Cheukting/mathqa huggingface dataset:
Question (physics): a train is 410 meter long is running at a speed of 45 km / hour . in what time will it pass a bridge of 140 meter length
Options: a ) 20 seconds , b ) 44 seconds , c ) 40 seconds , d ) 50 seconds , e ) none of these
Rationale: "explanation : speed = 45 km / hr = 45 * ( 5 / 18 ) m / sec = 25 / 2 m / sec total distance = 410 + 140 = 550 meter time = distance / speed = 550 ∗ 2 / 25 = 44 seconds option b"
Answer: b
Question (general): the sum of the fourth and twelfth term of an arithmetic progression is 20 . what is the sum of the first 15 terms of the arithmetic progression ?
Options: a ) 3 , b ) 1 / 3 , c ) 2 , d ) 9 , e ) 1 / 9
Rationale: "the sum of the first n terms of a g . p . is given by , where ' a ' is the first term of the g . p . , ' r ' is the common ratio and ' n ' is the number of terms in the g . p . therefore , the sum of the first 6 terms of the g . p will be equal to and sum of the first 3 terms of the g . p . will be equal to use the ratio between these two sums to find ' r ' the ratio of the sum of the first 6 terms : sum of first 3 terms = 9 : 1 i . e . or r 3 + 1 = 9 r 3 = 8 r = 2 the answer is c"
Answer: c
Question (general): the average ( arithmetic mean ) of 4 positive integers is 50 . if the average of 2 of these integers is 40 , what is the greatest possible value that one of the other 2 integers can have ?
Options: a ) 55 , b ) 65 , c ) 119 , d ) 109 , e ) 115
Rationale: "a + b + c + d = 200 a + b = 80 c + d = 120 greatest possible = 119 ( just less than 1 ) answer = c"
Answer: c
Question (general): if f ( x ) = 3 x ^ 4 - 4 x ^ 3 - 2 x ^ 2 + 6 x , then f ( - 1 ) =
Options: a ) - 2 , b ) - 1 , c ) 0 , d ) 1 , e ) 2
Rationale: "f ( - 1 ) = 3 ( - 1 ) ^ 4 - 4 ( - 1 ) ^ 3 - 2 ( - 1 ) ^ 2 + 6 ( - 1 ) = 3 + 4 - 2 - 6 = - 1 the answer is b ."
Answer: b
Question (gain): an uneducated retailer marks all his goods at 50 % above the cost price and thinking that he will still make 25 % profit , offers a discount of 25 % on the marked price . what is his actual profit on the sales ?
Options: a ) 12.50 % , b ) 13.50 % , c ) 14 % , d ) 14.50 % , e ) none
Rationale: "sol . let c . p . = rs . 100 . then , marked price = rs . 150 . s . p . = 75 % of rs . 150 = rs . 112.50 . ∴ gain % = 12.50 % . answer a"
Answer: a
Question (geometry): the mass of 1 cubic meter of a substance is 300 kg under certain conditions . what is the volume in cubic centimeters of 1 gram of this substance under these conditions ? ( 1 kg = 1,000 grams and 1 cubic meter = 1 , 000,000 cubic centimeters )
Options: a ) 3.33 , b ) 3.34 , c ) 3.53 , d ) 5.32 , e ) 3.92
Rationale: "300 kg - 1 cubic meter ; 300,000 g - 1 cubic meter ; 300,000 g - 1 , 000,000 cubic centimeters ; 1 g - 1 , 000,000 / 300,000 = 10 / 3 = 3.33 cubic centimeters . answer : a ."
Answer: a
Question (gain): a dishonest person wants to make a profit on the selling of milk . he would like to mix water ( costing nothing ) with milk costing 33 $ per litre so as to make a profit of 50 % on cost when he sells the resulting milk and water mixture for 36 $ . in what ratio should he mix the water and milk ?
Options: a ) 1 : 20 , b ) 1 : 10 , c ) 3 : 8 , d ) 3 : 4 , e ) 3 : 2
Rationale: "first of all , let ' s consider 1 liter of the stuff he is going to sell - - - naive customers think it ' s pure milk , but we know it ' s some milk - water mixture . he is going to sell this liter of milk - water for $ 36 . this $ 36 should be a 50 % increase over cost . here , we need to think about percentage increases as multipliers . using multipliers ( cost ) * 1.50 = $ 36 cost = 36 / 1.5 = 360 / 12 = $ 24 if he wants a 20 % increase over cost on the sale of one liter of his milk - water , the cost has to be $ 24 . well , a liter of milk costs $ 33 , so if he is going to use just $ 30 of milk in his mixture , that ' s 24 / 33 = 8 / 11 of a liter . if milk is 8 / 11 of the liter , then water is 3 / 11 of the liter , and the ratio of water to milk is 3 : 8 . answer choice ( c )"
Answer: c
Question (physics): a train 520 m long can cross an electric pole in 20 sec and then find the speed of the train ?
Options: a ) 88 kmph , b ) 94 kmph , c ) 72 kmph , d ) 16 kmph , e ) 18 kmph
Rationale: "length = speed * time speed = l / t s = 520 / 20 s = 26 m / sec speed = 26 * 18 / 5 ( to convert m / sec in to kmph multiply by 18 / 5 ) speed = 94 kmph answer : b"
Answer: b
Question (probability): in a throw of dice what is the probability of ge æ « ng number greater than 4
Options: a ) 1 / 2 , b ) 1 / 3 , c ) 1 / 5 , d ) 1 / 6 , e ) none of these
Rationale: "explanation : number greater than 4 is 5 & 6 , so only 2 number total cases of dice = [ 1,2 , 3,4 , 5,6 ] so probability = 2 / 6 = 1 / 3 answer : b"
Answer: b
Question (gain): in a particular state , 60 % of the counties received some rain on monday , and 65 % of the counties received some rain on tuesday . no rain fell either day in 25 % of the counties in the state . what percent of the counties received some rain on monday and tuesday ?
Options: a ) 12.5 % , b ) 40 % , c ) 50 % , d ) 60 % , e ) 67.5 %
Rationale: "60 + 65 + 25 = 150 % the number is 50 % above 100 % because 50 % of the counties were counted twice . the answer is c ."
Answer: c
Question (gain): two boys starts from the same place walking at the rate of 5 kmph and 5.5 kmph respectively in the same direction . what time will they take to be 8.5 km apart ?
Options: a ) 17 hr , b ) 14 hr , c ) 12 hr , d ) 19 hr , e ) 23 hr
Rationale: "relative speed = 5.5 - 5 = 0.5 kmph ( because they walk in the same direction ) distance = 8.5 km time = distance / speed = 8.5 / 0.5 = 17 hr answer is a"
Answer: a
Question (physics): two dogsled teams raced across a 300 mile course in wyoming . team a finished the course in 3 fewer hours than team q . if team a ' s average speed was 5 mph greater than team q ' s , what was team q ' s average mph ?
Options: a ) 12 , b ) 15 , c ) 18 , d ) 20 , e ) 25
Rationale: "this is a very specific format that has appeared in a handful of real gmat questions , and you may wish to learn to recognize it : here we have a * fixed * distance , and we are given the difference between the times and speeds of two things that have traveled that distance . this is one of the very small number of question formats where backsolving is typically easier than solving directly , since the direct approach normally produces a quadratic equation . say team q ' s speed was s . then team q ' s time is 300 / s . team a ' s speed was then s + 5 , and team a ' s time was then 300 / ( s + 5 ) . we need to find an answer choice for s so that the time of team a is 3 less than the time of team q . that is , we need an answer choice so that 300 / ( s + 5 ) = ( 300 / s ) - 3 . you can now immediately use number properties to zero in on promising answer choices : the times in these questions will always work out to be integers , and we need to divide 300 by s , and by s + 5 . so we want an answer choice s which is a factor of 300 , and for which s + 5 is also a factor of 300 . so you can rule out answers a and c immediately , since s + 5 wo n ' t be a divisor of 300 in those cases ( sometimes using number properties you get to the correct answer without doing any other work , but unfortunately that ' s not the case here ) . testing the other answer choices , if you try answer d , you find the time for team q is 15 hours , and for team a is 12 hours , and since these differ by 3 , as desired , d is correct ."
Answer: d
Question (general): the average salary of the employees in a office is rs . 120 / month . the avg salary of officers is rs . 460 and of non officers is rs 110 . if the no . of officers is 15 , then find the no of nonofficers in the office .
Options: a ) 400 , b ) 420 , c ) 430 , d ) 450 , e ) 510
Rationale: "let no . of non - officers be x 15 * 460 + x * 110 = ( x + 15 ) 120 x = 510 e"
Answer: e
Question (other): the h . c . f . of two numbers is 10 and the other two factors of their l . c . m . are 13 and 14 . the larger of the two numbers is :
Options: a ) 100 , b ) 120 , c ) 180 , d ) 140 , e ) 60
Rationale: "clearly , the numbers are ( 10 x 13 ) and ( 10 x 14 ) . larger number = ( 10 x 14 ) = 140 . answer : option d"
Answer: d
Question (gain): a and b began business with rs . 3000 and rs . 4000 after 8 months , a withdraws rs . 1000 and b advances rs . 1000 more . at the end of the year , their profits amounted to rs . 672 find the share of a .
Options: a ) 256 , b ) 388 , c ) 379 , d ) 277 , e ) 122
Rationale: "explanation : ( 3 * 8 + 2 * 4 ) : ( 4 * 8 + 5 * 4 ) 8 : 13 8 / 21 * 672 = 256 answer : a"
Answer: a
Question (general): a cricketer whose bowling average is 12.4 runs per wicket takes 5 wickets for 26 runs and there by decreases his average by 0.4 . the number age of the family now is ?
Options: a ) 17 , b ) 98 , c ) 88 , d ) 85 , e ) 83
Rationale: let the number of wickets taken till the last match be x . then , ( 12.4 x + 26 ) / ( x + 5 ) = 12 = 12.4 x + 26 = 12 x + 60 = 0.4 x = 34 = x = 340 / 4 = 85 . answer : d
Answer: d
Question (other): a began business with rs . 27000 and was joined afterwards by b with rs . 54000 . when did b join if the profits at the end of the year were divided in the ratio of 2 : 1 ?
Options: a ) 9 , b ) 6 , c ) 7 , d ) 8 , e ) 2
Rationale: 27 * 12 : 54 * x = 2 : 1 x = 3 12 - 3 = 9 answer : a
Answer: a
Question (general): in a recent election , james received 2.1 percent of the 2,000 votes cast . to win the election , a candidate needed to receive more than 46 percent of the vote . how many additional votes would james have needed to win the election ?
Options: a ) 901 , b ) 879 , c ) 990 , d ) 991 , e ) 1,001
Rationale: "james = ( 2.1 / 100 ) * 2000 = 42 votes to win = ( 46 / 100 ) * total votes + 1 = ( 46 / 100 ) * 2000 + 1 = 921 remaining voted needed to win election = 921 - 42 = 879 answer : option b"
Answer: b
Question (physics): a , band c can do a piece of work in 11 days , 20 days and 20 days respectively , working alone . how soon can the work be done if a is assisted by band c on alternate days ?
Options: a ) 7 days , b ) 8 days , c ) 9 days , d ) 10 days , e ) 11 days
Rationale: "( a + b ) ' s 1 day ' s work = 1 / 11 + 1 / 20 = 31 / 220 ( a + c ) ' s 1 day ' s work = 1 / 11 + 1 / 20 = 31 / 220 work done in 2 day ' s = 31 / 220 + 31 / 220 = 31 / 110 31 / 110 th work done in 2 days work done = 110 / 31 * 2 = 7 days ( approx ) answer : a"
Answer: a
Question (general): let c be defined as the sum of all prime numbers between 0 and 38 . what is c / 3
Options: a ) 155 , b ) 76.6 , c ) 61 , d ) 47 , e ) 43
Rationale: "prime numbers between 0 and 30 - 2 , 3 , 5 , 7 , 11 , 13 , 17 , 19 , 23 , 29 , 31 , 33 , 37 sum , c = 230 c / 3 = 76.6 answer b"
Answer: b
Question (general): out of 40 applicants to a law school , 15 majored in political science , 20 had a grade point average higher than 3.0 , and 10 did not major in political science and had a gpa equal to or lower than 3.0 . how many t applicants majored in political science and had a gpa higher than 3.0 ?
Options: a ) 5 , b ) 10 , c ) 15 , d ) 25 , e ) 35
Rationale: "total applicants = 40 political science = 15 and non political science = 40 - 15 = 25 gpa > 3.0 = 20 and gpa < = 3.0 = 20 10 non political science students had gpa < = 3.0 - - > 15 non political science students had gpa > 3.0 gpa > 3.0 in political science = total - ( gpa > 3.0 in non political science ) t = 20 - 15 = 5 answer : a"
Answer: a
Question (general): two numbers a and b are such that the sum of 5 % of a and 2 % of b is two - third of the sum of 6 % of a and 8 % of b . find the ratio of a : b .
Options: a ) 2 : 1 , b ) 1 : 2 , c ) 4 : 3 , d ) 10 : 3 , e ) 3 : 2
Rationale: explanation : 5 % of a + 2 % of b = 2 / 3 ( 6 % of a + 8 % of b ) 5 a / 100 + 2 b / 100 = 2 / 3 ( 6 a / 100 + 8 b / 100 ) ⇒ 5 a + 2 b = 2 / 3 ( 6 a + 8 b ) ⇒ 15 a + 6 b = 12 a + 16 b ⇒ 3 a = 10 b ⇒ ab = 10 / 3 ⇒ a : b = 10 : 3 answer : option d
Answer: d
Question (other): a man invests some money partly in 9 % stock at 96 and partly in 12 % stock at 120 . to obtain equal dividends from both , he must invest the money in the ratio ?
Options: a ) 16 : 18 , b ) 16 : 13 , c ) 16 : 15 , d ) 16 : 12 , e ) 16 : 11
Rationale: "for an income of re . 1 in 9 % stock at 96 , investment = rs . 96 / 9 = rs . 32 / 3 for an income re . 1 in 12 % stock at 120 , investment = rs . 120 / 12 = rs . 10 . ratio of investments = ( 32 / 3 ) : 10 = 32 : 30 = 16 : 15 answer : c"
Answer: c
Question (physics): 20 men do a work in 20 days . how many men are needed to finish the work in 10 days ?
Options: a ) 50 , b ) 20 , c ) 30 , d ) 10 , e ) 40
Rationale: "men required to finish the work in 10 days = 20 * 20 / 10 = 40 answer is e"
Answer: e
Question (general): if 5 a = 6 b and ab ≠ 0 , what is the ratio of a / 6 to b / 5 ?
Options: a ) 36 / 25 , b ) 10 / 12 , c ) 1 , d ) 1 / 5 , e ) 25 / 36
Rationale: "a nice fast approach is the first find a pair of numbers that satisfy the given equation : 5 a = 6 b here ' s one pair : a = 6 and b = 5 what is the ratio of a / 6 to b / 5 ? in other words , what is the value of ( a / 6 ) / ( b / 5 ) ? plug in values to get : ( a / 6 ) / ( b / 5 ) = ( 6 / 6 ) / ( 5 / 5 ) = 1 / 1 = 1 c"
Answer: c
Question (gain): a dishonest milkman wants to make a profit on the selling of milk . he would like to mix water ( costing nothing ) with milk costing rs . 33 per litre so as to make a profit of 25 % on cost when he sells the resulting milk and water mixture for rs . 36 in what ratio should he mix the water and milk ?
Options: a ) 1 : 20 , b ) 1 : 10 , c ) 1 : 8 , d ) 1 : 4 , e ) 21 : 124
Rationale: "water = w ( liter ) milk = m ( liter ) = = > cost = price x quantity = 0.33 m = = > revenue = price x quantity = 0.36 ( m + w ) = = > profit = 0.36 ( m + w ) - 0.33 m = 0.25 * ( 0.33 m ) [ 25 % of cost ] = = > 0.36 m + 0.36 w - 0.33 m = 0.0825 m = = > 0.0525 m = 0.36 w = = > m / w = 0.36 / 0.0525 = 124 / 21 - - or - - w / m = 21 / 124 e is correct ."
Answer: e
Question (physics): gary ’ s gas station serves an average of 15 cars per hour on saturdays , 10 cars per hour on sundays , and 9 cars per hour on all other days of the week . if the station is open from 6 a . m . to 10 p . m . every day , how many cars does gary ’ s station serve over the course of a typical week ?
Options: a ) 1,120 , b ) 1,200 , c ) 1,240 , d ) 1,280 , e ) 1,320
Rationale: 6 a . m . to 10 p . m . = 16 hours number of cars serviced on weekdays = ( 16 * 9 * 5 ) number of cars serviced on saturday = ( 16 * 15 ) number of cars serviced on sunday = ( 16 * 10 ) number of cars served in a week = 16 ( 45 + 15 + 10 ) = 16 * 70 = 1120 answer : a
Answer: a
Question (physics): x does a work in 20 days . y does the same work in 30 days . in how many days they together will do the same work ?
Options: a ) 10 , b ) 12 , c ) 20 , d ) 30 , e ) 15
Rationale: "x ' s 1 day ' s work = 1 / 20 y ' s 1 day ' s work = 1 / 30 ( x + y ) ' s 1 day ' s work = ( 1 / 20 + 1 / 30 ) = 1 / 12 both together will finish the work in 12 days . correct option is b"
Answer: b
Question (physics): jack and jill are marathon runners . jack can finish a marathon ( 42 km ) in 3.5 hours and jill can run a marathon in 4.2 hours . what is the ratio of their average running speed ? ( jack : jill )
Options: a ) 14 / 15 , b ) 15 / 14 , c ) 4 / 5 , d ) 6 / 5 , e ) can not be determined
Rationale: average speed of jack = distance / time = 42 / ( 7 / 2 ) = 84 / 7 average speed of jill = 42 / ( 4.2 ) = 10 ratio of average speed of jack to jill = ( 84 / 7 ) / 10 = 84 / 70 = 6 / 5 answer d
Answer: d
Question (general): a container contains 1000 liters of milk , from this container 10 liters of milk was taken out and replaced by water . this process was repeated further 2 times . how much milk is now contained by the container ?
Options: a ) 970.3 liters , b ) 1000.45 liters , c ) 879.65 liters , d ) 1020.56 liters , e ) 910.95 liters
Rationale: amount of milk left after 3 operations = 1000 ( 1 - 10 / 1000 ) ^ 3 = 1000 * 99 / 100 * 99 / 100 * 99 / 100 = 970.3 liters answer is a
Answer: a
Question (gain): the workforce of company x is 60 % female . the company hired 20 additional male workers , and as a result , the percent of female workers dropped to 50 % . how many employees did the company have after hiring the additional male workers ?
Options: a ) 145 , b ) 188 , c ) 189 , d ) 190 , e ) 191
Rationale: "let x be the total worker then 0.6 x = female worker and 0.4 x is male worker then 20 male worker added 06 x / ( 0.4 x + 20 ) = 50 / 100 or 60 x = 50 * ( 0.4 x + 100 ) = 20 x + 5000 or 40 x = 5000 , x = 500 / 4 = 125 total worker = 125 + 20 = 145 a"
Answer: a
Question (geometry): the ratio between the perimeter and the width of a rectangle is 5 : 1 . if the area of the rectangle is 216 sq . cm , what is the width of the rectangle ?
Options: a ) 12 cm , b ) 16 cm , c ) 18 cm , d ) 20 cm , e ) 22 cm
Rationale: "2 l + 2 w = 5 w l = 3 w / 2 w * l = 216 3 w ^ 2 / 2 = 216 w ^ 2 = 144 w = 12 the answer is a ."
Answer: a
Question (geometry): a squirrel runs up a cylindrical post , in a perfect spiral path making one circuit for each rise of 3 feet . how many feet does the squirrel travels if the post is 18 feet tall and 3 feet in circumference ?
Options: a ) 10 feet , b ) 12 feet , c ) 13 feet , d ) 15 feet , e ) 18 feet
Rationale: "total circuit = 18 / 3 = 6 total feet squirrel travels = 6 * 3 = 18 feet answer : e"
Answer: e
Question (geometry): in an electric circuit , two resistors with resistances 3 ohm and 5 ohm are connected in parallel . in this case , if r is the combined resistance of these two resistors , then the reciprocal of r is equal to the sum of the reciprocals of two resistors . what is the value ?
Options: a ) 15 ohms
b ) 15 / 8 ohms
c ) 1 / 8 ohms
d ) 8 / 15 ohms
e ) 8 ohms
Rationale: the wording is a bit confusing , though basically we are told that 1 / r = 1 / 3 + 1 / 5 , from which it follows that r = 15 / 8 ohms . answer : b .
Answer: b
Question (general): a and b enterd into a partnership investing rs . 16000 and rs . 12000 respectively . after 3 months , a withdrew rs . 5000 while b invested rs . 5000 more . after 3 more months . c joins the business with a capital of rs . 21000 . the share of b exceeds that of c , out of a total profit of rs . 26400 after one year by
Options: a ) rs . 2400 , b ) rs . 3000 , c ) rs . 3600 , d ) rs . 4800 , e ) none of these
Rationale: solution a : b : c = ( 16000 x 3 + 11000 x 9 ) : ( 12000 x 3 + 17000 x 9 ) : ( 21000 x 6 ) = 147 : 180 : 126 = 7 : 9 : 6 . ∴ difference of b and c ’ s shares = rs . ( 26400 x 9 / 22 - 26400 x 6 / 22 ) = rs . 3600 . answer c
Answer: c
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 $ 0.815 per pound ?
Options: a ) 1 : 3 , b ) 1 : 2 , c ) 6 : 1 , d ) 2 : 1 , e ) 3 : 1
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 ) = 0.815 0.9 – 0.1 x = 0.815 x = 0.85 thus ratio of both flours is 6 : 1 c"
Answer: c
Question (gain): if the cost price of 20 articles is equal to the selling price of 25 articles , what is the % profit or % loss made by the merchant ?
Options: a ) 25 % loss , b ) 25 % profit , c ) 20 % loss , d ) 20 % profit , e ) 5 % profit
Rationale: "explanatory answer approach : assume a value for cost price . compute cost price and selling price for the same number of articles let the cost price of 1 article be $ 1 . therefore , cost price of 20 articles = 20 * 1 = $ 20 the selling price of 25 articles = cost price of 20 articles = $ 20 . let us find the cost price of 25 articles . cost price of 25 articles = 25 * 1 = $ 25 . therefore , profit made on sale of 25 articles = selling price of 25 articles - cost price of 25 articles = 20 - 25 = - $ 5 . because the profit is in the negative , the merchant has made a loss of $ 5 . therefore , % loss = loss / cost price ∗ 100 % loss = 5 / 25 ∗ 100 = 20 % loss . choice c"
Answer: c
Question (physics): in a 500 m race , the ratio of the speeds of two contestants a and b is 3 : 4 . a has a start of 155 m . then , a wins by :
Options: a ) 60 m , b ) 20 m , c ) 40 m , d ) 20 m , e ) 23 m
Rationale: "to reach the winning post a will have to cover a distance of ( 500 - 155 ) m , i . e . , 345 m . while a covers 3 m , b covers 4 m . while a covers 345 m , b covers 4 x 345 / 3 m = 460 m . thus , when a reaches the winning post , b covers 460 m and therefore remains 40 m behind . a wins by 40 m . answer : c"
Answer: c
Question (general): dan ' s age after 16 years will be 6 times his age 4 years ago . what is the present age of dan ?
Options: a ) 8 , b ) 10 , c ) 12 , d ) 14 , e ) 16
Rationale: "let dan ' s present age be x . x + 16 = 6 ( x - 4 ) 5 x = 40 x = 8 the answer is a ."
Answer: a
Question (general): the ratio of two quantities is 10 : 7 . if each of the quantities is increased by 2 , their ratio changes to 15 : 11 then the greatest number is ?
Options: a ) 10 , b ) 12 , c ) 15 , d ) 16 , e ) 20
Rationale: "let the numbers be 10 x and 7 x then 10 x + 2 / 7 x + 2 = 15 / 11 110 x + 22 = 105 x + 30 5 x = 8 x = 1.6 greatest number = 10 * 1.6 = 16 answer is d"
Answer: d
Question (gain): by selling 20 pencils for a rupee a man loses 60 % . how many for a rupee should he sell in order to gain 60 % ?
Options: a ) 8 , b ) 9 , c ) 7 , d ) 6 , e ) 5
Rationale: "40 % - - - 20 160 % - - - ? 40 / 160 * 20 = 5 answer : e"
Answer: e
Question (gain): after decreasing 24 % in the price of an article costs rs . 1216 . find the actual cost of an article ?
Options: a ) 1667 , b ) 6789 , c ) 1200 , d ) 1600 , e ) 1421
Rationale: "cp * ( 76 / 100 ) = 1216 cp = 16 * 100 = > cp = 1600 answer : d"
Answer: d
Question (general): if ( 18 ^ a ) * 9 ^ ( 3 a – 1 ) = ( 2 ^ 3 ) ( 3 ^ b ) and a and b are positive integers , what is the value of a ?
Options: a ) 22 , b ) 11 , c ) 9 , d ) 6 , e ) 3
Rationale: 18 ^ a ) * 9 ^ ( 3 a – 1 ) = ( 2 ^ 3 ) ( 3 ^ b ) = 2 ^ a . 9 ^ a . 9 ^ ( 3 a – 1 ) = ( 2 ^ 3 ) ( 3 ^ b ) just compare powers of 2 from both sides ( no need to calculate powers of 3 , 9 as value of b is not asked ) answer = 3 answer : e
Answer: e
Question (physics): a student traveled 10 percent of the distance of the trip alone , continued another 30 miles with a friend , and then finished the last half of the trip alone . how many miles long was the trip ?
Options: a ) 75 , b ) 100 , c ) 125 , d ) 150 , e ) 175
Rationale: let x be the total length of the trip . 0.1 x + 30 miles + 0.5 x = x 30 miles = 0.4 x x = 75 miles the answer is a .
Answer: a
Question (gain): a bag marked at $ 250 is sold for $ 120 . the rate of discount is ?
Options: a ) 10 % , b ) 25 % , c ) 20 % , d ) 52 % , e ) 45 %
Rationale: "rate of discount = 130 / 250 * 100 = 52 % answer is d"
Answer: d
Question (physics): a can do a piece of work 30 days . b can do work in 45 days . in how many days they will complete the work together ?
Options: a ) 15 days , b ) 16 days , c ) 19 days , d ) 17 days , e ) 18 days
Rationale: "lcm = 90 , ratio = 30 : 45 = 2 : 3 no of days = 90 / ( 2 + 3 ) = 90 / 5 = 18 days answer : e"
Answer: e
Question (other): the ratio of 2 numbers is 3 : 7 and their h . c . f . is 12 . their l . c . m . is ?
Options: a ) 20 , b ) 24 , c ) 252 , d ) 136 , e ) 160
Rationale: "let the numbers be 3 x and 7 x their h . c . f . = 3 so the numbers are 3 * 12 , 7 * 12 = 36,84 l . c . m . = 252 answer is c"
Answer: c
Question (general): average between two sets of numbers is closer to the set with morenumbers ?
Options: a ) 70 , b ) 80 , c ) 85 , d ) 90 , e ) 95
Rationale: "if on a test three people answered 90 % of the questions correctly and two people answered 80 % correctly , then the average for the group is not 85 % but rather 3 × 90 + 2 × 805 = 4305 = 86.3 × 90 + 2 × 805 = 4305 = 86 . here , 90 has a weight of 3 = > it occurs 3 times . whereas 80 has a weight of 2 = > it occurs 2 times . so the average is closer to 90 than to 80 as we have just calculated . b"
Answer: b