = 6 / 13 ( 13000 ) = rs . 6000 answer : a"
Answer: a
Question (general): if the average ( arithmetic mean ) of x , x + 2 , and x + 4 is 103 , what is the value of x ?
Options: a ) 95 , b ) 97 , c ) 101 , d ) 85 , e ) 87
Rationale: "am of x , x + 2 , and x + 4 = x + ( x + 2 ) + ( x + 4 ) / 3 = 3 x + 6 / 3 = x + 2 given that x + 2 = 103 x = 101 answer : c"
Answer: c
Question (other): divide rs . 32000 in the ratio 1 : 7 ?
Options: a ) 12000 , 20000 , b ) 12000 , 200098 , c ) 4000 , 28000 , d ) 12000 , 20006 , e ) 12000 , 20001
Rationale: "1 / 8 * 32000 = 4000 7 / 8 * 32000 = 28000 answer : c"
Answer: c