euclaise/mathqa_programs huggingface dataset:
Problem: the area of a square field is 576 km 2 . how long will it take for a horse to run around at the speed of 12 km / h ?
Options: a ) 12 h , b ) 10 h , c ) 8 h , d ) 6 h , e ) none of these
Rationale: "area of field = 576 km 2 . then , each side of field = √ 576 = 24 km distance covered by the horse = perimeter of square field = 24 × 4 = 96 km ∴ time taken by horse = distances / peed = 96 / 12 = 8 h answer c"
Answer: c
Python program:
a = math.sqrt(576)
b = 4 * a
c = b / 12
Problem: a and b complete a work in 6 days . a can alone can do it in 10 days . if both can together can do the work in how many days ?
Options: a ) 7 , b ) 3.75 , c ) 2 , d ) 1 , e ) 8
Rationale: 1 / 6 + 1 / 10 = 8 / 30 = 4 / 15 15 / 4 = 3.75 days answer b
Answer: b
Python program:
a = 6 * 10
b = 6 + 10 
c = a / b
Problem: suppose you work for a manufacturing plant that pays you $ 12.50 an hour plus $ 0.16 for each widget you make . how many widgets must you produce in a 40 hour week to earn $ 620 ( before payroll deductions ) ?
Options: a ) 670 , b ) 710 , c ) 750 , d ) 790 , e ) 830
Rationale: total pay = 40 * $ 12.50 + $ 0.16 * x = 620 x = 120 / 0.16 = 750 the answer is c .
Answer: c
Python program:
a = 12 * 5
b = 620 - a
c = b / 0
Problem: what is the distance covered by a car if it travels with a speed of 160 kmh for 5 hours ?
Options: a ) 350 km , b ) 400 km , c ) 800 km , d ) 600 km , e ) 650 km
Rationale: distance = time x speed 5 x 160 = 800 answer : c
Answer: c
Python program:
a = 160 * 5
Problem: a cricketer scored 132 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 ) 70 % , e ) none of these
Rationale: "explanation : number of runs made by running = 132 - ( 12 x 4 + 2 x 6 ) = 132 - ( 60 ) = 72 now , we need to calculate 72 is what percent of 132 . = > 72 / 132 * 100 = 54.54 % answer : b"
Answer: b
Python program:
a = 12 * 4
b = 2 * 3
c = 2 * b
d = a + c 
e = 132 - d
f = e / 132
g = f * 100
Problem: a can do a piece of work in 80 days and b in 100 days . they work together for 20 days and then b goes away . in how many days will a finish the remaining work ?
Options: a ) 33 days , b ) 44 days , c ) 55 days , d ) 42 days , e ) 32 days
Rationale: "explanation : in this type of questions we first get the finishing of work in 1 minute for both pipes then we will add them to get the result , as : part finished by a in 1 day = 1 / 80 part finished by b in 1 day = 1 / 100 part finished by ( a + b ) in 1 day = 1 / 80 + 1 / 100 = 9 / 400 so ( a + b ) ' s 20 days work = 20 * 9 / 400 = 9 / 20 remaining work = 1 - 9 / 20 = 11 / 20 . number days to finish the remaining work by a = 80 * 11 / 20 = 44 days . option b"
Answer: b
Python program:
a = 1 / 80
b = 20 * a
c = 1 / 100
d = 20 * c
e = b + d 
f = 1 - e
g = 1 / 100
h = f / g
i = h + 20
Problem: pumps a , b , and c operate at their respective constant rates . pumps a and b , operating simultaneously , can fill a certain tank in 6 / 5 hours ; pumps a and c , operating simultaneously , can fill the tank in 3 / 2 hours ; and pumps b and c , operating simultaneously , can fill the tank in 1 hours . how many hours does it take pumps a , b , and c , operating simultaneously , to fill the tank .
Options: a ) 37 / 20 , b ) 1 / 2 , c ) 1 / 4 , d ) 1 , e ) 5 / 6
Rationale: "a + b = 6 / 5 ; a + c = 3 / 2 , b + c = 1 ; add then 2 * ( a + b + c ) = 6 / 5 + 3 / 2 + 1 = 37 / 10 a + b + c = 37 / 20 hrs a"
Answer: a
Python program:
a = 5 + 5 
b = 5 / 6
c = 6 + 6 
d = b + c 
e = a - d
f = e / 6
Problem: the marks obtained by polly and sandy are in the ratio 4 : 5 and those obtained by sandy and willy are in the ratio of 5 : 2 . the marks obtained by polly and willy are in the ratio of . . . ?
Options: a ) 2 : 1 , b ) 3 : 2 , c ) 4 : 3 , d ) 5 : 4 , e ) 6 : 5
Rationale: "polly : sandy = 4 : 5 sandy : willy = 5 : 2 polly : sandy : willy = 4 : 5 : 2 polly : willy = 4 : 2 = 2 : 1 the answer is a ."
Answer: a
Python program:
a = 4 * 5
b = 5 * 2
c = a / b
Problem: in a certain supermarket , a triangular display of cans is arranged in 9 rows , numbered 1 through 9 from top to bottom . each successively numbered row contains 3 more cans than the row immediately above it . if there are fewer than 120 cans in the entire display , how many cans are in the six row ?
Options: a ) 12 , b ) 14 , c ) 16 , d ) 18 , e ) 20
Rationale: "let x be the number of cans in row 1 . the total number of cans is x + ( x + 3 ) + . . . + ( x + 24 ) = 9 x + 3 ( 1 + 2 + . . . + 8 ) = 9 x + 3 ( 8 ) ( 9 ) / 2 = 9 x + 108 since the total is less than 120 , x must equal 1 . the number of cans in the 6 th row is 1 + 3 ( 5 ) = 16 the answer is c ."
Answer: c
Python program:
a = 3 + 3 
b = a * 3
c = 9 - 1
d = 3 * c
e = d / 2
f = e * 9
g = 120 - f
h = g / 9
i = math.floor(h)
j = b + i
Problem: a man ' s regular pay is $ 3 per hour up to 40 hours . overtime is twice the payment for regular time . if he was paid $ 168 , how many hours overtime did he work ?
Options: a ) 8 , b ) 21 , c ) 14 , d ) 12 , e ) 15
Rationale: "answer is : b at $ 3 per hour up to 40 hours , regular pay = $ 3 x 40 = $ 120 if total pay = $ 168 , overtime pay = $ 168 - $ 120 = $ 48 overtime rate ( twice regular ) = 2 x $ 3 = $ 6 per hour = > number of overtime hours = $ 48 / $ 6 = 8"
Answer: a
Python program:
a = 3 * 40
b = 168 - a
c = 3 * 2
d = b / c
Problem: if a is thrice as fast as b and together can do a work in 21 days . in how many days a alone can do the work ?
Options: a ) 36 , b ) 42 , c ) 28 , d ) 54 , e ) 45
Rationale: "a ’ s one day ’ s work = 1 / x b ’ s one day ’ s work = 1 / 3 x a + b ’ s one day ’ s work = 1 / x + 1 / 3 x = 1 / 21 = 3 + 1 / 3 x = 4 / 3 x = 1 / 21 x = 21 * 4 / 3 = 28 answer : c"
Answer: c
Python program:
a = 21 * 4
b = 3 / a
c = 1/(b)
Problem: at a local appliance manufacturing facility , the workers received a 20 % hourly pay raise due to extraordinary performance . if one worker decided to reduce the number of hours that he worked so that his overall pay would remain unchanged , by approximately what percent would he reduce the number of hours that he worked ?
Options: a ) 83 % , b ) 80 % , c ) 20 % , d ) 17 % , e ) 12 %
Rationale: "let ' s say he works usually 10 hours and earns 100 per hour . 10 * 100 = 1000 10 * 120 = 1200 ( this are the new earnings after the raise ) to figure out how much he needs to work with the new salary in order to earn the original 1000 : 1000 / 120 = 8.3333 so he can reduce his work by 1.6666 hours . which is > 15 % . answer d ."
Answer: d
Python program:
a = 20 - 1
Problem: a reduction of 12 % in the price of oil enables a house wife to obtain 6 kgs more for rs . 1200 , what is the reduced price for kg ?
Options: a ) 24 , b ) 27 , c ) 40 , d ) 28 , e ) 20
Rationale: "1200 * ( 12 / 100 ) = 144 - - - - 6 ? - - - - 1 = > rs . 24 answer : a"
Answer: a
Python program:
a = 1200 * 12
b = a / 100
c = b / 6
Problem: dick and jane each saved $ 3,000 in 1989 . in 1990 dick saved 8 percent more than in 1989 , and together he and jane saved a total of $ 5,000 . approximately what percent less did jane save in 1990 than in 1989 ?
Options: a ) 8 % , b ) 25 % , c ) 41 % , d ) 59 % , e ) 70 %
Rationale: "dick saved = $ 3240 jane saved = $ 1760 ( jane saved $ 1240 less than she did the prior year ) jane saved approximately $ 1240 / $ 3000 ( close to 41 % ) less in 1990 answer : c"
Answer: c
Python program:
a = 8 / 100
b = a + 1 
c = 2 - b
d = 1 - c
e = d * 100
Problem: the average of temperatures at noontime from monday to friday is 40 ; the lowest one is 30 , what is the possible maximum range of the temperatures ?
Options: a ) 20 , b ) 25 , c ) 50 , d ) 45 , e ) 75
Rationale: "average = 40 , sum of temperatures = 40 * 5 = 200 as the min temperature is 30 , max would be 200 - 4 * 30 = 80 - - > the range = 80 ( max ) - 30 ( min ) = 50 answer : c"
Answer: c
Python program:
a = 2 + 3 
b = 40 * a
c = 30 * 4
d = b - c
e = d - 30
Problem: in a parallelogram , the length of one diagonal and the perpendicular dropped on that diagonal are 30 and 20 metres respectively . find its area
Options: a ) 600 m 2
b ) 540 m 2
c ) 680 m 2
d ) 574 m 2
e ) none of these
Rationale: in a parallelogram . area = diagonal × length of perpendicular on it . = 30 × 20 = 600 m 2 answer a
Answer: a
Python program:
a = 30 * 20
Problem: a card is drawn from a pack of 52 cards . the probability of getting a queen of spade or an ace of club is :
Options: a ) 1 / 13 , b ) 1 / 26 , c ) 2 / 13 , d ) 1 / 52 , e ) 1 / 48
Rationale: "explanation : total outcomes = 52 favourable outcomes ( getting a queen of spade or an ace of club ) = 2 probability = 2 / 52 = 1 / 26 . answer : b"
Answer: b
Python program:
a = 4 * 4
b = 52 - a
c = b / 52
Problem: in a certain game , a large bag is filled with blue , green , purple and red chips worth 1 , 5 , x and 11 points each , respectively . the purple chips are worth more than the green chips , but less than the red chips . a certain number of chips are then selected from the bag . if the product of the point values of the selected chips is 11,000 , how many purple chips were selected ?
Options: a ) 1 , b ) 2 , c ) 3 , d ) 4 , e ) 5
Rationale: "11,000 = 1 * 5 ^ 3 * 8 * 11 the factor of 8 must come from the purple point value , so there is 1 purple chip . the answer is a ."
Answer: a
Python program:
a = 5 - 2
Problem: find large number from below question the difference of two numbers is 1370 . on dividing the larger number by the smaller , we get 6 as quotient and the 15 as remainder
Options: a ) 1245 , b ) 1345 , c ) 1455 , d ) 1577 , e ) 1641
Rationale: "let the smaller number be x . then larger number = ( x + 1370 ) . x + 1370 = 6 x + 15 5 x = 1355 x = 271 large number = 271 + 1370 = 1641 e"
Answer: e
Python program:
a = 1370 - 15
b = 6 - 1
c = a / b
d = c * 6
Problem: a , b and c started a partnership business by investing rs . 8000 , rs . 4000 , rs . 2000 respectively . at the end of the year , the profit were distributed among them . if c ' s share of profit is 36000 , what is the total profit ?
Options: a ) 70000 , b ) 60000 , c ) 80000 , d ) 90000 , e ) 252000
Rationale: "a : b : c = 8000 : 4000 : 2000 = 4 : 2 : 1 let total profit = p then p ã — 1 / 7 = 36000 p = ( 36000 ã — 7 ) / 1 = 252000 answer is e ."
Answer: e
Python program:
a = 8000 / 2000
b = a * 36000
c = 4000 / 2000
d = c * 36000
e = b + d 
f = e + 36000
Problem: find the area of the quadrilateral of one of its diagonals is 24 cm and its off sets 9 cm and 6 cm ?
Options: a ) 180 cm 2 , b ) 150 cm 2 , c ) 168 cm 2 , d ) 198 cm 2 , e ) 987 cm 2
Rationale: "1 / 2 * 24 ( 9 + 6 ) = 180 cm 2 answer : a"
Answer: a
Python program:
a = 1 / 2
b = 6 + 9 
c = a * b
d = c * 24
Problem: the average monthly salary of 18 employees in an organisation is rs . 2000 . if the manager ' s salary is added , then the average salary increases by rs . 200 . what is the manager ' s monthly salary ?
Options: a ) rs . 5800 , b ) rs . 3618 , c ) rs . 3600 , d ) rs . 3619 , e ) rs . 3610
Rationale: "manager ' s monthly salary = rs . ( 2200 * 19 - 2000 * 18 ) = rs . 5800 answer : a"
Answer: a
Python program:
a = 2000 + 200 
b = 18 + 1 
c = a * b
d = 2000 * 18
e = c - d
Problem: a , b and c started a business with capitals of rs . 8000 , rs . 10000 and rs . 12000 respectively . at the end of the year , the profit share of b is rs . 4000 . the difference between the profit shares of a and c is ?
Options: a ) 621 , b ) 276 , c ) 236 , d ) 1600 , e ) 211
Rationale: "explanation : ratio of investments of a , b and c is 8000 : 10000 : 12000 = 4 : 5 : 6 and also given that , profit share of b is rs . 4000 = > 5 parts out of 15 parts is rs . 4000 now , required difference is 6 - 4 = 2 parts required difference = 2 / 5 ( 4000 ) = rs . 1600 answer : d"
Answer: d
Python program:
a = 12000 / 10000
b = 8000 / 10000
c = a - b
d = c * 4000
Problem: in an election between the two candidates , the candidates who gets 70 % of votes polled is winned by 320 vote ’ s majority . what is the total number of votes polled ?
Options: a ) 750 , b ) 700 , c ) 800 , d ) 850 , e ) none of these
Rationale: "explanation : note : majority ( 40 % ) = difference in votes polled to win ( 70 % ) & defeated candidates ( 30 % ) 40 % = 70 % - 30 % 40 % - - - - - > 320 ( 40 * 8 = 320 ) 100 % - - - - - > 800 ( 100 * 8 = 800 ) answer : option c"
Answer: c
Python program:
a = 100 * 320
b = 100 - 70
c = 70 - b
d = a / c
Problem: what least number must be added to 1100 , so that the sum is completely divisible by 23 ?
Options: a ) 2 , b ) 3 , c ) 4 , d ) 5 , e ) 6
Rationale: "48 * 23 = 1104 1104 - 1100 = 4 answer : c"
Answer: c
Python program:
a = 4 * 10
b = a + 2 
c = b * 23
d = c - 1100
Problem: ( 3136 + 6160 ) / 28
Options: a ) 380 , b ) 350 , c ) 332 , d ) 310 , e ) none of these
Rationale: "explanation : as per bodmas rule , first we will solve the equation in bracket then we will go for division = ( 9296 ) / 28 = 332 option c"
Answer: c
Python program:
a = 4 + 1 
b = a ** 4
c = 3136 * b
Problem: a train 280 m long , running with a speed of 72 km / hr will pass a tree in
Options: a ) 14 sec , b ) 15 sec , c ) 16 sec , d ) 20 sec , e ) none
Rationale: "sol . speed = ( 72 x 5 / 18 ) m / sec . = 20 m / sec . time taken = ( 280 x 1 / 20 ) sec = 14 sec answer a"
Answer: a
Python program:
a = 72 * 1000
b = 280 / a
c = b * 3600
Problem: a man swims downstream 24 km and upstream 12 km taking 6 hours each time , what is the speed of the man in still water ?
Options: a ) 5 , b ) 8 , c ) 10 , d ) 4 , e ) 3
Rationale: "24 - - - 6 ds = 4 ? - - - - 1 12 - - - - 6 us = 2 ? - - - - 1 m = ? m = ( 4 + 2 ) / 2 = 3 answer : e"
Answer: e
Python program:
a = 12 / 6
b = 24 / 6
c = a + b 
d = c / 2
Problem: s is a set of 45 consecutive multiples of 5 . if the smallest number in s is 55 , then the greatest number in s is
Options: a ) 198 , b ) 275 , c ) 299 , d ) 402 , e ) 205
Rationale: "last term = first term + ( total no . of terms - 1 ) consecutive difference s is a set of 45 consecutive multiples of 5 . if the smallest number in s is 55 , then the greatest number in s is first term = 55 ; total terms = 45 ; difference = 5 55 + ( 44 ) 5 = 275 ans b"
Answer: b
Python program:
a = 45 - 1
b = a * 5
c = 55 + b
Problem: the sum of ages of 6 children born at the intervals of 3 years each is 75 years . what is the age of the youngest child ?
Options: a ) 10 , b ) 15 , c ) 6 , d ) 5 , e ) 8
Rationale: "let the ages of children be x , ( x + 3 ) , ( x + 6 ) , ( x + 9 ) , ( x + 12 ) , ( x + 15 ) years . then , x + ( x + 3 ) + ( x + 6 ) + ( x + 9 ) + ( x + 12 ) + ( x + 15 ) = 75 6 x = 30 x = 5 . age of the youngest child = x = 4 years . answer : d"
Answer: d
Python program:
a = 75 / 6
b = a - 3
c = b - 3
Problem: the sum of three consecutive integers is 312 . what is the sum of the next three consecutive integers ?
Options: a ) 315 , b ) 321 , c ) 330 , d ) 415 , e ) 424
Rationale: "a + ( a + 1 ) + ( a + 2 ) = 3 a + 3 = 312 ( a + 3 ) + ( a + 4 ) + ( a + 5 ) = ( 3 a + 3 ) + 9 = 312 + 9 = 321 answer : b ."
Answer: b
Python program:
a = 312 - 1
b = 2 * 1
c = a / b
d = c + 1
Problem: a can fill tank in 9 minutes , b can empty the tank in 18 minutes . . in what time the tank be filled , if both pipes work simultaneously ?
Options: a ) 14 minutes , b ) 15 minutes , c ) 16 minutes , d ) 17 minutes , e ) 18 minutes
Rationale: bigger no = 18 , ratio = 9 : 18 = 1 : 2 time taken to fill the tank = 18 / ( 2 - 1 ) = 18 minutes answer : e
Answer: e
Python program:
a = 1 / 9
b = 1 / 18
c = a - b
d = 1 / c
Problem: if you spend 1 / 4 of your salary during the first week of the month and 20 % of it during each of the coming 3 weeks , what part ( fraction ) of your salary will leave unspent at the end of the month ?
Options: a ) 2 / 20 , b ) 3 / 20 , c ) 4 / 20 , d ) 5 / 20 , e ) none
Rationale: solution : 1 / 4 + 3 ( 20 / 100 ) = 1 / 4 + 3 / 5 = 5 + 12 / 20 = 17 / 20 the sallary that will be spent = 17 / 20 unspend will be = 1 − 17 / 20 = 20 − 17 / 20 = 3 / 20 answer b
Answer: b
Python program:
a = 20 / 100
b = a * 3
c = 1 / 4
d = b + c 
e = 1 - d
Problem: find the l . c . m of 16 , 25 , 24 and 10 .
Options: a ) 1000 , b ) 1400 , c ) 1320 , d ) 1200 , e ) 1650
Rationale: "explanation : 4 x 5 x 2 x 3 x 5 x 2 = 1200 answer : option d"
Answer: d
Python program:
a = 3 ** 3
b = 2 ** 3
c = 4 + 1 
d = c ** 2
e = b * d
f = a * e
g = 24 / 2
h = g / 2
i = h / 3
j = 4 + 1 
k = i / j
l = 4 + 1 
m = k / l
n = f * m
Problem: a bag contains 6 green and 8 white balls . if two balls are drawn simultaneously , the probability that both are of the same colour is
Options: a ) 8 / 15 , b ) 2 / 5 , c ) 3 / 5 , d ) 11 / 15 , e ) 43 / 91
Rationale: "drawing two balls of same color from six green balls can be done in 6 c ₂ ways . similarly from eight white balls two can be drawn in ⁸ c ₂ ways . p = 6 c ₂ / ¹ ⁵ c ₂ + ⁸ c ₂ / ¹ ⁵ c ₂ = 43 / 91 answer : e"
Answer: e
Python program:
a = 6 + 8 
b = 8 / a
c = 8 - 1
d = 6 + 8 
e = d - 1
f = c / e
g = b * f
h = 6 + 8 
i = 6 / h
j = 6 - 1
k = 6 + 8 
l = k - 1
m = j / l
n = i * m
o = g + n
Problem: 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 2000 , the number of valid votes that the other candidate got , was :
Options: a ) 900 , b ) 750 , c ) 250 , d ) 600 , e ) 800
Rationale: "number of valid votes = 80 % of 2000 = 1600 valid votes polled by other candidate = 45 % of 2000 = ( 45 / 100 ) x 2000 = 900 answer = a"
Answer: a
Python program:
a = 20 / 100
b = 1 - a
c = 55 / 100
d = 1 - c
e = b * d
f = e * 2000
Problem: a man â € ™ s current age is ( 2 / 5 ) of the age of his father . after 14 years , he will be ( 1 / 2 ) of the age of his father . what is the age of father at now ?
Options: a ) 40 , b ) 45 , c ) 38 , d ) 50 , e ) 70
Rationale: let , father â € ™ s current age is a years . then , man â € ™ s current age = [ ( 2 / 5 ) a ] years . therefore , [ ( 2 / 5 ) a + 14 ] = ( 1 / 2 ) ( a + 14 ) 2 ( 2 a + 70 ) = 5 ( a + 14 ) a = 70 e
Answer: e
Python program:
a = 1 / 2
b = 14 * a
c = 14 - b
d = 1 / 2
e = 2 / 5
f = d - e
g = c / f
Problem: at a certain committee meeting only associate professors and assistant professors are present . each associate professor has brought 2 pencils and 1 chart to the meeting , while each assistant professor has brought 1 pencil and 2 charts . if a total of 10 pencils and 5 charts have been brought to the meeting , how many people are present ?
Options: a ) 5 , b ) 7 , c ) 8 , d ) 9 , e ) 10
Rationale: "say there are ' a ' associate professors . so we have 2 a pencils and a charts . say there are ' b ' assistant professors . so we have b pencils and 2 b charts . total pencils are 10 so 2 a + b = 10 total charts are 11 so a + 2 b = 5 add both : 3 a + 3 b = 15 so a + b = 5 total number of people = 5 a"
Answer: a
Python program:
a = 5 + 10 
b = 2 + 1 
c = a / b
Problem: a set of consecutive positive integers beginning with 1 is written on the blackboard . a student came along and erased one number . the average of the remaining numbers is 35 7 / 17 . what was the number erased ?
Options: a ) seven 7 , b ) 8 , c ) 9 , d ) 15 , e ) 17
Rationale: "2 ) the average of the new group of numbers is 35 7 / 17 . the denominator of that fraction tells us that the total number of terms in the new list must be a multiple of 17 : 17 , 34 , 51 , 68 , 85 , etc . 3 ) since we ' re removing 1 number from a list of consecutive positive integers , we could quickly limit down the possible number of terms in the original list : if new = 17 , old = 18 , but the numbers from 1 to 18 would not have an average in the mid - 30 s ( it would be much smaller ) . eliminate this option . if new = 34 , old = 35 , but we run into the same problem . the average wo n ' t match here either . eliminate this option . if new = 51 , old = 52 , same problem here . eliminate this option . if new = 68 , old = 69 . . . . here we have a group of numbers that might just be what we ' re looking for . in theold group , the average is themiddle term = 35 , which is really close to the new average once we remove a number . now , we just have to figure out which of the 5 answers was removed ( and that changed the new average to 35 7 / 17 ) . there are a couple of ways to do this math , but i ' m going to use the answers to save myself some steps : sum of 1 to 69 , inclusive = 69 ( 35 ) = 2415 remove answer b . . . . 2415 - 8 = 2407 new average = 2407 / 68 = 35 27 / 68 now , we can compare 27 / 68 to 7 / 17 27 / 68 and 28 / 68 this is really close , but is not the answer . eliminate b . the answer is either a or c . since 28 / 68 is a bigger fraction than 27 / 68 , we need the sum ( of the 68 integers ) to be bigger . . . which means we need to remove a smaller number . final answer : a"
Answer: a
Python program:
a = 7 / 17
b = 35 + a 
c = b * 2
d = math.floor(c)
e = d / 2
f = 7 / 17
g = 35 + f 
h = g * 2
i = math.floor(h)
j = i - 1
k = e * j
l = 7 / 17
m = 35 + l 
n = 7 / 17
o = 35 + n 
p = o * 2
q = math.floor(p)
r = q - 1
s = r - 1
t = m * s
u = k - t
Problem: a rectangular photograph is surrounded by a border that is 1 inch wide on each side . the total area of the photograph and the border is m square inches . if the border had been 4 inches wide on each side , the total area would have been ( m + 90 ) square inches . what is the perimeter of the photograph , in inches ?
Options: a ) 10 , b ) 20 , c ) 30 , d ) 40 , e ) 50
Rationale: "let x and y be the width and length of the photograph . ( x + 2 ) ( y + 2 ) = m and so ( 1 ) xy + 2 x + 2 y + 4 = m ( x + 8 ) ( y + 8 ) = m and so ( 2 ) xy + 8 x + 8 y + 64 = m + 90 let ' s subtract equation ( 1 ) from equation ( 2 ) . 6 x + 6 y + 60 = 90 2 x + 2 y = 10 , which is the perimeter of the photograph . the answer is a ."
Answer: a
Python program:
a = 4 * 2
b = a ** 2
c = 1 * 2
d = c ** 2
e = b - d
f = 90 - e
g = f / 2
Problem: manoj borrowed rs . 3900 from anwar at 6 % p . a . simple interest for 3 years . he then added some more money to the borrowed sum and lent it to ramu for the same time at 9 % p . a . simple interest . if manoj gains rs . 824.85 by way of interest on the borrowed sum as well as his own amount from the whole transaction , then what is the sum lent by him to ramu ?
Options: a ) 22877 , b ) 5655 , c ) 2778 , d ) 6787 , e ) 1771
Rationale: let the sum lent by manoj to ramu be rs . p . amount gained by manoj = p . 3.9 / 100 = 3900 . 3.6 / 100 = rs . 824.85 27 p = 70200 = 82485 p = ( 82485 + 70200 ) / 27 = 3055 + 2600 = rs . 5655 answer : b
Answer: b
Python program:
a = 9 / 100
b = a * 3
c = 3900 * b
d = 6 / 100
e = d * 3
f = 3900 * e
g = c - f
h = 824 - 85
i = 9 / 100
j = i * 3
k = h / j
l = 3900 + k
Problem: two trains are moving in opposite directions at 60 km / hr and 90 km / hr . their lengths are 2.10 km and 1.4 km respectively . the time taken by the slower train to cross the faster train in seconds is ?
Options: a ) 99 , b ) 277 , c ) 84 , d ) 96 , e ) 22
Rationale: "relative speed = 60 + 90 = 150 km / hr . = 150 * 5 / 18 = 125 / 3 m / sec . distance covered = 2.10 + 1.4 = 3.5 km = 3500 m . required time = 3500 * 3 / 125 = 84 sec . answer : c"
Answer: c
Python program:
a = 2 * 10
b = 60 * 1000
c = b / 3600
d = a / c
e = 1 * 4
f = 90 * 1000
g = f / 3600
h = e / g
i = d - h
Problem: the arithmetic mean and standard deviation of a certain normal distribution are 10.5 and 1 , respectively . what value is exactly 2 standard deviations less than the mean ?
Options: a ) 6 , b ) 8.5 , c ) 11.5 , d ) 12 , e ) 12.5
Rationale: "mean = 10.5 two standard deviations is 1 + 1 = 2 there could be two calues for this . mean + two standard deviations = 12.5 mean - two standard deviations = 8.5 answer choice has 8.5 and so b is the answer ."
Answer: b
Python program:
a = 2 * 1
b = 10 - 5
Problem: what is the measure of the angle e made by the diagonals of the any adjacent sides of a cube .
Options: a ) 30
b ) 45
c ) 60
d ) 75
e ) 90
Rationale: c . . 60 degrees all the diagonals are equal . if we take 3 touching sides and connect their diagonals , we form an equilateral triangle . therefore , each angle would be 60 . . c
Answer: c
Python program:
a = const_180 / 3