Cheukting/mathqa huggingface dataset:
Question (gain): mr . john used to purchase certain number of mangoes for $ 360 since the price of mangoes is reduced by 10 % he got 12 more mangoes today . find the original price of 135 mangoes .
Options: a ) 360 , b ) 380 , c ) 400 , d ) 450 , e ) 412
Rationale: mr . john used to purchase certain number of mangoes for $ 360 since the price of mangoes is reduced by 10 % he got 12 more mangoes today . find the original price of 120 mangoes . method 1 : let price per mango = x . let number of mangoes be n . then , nx = 360 . now price = 0.9 x ; number of mangoes = n + 12 . total amount = 0.9 x * ( n + 12 ) = 360 . nx = 0.9 nx + 10.8 x = > 0.1 nx = 10.8 x = > n = 108 = > x = 360 / 108 = 3.33 original price of 135 mangoes = 135 * 3.33 = 450 . answer d
Answer: d
Question (gain): a gambler has won 40 % of his 20 poker games for the week so far . if , all of a sudden , his luck changes and he begins winning 80 % of the time , how many more games must he play to end up winning 60 % of all his games for the week ?
Options: a ) 20 , b ) 25 , c ) 30 , d ) 35 , e ) 40
Rationale: "let x be the number of additional games the gambler needs to play . 0.4 ( 20 ) + 0.8 x = 0.6 ( x + 20 ) 0.2 x = 4 x = 20 the answer is a ."
Answer: a
Question (gain): the malibu country club needs to drain its pool for refinishing . the hose they use to drain it can remove 60 cubic feet of water per minute . if the pool is 60 feet wide by 100 feet long by 10 feet deep and is currently at 80 % capacity , how long will it take to drain the pool ?
Options: a ) 1000 , b ) 1400 , c ) 1200 , d ) 800 , e ) 1000
Rationale: "volume of pool = 60 * 100 * 10 cu . ft , 80 % full = 60 * 100 * 10 * 0.8 cu . ft water is available to drain . draining capacity = 60 cu . ft / min therefore time taken = 60 * 100 * 10 * 0.8 / 60 min = 800 min d"
Answer: d
Question (physics): walking at 4 / 5 of her normal speed , a worker is 10 minutes later than usual in reaching her office . the usual time ( in minutes ) taken by her to cover the distance between her home and her office is
Options: a ) 30 , b ) 35 , c ) 40 , d ) 45 , e ) 50
Rationale: "let v be her normal speed and let t be her normal time . d = ( 4 / 5 ) v * ( t + 10 ) since the distance is the same we can equate this to a regular day which is d = v * t v * t = ( 4 / 5 ) v * ( t + 10 ) t / 5 = 8 t = 40 the answer is c ."
Answer: c
Question (physics): find the length of the longest pole that can be placed in a room 12 m long , 8 m broad and 9 m high .
Options: a ) 10 m , b ) 12 m , c ) 17 m , d ) 19 m , e ) none
Rationale: solution length of longest pole = length of the diagonal of the room = √ ( 12 ) 2 + 82 + 92 ‹ = › √ 289 = 17 m . answer c
Answer: c
Question (geometry): a metallic sheet is of rectangular shape with dimensions 48 m x 36 m . from each of its corners , a square is cut off so as to make an open box . if the length of the square is 4 m , the volume of the box ( in m 3 ) is :
Options: a ) 4480 , b ) 5120 , c ) 6420 , d ) 8960 , e ) 7960
Rationale: "clearly , l = ( 48 - 8 ) m = 40 m , b = ( 36 - 8 ) m = 28 m , h = 8 m . volume of the box = ( 40 x 28 x 4 ) m 3 = 4480 m 3 . answer : option a"
Answer: a
Question (general): find the value of x in ( x + 1 ) / ( x + 3 ) = 5
Options: a ) 2.5 , b ) - 2.5 , c ) 3.0 , d ) 3.5 , e ) - 3.5
Rationale: "( x - 1 ) / ( x + 3 ) = 5 multiplying both sides with x + 3 gives x + 1 = 5 ( x + 3 ) = x + 1 = 5 x + 15 subtracting x from both sides gives 4 x + 15 = 1 subtracting 15 from both sides gives 4 x = - 14 dividing by 4 on both sides gives x = - 3.5 answer : e"
Answer: e
Question (physics): a and b can together finish a work in 40 days . they worked together for 10 days and then b left . after another 15 days , a finished the remaining work . in how many days a alone can finish the job ?
Options: a ) 10 , b ) 25 , c ) 60 , d ) 30 , e ) 20
Rationale: "a + b 10 days work = 10 * 1 / 40 = 1 / 4 remaining work = 1 - 1 / 4 = 3 / 4 3 / 4 work is done by a in 15 days whole work will be done by a in 15 * 4 / 3 = 20 days answer is e"
Answer: e
Question (general): if the radius of a cylinder is made 3 times and height is doubled , what is the new volume of the cylinder divided by the old one ?
Options: a ) 18 . , b ) 2 . , c ) 6 . , d ) 4 . , e ) 10 .
Rationale: let v and v ' be the original and the changed volume now v = pir ^ 2 h v ' = pi ( 3 r ) ^ 2 ( 2 h ) v ' = 18 v a ) 18
Answer: a
Question (physics): a train 110 m long is running with a speed of 82 km / hr . in what time will it pass a man who is running at 6 km / hr in the direction opposite to that in which the train is going ?
Options: a ) 7 sec , b ) 6 sec , c ) 8 sec , d ) 4.5 sec , e ) 2 sec
Rationale: "speed of train relative to man = 82 + 6 = 88 km / hr . = 88 * 5 / 18 = 24.44 m / sec . time taken to pass the men = 110 / 24.44 = 4.5 sec . answer : d"
Answer: d
Question (general): the average marks of a class of 35 students is 40 and that of another class of 45 students is 60 . find the average marks of all the students ?
Options: a ) 52.6 , b ) 52.4 , c ) 52.1 , d ) 51.2 , e ) 52.9
Rationale: "sum of the marks for the class of 35 students = 35 * 40 = 1400 sum of the marks for the class of 45 students = 45 * 60 = 2700 sum of the marks for the class of 80 students = 1400 + 2700 = 4100 average marks of all the students = 4100 / 80 = 51.2 . answer : d"
Answer: d
Question (geometry): abcd is a square where ab = √ 2016 . let x be a point on ab and y be a point on cd such that ax = cy . compute the area of trapezoid axyd .
Options: a ) 3008 , b ) 2002 , c ) 1008 , d ) 2016 , e ) 3000
Rationale: note that trapezoids axy d and bxy c are congruent , so the area of axy d is always 2016 / 2 = 1008 . correct answer c
Answer: c
Question (general): chris age after 9 years will be 5 times his age 5 years back . what is the present age of chris ?
Options: a ) a ) 20 , b ) b ) 25 , c ) c ) 15 , d ) d ) 22 , e ) e ) 16
Rationale: "chris present age = x after 9 years = x + 9 5 years back = x - 5 x + 9 = 5 ( x - 5 ) x = 16 answer is e"
Answer: e
Question (gain): the owner of a furniture shop charges his customer 20 % more than the cost price . if a customer paid rs . 8600 for a computer table , then what was the cost price of the computer table ?
Options: a ) rs . 6289 , b ) rs . 6298 , c ) rs . 6290 , d ) rs . 7166 , e ) rs . 7708
Rationale: "cp = sp * ( 100 / ( 100 + profit % ) ) = 8600 ( 100 / 120 ) = rs . 7166 . answer : d"
Answer: d
Question (geometry): what is the perimeter , in meters , of a rectangular garden 16 meters wide that has the same area as a rectangular playground 16 meters long and 12 meters wide ?
Options: a ) 48 , b ) 56 , c ) 60 , d ) 56 , e ) 192
Rationale: "say length of garden is l meters . then ( l * 16 ) = 16 * 12 [ given area is same . area = l * b ] therefore l works out to 12 meters . perimeter of garden = 2 * ( 12 + 16 ) = 56 meter . answer is d"
Answer: d
Question (other): mrs . evans gave a test to her freshmen economics class , which has 29 students enrolled and 19 of them answered question 1 correctly . if 24 answered question 2 correctly and 5 did not take the test then how many answered both questions correctly ?
Options: a ) 3 , b ) 9 , c ) 11 , d ) 17 , e ) 19
Rationale: "total number of enrolled students = 29 number of students who did not take test = 5 hence , number of students who took test = 29 - 5 = 24 number of students who answered q 2 correctly = 24 , therefore , all students who took test answered q 2 correctly . so , number of students who answered q 1 correctly , also answered q 2 correctly = 19 . number of students who answered both q 1 & q 2 correctly = 19 . answer : e"
Answer: e
Question (physics): the distance between west - town to east - town is 10 kilometers . two birds start flying simultaneously towards one another , the first leaving from west - town at a speed of 4 kilometers per minute and the second bird , leaving from east - town , at a speed of 1 kilometers per minute . what will be the distance , in kilometers , between the meeting point and west - town ?
Options: a ) 3 . , b ) 8 . , c ) 10 . , d ) 12 . , e ) 15 .
Rationale: "time taken by the birds to meet = 10 / ( 4 + 1 ) = 2 mins distance traveled by the bird traveling from west - town = 4 * 2 = 8 answer : b"
Answer: b
Question (general): if m is a positive integer and m ^ 2 is divisible by 33 , then the largest positive integer that must divide m is ?
Options: a ) 3 , b ) 6 , c ) 8 , d ) 11 , e ) 16
Rationale: "m ^ 2 is divisible by 33 so m ^ 2 must be multiple of 48 . if the value of m is multiples of 11 then it will satisfy the condition . if we if m is 12 or 24 or 36 then it ans is d but if m = 33 then answer should be 16 . is the question right ? or am i missing some thing ? d"
Answer: d
Question (gain): √ 2 percent of 2 √ 2 =
Options: a ) 5.0 , b ) 0.05 , c ) 1.0 , d ) 2.0 , e ) 4.0
Rationale: "the other solutions are great , but here ' s one more approach . first , we scan the answer choices to see that they are quite spread apart . this means we can also use someapproximation all test - takers must memorize the following approximations : √ 2 ≈ 1.4 so , √ 2 percent of 2 √ 2 ≈ 1.4 percent of ( 2 ) ( 1.4 ) ≈ ( 1.4 / 100 ) ( 2.8 ) ≈ 3.92 / 100 ≈ 0.03 check the answer choices to see that b is the only answer that ' s close . answer : b"
Answer: b
Question (general): a , b and c play a cricket match . the ratio of the runs scored by them in the match is a : b = 6 : 3 and b : c = 6 : 5 . if the total runs scored by all of them are 118 , the runs scored by b are ?
Options: a ) 24 , b ) 20.13 , c ) 30.93 , d ) 20.93 , e ) 10.93
Rationale: "a : b = 6 : 3 b : c = 6 : 5 a : b : c = 36 : 18 : 15 12 / 59 * 118 = 24 answer : a"
Answer: a
Question (physics): a man swims downstream 90 km and upstream 55 km taking 5 hours each time ; what is the speed of the current ?
Options: a ) 3.8 , b ) 3.5 , c ) 3.3 , d ) 3.2 , e ) 1.6
Rationale: "90 - - - 5 ds = 18 ? - - - - 1 55 - - - - 5 us = 11 ? - - - - 1 s = ? s = ( 18 - 11 ) / 2 = 3.5 answer : b"
Answer: b
Question (general): from a total of 5 boys and 6 girls , how many 4 - person committees can be selected if the committee must have exactly 2 boys and 2 girls ?
Options: a ) 16 , b ) 24 , c ) 60 , d ) 120 , e ) 150
Rationale: answer = e = 150 no of 4 person committees that can be formed = 5 c 2 * 6 c 2 = 150 answer e
Answer: e
Question (general): the simple interest on a sum of money will be rs . 1400 after 10 years . if the principal is trebled after 5 years what will be the total interest at the end of the tenth year ?
Options: a ) 2800 , b ) 3799 , c ) 1200 , d ) 2693 , e ) 1732
Rationale: "p - - - 10 - - - - 1400 p - - - 5 - - - - - 700 3 p - - - 5 - - - - - 2100 - - - - - - = > 2800 answer : a"
Answer: a
Question (general): if the price of a certain computer increased 30 percent from d dollars to 351 dollars , then 3 d =
Options: a ) 540 , b ) 570 , c ) 619 , d ) 649 , e ) 710
Rationale: "before price increase price = d after 30 % price increase price = d + ( 30 / 100 ) * d = 1.3 d = 351 ( given ) i . e . d = 351 / 1.3 = $ 270 i . e . 3 d = 3 * 270 = 710 answer : option e"
Answer: e
Question (physics): two cars start at the same time from opposite ends of a highway that is 175 miles long . one car is riding at 25 mph and the second car is riding at 45 mph . how long after they begin will they meet ?
Options: a ) 2 , b ) 2.5 , c ) 3 , d ) 3.5 , e ) 4
Rationale: "as cars are moving in opposite directions their speeds will be added . so their relative speeds : 45 + 25 = 70 mph total distance to be covered = 175 miles . time taken would be : 175 miles / 70 mph = 2.5 hours b is the answer ."
Answer: b
Question (general): how many seven - digit numbers that do not contain the digits 2 or 9 are there ?
Options: a ) 178546 , b ) 44786544 , c ) 435786 , d ) 1599678 , e ) 1835008
Rationale: "we can have 7 digits ( 1 , 3,4 , 5,6 , 7,8 ) for the first place ( million ' s place ) . and similarly 8 digits for hundred thousands , ten thousands , thousands , hundred ' s , tenth ' s and unit digit . ( 0,1 , 3,4 , 5,6 , 7,8 ) so in total 7 * 8 * 8 * 8 * 8 * 8 * 8 = 1835008 hence e"
Answer: e
Question (physics): the sum of two consecutive number is 67 . which is the larger number ?
Options: a ) 34 , b ) 43 , c ) 44 , d ) 45 , e ) 46
Rationale: "let consecutive number be x , x + 1 therefore sum of the consecutive number is x + x + 1 = 67 2 x + 1 = 67 2 x = 66 x = 33 therefore larger number is x + 1 = 34 answer : a"
Answer: a
Question (physics): a and b together can do a piece of work in 1 days . if a alone can do the same work in 20 days , then b alone can do the same work in ?
Options: a ) 0.35 days , b ) 0.45 days , c ) 0.55 days , d ) 0.25 days , e ) 0.95 days
Rationale: "b = 1 / 1 – 1 / 20 = 0.95 days answer : e"
Answer: e
Question (gain): in a school of 850 boys , 46 % of muslims , 28 % hindus , 10 % sikhs and the remaining of other communities . how many belonged to the other communities ?
Options: a ) a ) 136 , b ) b ) 627 , c ) c ) 153 , d ) d ) 721 , e ) e ) 159
Rationale: "46 + 28 + 10 = 84 % 100 – 84 = 16 % 850 * 16 / 100 = 136 answer : a"
Answer: a
Question (general): 45 % of x is greater than 1 / 3 rd of x by 110 . what is x ?
Options: a ) 100 , b ) 200 , c ) 300 , d ) 350 , e ) 943
Rationale: "45 x / 100 - x / 3 = 110 7 x / 60 = 110 x = 943 answer : e"
Answer: e
Question (other): there are 7 executives , including the ceo and cfo , that are asked to form a small team of 4 members . however , the ceo and cfo may not both be assigned to the team . given this constraint , how many ways are there to form the team ?
Options: a ) 25 , b ) 28 , c ) 30 , d ) 32 , e ) 35
Rationale: "the total number of ways to form a team of 4 is 7 c 4 = 35 . we need to subtract the number of teams that have both the ceo and the cfo . the number of teams with both the ceo and cfo is 5 c 2 = 10 . the number of ways to form an acceptable team is 35 - 10 = 25 . the answer is a ."
Answer: a
Question (general): a / ( b / c ) in the expression above , a , b , and c are different numbers and each is one of the numbers 2 , 3 , or 6 . what is the largest possible value of the expression ?
Options: a ) 2 / 18 , b ) 6 / 3 , c ) 30 / 2 , d ) 18 / 2 , e ) 6 / 18
Rationale: a / ( b / c ) = ( a * c ) / b the expression will have the largest value when numerator ( a * c ) is the largest . = ( 6 * 3 ) / 2 = 18 / 2 answer d
Answer: d
Question (physics): a work as fast as b . if b can complete a work in 8 days independently , the number of days in which a and b can together finish the work in ?
Options: a ) 2 days , b ) 2 2 / 3 days , c ) 4 days , d ) 5 days , e ) 6 days
Rationale: "ratio of rates of working of a and b = 2 : 1 ratio of times taken = 1 : 2 a ' s 1 day work = 1 / 4 b ' s 1 day work = 1 / 8 a + b 1 day work = 1 / 4 + 1 / 8 = 3 / 8 = > 8 / 3 = 2 2 / 3 a and b can finish the work in 2 2 / 3 days answer is b"
Answer: b
Question (gain): ravi purchased a refrigerator and a mobile phone for rs . 15000 and rs . 8000 respectively . he sold the refrigerator at a loss of 5 percent and the mobile phone at a profit of 10 percent . overall he make a .
Options: a ) 50 , b ) 288 , c ) 27 , d ) 200 , e ) 881
Rationale: "let the sp of the refrigerator and the mobile phone be rs . r and rs . m respectively . r = 15000 ( 1 - 5 / 100 ) = 15000 - 750 m = 8000 ( 1 + 10 / 100 ) = 8000 + 800 total sp - total cp = r + m - ( 15000 + 8000 ) = - 750 + 800 = rs . 50 as this is positive , an overall profit of rs . 50 was made . answer : a"
Answer: a
Question (general): a batsman makes a score of 87 runs in the 17 th inning and thus increases his average by 3 . find his average after 17 th inning .
Options: a ) 39 , b ) 88 , c ) 26 , d ) 87 , e ) 11
Rationale: "explanation : consider the avg for first 16 innings is x . then total runs scored till 16 innings is 16 x . total runs after 17 innings = 16 x + 87 . thus , 16 x + 8717 = x + 316 x + 8717 = x + 3 ⇒ x = 36 so his average after 17 innings = 39 . answer : a"
Answer: a
Question (geometry): the area of a square is equal to five times the area of a rectangle of dimensions 32 cm * 10 cm . what is the perimeter of the square ?
Options: a ) 289 cm
b ) 160 cm
c ) 829 cm
d ) 288 cm
e ) 289 cm
Rationale: area of the square = s * s = 5 ( 32 * 10 ) = 1600 = > s = 40 = 40 cm perimeter of the square = 4 * 40 = 160 cm . answer : b
Answer: b
Question (gain): working alone , mary can pave a driveway in 4 hours and hillary can pave the same driveway in 3 hours . when they work together , mary thrives on teamwork so her rate increases by 33.33 % , but hillary becomes distracted and her rate decreases by 50 % . if they both work together , how many hours will it take to pave the driveway ?
Options: a ) 2 hours , b ) 4 hours , c ) 5 hours , d ) 6 hours , e ) 7 hours
Rationale: initial working rates : mary = 1 / 4 per hour hillary = 1 / 3 per hour rate when working together : mary = 1 / 4 + ( 1 / 3 * 1 / 4 ) = 1 / 3 per hour hillary = 1 / 3 - ( 1 / 2 * 1 / 3 ) = 1 / 6 per hour together they work 1 / 3 + 1 / 6 = 1 / 2 per hour so they will need 2 hours to complete the driveway . the correct answer is a .
Answer: a
Question (general): if y is a positive number and 1 / 2 the square root of x is the cube root of y , then y =
Options: a ) 64 , b ) 32 , c ) 16 , d ) 4 , e ) 1
Rationale: 1 / 2 the square root of x is cube root of y . if y = 64 . . then 1 / 2 the square root of y = 4 and cube of y is 64 . option a .
Answer: a
Question (physics): the perimeter of a semi circle is 180 cm then the radius is ?
Options: a ) 22 , b ) 28 , c ) 35 , d ) 37 , e ) 13
Rationale: "36 / 7 r = 180 = > r = 35 answer : c"
Answer: c
Question (general): the sum of the ages of 4 children born at the intervals of 1 years each is 12 years . what is the age of the youngest child ?
Options: a ) 2.5 , b ) 1.5 , c ) 1 , d ) 3.5 , e ) 4.5
Rationale: "let x = the youngest child . each of the other four children will then be x + 1 , x + 2 , x + 3 we know that the sum of their ages is 12 so , x + ( x + 1 ) + ( x + 2 ) + ( x + 3 ) = 12 therefore the youngest child is 1.5 years old answer : b"
Answer: b
Question (general): what is the decimal equivalent of ( 1 / 2 ) ^ 2 ?
Options: a ) 0.0016 , b ) 0.0625 , c ) 0.16 , d ) 0.25 , e ) 0.5
Rationale: "( 1 / 2 ) ² = ( 1 / 2 ) ( 1 / 2 ) = 1 / 4 approach # 1 : use long division to divide 4 into 1 to get 1 / 4 = 0.25 d"
Answer: d
Question (general): when x is even , [ x ] = x / 2 + 1 , when x is odd [ x ] = 2 x + 1 then [ 6 ] * [ 3 ] = ?
Options: a ) [ 22 ] , b ) [ 44 ] , c ) [ 45 ] , d ) [ 28 ] , e ) [ 10 ]
Rationale: [ 6 ] * [ 3 ] = ( 6 / 2 + 1 ) ( 3 * 2 + 1 ) = [ 28 ] . ans - d
Answer: d
Question (general): the sum of all the integers a such that - 26 < a < 24 is
Options: a ) 0 , b ) - 2 , c ) - 25 , d ) - 49 , e ) - 51
Rationale: easy one - - 25 , - 24 , - 23 , - 22 , . . . . . . - 10 , 1 , 2 . . . . , 22 , 23 cancel everyhitng and we ' re left with - - 25 and - 24 a = - 49 . d is the answer .
Answer: d
Question (physics): in what time will a railway train 52 m long moving at the rate of 24 kmph pass a telegraph post on its way ?
Options: a ) 3 sec , b ) 4 sec , c ) 8 sec , d ) 6 sec , e ) 7 sec
Rationale: t = 52 / 24 * 18 / 5 = 8 sec answer : c
Answer: c
Question (geometry): find the smallest number which should be multiplied with 36963 to make it a perfect square .
Options: a ) 4 , b ) 7 , c ) 4 , d ) 3 , e ) 6
Rationale: "36963 = 111 * 111 * 3 required smallest number = 3 3 is the smallest number which should be multiplied with 36963 to make it a perfect square . answer : d"
Answer: d
Question (physics): one computer can upload 100 megabytes worth of data in 2 seconds . two computers , including this one , working together , can upload 1300 megabytes worth of data in 10 seconds . how long would it take for the second computer , working on its own , to upload 100 megabytes of data ?
Options: a ) 6.6 , b ) 7 , c ) 9 , d ) 11 , e ) 13
Rationale: "since the first computer can upload 100 megabytes worth of data in 2 seconds then in 2 * 10 = 20 seconds it can upload 10 * 100 = 1000 megabytes worth of data , hence the second computer in 20 seconds uploads 1300 - 1000 = 300 megabytes worth of data . the second computer can upload 100 megabytes of data in 6.6 seconds . answer : a ."
Answer: a
Question (gain): 6 / 9 of the population of the country of venezia lives in montague province , while the rest lives in capulet province . in the upcoming election , 80 % of montague residents support romeo , while 70 % of capulet residents support juliet ; each resident of venezia supports exactly one of these two candidates . rounded if necessary to the nearest percent , the probability that a juliet supporter chosen at random resides in capulet is
Options: a ) 64 % , b ) 41 % , c ) 45 % , d ) 72 % , e ) 78 %
Rationale: total population = 90 ( assume ) . 6 / 9 * 90 = 60 people from montague . 3 / 9 * 90 = 30 people from capulet . 0.2 * 60 = 12 people from montague support juliet . 0.7 * 30 = 21 people from capulet support juliet . the probability that a juliet supporter chosen at random resides in capulet is 21 / ( 12 + 21 ) = ~ 64 . answer : a
Answer: a
Question (general): if a 2 - b 2 = 10 and a * b = 5 , find a 4 + b 4 .
Options: a ) 50 , b ) 100 , c ) 150 , d ) 92 , e ) 25
Rationale: a 2 - b 2 = 10 : given a 4 + b 4 - 2 a 2 b 2 = 102 : square both sides and expand . a * b = 5 : given a 2 b 2 = 52 : square both sides . a 4 + b 4 - 2 ( 25 ) = 100 : substitute a 4 + b 4 = 150 correct answer c
Answer: c
Question (general): in an office , totally there are 2800 employees and 25 % of the total employees are males . 30 % of the males in the office are at - least 50 years old . find the number of males aged below 50 years ?
Options: a ) 390 , b ) 490 , c ) 400 , d ) 460 , e ) none of these
Rationale: number of male employees = 2800 * 25 / 100 = 700 required number of male employees who are less than 50 years old = 700 * ( 100 - 30 ) % = 700 * 70 / 100 = 490 . answer : b
Answer: b
Question (general): when 3 is added to half of one - third of one - fifth of a number , the result is one - fifteenth of the number . find the number ?
Options: a ) 32 , b ) 81 , c ) 60 , d ) 27 , e ) 90
Rationale: explanation : let the number be 3 + 1 / 2 [ 1 / 3 ( a / 5 ) ] = a / 15 = > 3 = a / 30 = > a = 90 answer : e
Answer: e
Question (general): how many integers between 314,700 and 458,600 have tens digit 1 and units digit 3 ?
Options: a ) 10,300 , b ) 10,030 , c ) 1,353 , d ) 1,352 , e ) 1,439
Rationale: "there is one number in hundred with 1 in the tens digit and 3 in the units digit : 13 , 113 , 213 , 313 , . . . the difference between 314,700 and 458,600 is 458,600 - 314,700 = 143,900 - one number per each hundred gives 143,900 / 100 = 1,439 numbers . answer : e ."
Answer: e
Question (general): a certain psychologist charges $ 20 more for the first hour of therapy than for each additional hour . if the total charge to a patient who receives 5 hours of therapy is $ 300 , what is the total charge to a patient who receives only 3 hours of therapy ?
Options: a ) $ 120 , b ) $ 135 , c ) $ 150 , d ) $ 165 , e ) $ 188
Rationale: "let the charge for first hour = x + 20 then charge for each additional hour = x x + 20 + 4 x = 300 = > 5 x = 280 = > x = 56 total charge for patient for 3 hours of therapy = x + 20 + 2 x = 3 x + 20 = 188 $ answer e"
Answer: e