Cheukting/mathqa huggingface dataset:
Question (physics): find the area of trapezium whose parallel sides are 20 cm and 18 cm long , and the distance between them is 11 cm .
Options: a ) 335 cm 2 , b ) 209 cm 2 , c ) 285 cm 2 , d ) 825 cm 2 , e ) 725 cm 2
Rationale: "area of a trapezium = 1 / 2 ( sum of parallel sides ) * ( perpendicular distance between them ) = 1 / 2 ( 20 + 18 ) * ( 11 ) = 209 cm 2 answer : b"
Answer: b
Question (physics): working alone , a can complete a certain kind of job in 3 hours . a and d , working together at their respective rates , can complete one of these jobs in 2 hours . in how many hours can d , working alone , complete one of these jobs ?
Options: a ) 2 , b ) 4 , c ) 6 , d ) 8 , e ) 10
Rationale: let total time taken by d to complete the job = d total time taken by a to complete the job = 3 work done by a in an hour 1 / a = 1 / 3 working together a and d can complete the job in 2 hours 1 / a + 1 / d = 1 / 2 = > 1 / d = 1 / 2 - 1 / a = 1 / 2 - 1 / 3 = 1 / 6 = > d = 6 hours answer c
Answer: c
Question (other): a class of boys stands in a single line , one boy is 19 th in order from both the ends , how many boys are there in the class ?
Options: a ) 37 , b ) 38 , c ) 27 , d ) 29 , e ) 11
Rationale: explanation : number of boys in the class = ( 18 + 1 + 18 ) = 37 answer : a ) 37
Answer: a
Question (general): what number must be added to 6 , 16 and 8 to get an average of 13 ?
Options: a ) 23 , b ) 22 , c ) 44 , d ) 33 , e ) 55
Rationale: b 22
Answer: b
Question (general): the average age of 30 students in a class is 15 years . if the age of teacher is also included , the average becomes 16 years , find the age of the teacher .
Options: a ) 46 , b ) 55 , c ) 43 , d ) 39 , e ) 54
Rationale: "explanation : if teacher ' s age is 15 years , there is no change in the average . but teacher has contributed 1 year to all the students along with maintaining his age at 16 . age of teacher = average age of all + total increase in age = 16 + ( 1 x 30 ) = 46 years answer : a"
Answer: a
Question (general): if x = the product of 7 distinct prime numbers , how many factors does x have besides 1 and itself ?
Options: a ) 108 , b ) 114 , c ) 120 , d ) 126 , e ) 132
Rationale: since x has 7 distinct prime factors , x has a total of 2 ^ 7 = 128 factors . besides 1 and itself , x has 126 factors . the answer is d .
Answer: d
Question (general): how many integers n are prime numbers in the range 200 < n < 220 ?
Options: a ) 1 , b ) 2 , c ) 3 , d ) 4 , e ) 5
Rationale: to test a number n on whether it is a prime number , take square root ( n ) . consider as it is if it is a natural number . otherwise , increase the sq . root to the next natural no . then divide given no . by all prime numbers below the sq . root obtained . if the no . is divisible by any of the prime numbers , then it is not a prime number ; else it is . square root of 200 or 220 is less than 15 so , lets check if any number between 200 and 220 is not divisible by prime numbers 2 , 35 , 711 ( < 15 ) . that ' s it . out : 201 , 202 , 203 , 204 , 205 , 206 , 207 , 208 , 209 , 210 , 212 , 213 , 214 , 215 , 216 , 217 , 218 , 219 only 211 is a prime number in the given range correct option : a
Answer: a
Question (gain): a sum of $ 800 amounts to $ 920 in 3 years at simple interest . if the interest rate is increased by 3 % it would amount to how much ?
Options: a ) $ 506 , b ) $ 774 , c ) $ 992 , d ) $ 854 , e ) $ 1021
Rationale: s . i = 920 - 800 = 120 p = $ 800 t = 3 years r = 100 * 120 / 800 * 3 = 5 % new rate = 5 + 3 = 8 % new s . i . = 800 * 8 * 3 / 100 = $ 192 new amount = 800 + 192 = $ 992 answer is c
Answer: c
Question (physics): a copy machine , working at a constant rate , makes 35 copies per minute . a second copy machine , working at a constant rate , makes 65 copies per minute . working together at their respective rates , how many copies do the two machines make in half an hour ?
Options: a ) 3,000 , b ) 2,700 , c ) 4,500 , d ) 5,400 , e ) 324,000
Rationale: "together the two machines make 35 + 65 = 100 copies per minute . so , in half an hour they will make 100 * 30 = 3,000 copies . answer : a ."
Answer: a
Question (gain): what will be the compound interest on a sum of rs . 28,000 after 3 years at the rate of 12 % p . a . ?
Options: a ) s . 10123.77 , b ) s . 10123.21 , c ) s . 10123.20 , d ) s . 10123.28 , e ) s . 11337.98
Rationale: "amount = [ 28000 * ( 1 + 12 / 100 ) 3 ] = 28000 * 28 / 25 * 28 / 25 * 28 / 25 = rs . 39337.984 c . i . = ( 39337.984 - 28000 ) = rs . 11337.98 answer : e"
Answer: e
Question (general): what is the greatest positive integer x such that 3 ^ x is a factor of 9 ^ 5 ?
Options: a ) 5 , b ) 9 , c ) 10 , d ) 20 , e ) 30
Rationale: "what is the greatest positive integer x such that 3 ^ x is a factor of 9 ^ 5 ? 9 ^ 5 = ( 3 ^ 2 ) ^ 5 = 3 ^ 10 c . 10"
Answer: c
Question (general): 10 % people of a village in sri lanka died by bombardment , 20 % of the remainder left the village on account of fear . if now the population is reduced to 4554 , how much was it in the beginning ?
Options: a ) 7349 , b ) 6300 , c ) 6325 , d ) 6939 , e ) 2989
Rationale: "x * ( 90 / 100 ) * ( 80 / 100 ) = 4554 x = 6325 answer : c"
Answer: c
Question (general): cost is expressed by the formula tb ^ 4 . if b is doubled , the new cost w is what percent of the original cost ?
Options: a ) w = 200 , b ) w = 600 , c ) w = 800 , d ) w = 1600 , e ) w = 50
Rationale: "original cost w , c 1 = t 1 * b 1 ^ 4 new cost c 2 = t 2 * b 2 ^ 4 . . . . only b is doubled so t 2 = t 1 and b 2 = 2 b 1 c 2 = t 2 * ( 2 b 1 ) ^ 4 = 16 ( t 1 * b 1 ^ 4 ) = 16 c 1 16 times c 1 = > 1600 % of c 1 ans d = 1600"
Answer: d
Question (physics): if a car went the first third of the distance at 80 kmh , the second third at 30 kmh , and the last third at 48 kmh , what was the average speed of the car for the entire trip ?
Options: a ) 36 kmh , b ) 40 kmh , c ) 42 kmh , d ) 45 kmh , e ) 50 kmh
Rationale: assume d / 3 = 240 ( this number is convenient because it is divisible by 80 , 30 and 48 ) so : 240 = 80 * t 1 = 3 hrs 240 = 30 * t 2 = 8 hrs 240 = 48 * t 3 = 5 hrs t = t 1 + t 2 + t 3 = 16 hrs d = rt ( 240 * 3 ) = r * 16 r = 45 answer : d
Answer: d
Question (general): a cement mixture is composed of 3 elements . by weight , 1 / 2 of the mixture is sand , 1 / 5 of the mixture is water , and the remaining 15 pounds of the mixture is gravel . what is the weight of the entire mixture in pounds ?
Options: a ) 30 , b ) 40 , c ) 50 , d ) 60 , e ) 80
Rationale: "let the total weight be x . sand content = ( 1 / 2 ) x water content = ( 1 / 5 ) x gravel = x - ( 1 / 2 ) x - ( 1 / 5 ) x = ( 3 / 10 ) x = 15 x = 50 then answer will be c = 50"
Answer: c
Question (other): the compound ratio of 2 / 3 , 6 / 7 , 4 / 3 and 1 / 8 is given by ?
Options: a ) 2 / 21 , b ) 1 / 48 , c ) 1 / 98 , d ) 1 / 96 , e ) 1 / 68
Rationale: "2 / 3 * 6 / 7 * 4 / 3 * 1 / 8 = 48 / 504 = 2 / 21 answer : a"
Answer: a
Question (physics): the center of a circle lies on the origin of the coordinate plane . if a point ( x , y ) is randomly selected inside of the circle , what is the probability that y > x or x > 0 ?
Options: a ) 7 / 8 , b ) 5 / 6 , c ) 3 / 8 , d ) 1 / 2 , e ) 3 / 4
Rationale: "the line y = x divides the circle into two equal areas . all the points above the line y = x satisfy the condition that y > x . all the points to the right of the y - axis satisfy the condition that x > 0 . the union of these two areas is 7 / 8 of the circle . the answer is a ."
Answer: a
Question (gain): reema took a loan of rs 900 with simple interest for as many years as the rate of interest . if she paid rs . 729 as interest at the end of the loan period , what was the rate of interest .
Options: a ) 5 % , b ) 6 % , c ) 7 % , d ) 8 % , e ) 9 %
Rationale: "explanation : let rate = r % then time = r years . = > 900 ∗ r ∗ r / 100 = 729 = > r 2 = 81 = > r = 9 % option e"
Answer: e
Question (other): of the 20 members of a kitchen crew , 17 can use the meat - cutting machine , 18 can use the bread - slicing machine , and 15 can use both machines . if one member is chosen at random , what is the probability that the member chosen will be someone who can not use either machine ?
Options: a ) 0 , b ) 1 / 10 , c ) 1 / 7 , d ) 1 / 4 , e ) 1 / 3
Rationale: you know how to solve for total number of people who can use at least one machine : total = n ( a ) + n ( b ) - n ( a and b ) total people who can use at least one machine = 17 + 18 - 15 = 20 so all 20 people know how to use at least one machine . hence , if you pick anyone , the probability is 0 that he would n ' t know how to use any machine . answer a
Answer: a
Question (general): the average of first 9 natural numbers is ?
Options: a ) 1.5 , b ) 2.5 , c ) 3.5 , d ) 4.5 , e ) 5.5
Rationale: "sum of 10 natural no . = 90 / 2 = 45 average = 45 / 10 = 4.5 answer : d"
Answer: d
Question (physics): buses a and b start from a common bus stop x . bus a begins to travel in a straight line away from bus b at a constant rate of 20 miles per hour . one hour later , bus b begins to travel in a straight line in the exact opposite direction at a constant rate of 80 miles per hour . if both buses travel indefinitely , what is the positive difference , in minutes , between the amount of time it takes bus b to cover the exact distance that bus a has covered and the amount of time it takes bus b to cover twice the distance that bus a has covered ?
Options: a ) 36 , b ) 72 , c ) 132 , d ) 144 , e ) 180
Rationale: 1 st part : - in 1 hr , bus a covers 30 miles . relative speed of bus abus b is ( 80 - 30 ) = 50 mph . so time required for bus b to cover the exact distance as a is 50 * t = 30 t = 3 / 5 = 36 min 2 nd part 80 * t = 2 d - b has to cover twice the distance 30 * ( t + 1 ) = d - a traveled 1 hr more and has to travel only only d so d / 30 - 2 d / 80 = 1 d = 120 t = 3 hrs = 180 min question asks for + ve difference between part 1 and part 2 in minutes = 180 - 36 = 132 min c
Answer: c
Question (other): a student committee on academic integrity has 132 ways to select a president and vice president from a group of candidates . the same person can not be both president and vice president . how many candidates are there ?
Options: a ) 7 , b ) 8 , c ) 9 , d ) 10 , e ) 12
Rationale: "xc 1 * ( x - 1 ) c 1 = 132 x ^ 2 - x - 132 = 0 ( x - 12 ) ( x + 11 ) = 0 x = 12 , - 11 - 11 ca n ' t possible . hence 12 should be the answer e"
Answer: e
Question (other): a grocery store bought some mangoes at a rate of 5 for a dollar . they were separated into two stacks , one of which was sold at a rate of 3 for a dollar and the other at a rate of for a dollar . what was the ratio of the number of mangoes in the two stacks if the store broke even after having sold all of its mangoes ?
Options: a ) 1 : 4 , b ) 16 : 9 , c ) 2 : 3 , d ) 1 : 2 , e ) 2 : 5
Rationale: the cost price of a mango = 1 / 5 dollars . the selling price of a mango from the first stack = 1 / 3 dollars - - > the profit from one mango = 1 / 3 - 1 / 5 = 2 / 15 = 4 / 30 dollars . the selling price of a mango from the second stack = 1 / 8 dollars - - > the loss from one mango = 1 / 5 - 1 / 8 = 3 / 40 dollars . the profit from one mango from the first stack is 4 times the loss from one mango from the second stack . the ratio is 4 / 30 * 40 / 3 = 16 / 9 b
Answer: b
Question (gain): if an investor puts $ 800 in a savings account that earns 10 percent annual interest compounded semiannually , how much money will be in the account after one year ?
Options: a ) $ 878 , b ) $ 880 , c ) $ 882 , d ) $ 884 , e ) $ 886
Rationale: "1.05 * 1.05 * 800 = $ 882 the answer is c ."
Answer: c
Question (gain): in an election between two candidates , one got 55 % of the total valid votes . 20 % of the votes were invalid . if the total number of votes was 7500 , what was the number of valid votes that the other candidate got ?
Options: a ) 2800 , b ) 2700 , c ) 2100 , d ) 2500 , e ) 3000
Rationale: "total no of votes = 7500 20 % invalid = > 80 % valid tot valid votes = 7500 * 80 / 100 = > valid for 2 nd candidate got 7500 * 80 / 100 * 45 / 100 = 2700 answer b"
Answer: b
Question (general): the average of first five multiples of 6 is ?
Options: a ) 6 , b ) 18 , c ) 9 , d ) 5 , e ) 7
Rationale: "average = 6 ( 1 + 2 + 3 + 4 + 5 ) / 5 = 90 / 5 = 18 . answer : b"
Answer: b
Question (gain): indu gave bindu rs . 625 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 ) 7 , d ) 4 , e ) 9
Rationale: "625 = d ( 100 / 4 ) 2 d = 1 answer : a"
Answer: a
Question (probability): a bag contains 3 red , 5 yellow and 4 green balls . 3 balls are drawn randomly . what is the probability that the balls drawn contain balls of different colours ?
Options: a ) 2 / 7 , b ) 3 / 5 , c ) 3 / 11 , d ) 1 / 4 , e ) 7 / 16
Rationale: "total number of balls = 3 + 5 + 4 = 12 n ( s ) = 12 c 3 = 12 * 11 * 10 / 3 * 2 = 220 n ( e ) = 3 c 1 * 5 c 1 * 4 c 1 = 3 * 5 * 4 = 60 probability = 60 / 220 = 3 / 11 answer is c"
Answer: c
Question (gain): the market value of a certain machine decreased by 10 percent of its purchase price each year . if the machine was purchased in 1982 for its market value of $ 8000 , what was its market value two years later ?
Options: a ) $ 8,000 , b ) $ 5,600 , c ) $ 3,200 , d ) $ 6,400 , e ) $ 800
Rationale: d market value in 1982 = $ 8000 market value in 1983 = $ 8000 - ( $ 8000 x 10 / 100 ) = 8000 - 800 = $ 7200 market value in 1984 = market value in 1983 - ( 10 % of $ 8000 ) = 7200 - 800 = $ 6400
Answer: d
Question (gain): two numbers are less than third number by 60 % and 74 % respectively . how much percent is the second number less than by the first ?
Options: a ) 18 % , b ) 29 % , c ) 35 % , d ) 41 % , e ) none of these
Rationale: "explanation : let the third number is x . then first number = ( 100 - 60 ) % of x = 40 % of x = 4 x / 10 second number is ( 26 x / 100 ) difference = 4 x / 10 - 26 x / 100 = 14 x / 10 so required percentage is , difference is what percent of first number = > ( 14 x / 100 * 10 / 4 x * 100 ) % = 35 % answer : c"
Answer: c
Question (physics): a 1400 m long train crosses a tree in 100 sec , how much time will it take to pass a platform 700 m long ?
Options: a ) 288 , b ) 190 , c ) 150 , d ) 188 , e ) 12
Rationale: "l = s * t s = 1400 / 100 s = 14 m / sec . total length ( d ) = 2100 m t = d / s t = 2100 / 14 t = 150 sec answer : c"
Answer: c
Question (general): the product of two positive integers is 675 and their difference is 2 . what is the bigger number ?
Options: a ) 21 , b ) 23 , c ) 25 , d ) 27 , e ) 29
Rationale: "let ' s use trial and error to find the two numbers . 25 * 23 = 575 ( too low ) 27 * 25 = 675 the answer is d ."
Answer: d
Question (general): during the last 4 years , a large truck company purchased diesel at rates of $ 1.2 , $ 1.3 , $ 1.8 and $ 2.1 per gallon . what was the mean cost of diesel over the 4 - year period if the company spends the same amount of dollars on diesel each year ?
Options: a ) $ 2.5 , b ) $ 2.55 , c ) $ 1.52 , d ) $ 3.25 , e ) $ 3.0
Rationale: finding the harmonic mean here . hm = 4 / ( 1 / 12 + 1 / 13 + 1 / 18 + 1 / 21 ) = 15.18 c
Answer: c
Question (general): after spending rs . 5000 on rent , rs . 1500 on milk , rs . 4500 on groceries , rs . 2500 on childrens education rs . 2000 on petrol and rs . 5200 on miscellaneous expenses , mr . kishore saved 10 % of his monthly salary . how much did he save in rs . ?
Options: a ) 2160 , b ) 2350 , c ) 2000 , d ) 2300 , e ) none of these
Rationale: "explanation : total exp = 5000 + 1500 + 4500 + 2500 + 2000 + 5200 = 20700 exp in % = 100 - 10 = 90 % , 20700 = 90 % saving = 10 % = 20700 x 10 / 90 = rs . 2300 answer : d"
Answer: d
Question (general): shekar scored 76 , 65 , 82 , 47 and 85 marks in mathematics , science , social studies , english and biology respectively . what are his average marks ?
Options: a ) 71 , b ) 69 , c ) 75 , d ) 85 , e ) 90
Rationale: "explanation : average = ( 76 + 65 + 82 + 47 + 85 ) / 5 = 355 / 5 = 71 hence average = 71 answer : a"
Answer: a
Question (gain): at an elementary school , 70 % of the faculty members are women and 60 % of the faculty members are married . if 2 ⁄ 3 of the men are single , what fraction of the women are married ?
Options: a ) 5 ⁄ 7 , b ) 7 ⁄ 10 , c ) 1 ⁄ 3 , d ) 7 ⁄ 30 , e ) 5 ⁄ 70
Rationale: "plugging in numbers for this . assume 100 faculty members . 70 faculty members are women 30 faculty members are men 60 total faculty members are married 1 / 3 of men are married ( 10 ) , which means 20 men are single 10 of the 60 married faculty members are men , which means that 50 women are married . 50 / 70 women are married , reduced to 5 / 7 ans a"
Answer: a
Question (general): how many multiples of 4 are there between 12 and 104 , inclusive ?
Options: a ) 21 , b ) 22 , c ) 23 , d ) 24 , e ) 25
Rationale: "the multiples of 4 are from 4 * 3 up to 4 * 26 . 26 - 3 + 1 = 24 . the answer is d ."
Answer: d
Question (general): a high school has 400 students 1 / 2 attend the airthmetic club , 5 / 8 attend the physics club and 3 / 4 attend the chemistry club . 3 / 8 attend all 3 clubs . if every student attends at least one club how many students attend exactly 2 clubs .
Options: a ) 80 , b ) 70 , c ) 60 , d ) 50 , e ) 30
Rationale: "a - club has 200 members ( 1 / 2 of 400 ) b - club has 250 members ( 5 / 8 of 400 ) c - club has 300 members ( 3 / 4 of 400 ) we can create an equation to solve this : 200 + 250 + 300 = n + x + 2 y where n is the number of students , x is the number of students in two clubs , and y is the number of students in three clubs . the question provides y for us ( 150 ) . 750 = 400 + x + 300 x = 50 d"
Answer: d
Question (general): how many kg of rice at rs . 6.60 per kg . be mixed with 56 kg of rice at rs . 9.60 per kg to get a mixture worth rs . 8.20 per kg
Options: a ) 56 kg , b ) 52 kg , c ) 44 kg , d ) 49 kg , e ) none of these
Rationale: explanation : by the rule of alligation , we have cost of 1 kg of 1 st kind rice cost of 1 kg of 2 nd kind rice 6.6 9.6 price of 1 kg of the mixture 8.2 9.6 - 8.2 = 1.4 8.2 - 6.6 = 1.6 quantity of 1 st kind rice : quantity of 2 nd kind rice = 1.4 : 1.6 = 7 : 8 quantity of 1 st kind rice : 56 = 7 : 8 = > quantity of 1 st kind rice = 56 × 78 = 49 answer : option d
Answer: d
Question (geometry): a box measuring 36 inches long by 45 inches wide by 18 inches deep is to be filled entirely with identical cubes . no space is to be left unfilled . what is the smallest number of cubes that can accomplish this objective ?
Options: a ) 32 , b ) 34 , c ) 38 , d ) 40 , e ) 42
Rationale: "least number of cubes will be required when the cubes that could fit in are biggest . 9 is the biggest number that could divide all three , 36 , 45 and 18 . thus side of cube must be 9 , and total number of cubes = 36 / 9 * 45 / 9 * 18 / 9 = 40 ans d ."
Answer: d
Question (geometry): the dimensions of a rectangular solid are 4 inches , 5 inches , and 12 inches . if a cube , a side of which is equal to one of the dimensions of the rectangular solid , is placed entirely within thespherejust large enough to hold the cube , what the ratio of the volume of the cube to the volume within thespherethat is not occupied by the cube ?
Options: a ) 10 : 17 , b ) 2 : 5 , c ) 5 : 16 , d ) 25 : 7 , e ) 10 : 21
Rationale: answer : e .
Answer: e
Question (physics): tanks a and b are each in the shape of a right circular cylinder . the interior of tank a has a height of 10 meters and a circumference of 8 meters , and the interior of tank b has a height of 8 meters and a circumference of 10 meters . the capacity of tank a is what percent of the capacity of tank b ?
Options: a ) 90 % , b ) 50 % , c ) 60 % , d ) 70 % , e ) 80 %
Rationale: "circumference of a = 2 ( pie ) r = 8 so r = 4 / pie volume = pie ( 4 / pie ) ^ 2 * 10 = 160 / pie circumference of b = 2 ( pie ) r = 10 so r = 5 / pie volume = pie ( 5 / pie ) ^ 2 * 8 = 200 / pie so ratio of capacities = 160 / 200 = 0.8 so capacity of a will be 80 % of the capacity of b answer : e"
Answer: e
Question (general): a person ' s present age is two - fifth of the age of his mother . after 8 years , he will be one - half of the age of his mother . how old is the mother at present
Options: a ) 38 , b ) 40 , c ) 42 , d ) 44 , e ) 45
Rationale: "explanation : let the mother ' s present age be x years . then , the person ' s present age = ( 2 / 5 x ) years . = > ( 2 / 5 x + 8 / 2 ) = 1 ( x + 8 ) = > 2 ( 2 x + 40 ) = 5 ( x + 8 ) = > x = 40 answer : option b"
Answer: b
Question (gain): in town x , 64 percent of the population are employed , and 47 percent of the population are employed males . what percent of the employed people in town x are females ?
Options: a ) 16 % , b ) 46 % , c ) 32 % , d ) 24 % , e ) 52 %
Rationale: "answer b male - employed - 64 % female - employed - 17 % total employed 64 % means total unemployed = 36 % therefore d and e are not correct because female unemployed has to be less than 36 % female - unemployed = 32 % male unemployed = 4 % 48 % + 4 % = 52 % 16 % + 32 % = 48 % plug in a and b in place of 32 % and the sum is not 100 % 17 / 64 = 26 d"
Answer: d
Question (general): when positive integer n is divided by positive integer j , the remainder is 18 . if n / j = 134.03 , what is value of j ?
Options: a ) 22 , b ) 56 , c ) 78 , d ) 112 , e ) 600
Rationale: "1 ) we know that decimal part of decimal quotient = { remainder / divisor } so 0.03 , the decimal part of the decimal quotient , must equal the remainder , 18 , divided by the divisor j . 0.03 = 18 / j 0.03 * j = 18 j = 18 / 0.03 = 1800 / 3 = 600 so j = 600 , answer = e ."
Answer: e
Question (gain): the present population of a town is 3744 . population increase rate is 20 % p . a . find the population of town before 2 years ?
Options: a ) 2500 , b ) 2600 , c ) 3500 , d ) 3600 , e ) 2050
Rationale: "p = 3744 r = 20 % required population of town = p / ( 1 + r / 100 ) ^ t = 3744 / ( 1 + 20 / 100 ) ^ 2 = 3744 / ( 6 / 5 ) ^ 2 = 2600 ( approximately ) answer is b"
Answer: b
Question (general): at joes steakhouse the hourly wage for a chef is 20 % greater than that of a dishwasher , and the hourly wage of a dishwasher is half as much as the hourly wage of a manager . if a managers wage is $ 6.50 per hour , how much less than a manager does a chef earn each hour ?
Options: a ) $ 2.6 , b ) $ 2.40 , c ) $ 3.40 , d ) $ 4.40 , e ) $ 5.40
Rationale: manager wages per hour = $ 6.50 dishwasher wages per hour = half of manager ' s wages . = 1 / 2 ( $ 6.50 ) = = > $ 3.25 chef wages per hour = 20 % greater than dishwasher wages - - > 20 % of $ 3.25 = ( 20 * ( $ 3.25 ) ) / 100 - - > ( $ 65 ) / 100 - - > $ 0.65 therefore , chef wages per hour = $ 3.25 + $ 0.65 = = > $ 3.9 difference of wages between manager and chef = $ 6.50 - $ 3.9 = = > $ 2.6 answer : a
Answer: a
Question (geometry): the cost of paint is 60 per kilograme . a kilogram paint covers 20 square feet . how much will it cost to paint the outside of a cube having each side 10 feet ?
Options: a ) 3000
b ) 900
c ) 1800
d ) 360
e ) none of these
Rationale: area of cube = 6 × ( side ) 2 = 6 × 10 × 10 = 600 square feet . cost to paint outside of the cube = 600 ⁄ 20 × 60 = 1800 answer c
Answer: c
Question (general): a man whose speed is 4.5 kmph in still water rows to a certain upstream point and back to the starting point in a river which flows at 0.5 kmph , find his average speed for the total journey ?
Options: a ) 4 , b ) 3.5 , c ) 3 , d ) 3.1 , e ) 2.8
Rationale: "m = 4.5 s = 2.5 ds = 7 us = 2 as = ( 2 * 7 * 2 ) / 9 = 3.1 answer : d"
Answer: d
Question (general): the original price of a suit is $ 160 . the price increased 25 % , and after this increase , the store published a 25 % off coupon for a one - day sale . given that the consumers who used the coupon on sale day were getting 25 % off the increased price , how much did these consumers pay for the suit ?
Options: a ) $ 140 , b ) $ 145 , c ) $ 150 , d ) $ 155 , e ) $ 160
Rationale: 0.75 * ( 1.25 * 160 ) = $ 150 the answer is c .
Answer: c