euclaise/mathqa_programs huggingface dataset:
Problem: on a certain road 10 % of the motorists exceed the posted speed limit and receive speeding tickets , but 20 % 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 ) 12.5 % , c ) 15 % , d ) 22 % , e ) 30 %
Rationale: "say there are 100 motorists . { # of motorists who exceed speed & receive tickets } + { # of motorists who exceed speed & do n ' t receive tickets } = { total # of motorist who exceed speed } ; given : { # of motorists who exceed speed & receive tickets } = 10 ; also , if { total # of motorist who exceed speed } = x , then 0.2 x = { # of motorists who exceed speed & do n ' t receive tickets } ; 10 + 0.2 x = x - - > x = 12.5 answer : b ."
Answer: b
Python program:
a = 10 / 100
b = 20 / 100
c = a * b
d = c * 100
e = 100 / d
Problem: a man can row downstream at the rate of 24 kmph and upstream at 7 kmph . find the man ’ s rate in still water and rate of current ?
Options: a ) 8.5 , b ) 8.0 , c ) 9.5 , d ) 9.0 , e ) 8.25
Rationale: "rate of still water = 1 / 2 ( down stream + upstream ) = 1 / 2 ( 24 + 7 ) = 15.5 kmph rate of current = 1 / 2 ( down stream - upstream ) = 1 / 2 ( 24 - 7 ) = 1 / 2 ( 17 ) = 8.5 kmph answer is a ."
Answer: a
Python program:
a = 24 - 7
b = a / 2
Problem: the average weight of 5 persons increases by 1.5 kg . if a person weighing 65 kg is replaced by a new person , what could be the weight of the new person ?
Options: a ) 76 kg , b ) 77 kg , c ) 72.5 kg , d ) data inadequate , e ) none of these
Rationale: "total weight increases = 5 × 1.5 = 7.5 kg so the weight of new person = 65 + 7.5 = 72.5 kg answer c"
Answer: c
Python program:
a = 5 * 1
b = 65 + a
Problem: two trains , one from howrah to patna and the other from patna to howrah , start simultaneously . after they meet , the trains reach their destinations after 4 hours and 16 hours respectively . the ratio of their speeds is ?
Options: a ) 4 : 5 , b ) 4 : 2 , c ) 4 : 4 , d ) 4 : 8 , e ) 4 : 1
Rationale: "let us name the trains a and b . then , ( a ' s speed ) : ( b ' s speed ) = √ b : √ a = √ 16 : √ 4 = 4 : 2 answer : b"
Answer: b
Python program:
a = math.sqrt(16)
b = math.sqrt(4)
c = a / b
Problem: on july 1 of last year , total employees at company e was decreased by 10 percent . without any change in the salaries of the remaining employees , the average ( arithmetic mean ) employee salary was 10 percent more after the decrease in the number of employees than before the decrease . the total of the combined salaries of all the employees at company e after july 1 last year was what percent e of thatbeforejuly 1 last year ?
Options: a ) 90 % , b ) 99 % , c ) 100 % , d ) 101 % , e ) 110 %
Rationale: "the total number of employees = n the average salary = x total salary to all emplyoees = xn after the total number of employees = n - 0.1 n = 0.9 n the average salary = x + 10 % of x = 1.1 x total salary to all emplyoees = 0.9 n ( 1.1 x ) total salary after as a % of total salary before e = [ 0.9 n ( 1.1 x ) ] / xn = 0.99 or 99 % = b"
Answer: b
Python program:
a = 10 * 10
Problem: when positive integer n is divided by 5 , the remainder is 1 . when n is divided by 7 , the remainder is 3 . what is the smallest positive integer k such that k + n is a multiple of 70 .
Options: a ) 3 , b ) 4 , c ) 12 , d ) 32 , e ) 35
Rationale: "first , let us say i have a number n which is divisible by 5 and by 7 . we all agree that it will be divisible by 35 , the lcm of 5 and 7 . now , if i have a number n which when divided by 5 gives a remainder 1 and when divided by 7 gives a remainder 1 , we can say the number is of the form n = 5 a + 1 e . g . 5 + 1 , 10 + 1 , 15 + 1 , 20 + 1 , 25 + 1 , 30 + 1 , 35 + 1 etc and n = 7 b + 1 e . g . 7 + 1 , 14 + 1 , 21 + 1 , 28 + 1 , 35 + 1 etc so when it is divided by the lcm , 35 , it will give 1 as remainder ( as is apparent above ) next , if i have a number n which when divided by 5 gives a remainder 1 and when divided by 7 gives a remainder 3 , we can say the number is of the form n = 5 a + 1 and n = 7 b + 3 now , the only thing you should try to understand here is that when n is divided by 5 and if i say the remainder is 1 , it is the same as saying the remainder is - 4 . e . g . when 6 is divided by 5 , remainder is 1 because it is 1 more than a multiple of 5 . i can also say it is 4 less than the next multiple of 5 , ca n ' t i ? 6 is one more than 5 , but 4 less than 10 . therefore , we can say n = 5 x - 4 and n = 7 y - 4 ( a remainder of 3 when divided by 7 is the same as getting a remainder of - 4 ) now this question is exactly like the question above . so when you divide n by 70 , remainder will be - 4 i . e . n will be 4 less than a multiple of 70 . so you must add 4 to n to make it a multiple of 70 d"
Answer: d
Python program:
a = 70 - reminder
Problem: the difference between the place values of 6 and 5 in the number 826533 is
Options: a ) 5500 , b ) 4500 , c ) 2500 , d ) 6970 , e ) none
Rationale: sol . = ( place value of 6 ) – ( place value of 5 ) = ( 6000 - 500 ) = 5500 answer a
Answer: a
Python program:
a = 10 * 6
b = a - 6
Problem: a works twice as fast as b . if b can complete a work in 12 days independently , the number of days in which a and b can together finish the work in :
Options: a ) 4 days , b ) 6 days , c ) 8 days , d ) 18 days , e ) 28 days
Rationale: "explanation : ratio of rates of working of a and b = 2 : 1 . so , ratio of times taken = 1 : 2 . b ' s 1 day ' s work = 1 / 12 a ' s 1 day ' s work = 1 / 6 ; ( 2 times of b ' s work ) ( a + b ) ' s 1 day ' s work = ( 1 / 6 + 1 / 12 ) = 3 / 12 = 1 / 4 so , a and b together can finish the work in 4 days . answer is a"
Answer: a
Python program:
a = 1 / 12
b = 1 / 12
c = 2 * b
d = a + c 
e = 1/(d)
Problem: if a student loses 5 kilograms , he will weigh twice as much as his sister . together they now weigh 104 kilograms . what is the student ' s present weight in kilograms ?
Options: a ) 70 , b ) 71 , c ) 72 , d ) 73 , e ) 74
Rationale: "let x be the weight of the sister . then the student ' s weight is 2 x + 5 . x + ( 2 x + 5 ) = 104 3 x = 99 x = 33 kg then the student ' s weight is 71 kg . the answer is b ."
Answer: b
Python program:
a = 104 - 5
b = a / 3
c = 104 - b
Problem: a football team lost 5 yards and then gained 13 . what is the team ' s progress ?
Options: a ) 2 , b ) 4 , c ) 5 , d ) 6 , e ) 8
Rationale: "for lost , use negative . for gain , use positive . progress = - 5 + 13 = 8 yards e"
Answer: e
Python program:
a = 13 - 5
Problem: find the value of x from logx 100 = 2
Options: a ) 10 , b ) 12 , c ) 13 , d ) 14 , e ) 15
Rationale: "solution : logb 1000 = 3 we can write it as , b 3 = 1000 b 3 = 103 so from the above equation b = 10 answer is a"
Answer: a
Python program:
a = 2 - 4
b = a * 100
Problem: x starts a business with rs . 52000 . y joins in the business after 6 months with rs . 26000 . what will be the ratio in which they should share the profit at the end of the year ?
Options: a ) 1 : 2 , b ) 2 : 3 , c ) 1 : 3 , d ) 4 : 1 , e ) none of these
Rationale: "explanation : ratio in which they should share the profit = ratio of the investments multiplied by the time period = 52000 * 12 : 26000 * 6 = 52 * 12 : 26 * 6 = 24 : 6 = 4 : 1 . answer : option d"
Answer: d
Python program:
a = 52000 * 12
b = 4 + 3 
c = 26000 * b
d = a / c
Problem: if x is equal to the sum of the even integers from 40 to 60 inclusive , and y is the number of even integers from 40 to 60 inclusive , what is the value of x + y ?
Options: a ) 550 , b ) 551 , c ) 560 , d ) 561 , e ) 572
Rationale: this is a perfect example of why you should not use formulas without understanding them properly . if you understand them , you will not make a mistake and will save time . the formula quoted by the original poster : n ( n + 1 ) is absolutely fine . but one needs to understand that n is the number of even terms starting from the first even term . ( i discuss why this is so here : sum of even numbers from 40 to 60 using this formula will be : 30 * 31 - 19 * 20 = 10 ( 3 * 31 - 19 * 2 ) = 550 since number of terms is 11 , required sum is 561 but , i would not use this formula for this question and would do it the way many of you have done : average = 50 ( it is the middle number ) , number of terms = 11 ( no formula again . any 10 consecutive integers have 5 even and 5 odd numbers . 41 to 60 will have 10 even integers and 40 is the 11 th one ) sum = 50 * 11 + 11 = 561 answer is d
Answer: d
Python program:
a = 60 - 40
b = a / 2
c = b + 1 
d = 2 * 40
e = 60 - 40
f = e / 2
g = f * 2
h = d + g 
i = c * h
j = i / 2
k = 60 - 40
l = k / 2
m = l + 1 
n = j + m
Problem: a monkey start climbing up a tree 17 ft tall . each hour it hops 3 ft and slips back 2 ft . how much time would it take the monkey to reach the top .
Options: a ) 15 hrs , b ) 18 hrs , c ) 19 hrs , d ) 17 hrs , e ) 16 hrs
Rationale: "if monkey hops 3 ft and slips back 2 ft in a hour , it means the monkey hops ( 3 ft - 2 ft ) = 1 ft / hr . similarly in 14 hrs it wil be 14 ft . bt since the height of the tree is 17 ft , so if the monkey hops up the tree in the next hr i . e 15 th hr then it reaches at the top of the tree . hence it takes 15 hrs for monkey to reach at the top answer : a"
Answer: a
Python program:
a = 3 - 2
b = 17 / a
c = b - 2
Problem: in a competitive examination in state a , 6 % candidates got selected from the total appeared candidates . state b had an equal number of candidates appeared and 7 % candidates got selected with 79 more candidates got selected than a . what was the number of candidates appeared from each state ?
Options: a ) 7000 , b ) 7900 , c ) 6000 , d ) 5000 , e ) 4000
Rationale: "state a and state b had an equal number of candidates appeared . in state a , 6 % candidates got selected from the total appeared candidates in state b , 7 % candidates got selected from the total appeared candidates but in state b , 79 more candidates got selected than state a from these , it is clear that 1 % of the total appeared candidates in state b = 79 = > total appeared candidates in state b = 79 x 100 = 7900 = > total appeared candidates in state a = total appeared candidates in state b = 7900"
Answer: b
Python program:
a = 7 - 6
b = a / 100
c = 79 / b
Problem: the price ratio of oranges to lemons is 2 : 3 . the price ratio of grapefruits to lemons is 3 : 5 . what is the ratio , by price , of grapefruit to oranges ?
Options: a ) 18 : 20 , b ) 10 : 9 , c ) 2 : 5 , d ) 5 : 2 , e ) 3 : 2
Rationale: let price of lemons be 30 ( since that is common ) so , price of oranges = 20 & price of lemons is = 30 further price of grapefruit will be 6 * 3 = 18 thus price , of grapefruit to oranges = 18 : 20 answer : a
Answer: a
Python program:
a = 3 / 5
b = a * 3
c = 2 / 3
d = c * 3
e = b / d
Problem: 20 carrots on a scale weigh 3.64 kg . when 4 carrots are removed from the scale , the average weight of the 16 carrots is 180 grams . what is the average weight ( in grams ) of the 4 carrots which were removed ?
Options: a ) 160 , b ) 170 , c ) 180 , d ) 190 , e ) 200
Rationale: "16 * 180 = 2880 . the other 4 carrots weigh a total of 760 grams . the average weight is 760 / 4 = 190 grams . the answer is d ."
Answer: d
Python program:
a = 16 * 180
b = a / 1000
c = 3 - 64
d = c / 4
e = d * 1000
Problem: a can do a particular work in 6 days . b can do the same work in 8 days . a and b signed to do it for rs . 3200 . they completed the work in 3 days with the help of c . how much is to be paid to c ?
Options: a ) rs . 380 , b ) rs . 600 , c ) rs . 420 , d ) rs . 400 , e ) rs . 480
Rationale: "explanation : amount of work a can do in 1 day = 1 / 6 amount of work b can do in 1 day = 1 / 8 amount of work a + b can do in 1 day = 1 / 6 + 1 / 8 = 7 / 24 amount of work a + b + c can do = 1 / 3 amount of work c can do in 1 day = 1 / 3 - 7 / 24 = 1 / 24 work a can do in 1 day : work b can do in 1 day : work c can do in 1 day = 1 / 6 : 1 / 8 : 1 / 24 = 4 : 3 : 1 amount to be paid to c = 3200 × ( 1 / 8 ) = 400 answer : option d"
Answer: d
Python program:
a = 1 / 3
b = 1 / 6
c = 1 / 8
d = b + c 
e = a - d
f = 3 * e
g = f * 3200
Problem: a train requires 10 seconds to pass a pole while it requires 40 seconds to cross a stationary train which is 300 mtrs long . find the speed of the train .
Options: a ) 36 kmph , b ) 42 kmph , c ) 48 kmph , d ) 52 kmph , e ) 64 kmph
Rationale: "in 10 s the train crosses the pole and in 40 sec the train crosses one more stationary train in 30 sec the train travels a distance of 300 mtrs speed = 300 / 30 = 10 m / s = 10 * 18 / 5 = 36 kmph answer : a"
Answer: a
Python program:
a = 40 - 10
b = 300 / a
c = b * const_3_6
Problem: two trains are running in opposite directions in the same speed . the length of each train is 120 meter . if they cross each other in 4 seconds , the speed of each train ( in km / hr ) is
Options: a ) 42 , b ) 36 , c ) 108 , d ) 120 , e ) 124
Rationale: "explanation : distance covered = 120 + 120 = 240 m time = 4 s let the speed of each train = v . then relative speed = v + v = 2 v 2 v = distance / time = 240 / 4 = 60 m / s speed of each train = v = 60 / 2 = 30 m / s = 30 × 36 / 10 km / hr = 108 km / hr answer : option c"
Answer: c
Python program:
a = 120 + 120 
b = a / 4
c = b / 2
d = const_3_6 * c
Problem: how many multiples of 7 are there between 700 and 1000 , inclusive ?
Options: a ) 43 , b ) 42 , c ) 22 , d ) 21 , e ) 20
Rationale: "there are exactly 301 numbers between 700 to 1000 . . 701 to 800 = 100 801 to 1000 = 200 . . . total 300 numbers , count 700 too . . 301 / 7 = 43 . . . ans option a ."
Answer: a
Python program:
a = 1000 - 700
b = a / 7
c = b + 1
Problem: at a certain bowling alley , it costs $ 0.50 to rent bowling shoes for the day and $ 2 to bowl 1 game . if a person has $ 12.80 and must rent shoes , what is the greatest number of complete games that person can bowl in one day ?
Options: a ) 7 , b ) 8 , c ) 6 , d ) 10 , e ) 11
Rationale: after renting bowling shoes the person is left with $ 12.80 - $ 0.5 = $ 12.30 , which is enough for 12.3 / 2 < 7 = ~ 6 . answer : c .
Answer: c
Python program:
a = 12 - 8
b = a / 2
Problem: if a * b * c = 130 , b * c * d = 65 , c * d * e = 750 and d * e * f = 250 the ( a * f ) / ( c * d ) = ?
Options: a ) 1 / 2 , b ) 2 / 3 , c ) 3 / 4 , d ) 4 / 3 , e ) none of these
Rationale: "explanation : a â ˆ — b â ˆ — c / b â ˆ — c â ˆ — d = 130 / 65 = > a / d = 2 d â ˆ — e â ˆ — f / c â ˆ — d â ˆ — e = 250 / 750 = > f / c = 1 / 3 a / d * f / c = 2 * 1 / 3 = 2 / 3 answer : b"
Answer: b
Python program:
a = 130 * 250
b = 750 * 65
c = a / b
Problem: a cistern can be filled by a tap in 4 hours while it can be emptied by another tap in 9 hours . if both the taps are opened simultaneously , then after how much time cistern will get filled ?
Options: a ) 7 hours , b ) 7.1 hours , c ) 7.2 hours , d ) 7.3 hours , e ) none of these
Rationale: "explanation : when we have question like one is filling the tank and other is empting it , then we subtraction as , filled in 1 hour = 1 / 4 empties in 1 hour = 1 / 9 net filled in 1 hour = 1 / 4 - 1 / 9 = 5 / 36 so cistern will be filled in 36 / 5 hours i . e . 7.2 hours option c"
Answer: c
Python program:
a = 1 / 4
b = 1 / 9
c = a - b
d = 1 / c
Problem: evaluate : 986 x 237 - 986 x 37
Options: a ) 197600 , b ) 168000 , c ) 278000 , d ) 192700 , e ) none of them
Rationale: "986 x 237 - 986 x 37 = 986 x ( 237 - 37 ) = 986 x 200 = 197200 . answer is d ."
Answer: d
Python program:
a = 237 * 986
b = a * 37
c = 986 - b
Problem: what is the sum of the odd integers from 25 to 55 , inclusive ?
Options: a ) 495 , b ) 550 , c ) 555 , d ) 600 , e ) 640
Rationale: "the mean is 40 . sum = mean ( # of elements ) there are 16 odd numbers between 25 - 55 inclusive . 16 * 40 = 640 e"
Answer: e
Python program:
a = 25 * 55
b = a / 4
Problem: in a class of students , 2 / 3 of the number of girls is equal to 1 / 4 of the total number of students . what is the ratio of boys to girls in the class ?
Options: a ) 1 / 3 , b ) 2 / 3 , c ) 4 / 3 , d ) 5 / 3 , e ) 7 / 3
Rationale: "( 2 / 3 ) g = ( 1 / 4 ) ( b + g ) 8 g = 3 b + 3 g 5 g = 3 b b / g = 5 / 3 . the answer is d ."
Answer: d
Python program:
a = 2 / 3
b = 1 / 4
c = a - b
d = 1 / 4
e = c / d
Problem: a portion of the 85 % solution of chemicals was replaced with an equal amount of 20 % solution of chemicals . as a result , 40 % solution of chemicals resulted . what part of the original solution was replaced ?
Options: a ) 5 / 13 , b ) 6 / 13 , c ) 9 / 13 , d ) 13 / 9 , e ) 13 / 6
Rationale: "let the original amount of 85 percent solution = x and amount replaced be y 0.85 ( x - y ) + 0.2 y = 0.4 x 0.85 x - 0.85 y + 0.2 y = 0.4 x 0.45 x = 0.65 y 9 x = 13 y y = 9 x / 13 so , amount replaced = 9 / 13 of original amount answer : c"
Answer: c
Python program:
a = 85 - 40
b = 85 - 20
c = a / b
Problem: rain is falling at a rate of 10 centimeters per hour all over north carolina . somewhere downtown in north carolina a group of people are waiting for the rain to stop . if the rain filled a round puddle the with a base area of 300 square centimeters and a depth of 30 centimeters , how long did the people wait for the rain to stop ?
Options: a ) 4 hours
b ) 11 hours
c ) 7 hours 15 minutes
d ) 3 hours
e ) 14 hours
Rationale: answer is : d , 3 hours the volume of the puddle is irrelevant and only height matters since rain fell all over the city . thus , it takes only 30 / 10 = 3 hours of rain to fill the puddle
Answer: d
Python program:
a = 30 / 10
Problem: the greatest number which on dividing 1442 and 1816 leaves remainders 12 and 6 respectively , is :
Options: a ) 123 , b ) 127 , c ) 235 , d ) 305 , e ) 10
Rationale: explanation : required number = h . c . f . of ( 1442 - 12 ) and ( 1816 - 6 ) = h . c . f . of 1430 and 1810 = 10 . answer : e
Answer: e
Python program:
a = 1816 - 6
b = 1442 - 12
c = math.gcd(a, b)
Problem: if the average ( arithmetic mean ) of x + 1 , x + 3 , and x + 5 is 0 , then x =
Options: a ) – 4 , b ) – 3 , c ) – 2 , d ) – 1 , e ) 0
Rationale: "( x + 1 + x + 3 + x + 5 ) / 3 = 0 = > 3 x + 9 = 0 = > x = - 3 answer b"
Answer: b
Python program:
a = 3 * 2
b = 1 * 2
c = a - b
Problem: a wooden box of dimensions 4 m x 2 m x 4 m is to carry rectangularboxes of dimensions 4 cm x 2 cm x 2 cm . the maximum number ofboxes that can be carried in the wooden box , is
Options: a ) 9800000 , b ) 2000000 , c ) 7500000 , d ) 1200000 , e ) none of these
Rationale: explanation : number = ( 400 * 200 * 400 ) / 4 * 2 * 2 = 2000000 answer : b
Answer: b
Python program:
a = 4 * 100
b = 2 * 100
c = a * b
d = 4 * 100
e = c * d
f = 4 * 2
g = f * 2
h = e / g
Problem: find the simple interest on rs . 750 for 9 months at 6 paisa per month ?
Options: a ) rs . 415 , b ) rs . 405 , c ) rs . 450 , d ) rs . 345 , e ) rs . 564
Rationale: "explanation : i = ( 750 * 9 * 6 ) / 100 = 405 answer : option b"
Answer: b
Python program:
a = 9 / 100
b = 750 * a
Problem: if two projectiles are launched at the same moment from 1182 km apart and travel directly towards each other at 460 km per hour and 525 km per hour respectively , how many minutes will it take for them to meet ?
Options: a ) 68 , b ) 72 , c ) 76 , d ) 80 , e ) 84
Rationale: the projectiles travel a total of 985 km per hour . the time to meet is 1182 / 985 = 1.2 hours = 72 minutes the answer is b .
Answer: b
Python program:
a = 460 + 525 
b = 1182 / a
c = b * const_60
Problem: a and b complete a work in 20 days . a alone can do it in 40 days . if both together can do the work in how many days ?
Options: a ) 1.0875 days , b ) 0.1875 days , c ) 0.0675 days , d ) 0.075 days , e ) 0.0175 days
Rationale: "1 / 20 + 1 / 40 = 0.075 days answer : d"
Answer: d
Python program:
a = 1/(20)
b = 1/(40)
c = a + b 
d = 1/(c)
Problem: a metallic sphere of radius 12 cm is melted and drawn into a wire , whose radius of cross section is 8 cm . what is the length of the wire ?
Options: a ) 16 cm , b ) 24 cm , c ) 28 cm , d ) 36 cm , e ) 39 cm
Rationale: "volume of the wire ( in cylindrical shape ) is equal to the volume of the sphere . π ( 8 ) ^ 2 * h = ( 4 / 3 ) π ( 12 ) ^ 3 = > h = 36 cm answer : d"
Answer: d
Python program:
a = 12 ** 3
b = 8 ** 2
c = a / b
d = 4 * c
e = d / 3
Problem: if 0.4 of a number is equal to 0.06 of another number , the ratio of the numbers is :
Options: a ) 2 : 3 , b ) 3 : 4 , c ) 3 : 20 , d ) 20 : 3 , e ) 22 : 1
Rationale: "expl : 0.4 a = 0.06 b - > a / b = 0.06 / 0.40 = 6 / 40 = 3 / 20 : . a : b = 3 : 20 answer : c"
Answer: c
Python program:
a = 0 * 6
b = 0 * 4
c = a / b
Problem: a group of people participate in some curriculum , 25 of them practice yoga , 18 study cooking , 10 study weaving , 4 of them study cooking only , 5 of them study both the cooking and yoga , 4 of them participate all curriculums . how many people study both cooking and weaving ?
Options: a ) 1 , b ) 2 , c ) 3 , d ) 4 , e ) 5
Rationale: "both cooking and weaving = 18 - ( 4 + 4 + 5 ) = 5 so , the correct answer is e ."
Answer: e
Python program:
a = 18 - 5
b = a - 4
c = b - 4
Problem: a $ 500 investment and a $ 1,500 investment have a combined yearly return of 22 percent of the total of the two investments . if the $ 500 investment has a yearly return of 7 percent , what percent yearly return does the $ 1,500 investment have ?
Options: a ) 29 % , b ) 20 % , c ) 27 % , d ) 25 % , e ) 12 %
Rationale: "the equation we can form the question : return on total investment = sum of individual investments ( 500 + 1500 ) ( 22 ) = ( 500 â ˆ — 7 ) + ( 1500 x ) , where x is the return on investment of 1500 . solving the equation , we get x = 27 % ( option c ) answer : c"
Answer: c
Python program:
a = 3 * 500
b = 500 + a 
c = 22 / 100
d = b * c
e = 7 / 100
f = 500 * e
g = d - f
h = 3 * 500
i = g / h
j = i * 100
Problem: joe went on a diet 3 months ago when he weighed 222 pounds . if he now weighs 198 pounds and continues to lose at the same average monthly rate , in approximately how many months will he weigh 170 pounds ?
Options: a ) 3 , b ) 3.5 , c ) 4 , d ) 4.5 , e ) 5
Rationale: "222 - 198 = 24 pounds lost in 3 months 24 / 3 = 8 , so joe is losing weight at a rate of 8 pounds per month . . . . in approximately how many months will he weigh 170 pounds ? a simple approach is to just list the weights . now : 198 lbs in 1 month : 190 lbs in 2 months : 182 lbs in 3 months : 174 lbs in 4 months : 166 lbs since 170 pounds is halfway between 174 and 166 , the correct answer must be 3.5 months . answer : b"
Answer: b
Python program:
a = 198 - 170
b = 222 - 198
c = b / 3
d = a / c
Problem: two cars are traveling in the same direction along the same route . the red car travels at a constant speed of 40 miles per hour , and the black car is traveling at a constant speed of 50 miles per hour . if the red car is 30 miles ahead of the black car , how many hours will it take the black car to overtake the red car ?
Options: a ) 0.1 , b ) 0.6 , c ) 1 , d ) 1.2 , e ) 3
Rationale: option e 20 + 40 t = 50 t t = 3
Answer: e
Python program:
a = 50 - 40
b = 30 / a
Problem: in a certain city , 60 percent of the registered voters are democrats and the rest are republicans . in a mayoral race , if 70 percent of the registered voters who are democrats and 20 percent of the registered voters who are republicans are expected to vote for candidate a , what percent of the registered voters are expected to vote for candidate a ?
Options: a ) 50 % , b ) 53 % , c ) 54 % , d ) 55 % , e ) 57 %
Rationale: "say there are total of 100 registered voters in that city . thus 60 are democrats and 40 are republicans . 60 * 0.70 = 42 democrats are expected to vote for candidate a ; 40 * 0.20 = 8 republicans are expected to vote for candidate a . thus total of 42 + 8 = 50 registered voters are expected to vote for candidate a , which is 50 % of the total number of registered voters . answer : a"
Answer: a
Python program:
a = 70 / 100
b = 60 * a
c = 100 - 60
d = 20 / 100
e = c * d
f = b + e