euclaise/mathqa_programs huggingface dataset:
Problem: a cylindrical container of radius 6 cm and height 15 cm is filled with ice - cream . the whole icecream has to be distributed to 10 children in equal cones with hemispherical tops . if the height of the conical portion is four times the radius of its base , find the radius of the ice - cream cone .
Options: a ) 1
b ) 2
c ) 3
d ) 4
e ) 5
Rationale: volume of given ice cream = ( pie ) * 6 ² * 15 = 540 ( pie ) dividing to 10 children volume given to a child = 54 ( pie ) let r be radius and h be the height of the cone , then ( pie ) r ² h / 3 + 2 ( pie ) r ³ / 3 = 54 ( pie ) also given h = 4 r 4 r ³ / 3 + 2 r ³ / 3 = 54 2 r ³ = 54 r ³ = 27 r = 3 answer : c
Answer: c
Python program:
a = volume_cylinder / (
b = a / 10
c = 1 / 3
d = c * math.pi
e = d * 4
f = 2 / 3
g = f * math.pi
h = e + g 
i = b / h
j = math.sqrt(i)
Problem: if 1 = 3 2 = 6 3 = 9 4 = 12 5 = 15 then 9 = ? hint : its a logic riddle not a mathematical riddle
Options: a ) 1 , b ) 2 , c ) 3 , d ) 4 , e ) 5
Rationale: c 3 as stated 3 = 9 = > 9 = 3 answer is c
Answer: c
Python program:
a = 3 + 3 
b = a * 9
c = b / 15
d = c - const_0_33
e = d - const_0_33
Problem: in a forest 170 deer were caught , tagged with electronic markers , then released . a week later , 50 deer were captured in the same forest . of these 50 deer , it was found that 5 had been tagged with the electronic markers . if the percentage of tagged deer in the second sample approximates the percentage of tagged deer in the forest , and if no deer had either left or entered the forest over the preceding week , what is the approximate number of deer in the forest ?
Options: a ) 150 , b ) 750 , c ) 1,250 , d ) 1,700 , e ) 2,500
Rationale: "the percentage of tagged deer in the second sample = 5 / 50 * 100 = 10 % . so , 170 tagged deers comprise 10 % of total # of deers - - > total # of deers = 170 * 10 = 1,700 . answer : d ."
Answer: d
Python program:
a = 50 * 5
Problem: in an examination , a student scores 5 marks for every correct answer and loses 2 marks for every wrong answer . if he attempts all 100 questions and secures 290 marks , the number of questions he attempts correctly , is :
Options: a ) 60 , b ) 80 , c ) 70 , d ) 45 , e ) 50
Rationale: "let the number of correct answers be x . number of incorrect answers = ( 100 â € “ x ) . 5 x â € “ 2 ( 100 â € “ x ) = 290 or 7 x = 490 or x = 70 . answer : c"
Answer: c
Python program:
a = 290 + 100 
b = 5 + 2 
c = a / b
Problem: there are 3 boats b 1 , b 2 and b 3 working together they carry 60 people in each trip . one day an early morning b 1 carried 50 people in few trips alone . when it stopped carrying the passengers b 2 and b 3 started carrying the people together . it took a total of 10 trips to carry 300 people by b 1 , b 2 and b 3 . it is known that each day on an average 300 people cross the river using only one of the 3 boats b 1 , b 2 and b 3 . how many trips it would take to b 1 , to carry 150 passengers alone ?
Options: a ) 15 , b ) 30 , c ) 25 , d ) 10 , e ) 15
Rationale: explanation : combined efficiency of all the three boats = 60 passenger / trip now , consider option ( a ) 15 trips and 150 passengers means efficiency of b 1 = 10 p / t which means in carrying 50 passengers b 1 must has taken 5 trips . so the rest trips equal to 5 ( 10 - 5 = 5 ) in which b 2 and b 3 together carried remaining 250 ( 300 - 50 = 250 ) passengers . therefore the efficiency of b 2 and b 3 = 250 / 5 = 50 p / t since , the combined efficiency of b 1 , b 2 and b 3 is 60 . which is same as given in the first statement hence option ( a ) is correct answer : a
Answer: a
Python program:
a = 300 / 2
b = a / 10
Problem: the average age of 12 men is increased by years when two of them whose ages are 21 years and 23 years are replaced by two new men . the average age of the two new men is
Options: a ) 22 , b ) 30 , c ) 34 , d ) 38 , e ) 27
Rationale: "total age increased = ( 12 * 2 ) years = 24 years . sum of ages of two new men = ( 21 + 23 + 24 ) years = 68 years average age of two new men = ( 68 / 2 ) years = 34 years . answer : c"
Answer: c
Python program:
a = 21 + 23 
b = a / 2
c = 1 * 12
d = b + c
Problem: a boat can travel with a speed of 24 km / hr in still water . if the speed of the stream is 4 km / hr , find the time taken by the boat to go 112 km downstream
Options: a ) 3 hours , b ) 4 hours , c ) 5 hours , d ) 6 hours , e ) 7 hours
Rationale: "explanation : speed of the boat in still water = 24 km / hr speed of the stream = 4 km / hr speed downstream = ( 22 + 5 ) = 28 km / hr distance travelled downstream = 112 km time taken = distance / speed = 112 / 28 = 4 hours answer : option b"
Answer: b
Python program:
a = 24 + 4 
b = 112 / a
Problem: find the l . c . m . of 72 , 108 and 2100 .
Options: a ) 37800 , b ) 37600 , c ) 37200 , d ) 37500 , e ) none of them
Rationale: 72 = 2 ^ 3 x 3 ^ 2 , 108 = 3 ^ 3 x 2 ^ 2 , 2100 = 2 ^ 2 x 5 ^ 2 x 3 x 7 . l . c . m . = 2 ^ 3 x 3 ^ 3 x 5 ^ 2 x 7 = 37800 . answer is a .
Answer: a
Python program:
a = 3 ** 3
b = 2 ** 3
c = 4 + 1 
d = c ** 2
e = b * d
f = a * e
g = 2100 / 2
h = g / 2
i = h / 3
j = 4 + 1 
k = i / j
l = 4 + 1 
m = k / l
n = f * m
Problem: the average of 10 numbers is calculated as 16 . it is discovered later on that while calculating the average , the number 55 was incorrectly read as 25 , and this incorrect number was used in the calculation . what is the correct average ?
Options: a ) 17 , b ) 19 , c ) 25 , d ) 31 , e ) 46
Rationale: "the total sum of the numbers should be increased by 30 . then the average will increase by 30 / 10 = 3 . the correct average is 19 . the answer is b ."
Answer: b
Python program:
a = 16 * 10
b = a - 25
c = b + 55 
d = c / 10
Problem: the average of 1 st 3 of 4 numbers is 16 and of the last 3 are 15 . if the sum of the first and the last number is 21 . what is the last numbers ?
Options: a ) 2 , b ) 4 , c ) 9 , d ) 5 , e ) 7
Rationale: "a + b + c = 48 b + c + d = 45 a + d = 21 a – d = 3 a + d = 21 2 d = 18 d = 9 answer c"
Answer: c
Python program:
a = 3 * 16
b = 21 - 16
c = b + 3 
d = a - c
e = d - 16
Problem: how many inches are in 2000 millimeters ? ( round your answer to the nearest hundredth of of an inch ) .
Options: a ) 48.74 inches , b ) 58.74 inches , c ) 78.74 inches , d ) 28.74 inches , e ) 88.74 inches
Rationale: one inch is the same as 25.4 mm . let x inches be the same as 1000 mm x = 1 inch * 2000 mm / 25.4 mm = 78.74 inches correct answer c
Answer: c
Python program:
a = 2000 / 10
b = a * const_0_3937
Problem: the average of 6 no . ' s is 6.40 . the average of 2 of them is 6.2 , while the average of the other 2 is 6.1 . what is the average of the remaining 2 no ' s ?
Options: a ) 2.3 , b ) 2.6 , c ) 6.9 , d ) 4.5 , e ) 4.6
Rationale: "sum of the remaining two numbers = ( 6.4 * 6 ) - [ ( 6.2 * 2 ) + ( 6.1 * 2 ) ] = 38.40 - ( 12.4 + 12.2 ) = 38.40 - 24.6 = 13.80 required average = ( 13.8 / 2 ) = 6.9 answer : c"
Answer: c
Python program:
a = 6 * 6
b = 2 * 6
c = 2 * 6
d = b + c 
e = a - d
f = e / 2
Problem: the current in a river is 6 mph . a boat can travel 20 mph in still water . how far up the river can the boat travel if the round trip is to take 10 hours ?
Options: a ) 69 miles , b ) 88 miles , c ) 96 miles , d ) 91 miles , e ) 112 miles
Rationale: "upstream speed = 20 - 6 = 14 mph downstream speed = 20 + 6 = 26 mph d / 14 + d / 26 = 10 hours solving for d we get d = 91 answer : d"
Answer: d
Python program:
a = 20 - 6
b = 20 + 6 
c = a * b
d = c * 10
e = 20 + 6 
f = 20 - 6
g = e + f 
h = d / g
Problem: a school has 6 maths 5 physics and 5 chemistry teachers each teacher can teach 4 subjects max what is he minimum number of teachers required
Options: a ) 2 , b ) 4 , c ) 5 , d ) 6 , e ) 7
Rationale: "total subjects = 6 + 5 + 5 = 16 max subjects by 1 teacher = 4 so , min of teachers required = 16 / 4 = 4 answer : b"
Answer: b
Python program:
a = 6 + 5 
b = a + 5 
c = b / 4
Problem: if a monkey can climb 6 meter & slip down 3 meter in alternate minutes , than how much time can be taken by the monkey to climb up to a height of 60 meter .
Options: a ) 36 min , b ) 37 min , c ) 38 min , d ) 39 min , e ) 32 min
Rationale: in 1 st min it climb 6 m and in 2 nd min it slips 3 m , so it final displacement is 3 m in 2 min . now for 51 m it has taken 34 min . in 35 min it goes to 57 m . in 36 min come down to 54 m . in 37 min it goes to 60 answer : b
Answer: b
Python program:
a = 60 - 6
b = 3 / 2
c = a / b
d = c + 1
Problem: on a map , 1.5 inches represent 24 miles . how many miles approximately is the distance if you measured 46 centimeters assuming that 1 - inch is 2.54 centimeters ?
Options: a ) 174.2 , b ) 212 , c ) 288.1 , d ) 290 , e ) 282.4
Rationale: "1.5 inch = 2.54 * 1.5 cm . so , 2.54 * 1.5 represents 24 miles . so for 46 cm . : 46 / ( 2.54 * 1.5 ) = x / 24 - - - > x = 24 * 46 / ( 3.81 ) = 290 answer will be d ."
Answer: d
Python program:
a = 46 / 2
b = 24 / 1
c = a * b
Problem: the cash realised on selling a 14 % stock is rs . 104.25 , brokerage being 1 / 4 % is ?
Options: a ) 104 , b ) 106 , c ) 102 , d ) 192 , e ) 122
Rationale: "cash realised = rs . ( 104.25 - 0.25 ) = rs . 104 . answer : a"
Answer: a
Python program:
a = 1 / 4
b = 104 - 25
Problem: how many numbers up to 200 are divisible by 2 and 3 both ?
Options: a ) 22 , b ) 33 , c ) 77 , d ) 28 , e ) 22
Rationale: explanation : 200 / 6 = 33 2 / 6 = > 33 numbers answer : b
Answer: b
Python program:
a = 2 * 3
b = 200 / a
c = math.floor(b)
Problem: a dog has 15 bones , then he finds 8 more bones . now how many bones does he have .
Options: a ) a ) 7 , b ) b ) 27 , c ) c ) 23 , d ) d ) 19 , e ) e ) 21
Rationale: 15 + 8 = 23 . answer is c .
Answer: c
Python program:
a = 15 + 8
Problem: last year manfred received 26 paychecks . each of his first 6 paychecks was $ 750 ; each of his remaining paychecks was $ 20 more than each of his first 6 paychecks . to the nearest dollar , what was the average ( arithmetic mean ) amount of his pay checks for the year ?
Options: a ) $ 752 , b ) $ 755 , c ) $ 765 , d ) $ 773 , e ) $ 775
Rationale: = ( 750 * 6 + 770 * 20 ) / 26 = 765 answer is c . posted from my mobile device
Answer: c
Python program:
a = 750 + 20 
b = a * 20
c = 6 * 750
d = b + c 
e = d / 26
Problem: what is the rate percent when the simple interest on rs . 800 amount to rs . 200 in 4 years ?
Options: a ) 5 % , b ) 7 % , c ) 6.25 % , d ) 2 % , e ) 4 %
Rationale: "200 = ( 800 * 4 * r ) / 100 r = 6.25 % answer : c"
Answer: c
Python program:
a = 100 * 200
b = 800 * 4
c = a / b
Problem: the sides of a cube are in the ratio 1 : 2 the ratio of their volume is ?
Options: a ) 1 : 6
b ) 1 : 4
c ) 1 : 0
d ) 1 : 2
e ) 1 : 1
Rationale: 1 : 4 answer : b
Answer: b
Python program:
a = volume_cube / (
b = 2 * a
Problem: a can do a piece of work in 12 days . he worked for 15 days and then b completed the remaining work in 10 days . both of them together will finish it in .
Options: a ) 12 1 / 2 days , b ) 10 1 / 2 days , c ) 12 1 / 3 days , d ) 10 1 / 3 days , e ) 11 1 / 2 days
Rationale: explanation : 15 / 25 + 10 / x = 1 = > x = 25 1 / 25 + 1 / 25 = 2 / 25 25 / 2 = 12 1 / 2 days answer a
Answer: a
Python program:
a = 1 / 12
b = 1 / 15
c = a - b
d = 1 / c
Problem: a train running at the speed of 6 km / hr crosses a pole in 2 seconds . find the length of the train ?
Options: a ) 150 , b ) 872 , c ) 3.33 , d ) 3.21 , e ) 30.1
Rationale: "speed = 6 * ( 5 / 18 ) m / sec = 5 / 3 m / sec length of train ( distance ) = speed * time 5 / 3 ) * 2 = 3.33 meter answer : c"
Answer: c
Python program:
a = 6 * 1000
b = a / 3600
c = b * 2
Problem: the denominator of a fraction is 5 greater than the numerator . if the numerator and the denominator are increased by 1 , the resulting fraction is equal to 7 â  „ 12 . what is the value of the original fraction ?
Options: a ) 6 / 11 , b ) 8 / 13 , c ) 11 / 16 , d ) 12 / 17 , e ) 14 / 19
Rationale: let the numerator be x . then the denominator is x + 5 . x + 1 / x + 6 = 7 / 12 . 12 x + 12 = 7 x + 42 . 5 x = 30 . x = 6 . the original fraction is 6 / 11 . the answer is a .
Answer: a
Python program:
a = 1 + 5 
b = 7 * a
c = b - 12
d = 12 - 7
e = c / d
f = 1 + 5 
g = 7 * f
h = g - 12
i = 12 - 7
j = h / i
k = j + 5 
l = e / k
Problem: if the sum of two positive integers is 22 and the difference of their squares is 44 , what is the product of the two integers ?
Options: a ) 108 , b ) 119 , c ) 120 , d ) 135 , e ) 143
Rationale: "let the 2 positive numbers x and y x + y = 22 - - 1 x ^ 2 - y ^ 2 = 44 = > ( x + y ) ( x - y ) = 44 - - 2 using equation 1 in 2 , we get = > x - y = 2 - - 3 solving equation 1 and 3 , we get x = 12 y = 10 product = 12 * 10 = 120 answer c"
Answer: c
Python program:
a = 44 / 22
b = 22 - a
c = 44 / 22
d = b / c
e = 44 / 22
f = 22 - e
g = 44 / 22
h = f / g
i = 44 / 22
j = h + i 
k = d * j
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 $ 660 ( before payroll deductions ) ?
Options: a ) 800 , b ) 900 , c ) 1000 , d ) 1100 , e ) 1200
Rationale: "total pay = 40 * $ 12.50 + $ 0.16 * x = 660 x = 160 / 0.16 = 1000 the answer is c ."
Answer: c
Python program:
a = 12 * 50
b = 660 - a
c = b / 0
Problem: in a stream running at 3 kmph , a motor boat goes 10 km upstream and back again to the starting point in 57 minutes . find the speed of motor boat in still water ?
Options: a ) 18 kmph , b ) 22 kmph , c ) 16 kmph , d ) 20 kmph , e ) none of these
Rationale: "explanation : let the speed of motor boat instill water be x kmph then , speed in downstream = ( x + 3 ) km and . speed in upstream = ( x - 3 ) kmph time taken to row 10 km & back = ( 10 / x + 3,10 / x - 3 ) 10 / x + 3 + 10 / x - 3 = 57 / 60 11 x 2 - 240 x - 44 = 0 ( x - 22 ) ( 11 x + 2 ) = 0 x = 22 or x = - 2 / 11 then x = 22 kmph answer : option b"
Answer: b
Python program:
a = 10 + 10 
b = 57 / const_60
c = a / b
Problem: in a can , there is a mixture of milk and water in the ratio 4 : 5 . if it is filled with an additional 4 litres of milk the can would be full and ratio of milk and water would become 6 : 5 . find the capacity of the can ?
Options: a ) 40 , b ) 44 , c ) 48 , d ) 22 , e ) none of these
Rationale: "let the capacity of the can be t litres . quantity of milk in the mixture before adding milk = 4 / 9 ( t - 4 ) after adding milk , quantity of milk in the mixture = 6 / 11 t . 6 t / 11 - 4 = 4 / 9 ( t - 4 ) 10 t = 396 - 176 = > t = 22 . answer : d"
Answer: d
Python program:
a = 6 / 5
b = a * 5
c = b - 4
d = 4 / c
e = 5 * d
f = 6 / 5
g = f * 5
h = g - 4
i = 4 / h
j = e + i 
k = j + 4
Problem: people were sitting in a circle . 7 th one is direct opposite to 18 th one . . then how many were there in that group ?
Options: a ) 21
b ) 22
c ) 23
d ) 24
e ) 20
Rationale: 7 th one is exactly opposite represents half of circle . with 7 and 18 total members are 12 for remaing half = 12 * 2 - 2 ( 7 th and 18 th ( already taken ) ) = 22 answer : b
Answer: b
Python program:
a = 18 - 7
b = 2 * a
Problem: a no . when divided by 221 gives a remainder 43 , what remainder will be obtainedby dividingthe same no . 17 ?
Options: a ) 3 , b ) 6 , c ) 9 , d ) 11 , e ) 14
Rationale: "221 + 43 = 264 / 17 = 9 ( remainder ) c"
Answer: c
Python program:
a = 221 + 43 
b = a / 17
Problem: there are 25 balls which are red , blue or green . if 8 balls are blue and the sum of green balls and blue balls is less than 17 , at most how many green balls are there ?
Options: a ) 8 , b ) 5 , c ) 6 , d ) 7 , e ) 10
Rationale: "r + g + b = 25 b = 8 b + g < 17 = > 8 + g < 17 = > g < 9 = > at most 8 green balls answer : a"
Answer: a
Python program:
a = 8 - 1
Problem: a waitress ' s income consists of her salary and tips . during one week , her tips were 11 / 4 of her salary . what fraction of her income for the week came from tips ?
Options: a ) 1 / 9 , b ) 1 / 6 , c ) 1 / 3 , d ) 4 / 9 , e ) 11 / 15
Rationale: "her tips were 11 / 4 of her salary . let ' s say her salary = $ 4 this mean her tips = ( 11 / 4 ) ( $ 4 ) = $ 11 so , her total income = $ 4 + $ 11 = $ 15 what fraction of her income for the week came from tips $ 11 / $ 15 = 11 / 15 = e"
Answer: e
Python program:
a = 11 + 4 
b = 11 / a
Problem: on a certain farm the ratio of horses to cows is 5 : 1 . if the farm were to sell 15 horses and buy 15 cows , the ratio of horses to cows would then be 17 : 7 . after the transaction , how many more horses than cows would the farm own ?
Options: a ) 30 , b ) 40 , c ) 50 , d ) 60 , e ) 70
Rationale: originally , there were 5 k horses and k cows . 7 ( 5 k - 15 ) = 17 ( k + 15 ) 35 k - 17 k = 255 + 105 18 k = 360 k = 20 the difference between horses and cows is ( 5 k - 15 ) - ( k + 15 ) = 4 k - 30 = 50 the answer is c .
Answer: c
Python program:
a = 15 * 17
b = 15 * 7
c = a + b 
d = 5 * 7
e = d - 17
f = c / e
g = 5 * f
h = g - 15
i = 15 * 17
j = 15 * 7
k = i + j 
l = 5 * 7
m = l - 17
n = k / m
o = n + 15 
p = h - o
Problem: in an examination , a student scores 4 marks for every correct answer and loses 1 mark for every wrong answer . if he attempts all 50 questions and secures 130 marks , the no of questions he attempts correctly is :
Options: a ) a ) 36 , b ) b ) 38 , c ) c ) 90 , d ) d ) 88 , e ) e ) 37
Rationale: "let the number of correct answers be x . number of incorrect answers = ( 60 – x ) . 4 x – ( 50 – x ) = 130 = > 5 x = 180 = > x = 36 answer : a"
Answer: a
Python program:
a = 130 + 50 
b = 4 + 1 
c = a / b
Problem: the banker ' s gain on a sum due 6 years hence at 12 % per annum is rs . 684 . what is the banker ' s discount ?
Options: a ) 1240 , b ) 1120 , c ) 1190 , d ) 1634 , e ) none of these
Rationale: "explanation : td = ( bg × 100 ) / tr = ( 684 × 100 ) / ( 6 × 12 ) = rs . 950 bg = bd – td = > 684 = bd - 950 = > bd = 684 + 950 = 1634 answer : option d"
Answer: d
Python program:
a = 684 * 100
b = 12 * 6
c = a / b
d = 684 + c
Problem: a sum of money at simple interest amounts to $ 780 in 3 years and to $ 930 in 4 years . the sum is :
Options: a ) $ 153 , b ) $ 698 , c ) $ 330 , d ) $ 549 , e ) $ 675
Rationale: "c $ 330 s . i . for 1 year = $ ( 930 - 780 ) = $ 150 . s . i . for 3 years = $ ( 150 x 3 ) = $ 450 . principal = $ ( 780 - 450 ) = $ 330 ."
Answer: c
Python program:
a = 930 - 780
b = a * 2
c = b / 4
d = 780 - c
Problem: what is 15 percent of 44 ?
Options: a ) 6.6 , b ) 7.8 , c ) 8.9 , d ) 9.4 , e ) 10.2
Rationale: "( 15 / 100 ) * 44 = 6.6 the answer is a ."
Answer: a
Python program:
a = 3 + 2 
b = a * 2
c = 3 * 4
d = c * 100
e = b * d
f = 3 + 4 
g = 3 + 2 
h = f * g
i = 3 + 2 
j = i * 2
k = h * j
l = e + k 
m = 3 + 3 
n = l + m 
o = 15 * n
p = o / 100
Problem: the price of commodity x increases by 45 cents every year , while the price of commodity y increases by 20 cents every year . in 2001 , the price of commodity x was $ 5.20 and the price of commodity y was $ 7.30 . in which year will the price of commodity x be 90 cents more than the price of commodity y ?
Options: a ) 2010 , b ) 2011 , c ) 2012 , d ) 2013 , e ) 2014
Rationale: "the price of commodity x increases 25 cents each year relative to commodity y . the price difference is $ 2.10 and commodity x needs to be 90 cents more than commodity y . $ 3.00 / 25 cents = 12 years the answer is 2001 + 12 years = 2013 . the answer is d ."
Answer: d
Python program:
a = 90 / 100
b = 7 - 30
c = a + b 
d = 45 / 100
e = 7 - 30
f = d - e
g = c / f
h = 2001 + g
Problem: 1 , 1 , 3 , 9 , 5 , 25 , 7 , 49 _ , 81
Options: a ) 6 , b ) 7 , c ) 8 , d ) 9 , e ) 10
Rationale: "as seq is 1 , 1 , 3 , 9 , 5 , 25 , 7 , 49 9 , 81 two series are there . 1 , 3,5 , 7,9 . . . odd numbers and 1 , 9,25 , 49,81 . . square of odd numbers answer : d"
Answer: d
Python program:
a = negate - (
Problem: a shopkeeper cheats both his supplier and customer by using faulty weights . when he buys from the supplier , he takes 20 % more than the indicated weight . when he sells to his customer , he gives the customer a weight such that 10 % of that is added to the weight , the weight claimed by the trader is obtained . if he charges the cost price of the weight that he claims , find his profit percentage .
Options: a ) 20 % , b ) 32 % , c ) 23.365 % , d ) 22.109 % , e ) 2 %
Rationale: anyways , one can infer that he ' steals ' 20 % from suppliers and then charges 10 % extra to customers so basically 1.2 * 1.1 = 1.32 given that 1 is start point , we get 32 % more hence answer is b
Answer: b
Python program:
a = 20 + 100 
b = 10 + 100 
c = b / 100
d = a * c
e = d - 100
Problem: of 3 numbers , the third is 4 times the second and the second is two times the first . if their average is 165 , the smallest of the 3 numbers is :
Options: a ) 18 , b ) 19 , c ) 45 , d ) 21 , e ) 22
Rationale: explanation : let first number be x . so , 2 nd no . = 2 x & 3 rd no . = 8 x . so , x + 2 x + 8 x = 165 × 3 = 495 11 x = 495 / 11 x = 495 / 11 hence , smallest number x = 45 answer : c
Answer: c
Python program:
a = 165 * 3
b = 4 * 2
c = b + 3 
d = a / c
Problem: a train travels at the rate of 10 miles / hr for the first hour of a trip , at 20 miles / hr for the second hour , at 30 miles / hr for the third hour and so on . how many hours will it take the train to complete a 550 - mile journey ? assume that the train makes no intermediate stops .
Options: a ) 8 , b ) 8.5 , c ) 9 , d ) 9.5 , e ) 10
Rationale: "a train travels at the rate of 10 miles / hr for the first hour of a trip , at 20 miles / hr for the second hour , at 30 miles / hr for the third hour and so on . how many hours will it take the train to complete a 550 - mile journey ? assume that the train makes no intermediate stops . i think the easiest way to solve this problem would be simply to count the number of miles it travels per hour ( and in total ) hour miles / hour total miles 1 10 10 2 20 30 3 30 60 4 40 100 5 50 150 6 60 210 7 70 280 8 80 360 9 90 450 10 100 550 it takes a total of nine hours to cover the 550 mile distance . answer : e"
Answer: e
Python program:
a = 10 + 20 
b = 30 + a 
c = 550 / b
Problem: ifaequals the sum of the even integers from 2 to 20 , inclusive , andbequals the sum of the odd integers from 1 to 19 , inclusive , what is the value of ( a - b ) / 2 ?
Options: a ) 1 , b ) 10 , c ) 19 , d ) 5 , e ) 2
Rationale: "answer is 10 yes ! there is really a faster way to solve it . sum of consecutive odd or even integers = ( no . of odd or even ints ) * ( first int + last int ) / 2 here a = sum of even ints from 2 to 20 , inclusive number of even ints = 10 , first int + last int = 2 + 20 = 22 a = 10 * 22 / 2 = 110 b = sum of odd ints from 1 to 19 , inclusive number of odd ints = 10 , first int + last int = 1 + 19 = 20 a = 10 * 20 / 2 = 100 ( a - b ) / 2 = 110 - 100 = 10 / 2 = 5 ans : d"
Answer: d
Python program:
a = 20 / 2
b = 20 / 2
c = b + 1 
d = a * c
e = 19 + 1 
f = e / 2
g = 19 - 1
h = g / 2
i = h + 1 
j = f * i
k = d - j
Problem: in a certain diving competition , 5 judges score each dive on a scale from 1 to 10 . the point value of the dive is obtained by dropping the highest score and the lowest score and multiplying the sum of the remaining scores by the degree of difficulty . if a dive with a degree of difficulty of 3.2 received scores of 7.5 , 7.8 , 9.0 , 6.0 , and 8.5 , what was the point value of the dive ?
Options: a ) 68.8 , b ) 73.6 , c ) 75.2 , d ) 76.16 , e ) 81.6
Rationale: degree of difficulty of dive = 3.2 scores are 6.0 , 7.5 , 8.0 , 8.5 and 9.0 we can drop 6.0 and 9.0 sum of the remaining scores = ( 7.5 + 7.8 + 8.5 ) = 23.8 point of value of the dive = 23.8 * 3.2 = 76.16 answer d
Answer: d
Python program:
a = 7 + 5 
b = a + 8 
c = b * 3
Problem: the workforce of company x is 60 % female . the company hired 28 additional male workers , and as a result , the percent of female workers dropped to 55 % . how many employees did the company have after hiring the additional male workers ?
Options: a ) 160 , b ) 220 , c ) 336 , d ) 360 , e ) 420
Rationale: "let ' s xx be total quantity of employees 0.6 x = females before adding men 0.55 ( x + 28 ) = females after adding men as quantity of women does n ' t change we can make an equation : 0.6 x = 0.55 ( x + 28 ) 0.05 x = 15.4 x = 308 - this is quantity of employees before adding 28 men so after adding it will be 336 answer is c"
Answer: c
Python program:
a = 55 / 100
b = a * 28
c = 60 / 100
d = 55 / 100
e = c - d
f = b / e
g = f + 28