euclaise/mathqa_programs huggingface dataset:
Problem: how many different pairs of positive integers ( a , b ) satisfy the equation 1 / a + 1 / b = 34 / 53 ?
Options: a ) 6 , b ) 3 , c ) 2 , d ) 1 , e ) 0
Rationale: "there is no certain way to solve 2 unknown with 1 equation . the best way is to look at the question and retrospect the most efficient way . in this question , a and b are only positive integers . so that is a big relief . now , we can start with putting a = 1,2 , . . and so on till the time we are confident about one of the options . so , we start with a = 1 , we get b as - ve . out a = 2 , we get b as 6 . yes ( now ( a , b ) = ( 2,6 ) . we can directly see that ( a , b ) = ( 6,2 ) will also satisfy . so we have 2 possible solutions ) a = 3 , we get b as 3 . yes ( now we have 3 possible solutions ) a = 4 , we get b as fraction . out a = 5 , we get b again as some fraction . out a = 6 already taken . we have a , b options left . c , d , e are out . a is 6 . to have 6 as the answer , we will need one more pair like 2,6 and one more solution where a = b . when a = b , we have only 1 solution = 3 . so , one more solution , where a = b is not possible . so , answer will be c ."
Answer: c
Python program:
a = 34 / 53
Problem: in a house , there are 4 birds , 3 dogs , and 18 cats living with the human family . if the total number of feet in the house are 74 more than the number of heads in the house , how many family members are there ?
Options: a ) 1 , b ) 3 , c ) 5 , d ) 7 , e ) 9
Rationale: explanation : let number of family members be x . then , total number of feet = 2 x 4 + 4 x 3 + 4 x 18 + 2 x = 2 x + 92 . total number of heads = 4 + 3 + 18 + x = 25 + x . therefore ( 2 x + 92 ) = ( 25 + x ) + 74 or x = 7 . answer : d
Answer: d
Python program:
a = 18 / 3
b = a + 1
Problem: what will be the fraction of 33.33 %
Options: a ) 1 / 4 , b ) 1 / 5 , c ) 1 / 3 , d ) 1 / 8 , e ) none of above
Rationale: "explanation : it will 33.33 * 1 / 100 = 1 / 3 answer : option c"
Answer: c
Python program:
a = 33 / 33
b = circle_area / (
Problem: the ratio of the adjacent angles of a parallelogram is 6 : 9 . also , the ratio of the angles of quadrilateral is 5 : 6 : 7 : 12 . what is the sum of the smaller angle of the parallelogram and the second largest angle of the quadrilateral ?
Options: a ) 168 ° , b ) 228 ° , c ) 156 ° , d ) 224 ° , e ) none of these
Rationale: "the measures of the adjacent angles of a parallelogram add up to be 180 ° given so , 6 x + 9 x = 180 ° or , 15 x = 180 ° or , x = 12 ° hence the angles of the parallelogram are 72 ° and 108 ° further it is given we know sum of all the four angles of a quadrilateral is 360 ° so , 5 y + 6 y + 7 y + 12 y = 360 ° or , 5 y + 6 y + 7 y + 12 y = 360 ° or , 30 y = 360 ° or , y = 12 ° hence the angles of the quadrilateral are 60 ° , 72 , 84 ° and 144 ° will be 72 ° + 84 ° = 156 ° answer : c"
Answer: c
Python program:
a = 6 * 2
b = a * 10
c = b + 100 
d = c * 2
e = 5 + 6 
f = e + 7 
g = f + 12 
h = d / g
i = h * 9
Problem: the h . c . f . of two numbers is 12 and their difference is 12 . the numbers are
Options: a ) 66 , 78 , b ) 70 , 82 , c ) 94 , 106 , d ) 84 , 96 , e ) none
Rationale: "solution out of the given numbers , the two with h . c . f . 12 and difference 12 are 84 and 96 answer d"
Answer: d
Python program:
a = 3 + 4 
b = 12 * a
Problem: if the length and breadth of a room are increased by y feet each , the perimeter increases by 16 feet . find y
Options: a ) 8
b ) 2
c ) 6
d ) 4
e ) 3
Rationale: 2 ( l + b ) = x ; 2 ( l + y + b + y ) = x + 16 ; 2 ( l + b ) + 4 y = x + 16 ; x + 4 y = x + 16 ; y = 4 answer : d
Answer: d
Python program:
a = 16 / 4
Problem: jack and paul are running 1000 m . jack runs 1.5 km / hr faster than paul but also finishes the race 1.5 sec earlier . what is the speed of jack ? ?
Options: a ) 19.6 , b ) 20.6 , c ) 21.6 , d ) 22.6 , e ) 23.6
Rationale: distance ( given ) 1000 m paul speed ( let ) = x m / s time ( paul take ) = 1000 / x sec jack speed = x + 1.5 * ( 5 / 18 ) m / s tym ( jack ) = 1000 / ( x + 7.5 / 18 ) s tym ( paul ) - tym ( jack ) = 1.5 solving for x we get 20.20 speed of jack is 20.20 + 7.5 / 18 = 20.61 answer : b
Answer: b
Python program:
a = 1 * 5
b = a * 100
c = b / 2
d = 1 * 5
e = d / 2
f = c - e
Problem: the speed of boat in still water is 20 km / hr . if it travels 26 km downstream and 14 km upstream in same time , what is the speed of the stream ?
Options: a ) 6 , b ) 7 , c ) 8 , d ) 9 , e ) 2
Rationale: explanation : let x be speed of stream speed of boat downstream = ( 20 + x ) speed of boat upstream = ( 20 – x ) it is given that boat takes same time to travel 26 km downstream and 14 km upstream [ 26 / ( 20 + x ) ] = [ 14 / ( 20 – x ) ] 520 – 26 x = 280 + 14 x 40 x = 240 x = 6 km / hr answer : a
Answer: a
Python program:
a = 20 * 26
b = 20 * 14
c = a - b
d = 26 + 14 
e = c / d
Problem: on my sister ' s birthday , she was 147 cm in height , having grown 5 % since the year before . how tall was she the previous year ?
Options: a ) 145 cm , b ) 140 cm , c ) 142 cm , d ) 138 cm , e ) 135 cm
Rationale: "let the previous year ' s height be x . 1.05 x = 147 x = 140 the answer is b ."
Answer: b
Python program:
a = 147 * 5
b = a / 100
c = 147 - b
Problem: if the sum of the 4 th term and the 12 th term of an arithmetic progression is 10 , what is the sum of the first 15 terms of the progression ?
Options: a ) 65 , b ) 75 , c ) 60 , d ) 55 , e ) 50
Rationale: "4 th term + 12 th term = 10 i . e . , ( a + 3 d ) + ( a + 11 d ) = 10 now , sum of first 15 terms = ( 15 / 2 ) * [ 2 a + ( 15 - 1 ) d ] = ( 15 / 2 ) * [ 2 a + 14 d ] = ( 15 / 2 ) * 10 - - - - - - - - - - - - - - - from ( 1 ) = 75 answer : b"
Answer: b
Python program:
a = 15 / 2
b = a * 10
Problem: during a certain season , a team won 65 percent of its first 100 games and 50 percent of its remaining games . if the team won 70 percent of its games for the entire season , what was the total number of games that the team played ?
Options: a ) 80 , b ) 75 , c ) 56 , d ) 50 , e ) 105
Rationale: "we are first given that a team won 65 percent of its first 100 games . this means the team won 0.65 x 100 = 65 games out of its first 100 games . we are next given that the team won 50 percent of its remaining games . if we use variable t to represent the total number of games in the season , then we can say t – 100 equals the number of remaining games in the season . thus we can say : 0.5 ( t – 100 ) = number of wins for remaining games 0.5 t – 50 = number of wins for remaining games lastly , we are given that team won 70 percent of all games played in the season . that is , they won 0.7 t games in the entire season . with this we can set up the equation : number of first 100 games won + number of games won for remaining games = total number of games won in the entire season 65 + 0.5 t – 50 = 0.7 t 15 = 0.2 t 150 = 2 t 75 = t answer is b ."
Answer: b
Python program:
a = 65 - 70
b = 70 / 100
c = 50 / 100
d = b - c
e = a / d
f = 100 + e
Problem: worker a takes 8 hours to do a job . worker b takes 10 hours to do a job . how long should it take both a and b , working together to do same job .
Options: a ) 4 / 9 , b ) 2 4 / 9 , c ) 3 4 / 9 , d ) 4 4 / 9 , e ) none of these
Rationale: "explanation : in this type of questions , first we need to calculate 1 hours work , then their collective work as , a ' s 1 hour work is 1 / 8 b ' s 1 hour work is 1 / 10 ( a + b ) ' s 1 hour work = 1 / 8 + 1 / 10 = 9 / 40 so both will finish the work in 40 / 9 hours = 4 4 / 9 option d"
Answer: d
Python program:
a = 1 / 8
b = 1 / 10
c = a + b 
d = 1 / c
Problem: a man can row downstream at 18 kmph and upstream at 12 kmph . find the speed of the man in still water and the speed of stream respectively ?
Options: a ) 3 , b ) 5 , c ) 6 , d ) 4 , e ) 9
Rationale: "let the speed of the man in still water and speed of stream be x kmph and y kmph respectively . given x + y = 18 - - - ( 1 ) and x - y = 12 - - - ( 2 ) from ( 1 ) & ( 2 ) 2 x = 30 = > x = 15 , y = 3 . answer : a"
Answer: a
Python program:
a = 18 + 12 
b = a / 2
c = b / 2
Problem: the weight of a glass of jar is 25 % of the weight of the jar filled with coffee beans . after some of the beans have been removed , the weight of the jar and the remaining beans is 60 % of the original total weight . what fraction part of the beans remain in the jar ?
Options: a ) 1 / 5 , b ) 1 / 3 , c ) 2 / 5 , d ) 1 / 2 , e ) 7 / 15
Rationale: "let weight of jar filled with beans = 100 g weight of jar = 25 g weight of coffee beans = 75 g weight of jar and remaining beans = 60 g weight of remaining beans = 35 g fraction remaining = 35 / 75 = 7 / 15 answer is e ."
Answer: e
Python program:
a = 60 - 25
b = 100 - 25
c = a / b
Problem: one ton has 2500 pounds , and one pound has 16 ounces . how many packets containing wheat weighing 16 pounds and 4 ounces each would totally fill a gunny bag of capacity 13 tons ?
Options: a ) 2000 , b ) 1700 , c ) 2350 , d ) 2500 , e ) 8000
Rationale: "16 pounds and 4 ounces = 16 * 16 + 4 = 260 ounces . 13 tons = 13 * 2500 pound = 13 * 2500 * 16 ounces . hence the answer is ( 13 * 2500 * 16 ) / 260 = 2000 . answer : a ."
Answer: a
Python program:
a = 13 * 2500
b = a * 16
c = 16 * 16
d = c + 4 
e = b / d
Problem: in an examination , there were 2,000 candidates , out of which 900 candidates were girls and rest were boys . if 28 % of the boys and 32 % of the girls passed , then the total percentage of failed candidates is ?
Options: a ) 35.67 % , b ) 64.75 % , c ) 68.57 % , d ) 70.20 % , e ) none of these
Rationale: girls = 900 , boys = 1100 passed = ( 28 % of 1100 ) + ( 32 % of 900 ) = 308 + 288 = 596 failed = 2000 - 596 = 1404 failed % = [ ( 1404 / 2000 ) x 100 ] % = 70.2 % . answer : d
Answer: d
Python program:
a = 100 * 10
b = 2 * a
c = 28 / 100
d = 100 * 10
e = 2 * d
f = e - 900
g = c * f
h = b - g
i = 32 / 100
j = i * 900
k = h - j
l = 100 * 10
m = 2 * l
n = k / m
o = n * 100
Problem: an amount of money is to be distributed among faruk , vasim and ranjith in the ratio 3 : 3 : 7 . if vasims share is rs . 1500 , what is the difference between faruk ' s and ranjith ' s shares ?
Options: a ) s 1200 , b ) s 1500 , c ) s 1600 , d ) s 2000 , e ) s 1700
Rationale: "explanation : let p = faruk , q = vasim , r = ranjith let p = 3 x , q = 3 x and r = 7 x . then , 5 x = 1500 ? x = 500 . p = 1500 , q = 1500 and r = 3500 . hence , ( r - p ) = ( 3500 - 1500 ) = 2000 answer : d"
Answer: d
Python program:
a = 1500 / 3
b = 7 - 3
c = a * b
Problem: a , b and c are employed to do apiece of work for rs . 529 . a and c are supposed to finish 19 / 23 of the work together . how much shall be paid to b ?
Options: a ) 10 , b ) 11 , c ) 12 , d ) 14 , e ) 16
Rationale: c 12 12 men can complete a work in 18 days . six days after they started working , 4 more men joined them . how many days will all of them together complete the remaining work ?
Answer: c
Python program:
a = 19 / 23
b = a * 529
c = 529 - b
d = c + 4 
e = 4 + 4 
f = d / e
Problem: a train 990 m long is running at a speed of 78 km / hr . if it crosses a tunnel in 1 min , then the length of the tunnel is ?
Options: a ) 2898 , b ) 277 , c ) 310 , d ) 297 , e ) 435
Rationale: "speed = 78 * 5 / 18 = 65 / 3 m / sec . time = 1 min = 60 sec . let the length of the train be x meters . then , ( 990 + x ) / 60 = 65 / 3 x = 310 m . answer : c"
Answer: c
Python program:
a = 78 - 1
b = a * const_0_2778
c = 990 / b
Problem: calculate how many days it will take for 5 boys to paint a 30 m long fence if 2 boys can paint a 20 m long fence in 3 days ,
Options: a ) 6.80 days , b ) 4.80 days , c ) 3.80 days , d ) 2 days , e ) 1.80 days
Rationale: "the length of wall painted by one boy in one day = 20 / 2 * 1 / 3 = 3.33 m no . of days required to paint 50 m cloth by 8 boys = 30 / 5 * 1 / 3.33 = 1.80 days . e"
Answer: e
Python program:
a = 2 * 3
b = a * 30
c = 20 * 5
d = b / c
Problem: find the value of ( 28 + 48 / 69 ) × 69
Options: a ) 1980 , b ) 1982 , c ) 1930 , d ) 1988 , e ) 1680
Rationale: "= ( 28 + 48 / 69 ) × 69 = ( 1932 + 48 ) / 69 × 69 = 1980 / 69 × 69 = 1980 answer is a ."
Answer: a
Python program:
a = 48 / 69
b = a + 28 
c = b * 69
Problem: a soccer store typically sells replica jerseys at a discount of 20 percent to 50 percent off list price . during the annual summer sale , everything in the store is an additional 20 percent off the original list price . if a replica jersey ' s list price is $ 80 , approximately what percent of the list price is the lowest possible sale price ?
Options: a ) 20 , b ) 25 , c ) 30 , d ) 40 , e ) 50
Rationale: "let the list price be 2 x for min sale price , the first discount given should be 50 % , 2 x becomes x here now , during summer sale additional 20 % off is given ie sale price becomes 0.8 x it is given lise price is $ 80 = > 2 x = 80 = > x = 50 and 0.8 x = 32 so lowest sale price is 32 , which is 40 % of 80 hence , e is the answer"
Answer: e
Python program:
a = 80 / 2
Problem: a new tower has just been built at the verbico military hospital ; the number of beds available for patients at the hospital is now 4 times the number available before the new tower was built . currently , 1 / 3 of the hospital ' s original beds , as well as 1 / 5 of the beds in the new tower , are occupied . for the purposes of renovating the hospital ' s original wing , all of the patients in the hospital ' s original beds must be transferred to beds in the new tower . if patients are neither admitted nor discharged during the transfer , what fraction of the beds in the new tower will be unoccupied once the transfer is complete ?
Options: a ) 11 / 30 , b ) 29 / 60 , c ) 17 / 30 , d ) 31 / 45 , e ) 11 / 15
Rationale: "i think d - 31 / 45 is the correct answer . here goes : lets assume originally the number of beds = x after the new tower , the total combined no of beds = 4 x so old = x , new = 3 x now 1 / 3 of x are occupied and 1 / 5 of 3 x are occupied which simplifies to ( 3 / 5 ) x we are shifting 1 / 3 of x to the new ward so there will now be : 1 / 3 of x plus 3 / 5 of x occupied in the new ward . add them up to get 14 / 15 of x there are 3 x beds in new tower so ratio is : ( 14 / 15 ) x / 3 x = 14 / 45 of x subtract that from 45 / 45 of x and you get the number of un - occupied beds to total capacity of new tower = 31 / 45 d"
Answer: d
Python program:
a = 4 * 3
b = a + 1 
c = 1 / 3
d = 1 / 5
e = c * d
f = b * e
Problem: if jake loses 32 pounds , he will weigh twice as much as his sister . together they now weigh 212 pounds . what is jake ’ s present weight , in pounds ?
Options: a ) 131 , b ) 135 , c ) 139 , d ) 152 , e ) 188
Rationale: lets say j is the weight of jack and s is the wt of his sister . if he loses 32 pounds , he s twice as heavy as his sister . j - 32 = 2 * s also , together they weight 212 pounds j + s = 212 solvong the 2 equation , we get j = 152 pounds ! d
Answer: d
Python program:
a = 212 - 32
b = a / 3
c = b * 2
d = c + 32
Problem: a train 125 m long passes a man , running at 5 km / hr in the same direction in which the train is going , in 10 sec . the speed of the train is ?
Options: a ) 225 km / hr , b ) 50 km / hr , c ) 99 km / hr , d ) 88 km / hr , e ) 66 km / hr
Rationale: "speed of the train relative to man = 125 / 10 = 25 / 2 m / sec . = 25 / 2 * 18 / 5 = 45 km / hr let the speed of the train be x km / hr . then , relative speed = ( x - 5 ) km / hr . x - 5 = 45 = > x = 50 km / hr . answer : b"
Answer: b
Python program:
a = 5 * const_0_2778
b = a * 5
c = 125 - b
d = c / 5
e = d / const_0_2778
Problem: how many cuboids of length 6 m , width 4 m and height 3 m can be farmed from a cuboid of 18 m length , 15 m width and 2 m height .
Options: a ) 2.6 , b ) 5.8 , c ) 6.2 , d ) 7.5 , e ) 1.2
Rationale: "( 18 ã — 15 ã — 2 ) / ( 6 ã — 4 ã — 3 ) = 7.5 answer is d ."
Answer: d
Python program:
a = 18 * 15
b = a * 2
c = 6 * 4
d = c * 3
e = b / d
Problem: how many seconds will a train 100 meters long take to cross a bridge 180 meters long if the speed of the train is 36 kmph ?
Options: a ) 26 , b ) 72 , c ) 28 , d ) 82 , e ) 27
Rationale: "explanation : d = 100 + 180 = 280 s = 36 * 5 / 18 = 10 mps t = 280 / 10 = 28 sec answer : option c"
Answer: c
Python program:
a = 180 + 100 
b = 36 * const_0_2778
c = a / b
Problem: there are 36 students in a certain geometry class . if one third of the students are boys and one fourth of the boys are under 6 feet tall , how many boys in the class are under 6 feet tall ?
Options: a ) 3 , b ) 12 , c ) 18 , d ) 24 , e ) 27
Rationale: total students = 36 one third of the students are boys = 1 / 3 * 36 = 12 one fourth of the boys are under six feet tall = 1 / 4 * 12 = 3 . . . therefore number of boys in the class under six feet tall = 3 . . . answer a . . . . alternatively . . . number of boys in the class under six feet tall = 1 / 4 of 1 / 3 of total students = 1 / 4 * 1 / 3 * 36 = 3 . . . answer a
Answer: a
Python program:
a = 36 / 3
b = a / 4
Problem: find the area of the quadrilateral of one of its diagonals is 30 cm and its off sets 9 cm and 6 cm ?
Options: a ) 225 cm 2 , b ) 150 cm 2 , c ) 127 cm 2 , d ) 177 cm 2 , e ) 187 cm 2
Rationale: "1 / 2 * 30 ( 9 + 6 ) = 225 cm 2 answer : a"
Answer: a
Python program:
a = 1 / 2
b = 6 + 9 
c = a * b
d = c * 30
Problem: a cricketer scored 138 runs which included 12 boundaries and 2 sixes . what percent of his total score did he make by running between the wickets .
Options: a ) 46.2 % , b ) 54.54 % , c ) 63 % , d ) 56.52 % , e ) none of these
Rationale: explanation : number of runs made by running = 138 - ( 12 x 4 + 2 x 6 ) = 138 - ( 60 ) = 78 now , we need to calculate 72 is what percent of 138 . = > 78 / 138 * 100 = 56.52 % answer : d
Answer: d
Python program:
a = 12 * 4
b = 2 * 3
c = 2 * b
d = a + c 
e = 138 - d
f = e / 138
g = f * 100
Problem: if the height of a triangle is decreased by 40 % , land its base is increased by 40 % , what will be the effect on its area ?
Options: a ) no change
b ) 16 % increase
c ) 8 % decrease
d ) 16 % decrease
e ) none of thes
Rationale: regd effect = ∣ ∣ 40 − 40 − 40 × 40100 ∣ ∣ % = − 16 % | 40 − 40 − 40 × 40100 | % = − 16 % i . e . , the area will decrease by 16 % answer d
Answer: d
Python program:
a = 100 - 40
b = 100 + 40 
c = a * b
d = c / 100
e = 100 - d
Problem: p and q invested in a shop . the profits were divided in the ratio of 2 : 3 respectively . if p invested rs . 40,000 , the amount invested by q is :
Options: a ) 35000 , b ) 40000 , c ) 50000 , d ) 60000 , e ) none
Rationale: "suppose q invested rs . y . then , 40000 / y = 2 / 3 or y = [ 40000 x 3 / 2 ] = 60000 . answer d"
Answer: d
Python program:
a = 40 / 0
b = a * 3
Problem: if taxi fares were $ 8.00 for the first 1 / 5 mile and $ 0.8 for each 1 / 5 mile there after , then the taxi fare for a 8 - mile ride was
Options: a ) $ 39.00 , b ) $ 39.10 , c ) $ 39.25 , d ) $ 39.30 , e ) $ 39.20
Rationale: in 8 miles , initial 1 / 5 mile charge is $ 8 rest of the distance = 8 - ( 1 / 5 ) = 39 / 5 rest of the distance charge = 39 ( 0.8 ) = $ 31.2 ( as the charge is 0.8 for every 1 / 5 mile ) = > total charge for 4 miles = 8 + 31.2 = 39.2 answer is e
Answer: e
Python program:
a = 1 / 5
b = 8 / a
c = b - 1
d = c * 0
e = 8 + d
Problem: with both valves open , the pool will be filled with water in 48 minutes . the first valve alone would fill the pool in 2 hours . if the second valve emits 50 cubic meters of water more than the first every minute , then what is the capacity q of the pool ?
Options: a ) 9000 cubic meters , b ) 10500 cubic meters , c ) 11750 cubic meters , d ) 12000 cubic meters , e ) 12500 cubic meters
Rationale: "d . 12000 cubic meters . if both hte valves fill the pool in 48 minutes and valve 1 only fills in 120 minutes then valve 2 alone will fill the pool in ( 48 * 120 ) / ( 120 - 48 ) = 80 minutes . now , if valve 1 admits x cubic meter of water per minute then the capacity of pool will be 120 x and also 80 ( x + 50 ) . or , 120 x = 80 ( x + 50 ) . or x = 100 . hence , the capacity of pool = 120 x = 12000 cubic meters ."
Answer: d
Python program:
a = 48 / const_60
b = 4 + 1 
c = a * b
d = const_60 * c
e = 50 * d
Problem: how many diagonals does a 63 - sided convex polygon have ?
Options: a ) 1890 , b ) 1953 , c ) 3780 , d ) 3843 , e ) 3906
Rationale: "a 63 - sided convex polygon has 63 vertices . if we examine a single vertex , we can see that we can connect it with 60 other vertices to create a diagonal . note : there are 60 options because we ca n ' t connect the vertex to itself , and we ca n ' t connect it to its adjacent vertices , since this would not create a diagonal . if each of the 63 vertices can be connected with 60 vertices to create a diagonal then . . . . . . the total number of diagonals = ( 63 ) ( 60 ) = 3780 however , before we select answer choice c , we must recognize that we have counted every diagonal twice . for example , we might connect vertex a with vertex f and count that as 1 diagonal , and at the same time we connect vertex f with vertex a and count that as 1 diagonal . of course these diagonals are the same . to account for counting each diagonal twice , we must divide 3780 by 2 to get : 1890 answer : a"
Answer: a
Python program:
a = math.factorial(63)
b = 63 - 2
c = math.factorial(b)
d = math.factorial(2)
e = c * d
f = a / e
Problem: in a graduating class , the difference between the highest and lowest salaries is $ 100000 . the median salary is $ 50000 higher than the lowest salary and the average salary is $ 20000 higher than the median . what is the minimum number of students t in the class ?
Options: a ) a ) 10 , b ) b ) 12 , c ) c ) 15 , d ) d ) 20 , e ) e ) 25
Rationale: the difference between the highest and lowest salaries is $ 100000 . so there are at least 2 people - say one with salary 0 and the other with 100 k . no salary will be outside this range . median = 50 k more than lowest . so median is right in the center of lowest and highest since lowest and highest differ by 100 k . in our example , median = 50 k . since there are more than 2 people , there would probably be a person at 50 k . mean = 20 k more than median so in our example , mean salary = 70 k on the number line , 0 . . . . . . . . 50 k ( median ) . . . . . . . . 100 k mean = 70 k so there must be people more toward 100 k to bring the mean up to 70 k . since we want to add minimum people , we will add people at 100 k to quickly make up the right side deficit . 0 and 50 k are ( 70 k + 20 k ) = 90 k away from 70 k . 100 k is 30 k away from 70 k . to bring the mean to 70 k , we will add two people at 100 k each to get : 0 . . . . 50 k . . . . . 100 k , 100 k , 100 k but when we add more people to the right of 70 k , the median will shift to the right . we need to keep the median at 50 k . so every time we add people to the right of 70 k , we need to add people at 50 k too to balance the median . 50 k is 20 k less than 70 k while 100 k is 30 k more than 70 k . to keep the mean same , we need to add 2 people at 100 k for every 3 people we add at 50 k . so if we add 3 people at 50 k and 2 people at 100 k , we get : 0 , . . . 50 k , 50 k , 50 k , 50 k , . . . 100 k , 100 k , 100 k , 100 k , 100 k the median is not at 50 k yet . add another 3 people at 50 k and another 2 at 100 k to get 0 , 50 k , 50 k , 50 k , 50 k , 50 k , 50 k , 50 k , 100 k , 100 k , 100 k , 100 k , 100 k , 100 k , 100 k now the median is 50 k and mean is 70 k . total number of people is 15 . answer ( c )
Answer: c
Python program:
a = 50000 + 20000 
b = 50000 + 20000 
c = 100000 - b
d = c - 20000
e = a / d
f = e * 2
g = f + 1
Problem: uncle bruce is baking chocolate chip cookies . he has 36 ounces of dough ( with no chocolate ) and 20 ounces of chocolate . how much chocolate is left over if he uses all the dough but only wants the cookies to consist of 10 % chocolate ?
Options: a ) 18 , b ) 20 , c ) 16 , d ) 22 , e ) 24
Rationale: "first , you must find the total weight of the mixture given that 80 % of it will be dough . 90 % * total = 36 = > ( 9 / 10 ) total = 36 = > total = 360 / 9 = > total = 40 oz , from there , you must find 10 % of the total 40 oz of the mixture . 10 % * total = > ( 1 / 10 ) ( 40 ) = 4 oz choclate used , not forgetting that the question asks how much chocolate is left over we must subtract the chocolate used from the initial chocolate . 20 - 4 = 16 oz chocolate left over . answer : c"
Answer: c
Python program:
a = 10 / 100
b = a * 10