Cheukting/mathqa huggingface dataset:
Question (general): two kinds of vodka are mixed in the ratio 1 : 5 and 5 : 1 and they are sold fetching the profit 10 % and 20 % respectively . if the vodkas are mixed in equal ratio and the individual profit percent on them are increased by 4 / 3 and 5 / 3 times respectively , then the mixture will fetch the profit of
Options: a ) 21 % , b ) 20 % , c ) 21 % 18 % , d ) 23 % , e ) can not be determined
Rationale: "the profit on the first kind of vodka = x % ; the profit on the second kind of vodka = y % . when they are mixed in the ratio 1 : 2 ( total of 3 parts ) the average profit is 10 % : ( x + 2 y ) / 3 = 10 . when they are mixed in the ratio 2 : 1 ( total of 3 parts ) the average profit is 20 % : ( 2 x + y ) / 3 = 20 . solving gives : x = 30 % and y = 0 % . after the individual profit percent on them areincreased by 4 / 3 and 5 / 3 times respectively the profit becomes 40 % and 0 % , on the first and te second kinds of vodka , respectively . if they are mixed in equal ratio ( 1 : 1 ) , then the mixture will fetch the profit of ( 40 + 0 ) / 2 = 20 % . answer : c"
Answer: c
Question (other): a salesman sold twice as much pears in the afternoon than in the morning . if he sold $ 360 kilograms of pears that day , how many kilograms did he sell in the morning and how many in the afternoon ?
Options: a ) 120 , b ) 180 , c ) 240 , d ) 280 , e ) 320
Rationale: "let x be the number of kilograms he sold in the morning . then in the afternoon he sold 2 x kilograms . so , the total is x + 2 x = 3 x . this must be equal to 360 . 3 x = 360 x = 3603 x = 120 therefore , the salesman sold 120 kg in the morning and 2 ⋅ 120 = 240 kg in the afternoon . so answer is c ."
Answer: c
Question (general): the average of the marks of 25 students in a class is 70 . if the marks of each student are doubled , find the new average ?
Options: a ) 140 , b ) 100 , c ) 85 , d ) 160 , e ) 190
Rationale: "sum of the marks for the 25 students = 25 * 70 = 1750 . the marks of each student are doubled , the sum also will be doubled . the new sum = 1750 * 2 = 3500 . so , the new average = 3500 / 25 = 140 . answer : a"
Answer: a
Question (physics): a train after traveling for 50 km meets with an accident and then proceeds at 3 / 4 of its former speed and arrives at its destination 35 minutes late . had the accident occurred 24 km farther , it would have reached the destination only 25 minutes late . what is the speed w of the train .
Options: a ) a ) 45 , b ) b ) 33 , c ) c ) 48 , d ) d ) 55 , e ) e ) 61
Rationale: "let y be the balance distance to be covered and x be the former speed . a train after traveling for 50 km meets with an accident and then proceeds at 3 / 4 of its former speed and arrives at its destination 35 minutes late so , y / ( 3 x / 4 ) - y / x = 35 / 60 4 y / 3 x - y / x = 7 / 12 y / x ( 4 / 3 - 1 ) = 7 / 12 y / x * 1 / 3 = 7 / 12 y / x = 7 / 4 4 y - 7 x = 0 . . . . . . . . 1 had the accident occurred 24 km farther , it would have reached the destination only 25 minutes late so , ( y - 24 ) / ( 3 x / 4 ) - ( y - 24 ) / x = 25 / 60 4 ( y - 24 ) / 3 x - ( y - 24 ) / x = 5 / 12 ( y - 24 ) / x ( 4 / 3 - 1 ) = 5 / 12 ( y - 24 ) / x * 1 / 3 = 5 / 12 ( y - 24 ) * 12 = 3 x * 5 ( y - 24 ) * 4 = 5 x 4 y - 5 x = 96 . . . . . . . 2 eq 2 - eq 1 2 x = 96 x = 48 = w ans = c"
Answer: c
Question (physics): amit and ananthu can do a work in 10 days and 20 days respectively . amit started the work and left after 2 days . ananthu took over and completed the work . in how many days was the total work completed ?
Options: a ) 18 days , b ) 20 days , c ) 23 days , d ) 25 days , e ) 27 days
Rationale: amit ’ s one day ’ s work = 1 / 10 amit ’ s 2 day ’ s work = 1 / 10 * 2 = 1 / 5 work left = 1 - 1 / 5 = 4 / 5 ananthu ’ s one day ’ s work = 1 / 20 ananthu can do work in = 4 / 5 * 20 = 16 days so total days = 16 + 2 = 18 days answer : a
Answer: a
Question (other): there are two positive numbers in the ratio 4 : 8 . if the larger number exceeds the smaller by 16 , then find the smaller number ?
Options: a ) 25 , b ) 20 , c ) 77 , d ) 88 , e ) 44
Rationale: "let the two positive numbers be 5 x and 8 x respectively . 8 x - 4 x = 16 4 x = 16 = > x = 4 = > smaller number = 5 x = 20 . answer : b"
Answer: b
Question (other): cheese , bologna , and peanut butter sandwiches were made for a picnic in a ratio of 1 to 7 to 8 . if a total of 80 sandwiches were made , how many bologna sandwiches were made ?
Options: a ) 15 , b ) 30 , c ) 35 , d ) 42 , e ) 48
Rationale: for deciding such task we should calculate all parts 1 + 7 + 8 = 16 parts and we should calculate how many sandwiches holds 1 part : 80 / 16 = 5 sandwiches in one part for bologna we have 7 parts so : 7 * 5 = 35 answer is c
Answer: c
Question (general): for the past n days , the average ( arithmetic mean ) daily production at a company was 50 units . if today ' s production of 110 units raises the average to 55 units per day , what is the value of n ?
Options: a ) 9 , b ) 11 , c ) 13 , d ) 15 , e ) 17
Rationale: "the daily production was raised by 5 units for n days , which has a weighting of 5 n . 5 n = 110 - 55 = 55 n = 11 the answer is b ."
Answer: b
Question (physics): a train is 360 meter long is running at a speed of 50 km / hour . in what time will it pass a bridge of 140 meter length ?
Options: a ) 87 , b ) 69 , c ) 36 , d ) 72 , e ) 21
Rationale: "speed = 50 km / hr = 50 * ( 5 / 18 ) m / sec = 125 / 9 m / sec total distance = 360 + 140 = 500 meter time = distance / speed = 500 * ( 9 / 125 ) = 36 seconds answer : c"
Answer: c
Question (general): the population of locusts in a certain swarm doubles every two hours . if 4 hours ago there were 1,000 locusts in the swarm , in approximately how many hours will the swarm population exceed 128,000 locusts ?
Options: a ) 12 , b ) 8 , c ) 4 , d ) 10 , e ) 16
Rationale: - 4 hours : 1,000 - 2 hours : 2,000 now : 4,000 + 2 hours : 8,000 + 4 hours : 16,000 + 6 hours : 32,000 + 8 hours : 64,000 + 10 hours : 128,000 answer : d
Answer: d
Question (gain): the cash difference between the selling prices of an book at a profit of 12 % and 20 % is $ 3 . the ratio of the two selling prices is :
Options: a ) 55 : 23 , b ) 52 : 33 , c ) 52 : 53 , d ) 45 : 53 , e ) 14 : 15
Rationale: "let c . p . of the book be $ x . then , required ratio = 112 % of x / 120 % of x = 112 / 120 = 14 / 15 = 14 : 15 e"
Answer: e
Question (general): mixture contains alcohol and water in the ratio 4 : 3 . if 5 liters of water is added to the mixture , the ratio becomes 4 : 5 . find the quantity of alcohol in the given mixture .
Options: a ) 10 , b ) 99 , c ) 27 , d ) 22 , e ) 29
Rationale: "let the quantity of alcohol and water be 4 x litres and 3 x litres respectively 20 x = 4 ( 3 x + 5 ) 8 x = 20 x = 2.5 quantity of alcohol = ( 4 x 2.5 ) litres = 10 litres . answer : a"
Answer: a
Question (physics): a train 310 m long is running at a speed of 45 km / hr . in what time will it pass a bridge 140 m long ?
Options: a ) 40 , b ) 56 , c ) 41 , d ) 36 , e ) 34
Rationale: "speed = 45 * 5 / 18 = 25 / 2 m / sec total distance covered = 310 + 140 = 450 m required time = 450 * 2 / 25 = 36 sec answer : option d"
Answer: d
Question (gain): a merchant gets a 5 % discount on each meter of fabric he buys after the first 2,000 meters and a 7 % discount on every meter after the next 1,500 meters . the price , before discount , of one meter of fabric is $ 2 , what is the total amount of money the merchant spends on 6,500 meters of fabric ?
Options: a ) $ 11,320 , b ) $ 12,430 , c ) $ 13,540 , d ) $ 14,650 , e ) $ 15,760
Rationale: "for first 2000 meters he does not get any discount . the price is 2 * 2000 = $ 4000 for next 1500 meters , he gets a 5 % discount . the price is 1.9 * 1500 = $ 2850 for the next 1500 meters , he gets a 7 % discount . the price is 1.86 * 3000 = $ 5580 the total price is $ 4000 + $ 2850 + $ 5580 = $ 12,430 the answer is b ."
Answer: b
Question (physics): two pipes a and b can fill a tank in 36 hours and 46 hours respectively . if both the pipes are opened simultaneously , how much time will be taken to fill the tank ?
Options: a ) 20.195 hrs , b ) 21.195 hrs , c ) 22.195 hrs , d ) 23.195 hrs , e ) 20.495 hrs
Rationale: "a fill in one hour = 1 / 36 b fill in one hour = 1 / 46 both fill in one hour = 1 / 36 + 1 / 46 = 82 / 1656 time taken by both pipes = 1656 / 82 = 20.195 hrs answer : a"
Answer: a
Question (general): a grocer has a sale of rs . 5435 , rs . 5927 , rs . 5855 , rs . 6230 and rs . 5562 for 5 consecutive months . how much sale must he have in the sixth month so that he gets an average sale of rs . 5500 ?
Options: a ) 4991 , b ) 5991 , c ) 3991 , d ) 6542 , e ) 6995
Rationale: "total sale for 5 months = rs . ( 5435 + 5927 + 5855 + 6230 + 5562 ) = rs . 29009 . required sale = rs . [ ( 5500 x 6 ) - 29009 ] = rs . ( 33000 - 29009 ) = rs . 3991 answer : option c"
Answer: c
Question (general): find the result of equation of the ellipse whose foci are at ( 0 , - 5 ) and ( 0 , 5 ) and the length of its major axis is 14 .
Options: a ) 5 , b ) 4 , c ) 3 , d ) 2 , e ) 1
Rationale: from the coordinates of the foci , c = 5 and the major axis is the y axis . from the length of the major axis , we obtain a = 7 . also b 2 = a 2 - c 2 = 24 . the equation of the ellipse is given by x 2 / 24 + y 2 / 49 = 1 correct answer is e ) 1
Answer: e
Question (general): if p represents the product of the first 16 positive integers , then p is not a multiple of
Options: a ) 99 , b ) 84 , c ) 72 , d ) 65 , e ) 51
Rationale: "answer is e . since prime factor of 51 is 3 x 17 . 17 is a prime number and not part of the first 15 positive integers . a ) 9 x 11 b ) 12 x 7 c ) 12 x 6 d ) 13 x 5 e ) 3 x 17"
Answer: e
Question (general): if 12 machine can finish a job in 40 days , then how many more machines would be needed to finish the job in one - fourth less time ?
Options: a ) a . 4 , b ) b . 8 , c ) c . 10 , d ) d . 12 , e ) e . 16
Rationale: you might think of this in a management context - we can use the principle of ' person - hours ' to solve any problem where we have identical workers . so , using simpler numbers , suppose you know that 6 identical employees , working simultaneously , would finish a job in 5 hours . then that job requires 6 * 5 = 30 total hours of person - work . if instead you wanted the job done in 3 hours , you ' d assign 30 / 3 = 10 employees to do the job , because you want to get a total of 30 hours of work from the employees . we can solve this problem identically . if 12 machines ( identical ones , i assume ) work simultaneously for 40 days , they will do a total of 12 * 40 machine - days of work . so the job requires 12 * 40 days of machine work in total . we instead want the job done in 1 / 4 less time , so in 30 days . so we ' ll need 12 * 40 / 30 = 16 machines , or 4 additional machines . a
Answer: a
Question (general): following an increase in prices , the price of a candy box was 20 pounds and the price of a can of soda was 6 pounds . if the price of a candy box was raised by 25 % , and the price of a can of soda was raised by 50 % . what was the price of a box of candy plus a can of soda before prices were raised ?
Options: a ) 11 . , b ) 20 . , c ) 13 . , d ) 14 . , e ) 14.5
Rationale: "price of candy before price increase = 20 / 1.25 = 16 price of soda before price increase = 6 / 1.5 = 4 total price = 16 + 4 = 20 b is the answer"
Answer: b
Question (geometry): a rectangular farm has to be fenced one long side , one short side and the diagonal . if the cost of fencing is rs . 14 per meter . the area of farm is 1200 m 2 and the short side is 30 m long . how much would the job cost ?
Options: a ) 1276 , b ) 1680 , c ) 2832 , d ) 1299 , e ) 1236
Rationale: "explanation : l * 30 = 1200 è l = 40 40 + 30 + 50 = 120 120 * 14 = 1680 answer : option b"
Answer: b
Question (physics): . a car covers a distance of 810 km in 5 hours . find its speed ?
Options: a ) 104 , b ) 55 , c ) 162 , d ) 174 , e ) 2761
Rationale: "810 / 5 = 162 kmph answer : c"
Answer: c
Question (other): the compounded ratio of ( 2 : 3 ) , ( 6 : 11 ) and ( 11 : 2 ) is
Options: a ) 2 : 0 , b ) 2 : 1 , c ) 2 : 9 , d ) 2 : 2 , e ) 2 : 5
Rationale: answer : b ) 2 : 1
Answer: b
Question (general): in a photography exhibition , some photographs were taken by octavia the photographer , and some photographs were framed by jack the framer . jack had framed 24 photographs taken by octavia , and 12 photographs taken by other photographers . if 36 of the photographs in the exhibition were taken by octavia , how many photographs were either framed by jack or taken by octavia ?
Options: a ) 36 , b ) 48 , c ) 72 , d ) 96 , e ) 108
Rationale: the number of photographs either framed by jack or taken by octavia = { jack } + { octavia } - { overlap } = 36 + 36 - 24 = 48 ( { overlap } is green box ) . answer : b
Answer: b
Question (physics): a train 360 m long is running at a speed of 45 kmph . in what time will it pass a bridge 140 m long ?
Options: a ) 40 sec , b ) 42 sec , c ) 45 sec , d ) 48 sec , e ) 49 sec
Rationale: "speed of the train 45 * 5 / 18 = 25 / 2 m / sec time = ( 360 + 140 ) / 25 / 2 = 500 * 2 / 25 = 40 sec answer : a"
Answer: a
Question (general): what is value of ( p + q ) / ( p - q ) if p / q = 7 ?
Options: a ) 1 / 3 , b ) 2 / 3 , c ) 4 / 3 , d ) 5 / 3 , e ) none of these
Rationale: explanation : ( p + q ) / ( p - q ) = ( p / q + 1 ) / ( p / q - 1 ) = ( 7 + 1 ) / ( 7 - 1 ) = 4 / 3 . answer : c
Answer: c
Question (physics): find the area of a cuboid of length 8 cm , breadth 6 cm . and height 9 cm .
Options: a ) 400 cm cube , b ) 410 cm cube , c ) 420 cm cube , d ) 432 cm cube , e ) 480 cm cube
Rationale: "area of a cuboid = lxbxh = 8 cm x 6 cm x 9 cm = 432 cm cube answer : d"
Answer: d
Question (general): if | 5 x - 20 | = 100 , then find the sum of the values of x ?
Options: a ) 1 , b ) - 2 , c ) 8 , d ) - 3 , e ) 4
Rationale: "| 5 x - 20 | = 100 5 x - 20 = 100 or 5 x - 20 = - 100 5 x = 120 or 5 x = - 80 x = 24 or x = - 16 sum = 24 - 16 = 8 answer is c"
Answer: c
Question (general): a windmill is taking advantage of strong air currents in order to produce electrical energy . on a typical day the wind speed is around 20 mph and in that speed the windmill produces 400 kw / h ( kilowatts per hour ) . on a stormy day a windmill produces 20 % more energy . how much kw / h can 3 windmills produce in two hours on a stormy day ?
Options: a ) 2880 . , b ) 4860 . , c ) 5780 , d ) 5760 , e ) 6380 .
Rationale: normal day = 400 kw / h stormy day = 400 * 1.2 = 480 kw / h 3 windmills for 2 hours on stormy day 480 * 3 * 2 = 2880 answer : a
Answer: a
Question (general): john has 10 pairs of matched socks . if he loses 13 individual socks , what is the greatest number of pairs of matched socks he can have left ?
Options: a ) 7 , b ) 3 , c ) 5 , d ) 4 , e ) 1
Rationale: "because we have to maximize the pair of matched socks , we will remove 6 pairs ( 12 socks ) out of 10 pairs 1 sock from the 7 th pair . thus the no of matching socks pair remaining = 10 - 7 = 3 answer b"
Answer: b
Question (general): arjun started a business with rs . 20,000 and is joined afterwards by anoop with rs . 30 , 000 . after how many months did anoop join if the profits at the end of the year are divided equally ?
Options: a ) 3 , b ) 4 , c ) 5 , d ) 6 , e ) 7
Rationale: "suppose anoop joined after 3 months . then , 20000 * 12 = 30000 * ( 12 – x ) = > 120000 = 30000 x = > x = 4 . answer : b"
Answer: b
Question (geometry): the points a ( 0 , 0 ) , b ( 0 , 4 a - 5 ) and c ( 2 a + 1 , 2 a + 5 ) form a triangle . if angle abc = 90 , what is the area of triangle abc ?
Options: a ) 80 , b ) 82.5 , c ) 78.5 , d ) 75.5 , e ) 74
Rationale: "1 / 2 bh = 1 / 2 ( 2 a + 1 ) ( 2 a + 5 ) now 4 a - 5 = 2 a + 5 2 a = 10 , a = 5 therefore , a ( 0,0 ) ; b ( 0,15 ) ; c ( 10,15 ) 1 / 2 * 11 * 15 = 82.5 answer : b"
Answer: b
Question (gain): ramesh purchased a refrigerator for rs . 12500 after getting a discount of 20 % on the labelled price . he spent rs . 125 on transport and rs . 250 on installation . at what price should it be sold so that the profit earned would be 18 % if no discount was offered ?
Options: a ) 17608 , b ) 17606 , c ) 17604 , d ) 17600 , e ) 18880
Rationale: "price at which the tv set is bought = rs . 12,500 discount offered = 20 % marked price = 12500 * 100 / 80 = rs . 15625 the total amount spent on transport and installation = 125 + 250 = rs . 375 \ total price of tv set = 15625 + 375 = rs . 16000 the price at whichthe tv should be sold to get a profit of 18 % if no discount was offered = 16000 * 118 / 100 = rs . 18880 . answer : e"
Answer: e
Question (geometry): a hall is 15 meters long and 15 meters wide . if the sum of the areas of the floor and the ceiling is equal to the sum of the areas of four walls , what is the volume of the hall ( in cubic meters ) ?
Options: a ) 975.5 , b ) 1250.5 , c ) 1465.5 , d ) 1687.5 , e ) 1824.5
Rationale: "2 hl + 2 hw = 2 lw h = lw / ( l + w ) volume = lwh = ( lw ) ^ 2 / ( l + w ) = 1687.5 the answer is d ."
Answer: d
Question (geometry): what is the total surface area in square meters of a rectangular solid whose length is 9 meters , width is 8 meters , and depth is 5 meters ?
Options: a ) 152 m 2 , b ) 162 m 2 , c ) 180 m 2 , d ) 300 m 2 , e ) 314 m 2
Rationale: "surface area of a cuboid = 2 ( lb + bh + lh ) = 2 ( 9 * 8 + 8 * 5 + 9 * 5 ) = 2 ( 72 + 40 + 45 ) = 2 * 157 = 314 m 2 answer : e"
Answer: e
Question (other): how many multiples of 7 are there between 10 and 100 ( both are inclusive ) ?
Options: a ) 11 , b ) 13 , c ) 15 , d ) 17 , e ) 21
Rationale: "7 multiples are 14 , 21,28 , - - - - - - - - - , 98 it should be mentioned whether 10 and 100 are inclusive . the answer is ( 98 - 14 ) / 7 + 1 = 13 answer is b"
Answer: b
Question (physics): a car traveling at a certain constant speed takes 4 seconds longer to travel 1 km than it would take to travel 1 km at 80 km / hour . at what speed , in km / hr , is the car traveling ?
Options: a ) 70 , b ) 72 , c ) 74 , d ) 75 , e ) 78
Rationale: "time to cover 1 kilometer at 80 kilometers per hour is 1 / 80 hours = 3,600 / 80 seconds = 45 seconds ; time to cover 1 kilometer at regular speed is 45 + 4 = 49 seconds = 49 / 3,600 hours = 1 / 74 hours ; so , we get that to cover 1 kilometer 1 / 74 hours is needed - - > regular speed 74 kilometers per hour ( rate is a reciprocal of time or rate = distance / time ) . answer : c"
Answer: c
Question (gain): a , b and c invested rs . 6300 , rs . 4200 and rs . 10500 respectively , in a partnership business . find the share of a in profit of rs . 12500 after a year ?
Options: a ) 3630 , b ) 2881 , c ) 2887 , d ) 3750 , e ) 2212
Rationale: 6300 : 4200 : 10500 3 : 2 : 5 3 / 10 * 12100 = 3750 . answer : d
Answer: d
Question (other): two numbers are in the ratio of 2 : 3 . if 20 be subtracted from each , they are in the ratio of 10 : 17 . find the numbers ?
Options: a ) 70,105 , b ) 60,88 , c ) 80,120 , d ) 60,84 , e ) 60,81
Rationale: "( 2 x - 20 ) : ( 3 x - 20 ) = 10 : 17 x = 35 = > 70,105 answer : a"
Answer: a
Question (gain): a student needs 30 % of the marks on a test to pass the test . if the student gets 80 marks and fails the test by 100 marks , find the maximum marks set for the test .
Options: a ) 400 , b ) 600 , c ) 800 , d ) 1000 , e ) 1200
Rationale: "30 % = 180 marks 1 % = 6 marks 100 % = 600 marks the answer is b ."
Answer: b
Question (physics): to asphalt 1 km road , 30 men spent 12 days working 8 hours per day . how many days , 20 men will spend to asphalt a road of 2 km working 8 hours a day ?
Options: a ) 40 , b ) 36 , c ) 42 , d ) 44 , e ) 46
Rationale: "man - hours required to asphalt 1 km road = 30 * 12 * 8 = 2880 man - hours required to asphalt 2 km road = 2880 * 2 = 5760 man - hours available per day = 20 * 8 = 160 therefore number of days = 5760 / 240 = 36 days ans = b"
Answer: b
Question (general): if x and j are integers and 2 x – j = 11 , then 4 x + j can not be
Options: a ) – 5 , b ) 1 , c ) 13 , d ) 17 , e ) 551
Rationale: 2 x - j = 11 . . . . j = 2 x - 11 4 x + j = 4 x + 2 x - 11 = 6 x - 11 6 x - 11 = - 5 . . . x = 1 6 x - 11 = 1 . . . x = 2 6 x - 11 = 13 . . . x = 4 6 x - 11 = 17 . . x is not integer 6 x - 11 = 551 . . x is not integer i think the choice e is 55 not 551 . otherwise both de can not be solution = d
Answer: d
Question (general): 15.06 * 0.001 = ?
Options: a ) 15060000 , b ) 0.001506 , c ) 0.01506 , d ) 0.1506 , e ) none of these
Rationale: "explanation : clearly after decimal 5 digits should be there . option c"
Answer: c
Question (geometry): a small table has a length of 12 inches and a breadth of b inches . cubes are placed on the surface of the table so as to cover the entire surface . the maximum side of such cubes is found to be 4 inches . also , a few such tables are arranged to form a square . the minimum length of side possible for such a square is 48 inches . find b .
Options: a ) 8 , b ) 16 , c ) 24 , d ) 32 , e ) 48
Rationale: "from the info that the maximum sides of the cubes is 4 , we know that the gcf of 12 ( = 2 ^ 2 * 3 ) and ` ` b ' ' is 4 ( = 2 ^ 2 ) , so ` ` b ' ' = 2 ^ x , where x > = 2 . from the second premise , we know that the lcm of 12 ( 2 ^ 2 * 3 ) and ` ` b ' ' is 48 ( 2 ^ 4 * 3 ) , so ` ` b ' ' = 2 ^ 4 or 2 ^ 4 * 3 ( 16 or 48 ) . combining 2 premises shows the answer is b ( 16 ) ."
Answer: b
Question (gain): an investment yields an interest payment of $ 228 each month . if the simple annual interest rate is 9 % , what is the amount of the investment ?
Options: a ) $ 28,300 , b ) $ 30,400 , c ) $ 31,300 , d ) $ 32,500 , e ) $ 35,100
Rationale: "let the principal amount = p simple annual interest = 9 % simple monthly interest = ( 9 / 12 ) = ( 3 / 4 ) % ( 3 / 4 ) * ( p / 100 ) = 228 = > p = ( 228 * 4 * 10 ^ 2 ) / 3 = 76 * 4 * 10 ^ 2 = 304 * 10 ^ 2 answer b"
Answer: b
Question (gain): on a certain road 10 % of the motorists exceed the posted speed limit and receive speeding tickets , but 24 % of the motorists who exceed the posted speed limit do not receive speeding tickets . what percent of the motorists on the road exceed the posted speed limit ?
Options: a ) 10.5 % , b ) 13.2 % , c ) 15 % , d ) 22 % , e ) 30 %
Rationale: "answer is b . this question is in the og and thus well explained by ets . those who exceed : x so x = 10 % + 0,24 x id est x = 13.2 %"
Answer: b
Question (general): joe ’ s average ( arithmetic mean ) test score across 4 equally weighted tests was 45 . he was allowed to drop his lowest score . after doing so , his average test score improved to 50 . what is the lowest test score that was dropped ?
Options: a ) 20 , b ) 30 , c ) 55 , d ) 65 , e ) 80
Rationale: "the arithmetic mean of 4 equally weighted tests was 45 . so what we can assume is that we have 4 test scores , each 45 . he dropped his lowest score and the avg went to 50 . this means that the lowest score was not 45 and other three scores had given the lowest score 5 each to make it up to 45 too . when the lowest score was removed , the other 3 scores got their 5 back . so the lowest score was 3 * 5 = 15 less than 45 . so the lowest score = 45 - 15 = 30 answer ( b )"
Answer: b
Question (general): if y > 0 , ( 4 y ) / 20 + ( 3 y ) / 10 is what percent of y ?
Options: a ) 40 % , b ) 50 % , c ) 60 % , d ) 70 % , e ) 80 %
Rationale: "can be reduced to 2 y / 10 + 3 y / 10 = y / 2 = 50 % answer b"
Answer: b
Question (gain): in how many years rs 100 will produce the same interest at 5 % as rs . 600 produce in 4 years at 10 %
Options: a ) 44 , b ) 52 , c ) 50 , d ) 46 , e ) 48
Rationale: "explanation : clue : firstly we need to calculate the si with prinical 600 , time 4 years and rate 10 % , it will be rs . 240 then we can get the time as time = ( 100 * 240 ) / ( 100 * 5 ) = 48 option e"
Answer: e