Cheukting/mathqa huggingface dataset:
Question (probability): out of 10 students in a class , 4 are from maharashtra , 3 are from karnataka , and 3 are from goa . four students are to be selected at random . what are the chances that at least one is from karnataka ?
Options: a ) 1 / 3 , b ) 4 / 9 , c ) 5 / 6 , d ) 3 / 7 , e ) 1 / 4
Rationale: "total possible ways of selecting 4 students out of 10 = 10 c 4 = ( 10 * 9 * 8 * 7 ) / ( 4 * 3 * 2 * 1 ) = 210 the number of ways of selecting a 4 students in which no student belongs to karnataka = 7 c 4 number of ways of selecting atleast one student from karnataka = 15 c 4 - 7 c 4 = 175 probability = 175 / 210 = 5 / 6 answer is c"
Answer: c
Question (gain): a sum was put at simple interest at a certain rate for 3 years had it been put at 3 % higher rate , it would have fetched 81 more . find the sum .
Options: a ) 500 , b ) 600 , c ) 700 , d ) 800 , e ) 900
Rationale: "difference in s . i . = p × t / 100 ( r 1 − r 2 ) ⇒ 81 = p × 3 x 3 / 100 ( ∵ r 1 - r 2 = 2 ) ⇒ p = 81 × 100 / 3 x 3 = 900 answer e"
Answer: e
Question (other): the least whole number which when subtracted from both the terms of the ratio 6 : 7 to give a ratio less than 16 : 21 , is
Options: a ) 3 , b ) 4 , c ) 5 , d ) 6 , e ) 7
Rationale: "explanation : let x is subtracted . then , ( 6 − x ) / ( 7 − x ) < 16 / 21 21 ( 6 — x ) < 16 ( 7 — x ) = > 5 x > 14 = x > 2.8 least such number is 3 option a"
Answer: a
Question (gain): the total cost of 100 paper plates and 200 paper cups is $ 6.00 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 = $ 6.00 just divide the equation by 5 and you will get what u are looking for 20 p + 40 c = $ 1.20 therefore oa is c
Answer: c
Question (general): if the price of sugar rises from rs . 3 per kg to rs . 5 per kg , a person , to have no increase in the expenditure on sugar , will have to reduce his consumption of sugar by
Options: a ) 15 % , b ) 20 % , c ) 25 % , d ) 30 % , e ) 40 %
Rationale: sol . let the original consumption = 100 kg and new consumption = x kg . so , 100 x 3 = x × 5 = x = 60 kg . ∴ reduction in consumption = 40 % . answer e
Answer: e
Question (physics): a 1200 m long train crosses a tree in 120 sec , how much time will i take to pass a platform 300 m long ?
Options: a ) 176 sec , b ) 190 sec , c ) 178 sec , d ) 150 sec , e ) 276 sec
Rationale: "l = s * t s = 1200 / 120 s = 10 m / sec . total length ( d ) = 1500 m t = d / s t = 1500 / 10 t = 150 sec answer : d"
Answer: d
Question (general): find the average of all prime numbers between 30 and 50 .
Options: a ) 30 , b ) 33.6 , c ) 39.8 , d ) 44.9 , e ) none
Rationale: "sol . there are five prime numbers between 30 and 50 . they are 31 , 37 , 41 , 43 and 47 ∴ required average = [ 31 + 37 + 41 + 43 + 47 / 5 ] = 199 / 5 = 39.8 answer c"
Answer: c
Question (other): there are 2 available positions and 50 candidates , one half of whom are democrats and another half are republicans . if it was decided that the positions would be filled at random , then what is the probability w that the both positions will be taken by members of just one party ?
Options: a ) 1 / 25 , b ) 12 / 49 , c ) 1 / 4 , d ) 24 / 49 , e ) 1 / 2
Rationale: "w probability of one party having both spots : ( 1 / 2 ) * ( 24 / 49 ) = 12 / 49 ( 1 / 2 ) or ( 25 / 50 ) because it does not matter which party or which person gets the first spot . ( 24 / 49 ) because after one person from a particular party is chosen , there are 24 members of the same party left out of 49 total candidates . since this result can happen for both parties , ( 12 / 49 ) + ( 12 / 49 ) = ( 24 / 49 ) answer : d"
Answer: d
Question (general): a gambler bought $ 3,000 worth of chips at a casino in denominations of $ 30 and $ 100 . that evening , the gambler lost 16 chips , and then cashed in the remainder . if the number of $ 30 chips lost was 2 more or 2 less than the number of $ 100 chips lost , what is the largest amount of money that the gambler could have received back ?
Options: a ) $ 2,040 , b ) $ 2,120 , c ) $ 1,960 , d ) $ 1,920 , e ) $ 2,030
Rationale: "in order to maximize the amount of money that the gambler kept , we should maximize # of $ 30 chips lost and minimize # of $ 100 chips lost , which means that # of $ 30 chips lost must be 2 more than # of $ 100 chips lost . so , if # of $ 30 chips lost is x then # of $ 100 chips lost should be x - 2 . now , given that total # of chips lost is 16 : x + x - 2 = 16 - - > x = 9 : 9 $ 30 chips were lost and 9 - 2 = 7 $ 100 chips were lost . total worth of chips lost is 9 * 30 + 7 * 100 = $ 970 , so the gambler kept $ 3,000 - $ 970 = $ 2,030 . answer : e"
Answer: e
Question (gain): an association of mathematics teachers has 1,260 members . only 445 of these members cast votes in the election for president of the association . what percent of the total membership voted for the winning candidate if the winning candidate received 60 percent of the votes cast ?
Options: a ) 75 % , b ) 58 % , c ) 42 % , d ) 34 % , e ) 22 %
Rationale: "total umber of members = 1260 number of members that cast votes = 445 since , winning candidate received 60 percent of the votes cast number of votes for winning candidate = ( 60 / 100 ) * 445 = 267 percent of total membership that voted for winning candidate = ( 267 / 1260 ) * 100 = 21.19 % answer e"
Answer: e
Question (geometry): what is the smallest positive integer x , such that 5000 x is a perfect cube ?
Options: a ) 4 , b ) 6 , c ) 8 , d ) 25 , e ) 18
Rationale: "take out the factors of 5000 that will come 10 ^ 3 * 5 . for perfect cube you need every no . raise to the power 3 . for 5000 x to be a perfect cube , you need two 5 that means 25 . d is the answer ."
Answer: d
Question (physics): a leak in the bottom of a tank can empty the full tank in 6 hours . an inlet pipe fills water at the rate of 6 litres a minute . when the tank is full , the inlet is opened and due to the leak , the tank is empty in 12 hours . how many litres does the cistern hold ?
Options: a ) 7580 , b ) 7960 , c ) 8290 , d ) 4320 , e ) none
Rationale: "solution work done by the inlet in 1 hour = ( 1 / 6 - 1 / 12 ) = 1 / 12 . work done by the inlet in 1 min . = ( 1 / 12 × 1 / 60 ) = 0.001389 volume of 0.001389 part = 6 litres . therefore , volume of whole = 1 / 0.001389 x 6 ‹ = › 4320 litres . answer d"
Answer: d
Question (physics): maxwell leaves his home and walks toward brad ' s house . one hour later , brad leaves his home and runs toward maxwell ' s house . if the distance between their homes is 24 kilometers , maxwell ' s walking speed is 4 km / h , and brad ' s running speed is 6 km / h . what is the total time it takes maxwell before he meets up with brad ?
Options: a ) 3 , b ) 4 , c ) 5 , d ) 6 , e ) 8
Rationale: "total distance = 24 kms maxwell speed = 4 kms / hr maxwell travelled for 1 hour before brad started , therefore maxwell traveled for 4 kms in 1 hour . time taken = total distance / relative speed total distance after brad started = 20 kms relative speed ( opposite side ) ( as they are moving towards each other speed would be added ) = 6 + 4 = 10 kms / hr time taken to meet brad after brad started = 20 / 10 = 2 hrs distance traveled by maxwell = maxwell ' s speed * time taken = 4 * 2 = 8 + 4 = 12 kms . . . therefore total time taken by maxwell to meet brad = distance travelled by maxwell / maxwell ' s speed = 12 / 4 = 3 hrs . . . answer a"
Answer: a
Question (physics): one robot builds a robot in 1 hour , another one builds a robot in 2 hours . the 2 robots work together and when a new robot is complete , it joins the others , working at a constant rate of one robot in 2 hours . how much time will it take until there are 3 robots altogether , if the robots build only one robot at a time ?
Options: a ) 40 min , b ) 94 min , c ) 110 min , d ) 112 min , e ) 120 min
Rationale: "first the 2 robots work at the rate of 1 + 1 / 2 = 3 / 2 so they complete one robot in 2 / 3 rd of an hour = 40 minutes - ( 1 ) and now we have 3 robots in 40 minutes answer - a"
Answer: a
Question (general): if 20 percent of the students at a certain school went to a camping trip and took more than $ 100 , and 75 percent of the students who went to the camping trip did not take more than $ 100 , what percentage of the students at the school went to the camping trip ?
Options: a ) 95 , b ) 90 , c ) 85 , d ) 80 , e ) 75
Rationale: "let x be the number of students in the school . 0.2 x students went to the trip and took more than 100 $ . they compose ( 100 - 75 ) = 25 % of all students who went to the trip . therefore the toal of 0.2 x / 0.25 = 0.8 x students went to the camping which is 80 % . the answer is d"
Answer: d
Question (other): in a group of 400 readers who read science fiction or literacy works or both , 250 read science fiction and 230 read literacy works . how many read both science fiction and literacy works ?
Options: a ) 70 , b ) 80 , c ) 90 , d ) 100 , e ) 110
Rationale: "consider total number of reader n ( s u l ) = 400 people who read science fiction n ( s ) = 250 people who read literacy works n ( l ) = 230 both science fiction and literacy n ( s ∩ l ) = ? n ( s u l ) = n ( s ) + n ( l ) - n ( s ∩ l ) 400 = 250 + 230 - n ( s ∩ l ) n ( s ∩ l ) = 480 - 400 n ( s ∩ l ) = 80 so people read both science fiction and literacy works are 80 answer : b"
Answer: b
Question (physics): if 12 men and 16 boys can do a piece of work in 5 days and 13 men together will 24 boys can do it in 4 days . compare the daily work done by a man with that of a boy ?
Options: a ) 2 : 5 , b ) 2 : 9 , c ) 2 : 4 , d ) 2 : 1 , e ) 2 : 2
Rationale: 12 m + 16 b - - - - - 5 days 13 m + 24 b - - - - - - - 4 days 60 m + 80 b = 52 m + 96 b 8 m = 16 b = > 1 m = 2 b m : b = 2 : 1 answer : d
Answer: d
Question (physics): the pilot of a small aircraft with a 40 - gallon fuel tank wants to fly to cleveland , which is 480 miles away . the pilot recognizes that the current engine , which can fly only 10 miles per gallon , will not get him there . by how many miles per gallon must the aircraft ’ s fuel efficiency be improved to make the flight to cleveland possible ?
Options: a ) 2 , b ) 4 , c ) 12 , d ) 40 , e ) 160
Rationale: "actual miles / gallon is = 480 / 40 = 12 miles / gallon . current engine miles / gallon is 10 miles / gallon . additional 2 miles / gallon is required to match the actual mileage . imo option a ."
Answer: a
Question (general): a certain bus driver is paid a regular rate of $ 12 per hour for any number of hours that does not exceed 40 hours per week . for any overtime hours worked in excess of 40 hours per week , the bus driver is paid a rate that is 75 % higher than his regular rate . if last week the bus driver earned $ 976 in total compensation , how many total hours did he work that week ?
Options: a ) 60 , b ) 68 , c ) 65 , d ) 64 , e ) 61
Rationale: "for 40 hrs = 40 * 12 = 480 excess = 976 - 480 = 496 for extra hours = . 75 ( 12 ) = 9 + 12 = 21 number of extra hrs = 496 / 21 = 23.62 total hrs = 40 + 23.62 = 63.62 = 64 approx . answer d 64"
Answer: d
Question (general): three numbers are in the ratio 3 : 4 : 5 and their average is 36 . the largest number is :
Options: a ) 30 , b ) 98 , c ) 27 , d ) 21 , e ) 45
Rationale: "explanation : let the numbers be 3 x , 4 x and 5 x , then , ( 3 x + 4 x + 5 x ) / 3 = 36 = > 12 x = 36 * 3 = > x = 9 largest number 5 x = 5 * 9 = 45 answer : e"
Answer: e
Question (physics): 5 cats can catch 5 mice in 5 minutes . how many cats does it take to catch 100 mice in 100 minutes ?
Options: a ) 1 , b ) 2 , c ) 3 , d ) 4 , e ) 5
Rationale: let x be no . of cat 5 cat catch 5 mice in 5 min 5 cat catch 1 mice in ( 5 / 5 = 1 min ) 1 cat catch 1 mice in 1 * 5 = 5 min 1 cat catch 100 mice in 5 * 100 min x cat catch 100 mice in ( 5 * 100 ) / x min a / q ( 5 * 100 ) / x = 100 = > 5 * 100 = x * 100 = > x = 5 answer : e
Answer: e
Question (general): the tax on a commodity is diminished by 19 % and its consumption increased by 15 % . the effect on revenue is ?
Options: a ) 2 % , b ) 8.85 % , c ) 5.85 % , d ) 6.85 % , e ) 1 %
Rationale: "100 * 100 = 10000 81 * 115 = 9315 - - - - - - - - - - - 10000 - - - - - - - - - - - 685 100 - - - - - - - - - - - ? = > 6.85 % decrease answer : d"
Answer: d
Question (physics): when a train travels at a speed of 60 kmph , it reaches the destination on time . when the same train travels at a speed of 50 kmph , it reaches its destination 15 min late . what is the length of journey ?
Options: a ) 75 km , b ) 50 km , c ) 60 km , d ) 85 km , e ) 95 km
Rationale: "let x be the time reached with the speed 60 km / h 50 km / h - - - - > x + 15 distance is equal so 60 ( km / h ) × xhr = 50 ( km / h ) × ( x + 15 ) hr so 60 x = 50 x + 750 so the would be in km and x = 75 so 75 km answer : a"
Answer: a
Question (general): if x is less than y by 40 % then y exceed x by :
Options: a ) 33.33 % , b ) 25 % , c ) 75 % , d ) 66.66 % , e ) none of these
Rationale: "using formula ( x / ( 100 - x ) * 100 ) where x is percentage decrease ( here it is 40 % ) = > 40 / ( 100 - 40 ) * 100 = 66.66 % answer : d"
Answer: d
Question (physics): p is 20 % more efficient than q . p can complete a work in 22 days . if p and q work together , how many days will it take to complete the same work ?
Options: a ) 8 , b ) 11 , c ) 12 , d ) 15 , e ) 16
Rationale: "the work done by p in 1 day = 1 / 22 let work done by q in 1 day = q q × ( 120 / 100 ) = 1 / 22 q = 100 / ( 22 × 120 ) = 10 / ( 22 × 12 ) the work done by p and q in 1 day = 1 / 22 + 10 / ( 22 × 12 ) = 22 / ( 22 × 12 ) = 1 / 12 p and q together can do the work in 12 days . the answer is c ."
Answer: c
Question (general): a school has 4 section of chemistry in class x having 55 , 35 , 45 and 42 students . the mean marks obtained in chemistry test are 50 , 60 , 55 and 45 respectively for the 4 sections . determine the overall average of marks per student .
Options: a ) 50.15 , b ) 52.06 , c ) 51.25 , d ) 53.06 , e ) none of the above
Rationale: "required average marks = 55 ã — 50 + 35 ã — 60 + 45 ã — 55 + 42 ã — 45 / 55 + 35 + 45 + 42 = 2750 + 2100 + 2475 + 1890 / 162 = 9215 â  „ 177 = 52.06 answer b"
Answer: b
Question (general): rs . 2600 is divided so that 4 times the first share , thrice the 2 nd share and twice the third share amount to the same . what is the value of the third share ?
Options: a ) s . 1200 , b ) s . 1542 , c ) s . 1528 , d ) s . 1540 , e ) s . 1549
Rationale: "a + b + c = 2600 4 a = 3 b = 2 c = x a : b : c = 1 / 4 : 1 / 3 : 1 / 2 = 3 : 4 : 6 6 / 13 * 2600 = rs . 1200 answer : a"
Answer: a
Question (general): the difference of two numbers is 1355 . on dividing the larger number by the smaller , we get 6 as quotient and the 15 as remainder . what is the smaller number ?
Options: a ) 240 , b ) 270 , c ) 295 , d ) 268 , e ) 252
Rationale: "let the smaller number be x . then larger number = ( x + 1355 ) . x + 1355 = 6 x + 15 5 x = 1340 x = 268 smaller number = 270 . answer d"
Answer: d
Question (gain): if a radio is purchased for rs 490 and sold for rs 465.50 find the loss % ?
Options: a ) 5 % , b ) 4 % , c ) 6 % , d ) 8 % , e ) 7 %
Rationale: c . p = rs 490 s . p = rs 465.50 loss = c . p - s . p = 490 - 465.50 = rs 24.50 loss % = ( loss * 100 ) / c . p % = ( 24.50 * 100 ) / 490 % = 5 % answer a 5 %
Answer: a
Question (general): if a person cover 3 / 5 part of his journey by train , 7 / 20 part of his journey by bus and rest 6.5 km . by walk . what is total distance of his journey ?
Options: a ) 65 km , b ) 100 km , c ) 120 km , d ) 130 km , e ) 75 km
Rationale: let total distance be = x km . then , 3 x / 5 + 7 x / 20 + 6.5 = x ; 12 x + 7 x + 130 = 20 x ; x = 130 hence total distance = 130 km . answer d
Answer: d
Question (other): water consists of hydrogen and oxygen , and the approximate ratio , by mass , of hydrogen to oxygen is 2 : 16 . approximately how many grams of oxygen are there in 144 grams of water ?
Options: a ) 16 , b ) 72 , c ) 112 , d ) 128 , e ) 142
Rationale: "see h / o = 2 / 16 add 1 to both sides : h / o + 1 = 2 / 16 + 1 take lcm ( h + o ) / o = ( 2 + 16 ) / 16 water / o = 18 / 16 now that we have the water to oxygen ratio , put in the amount of water i . e . 144 gm = > o = 144 * 16 / 18 = 128 answer : d"
Answer: d
Question (other): the h . c . f . of two numbers is 16 and the other two factors of their l . c . m . are 13 and 14 . the larger of the two numbers is :
Options: a ) 276 , b ) 299 , c ) 224 , d ) 345 , e ) 365
Rationale: "clearly , the numbers are ( 16 x 13 ) and ( 16 x 14 ) . larger number = ( 23 x 14 ) = 224 . answer : option c"
Answer: c
Question (physics): at a certain resort , each of the 39 food service employees is trained to work in a minimum of 1 restaurant and a maximum of 3 restaurants . the 3 restaurants are the family buffet , the dining room , and the snack bar . exactly 21 employees are trained to work in the family buffet , 18 are trained to work in the dining room , and 12 are trained to work in the snack bar . if 4 employees are trained to work in exactly 2 restaurants , how many employees are trained to work in all 3 restaurants ?
Options: a ) 2 , b ) 3 , c ) 4 , d ) 5 , e ) 6
Rationale: "39 = 21 + 18 + 12 - 4 - 2 x 2 x = 21 + 18 + 12 - 4 - 39 = 47 - 39 = 8 x = 4 c"
Answer: c
Question (general): how many 4 digit number contain number 2 ?
Options: a ) 3168 , b ) 3268 , c ) 3368 , d ) 3468 , e ) 3568
Rationale: "total 4 digit no . = 9 * 10 * 10 * 10 = 9000 not containing 2 = 8 * 9 * 9 * 9 = 5832 total 4 digit number contain 2 = 9000 - 5832 = 3168 answer : a"
Answer: a
Question (gain): a bookstore has a shelf that contains biographies which normally sell for $ 20 each and mysteries that normally sell for $ 12 each . during a sale , the biographies and mysteries are discounted at different rates so that a customer saves a total of $ 19 from the normal price by buying 5 discounted biographies and 3 discounted mysteries . if the sum of the discount rates for the two types of books is 43 percent , what is the discount rate on mysteries ?
Options: a ) 24 % , b ) 25 % , c ) 30 % , d ) 37.5 % , e ) 40 %
Rationale: let b be the discount on biographies and m be the discount on mysteries so . , b + m = 0.435 - - - - - ( 1 ) and ( 20 * 5 + 12 * 3 ) - ( 20 * 5 * ( 1 - b ) + 12 * 3 * ( 1 - m ) ) = 19 - - > 100 ( 1 - ( 1 - b ) ) + 36 ( 1 - ( 1 - m ) = 19 100 b + 36 m = 19 - - - - - - ( 2 ) solving 12 . , we get m = 0.375 = 37.5 % d
Answer: d
Question (general): calculate the average of all the numbers between 15 and 55 which are divisible by 4 .
Options: a ) 39 , b ) 33 , c ) 34 , d ) 30 , e ) 36
Rationale: explanation : numbers divisible by 4 are 16,20 , 24,28 , 32,36 , 40,44 , 48,52 , , , average = ( 16 + 20 + 24 + 28 + 32 + 36 + 40 + 44 + 48 + 52 ) / 10 = 340 / 10 = 34 answer : c
Answer: c
Question (general): what is the remainder when 9 ^ 1 + 9 ^ 2 + 9 ^ 3 + . . . + 9 ^ 9 is divided by 9 ?
Options: a ) 2 , b ) 3 , c ) 0 , d ) 5 , e ) none of the above
Rationale: "notice that in the brackets we have the sum of 9 odd multiples of 9 , which yields remainder of 0 upon division by 9 . answer : c"
Answer: c
Question (gain): by selling an article at rs . 800 , a shopkeeper makes a profit of 25 % . at what price should he sell the article so as to make a loss of 25 % ?
Options: a ) rs . 488 , b ) rs . 480 , c ) rs . 482 , d ) rs . 487 , e ) rs . 481
Rationale: "sp = 800 profit = 25 % cp = ( sp ) * [ 100 / ( 100 + p ) ] = 800 * [ 100 / 125 ] = 640 loss = 25 % = 25 % of 640 = rs . 160 sp = cp - loss = 640 - 160 = rs . 480 answer : b"
Answer: b
Question (general): if ( a + b ) = 16 , ( b + c ) = 9 and ( c + d ) = 3 , what is the value of ( a + d ) ?
Options: a ) 10 . , b ) 8 . , c ) 7 . , d ) 2 . , e ) - 2 .
Rationale: "given a + b = 16 = > a = 16 - b - - > eq 1 b + c = 9 c + d = 3 = > d = 3 - c - - > eq 2 then eqs 1 + 2 = > a + d = 16 - b + 3 - c = > 19 - ( b + c ) = > 19 - 9 = 10 . option a . . ."
Answer: a
Question (general): rs . 880 is divided amongst a , b , c so that 4 times a ' s share , 5 times b ' s share and 10 times c ' s share are all equal . find c ' s share ?
Options: a ) 177 , b ) 150 , c ) 817 , d ) 160 , e ) 616
Rationale: a + b + c = 880 4 a = 5 b = 10 c = x a : b : c = 1 / 4 : 1 / 5 : 1 / 10 = 5 : 4 : 2 2 / 11 * 880 = rs . 160 answer : d
Answer: d
Question (other): divide $ 900 among a , b in the ratio 1 : 2 . how many $ that a get ?
Options: a ) $ 50 , b ) $ 300 , c ) $ 150 , d ) $ 250 , e ) $ 600
Rationale: "sum of ratio terms = 1 + 2 = 3 a = 900 * 1 / 3 = $ 300 answer is b"
Answer: b
Question (other): what is the square root of 169 ?
Options: a ) 8 , b ) 16 , c ) 13 , d ) 42 , e ) 25
Rationale: "13 x 13 = 169 answer c"
Answer: c
Question (physics): a car is running at a speed of 96 kmph . what distance will it cover in 14 sec ?
Options: a ) 378 m , b ) 350 m , c ) 380 m , d ) 200 m , e ) 250 m
Rationale: "speed = 96 kmph = 96 * 5 / 18 = 27 m / s distance covered in 14 sec = 27 * 14 = 378 m answer is a"
Answer: a
Question (general): in a certain aquarium , the number of red fish is 3 times the number of the green fish , and the number of blue fish is half the number of the red fish . if the ratio of green fish to red fish were to be doubled , and the ratio of red fish to blue fish were to be doubled , then the ratio of blue fish to green fish in that aquarium would be
Options: a ) 3 : 2 , b ) 1 : 1 , c ) 1 : 2 , d ) 3 : 4 , e ) 3 : 8
Rationale: lots of little places to make a mistake or panic here . = ) r = 3 g b = r / 2 g / r = 1 / 3 - - - - > doubled g / r = 2 / 3 r / b = 2 - - - - > doubled r / b = 4 b / g = ( b / r ) * ( r / g ) = ( 1 / 4 ) * ( 3 / 2 ) = 3 / 8 answer : e
Answer: e
Question (general): in what proportion must flour at $ 0.8 per pound be mixed with flour at $ 0.9 per pound so that the mixture costs $ 0.845 per pound ?
Options: a ) 1 : 3 , b ) 1 : 2 , c ) 1 : 1 , d ) 2 : 1 , e ) 5 : 4
Rationale: "using weighted average method : let x be the proportion in which the $ 0.8 per pound flour is mixed with $ 0.9 per pound flour . thus 0.8 * x + 0.9 * ( 1 - x ) = 0.845 0.9 – 0.1 x = 0.845 x = 0.55 thus ratio of both flours is 5 : 4 e"
Answer: e
Question (physics): a car drives 90 miles on local roads at 30 mph , and 75 miles on the highway at 60 mph , what is the average speed of the entire trip ?
Options: a ) 36 mph , b ) 40 mph , c ) 39 mph , d ) 42 mph , e ) 38 mph
Rationale: so the answer is plainly c . . . . we have a general relation for speed , time and distance : v ( velocity ) * t ( time ) = d ( distance ) for first part we have d = 90 miles , and v = 30 mph so we can obtain time : 30 * t = 90 or t = 90 / 30 = 3 hours the needed time to cover 90 miles in the same way we should divide 75 to 60 to find the needed time to cover 75 miles , so t = 1.25 hours so the total time for covering total distance would be 3 + 1.25 = 4.25 hours and total distance is 90 + 75 = 165 miles final stage : average speed is total distance divide to total time : 165 / 4.25 = 38.8 miles per hour rounded up to 39 mph . . . .
Answer: c
Question (general): in a mixture of 45 litres the ratio of milk to water is 4 : 1 . additional 18 litres of water is added to the mixture . find the ratio of milk to water in the resulting mixture .
Options: a ) 2 / 1 , b ) 4 / 3 , c ) 2 / 3 , d ) 3 / 4 , e ) 3 / 2
Rationale: given that milk / water = 4 x / x and 4 x + x = 45 - - > x = 9 . thus milk = 4 x = 36 liters and water = x = 9 liters . new ratio = 36 / ( 9 + 18 ) = 36 / 27 = 4 / 3 . answer : b .
Answer: b
Question (gain): a man sold 20 articles for $ 60 and gained 20 % . how many articles should he sell for $ 90 to incur a loss 20 % ?
Options: a ) 45 , b ) 36 , c ) 40 , d ) 50 , e ) 48
Rationale: "production cost per article : $ 60 * ( 100 % - 20 % ) / 20 = $ 2.40 required production costs for a loss of 20 % : $ 90 * ( 100 % + 20 % ) = $ 108 number of articles to be sold for $ 108 to incur a 20 % loss : $ 108 / $ 2.40 = 45 thus , solution a is correct ."
Answer: a
Question (general): if x > 3000 , then the value of ( 3 x ) / ( 2 x ^ 1.21 - 1111 ^ 1.3 ) is closest to ?
Options: a ) 1 / 6 , b ) 1 / 3 , c ) 10 / 21 , d ) 4 / 10 , e ) 3 / 2
Rationale: "assume x = 3002 ( 3 x ) / ( 2 x ^ 1.21 - 1111 ^ 1.3 ) = 9006 / ( 2 * ( 3002 ) ^ 1.21 - 1111 ^ 1.3 ) = 9006 / 23154 = = 4 / 10 d"
Answer: d