euclaise/mathqa_programs huggingface dataset:
Problem: at a certain restaurant , the price of a sandwich is $ 4.00 more than the price of a cup of coffee . if the price of a sandwich and a cup of coffee is $ 7.35 , including a sales tax of 5 % , what is the price of a cup of coffee , excluding the sales tax ?
Options: a ) $ 1.50 , b ) $ 3.00 , c ) $ 4.00 , d ) $ 5.50 , e ) $ 7.00
Rationale: let the price of sandwich = s price of coffee = c s = c + 4 = > s - c = 4 - - 1 the price of a sandwich and a cup of coffee is $ 7.35 , including a sales tax of 5 % , 1.05 ( s + c ) = 7.35 = > s + c = 7 - - 2 from equations 1 and 2 , we get s = 5.5 $ c = 1.5 $ answer a
Answer: a
Python program:
a = 1 / 5
b = 7 * 35
c = b / 10
d = 7 * 35
e = d / 10
f = c + e 
g = f - 5
h = a + g 
i = h - 1
Problem: what will be the percentage increase in the area of the cube ' s surface if each of the cube ' s edges grows by 30 % ?
Options: a ) 70 %
b ) 69 %
c ) 80 %
d ) 82 %
e ) 55 %
Rationale: the question is very easy . my logic is the following : a surface = 6 * a ^ 2 after 30 % increase a surface = 6 * ( ( 1.3 a ) ^ 2 ) = 6 * 1.69 * a ^ 2 the increase in the surface area = ( 6 * 1.69 * a ^ 2 - 6 * a ^ 2 ) / 6 * a ^ 2 = ( 6 * a ^ 2 ( 1.69 - 1 ) ) / ( 6 * a ^ 2 ) = 1.69 - 1 = 0.69 = 69 % answer : b
Answer: b
Python program:
a = 30 / 100
b = 1 + a 
c = b ** 2
d = c - 1
e = d * 100
Problem: if a , b , c , d , e and f are integers and ( ab + cdef ) < 0 , then what is the maximum number a of integers that can be negative ?
Options: a ) 2 , b ) 3 , c ) 4 , d ) 5 , e ) 6
Rationale: minimuum should be 1 maximum should be 4 : 1 out of a or b to make the multiplication negative 3 out of c , d , e or f to make the multiplication negative . negative + negative < 0 answer : c maximum will be 5 . . you dont require both the multiplicatin to be negative for entire equation to be negative . . . any one a or b can be negative to make ab negative and it can still be more ( away from 0 ) than the multiplication of 4 other - ve numbers . . . actually by writing minimum required as 1 out of 6 , you are actually meaning 5 out of 6 also possible as you will see a = 5 or 1 will give you same equation . . ans d
Answer: d
Python program:
a = 10 / 2
b = a + 0
Problem: ritesh and co . generated revenue of rs . 1,500 in 2006 . this was 12.5 % of its gross revenue . in 2007 , the gross revenue grew by rs . 2,500 . what is the percentage increase in the revenue in 2007 ?
Options: a ) 12.5 % , b ) 20.83 % , c ) 25 % , d ) 50 % , e ) none of these
Rationale: "explanation : given , ritesh and co . generated revenue of rs . 1,500 in 2006 and that this was 12.5 % of the gross revenue . hence , if 1250 is 12.5 % of the revenue , then 100 % ( gross revenue ) is : = > ( 100 / 12.5 ) × 1500 . = > 12,000 . hence , the total revenue by end of 2007 is rs . 12,000 . in 2006 , revenue grew by rs . 2500 . this is a growth of : = > ( 2500 / 12000 ) × 100 . = > 20.83 % . answer : b"
Answer: b
Python program:
a = 1 + 4 
b = 2 * a
c = b * 100
d = 2 * c
e = 1 + 4 
f = e * 100
g = d + f 
h = 1 + 4 
i = 2 * h
j = i * 100
k = 2 + 4 
l = k * 100
m = j + l 
n = 12 / 5
o = m / n
p = g / o
q = p * 100
Problem: if x is a number such that x ^ 2 + 4 x - 5 = 0 and x ^ 2 - 5 x + 4 = 0 , then x =
Options: a ) 5 , b ) 4 , c ) 1 , d ) - 4 , e ) - 5
Rationale: "x ^ 2 + 4 x - 5 = ( x + 5 ) ( x - 1 ) = 0 then x = - 5 or x = 1 . x ^ 2 - 5 x + 4 = ( x - 4 ) ( x - 1 ) = 0 then x = 4 or x = 1 . thus x = 1 . the answer is c ."
Answer: c
Python program:
a = 4 + 5 
b = 2 + 5 
c = a / b
Problem: if the ratio of two number is 3 : 4 and lcm of the number is 180 then what is the number .
Options: a ) 15 , b ) 20 , c ) 25 , d ) 30 , e ) 35
Rationale: "product of two no = lcm * hcf 3 x * 4 x = 180 * x x = 15 answer : a"
Answer: a
Python program:
a = 3 * 4
b = 180 / a
Problem: calculate the average marks of a student who obtained 56 , 60 , 72 , 85 and 80 marks ( out of 100 ) in geography , history and government , art , computer science and modern literature ?
Options: a ) 71.6 , b ) 70.6 , c ) 80.6 , d ) 60.6 , e ) 50.6
Rationale: explanation : average = ( 56 + 60 + 72 + 85 + 80 ) / 5 = 70.6 . answer : b ) 70.6
Answer: b
Python program:
a = 56 + 60 
b = 72 + 85 
c = a + b 
d = c + 80 
e = 2 + 3 
f = d / e
Problem: find the 21 th term of an arithmetic progression whose first term is 3 and the common difference is 5 .
Options: a ) 100 , b ) 102 , c ) 103 , d ) 150 , e ) 46
Rationale: "n th term of a . p = a + ( n - 1 ) * d = 3 + ( 21 - 1 ) * 5 , = 3 + 100 = 103 . answer : c"
Answer: c
Python program:
a = 21 - 1
b = a * 5
c = b + 3
Problem: in δ pqs above , if pq = 6 and ps = 7 , then
Options: a ) 9 / 4 , b ) 12 / 5 , c ) 16 / 5 , d ) 15 / 4 , e ) 21 / 4
Rationale: "there are two ways to calculate area of pqs . area remains same , so both are equal . 6 * 7 / 2 = pr * 8 / 2 pr = 21 / 4 e"
Answer: e
Python program:
a = 7 / 6
Problem: it was calculated that 75 men could complete a piece of work in 30 days . when work was scheduled to commence , it was found necessary to send 25 men to another project . how much longer will it take to complete the work ?
Options: a ) 20 days . , b ) 30 days . , c ) 25 days . , d ) 28 days . , e ) 45 days .
Rationale: "one day work = 1 / 30 one man ’ s one day work = 1 / ( 30 * 75 ) now : no . of workers = 50 one day work = 50 * 1 / ( 30 * 75 ) the total no . of days required to complete the work = ( 75 * 30 ) / 50 = 45 answer : e"
Answer: e
Python program:
a = 75 / 25
b = 30 * a
Problem: a committee is reviewing a total of 20 x black - and - white films and 6 y color films for a festival . if the committee selects y / x % of the black - and - white films and all of the color films , what fraction w of the selected films are in color ?
Options: a ) 1 / 130 , b ) 1 / 5 , c ) 3 / 13 , d ) 10 / 13 , e ) 30 / 31
Rationale: "it ' s y / xpercentnot y / x . if x = 20 and y = 10 . then : 20 x = 400 black - and - white films ; 6 y = 60 color films . y / x % = 10 / 20 % = 0.5 % of the black - and - white films , so 2 black - and - white films and all 60 color films , thus total of 62 films were selected . color films thus compose w 60 / 62 = 30 / 31 of the selected films . answer : e ."
Answer: e
Python program:
a = 20 / 100
b = a + 6 
c = 6 / b
Problem: the slant height of a cone is 13 cm and radius of the base is 9 cm , find the curved surface of the cone ?
Options: a ) 367 , b ) 378 , c ) 365 , d ) 26 , e ) 28
Rationale: "π * 13 * 9 = 367 answer : a"
Answer: a
Python program:
a = math.pi * 9
b = a * 13
Problem: a number increased by 20 % gives 480 . the number is
Options: a ) 200 , b ) 400 , c ) 300 , d ) 450 , e ) 500
Rationale: "formula = total = 100 % , increse = ` ` + ' ' decrease = ` ` - ' ' a number means = 100 % that same number increased by 20 % = 120 % 120 % - - - - - - - > 480 ( 120 × 4 = 480 ) 100 % - - - - - - - > 400 ( 100 × 4 = 400 ) b )"
Answer: b
Python program:
a = 20 / 100
b = 1 + a 
c = 480 / b
Problem: a person spends 1 / 3 rd of the money with him on clothes , 1 / 5 th of the remaining on food and 1 / 4 th of the remaining on travel . now , he is left with rs 400 . how much did he have with him in the beginning ?
Options: a ) s 200 , b ) s 1000 , c ) s 300 , d ) s 450 , e ) s 550
Rationale: "suppose the amount in the beginning was rs ’ x ’ money spent on clothes = rs 1 x / 3 balance = rs 2 x / 3 money spent on food = 1 / 5 of 2 x / 3 = rs 2 x / 15 balance = 2 x / 3 - 2 x / 15 = rs 8 x / 15 money spent on travel = 1 / 4 of 8 x / 15 = rs 2 x / 15 = 8 x / 15 - 2 x / 15 = 6 x / 15 = rs 2 x / 5 therefore 2 x / 5 = 400 = 1000 answer : b"
Answer: b
Python program:
a = 1 / 3
b = 1 - a
c = 1 / 3
d = 1 - c
e = d / 5
f = b - e
g = 1 / 3
h = 1 - g
i = 1 / 3
j = 1 - i
k = j / 5
l = h - k
m = l / 4
n = f - m
o = 400 / n
Problem: in what time will a train 200 metres long cross an electric pole , if its speed be 124 km / hr ?
Options: a ) 4.8 sec , b ) 5.9 sec , c ) 5.0 sec , d ) 5.4 sec , e ) 5.8 sec
Rationale: "solution speed = ( 124 x 5 / 18 ) m / sec = 34.44 m / sec time taken = ( 200 / 34.44 ) sec = 5.8 sec . answer e"
Answer: e
Python program:
a = 124 * const_0_2778
b = 200 / a
Problem: the h . c . f of two numbers is 23 and the other two factors of their l . c . m are 15 and 16 . the larger of the two numbers is :
Options: a ) 338 , b ) 278 , c ) 322 , d ) 368 , e ) 121
Rationale: clearly , the numbers are ( 23 * 15 ) and ( 23 * 16 ) . larger number = ( 23 * 16 ) = 368 . answer : d
Answer: d
Python program:
a = 23 * 16
Problem: a train of 45 carriages , each of 60 meters length , when an engine also of 60 meters length is running at a speed of 60 kmph . in what time will the train cross a bridge 1.5 km long ?
Options: a ) 6 , b ) 3 , c ) 4.2 , d ) 9 , e ) 4
Rationale: "d = 45 * 60 + 1500 = 4200 m t = 4200 / 60 * 18 / 5 = 252 sec = 4.2 mins answer : c"
Answer: c
Python program:
a = 45 + 1 
b = a * 60
c = b / 1000
d = c + 1
Problem: mike needs 30 % to pass . if he scored 212 marks and falls short by 13 marks , what was the maximum marks he could have got ?
Options: a ) 343 , b ) 377 , c ) 750 , d ) 367 , e ) 232
Rationale: "if mike had scored 13 marks more , he could have scored 30 % therefore , mike required 212 + 13 = 225 marks let the maximum marks be m . then 30 % of m = 225 ( 30 / 100 ) × m = 225 m = ( 225 × 100 ) / 30 m = 22500 / 30 m = 750 answer : c"
Answer: c
Python program:
a = 212 + 13 
b = 30 / 100
c = a / b
Problem: a merchant gets a 5 % discount on each meter of fabric he buys after the first 2,000 meters and a 7 % discount on every meter after the next 1,500 meters . the price , before discount , of one meter of fabric is $ 2 , what is the total amount of money the merchant spends on 7,000 meters of fabric ?
Options: a ) $ 13,360 , b ) $ 14,450 , c ) $ 15,720 , d ) $ 16,780 , e ) $ 17,240
Rationale: "for first 2000 meters he does not get any discount . the price is 2 * 2000 = $ 4000 for next 1500 meters , he gets a 5 % discount . the price is 1.9 * 1500 = $ 2850 for the next 1500 meters , he gets a 7 % discount . the price is 1.86 * 3500 = $ 6510 the total price is $ 4000 + $ 2850 + $ 6510 = $ 13,360 the answer is a ."
Answer: a
Python program:
a = 2 * 3
b = a * 100
Problem: when 100 is divided by positive integer x , the remainder is 4 . what is the remainder when 196 is divided by x ?
Options: a ) 2 , b ) 3 , c ) 4 , d ) 6 , e ) 8
Rationale: "f 100 / x leaves a reminder 4 then ( 100 - 4 ) i . e . 96 is divisible by x so ( 100 + 96 ) / x leaves a reminder rem ( 100 / x ) + rem ( 96 / x ) = > 4 + 0 = 4 answer : c"
Answer: c
Python program:
a = 196 - 100
b = 100 - a
Problem: a fair price shopkeeper takes 10 % profit on his goods . he lost 50 % goods during theft . his loss percent is :
Options: a ) 72 % , b ) 45 % , c ) 32 % , d ) 12 % , e ) 22 %
Rationale: "explanation : suppose he has 100 items . let c . p . of each item be re . 1 . total cost = rs . 100 . number of items left after theft = 50 . s . p . of each item = rs . 1.10 total sale = 1.10 * 50 = rs . 55 hence , loss % = 45 / 100 * 100 = 45 % answer : b"
Answer: b
Python program:
a = 100 + 10 
b = 100 + 10 
c = b * 50
d = c / 100
e = a - d
f = 100 - e
Problem: a sum was put a simple interest at a certain rate for 4 years . had it been put at 3 % higher rate , it would have fetched rs . 120 more . the sum is :
Options: a ) s . 750 , b ) s . 1000 , c ) s . 1250 , d ) s . 1500 , e ) s . 1750
Rationale: explanation : let the sub be rs . x and the initial rate be r % . then x ã — ( r + 3 ) ã — 4 / 100 â ˆ ’ x ã — r ã — 4 / 100 = 120 â ‡ ’ x ã — 3 ã — 4 / 100 = 120 â ‡ ’ x ã — 4 / 100 = 40 â ‡ ’ 4 x = 4000 â ‡ ’ x = 1000 answer : option b
Answer: b
Python program:
a = 120 / 4
b = a / 3
c = b * 100
Problem: √ ( 14 ) ^ 2
Options: a ) 7 , b ) 14 , c ) 49 , d ) 21 , e ) none of these
Rationale: "explanation √ ( 14 ) ^ 2 = ? or , ? = 14 answer b"
Answer: b
Python program:
a = 14 ** 2
b = math.sqrt(a)
Problem: in a graduating class of 236 students , 144 took geometry and 119 took biology . what is the difference between the greatest possible number and the smallest possible number of students that could have taken both geometry and biology ?
Options: a ) 144 , b ) 119 , c ) 113 , d ) 117 , e ) 31
Rationale: "greatest possible number taken both should be 144 ( as it is maximum for one ) smallest possible number taken both should be given by total - neither = a + b - both both = a + b + neither - total ( neither must be 0 to minimize the both ) so 144 + 119 + 0 - 236 = 27 greatest - smallest is 144 - 27 = 117 so answer must be d . 117"
Answer: d
Python program:
a = 144 + 119 
b = a - 236
c = 119 - b
Problem: bruce purchased 8 kg of grapes at the rate of 70 per kg and 9 kg of mangoes at the rate of 55 per kg . how much amount did he pay to the shopkeeper ?
Options: a ) 1040 , b ) 1050 , c ) 1055 , d ) 1065 , e ) 1075
Rationale: "cost of 8 kg grapes = 70 × 8 = 560 . cost of 9 kg of mangoes = 55 × 9 = 490 . total cost he has to pay = 560 + 490 = 1055 c"
Answer: c
Python program:
a = 8 * 70
b = 9 * 55
c = a + b
Problem: initially , the men and women in a room were in the ratio of 4 : 5 . then , 2 men entered the room and 3 women left the room . then , the number of women doubled . now there are 14 men in the room . how many r women are currently in the room ?
Options: a ) 12 , b ) 14 , c ) 15 , d ) 24 , e ) 36
Rationale: "the number of women doubled means that they have become 24 from 12 . . and we have to tell the current strength so 24 is the answer . . let the number be 4 x and 5 x . . given 4 x + 2 = 14 . . so x = 3 . . women number = 5 * 3 - 3 = 12 , then doubled = 24 . . ans d"
Answer: d
Python program:
a = 14 - 2
b = 5 * a
c = b / 4
d = c - 3
e = 2 * d
Problem: paul ' s salary was decreased by 50 % and subsequently increased by 50 % . how much percent does he lose ?
Options: a ) 0 , b ) 25 , c ) 50 , d ) 30 , e ) 40
Rationale: let the original salary = $ 100 new final salary = 150 % of ( 50 % of rs . 100 ) = $ ( ( 150 / 100 ) * ( 50 / 100 ) * 100 ) = $ 75 . decrease = 25 % answer option b ) 25 .
Answer: b
Python program:
a = 50 * 50
b = a / 100
c = 50 + b 
d = 100 - c
Problem: a certain list consists of 21 different numbers . if n is in the list and n is 4 times the average ( arithmetic mean ) of the other 20 numbers in the list , then n is what fraction u of the sum of the 21 numbers in the list ?
Options: a ) 1 / 20 , b ) 1 / 6 , c ) 1 / 5 , d ) 4 / 21 , e ) 5 / 21
Rationale: "this is how i used to calculate which i think works pretty well : if you let the average of the 20 other numbers equal a , can you write this equation for sum of the list ( s ) n + 20 a = s the question tells us that n = 4 a plug this back into the first equation and you get that the sum is 24 a 4 a + 20 a = 24 a therefore fraction u of n to the total would be 4 a / 24 a or 1 / 6 answer b"
Answer: b
Python program:
a = 1 * 1
b = 20 / 4
c = b + 21 
d = c / 4
e = d * 2
f = e - 4
g = f - 3
h = a / g
Problem: if an object travels 80 feet in 4 seconds , what is the object ’ s approximate speed in miles per hour ? ( note : 1 mile = 5280 feet )
Options: a ) 7.25 , b ) 9.47 , c ) 11.58 , d ) 13.64 , e ) 15.92
Rationale: "80 feet / 4 seconds = 20 feet / second ( 20 feet / second ) * ( 3600 seconds / hour ) * ( 1 mile / 5280 feet ) = 13.64 miles / hour ( approximately ) the answer is d ."
Answer: d
Python program:
a = 80 / 5280
b = 1 / 3600
c = 4 * b
d = a / c
Problem: two different primes may be said torhymearound an integer if they are the same distance from the integer on the number line . for instance , 3 and 7 rhyme around 5 . what integer t between 1 and 20 , inclusive , has the greatest number of distinct rhyming primes around it ?
Options: a ) 12 , b ) 15 , c ) 17 , d ) t = 18 , e ) 20
Rationale: "since we are concerned with integers between 1 and 20 , write down the primes till 40 . 2 , 3 , 5 , 7 , 11 , 13 , 17 , 19 , 23 , 29 , 31 , 37 ( you should be very comfortable with the first few primes . . . ) 2 , 3 , 5 , 7 , 11,12 , 13 , 17 , 19 , 23 , 29 , 31 , 37 - three pairs ( 11,13 ) , ( 7,17 ) , ( 5 , 19 ) 2 , 3 , 5 , 7 , 11 , 13 , 15,17 , 19 , 23 , 29 , 31 , 37 - three pairs ( 13 , 17 ) , ( 11 , 19 ) , ( 7 , 23 ) 2 , 3 , 5 , 7 , 11 , 13,17 , 19 , 23 , 29 , 31 , 37 - three pairs ( 11 , 23 ) , ( 5 , 29 ) , ( 3 , 31 ) 2 , 3 , 5 , 7 , 11 , 13 , 17 , 18,19 , 23 , 29 , 31 , 37 - four pairs ( 17 , 19 ) , ( 13 , 23 ) , ( 7 , 29 ) , ( 5 , 31 ) 2 , 3 , 5 , 7 , 11 , 13 , 17 , 19 , 20,23 , 29 , 31 , 37 - definitely can not be more than 4 since there are only 4 primes more than 20 . so must be less than 4 pairs . ignore . answer ( d ) ."
Answer: d
Python program:
a = 3 * 2
b = a * 3
Problem: what is the greatest prime factor of 42 ^ 2 + 75 ^ 2 + 6300
Options: a ) 3 , b ) 7 , c ) 11 , d ) 13 , e ) 79
Rationale: "42 ^ 2 = ( 50 - 8 ) ( 50 - 8 ) = 1764 75 ^ 2 = ( 100 - 25 ) ( 100 - 25 ) = 5625 1764 + 5625 + 6300 = 13689 this number is divisible by 3 and 9 divide by 9 and get 1521 , the sum of this number is again a multiple of 9 , thus we can divide it one more time by 9 . we get 169 , and 169 is 13 ^ 2 . thus the answer is 13 . answer : d"
Answer: d
Python program:
a = 42 * 2
b = a + 1 
c = b / 6300
d = c + 3 
e = d + 3
Problem: 12 men can complete a piece of work in 30 days . in how many days can 10 men complete that piece of work ?
Options: a ) 23 , b ) 27 , c ) 36 , d ) 27 , e ) 11
Rationale: "12 * 30 = 10 * x = > x = 36 days answer : c"
Answer: c
Python program:
a = 30 * 12
b = a / 10
Problem: if a - b = 4 and a ^ 2 + b ^ 2 = 80 , find the value of ab
Options: a ) 10 , b ) 12 , c ) 15 , d ) 18 , e ) 32
Rationale: "2 ab = ( a ^ 2 + b ^ 2 ) - ( a - b ) ^ 2 = 80 - 16 = 64 = > ab = 32 answer : e"
Answer: e
Python program:
a = math.sqrt(80)
b = a - 4
c = b / 2
d = 4 + c 
e = math.sqrt(80)
f = e - 4
g = f / 2
h = d * g
i = h * 2
Problem: the timing of a college is from 11 p . m to 4.20 p . m . five lectures are held in the given duration and a break of 5 minutes after each lecture is given to the students . find the duration of each lecture .
Options: a ) 56 minutes , b ) 52 minutes , c ) 30 minutes , d ) 48 minutes , e ) 44 minutes
Rationale: "explanation : total time a student spends in college = 5 hours 20 minutes = 280 minutes as there are 5 lectures , the number of breaks between lectures is 4 . total time of the break = 20 minutes hence , the duration of each lecture is = ( 280 â € “ 20 ) / 5 = 52 minutes answer b"
Answer: b
Python program:
a = 4 * 20
b = a / 5
Problem: efrida and frazer who live 10 miles apart , meet at a restaurant that is directly north of efrida ' s home and directly east of frazer ' s home . if the restaurant is three miles closer to efrida ' s home , than to frazer ' s home , how many miles is the restaurant from frazer ' s home ?
Options: a ) 6 , b ) 7 , c ) 8 , d ) 10 , e ) 11
Rationale: "it ' s a simple geometry problem . look at the diagram below : answer : b ."
Answer: b
Python program:
a = 10 ** 2
b = 2 ** 2
c = a - b
d = c / 2
e = math.sqrt(d)
f = e + 2
Problem: a man performs 3 / 5 of the total journey by rail , 17 / 20 by bus and the remaining 6.5 km on foot . his total journey is ?
Options: a ) 130 , b ) 152 , c ) 225 , d ) 260 , e ) 180
Rationale: "let the total journey be x km then , ( 3 x / 5 ) + ( 7 x / 20 ) + 6.5 = x 12 x + 7 x + 20 * 6.5 = 20 x x = 130 km answer is a"
Answer: a
Python program:
a = 20 * 6
Problem: find the fraction which has the same ratio to 2 / 3 that 3 / 5 has to 6 / 7
Options: a ) 1 / 5 , b ) 2 / 22 , c ) 3 / 4 , d ) 7 / 15 , e ) 5 / 6
Rationale: "p : 2 / 3 = 3 / 5 : 6 / 7 as the product of the means is equal to the product of the extremes . p * 6 / 7 = 2 / 3 * 3 / 5 p * 6 / 7 = 6 / 15 p = 7 / 15 = > p = 7 / 15 answer : d"
Answer: d
Python program:
a = 3 / 5
b = 6 / 7
c = a / b
d = 2 / 3
e = c * d
Problem: how many of the positive divisors g of 120 are also multiples of 4 not including 120 ?
Options: a ) 3 . , b ) 4 . , c ) 5 . , d ) 7 . , e ) 8 .
Rationale: "4 , 8,12 , 20,24 , 40,60 . ( 7 ) is the answer other way : factors of 120 = 2 ^ 3 * 3 * 5 separate 2 ^ 2 ( which means 4 ) now , calculate the number of other factors . g = 2 * 3 * 5 = total positive factors are 2 * 2 * 2 = 8 this 8 factors include 120 so subtract 1 from 8 ans is 7 = d"
Answer: d
Python program:
a = 120 / 4
b = a / 2
c = b / 3
Problem: ( 9568422 x 558 ) = ?
Options: a ) 5846381256 , b ) 5339179476 , c ) 5346381356 , d ) 5846381406 , e ) 5346381456
Rationale: 9568422 x 558 = 5339179476 ans b
Answer: b
Python program:
a = 4 + 1 
b = a ** 4
c = 9568422 * b
Problem: in a certain math department , students are required to enroll in either calculus or trigonometry , each of which is offered in beginner and advanced courses . the number of students enrolled in trigonometry is 50 % greater than the number of students enrolled in calculus , and 70 % of calculus students are enrolled in the beginner course . if 4 / 5 of students are in the beginner courses , and one student is selected at random , what is the probability that an advanced trigonometry student is selected ?
Options: a ) 8 % , b ) 16 % , c ) 20 % , d ) 24 % , e ) 40 %
Rationale: "let x be the number of students in calculus . then the number of students in trigonometry is 1.5 x the number of students on beginner calculus is 0.7 x the number of students in beginner trigonometry is 4 / 5 * ( 2.5 x ) - 0.7 x = 1.3 x the number of students in advanced trigonometry is 0.2 x the percentage in advanced trigonometry is 0.2 x / 2.5 x = 8 % the answer is a ."
Answer: a
Python program:
a = 50 * 2
b = a + 50 
c = 50 * 2
d = b + c 
e = 4 / 5
f = d * e
g = f - 70
h = 50 * 2
i = h + 50 
j = 50 * 2
k = i + j 
l = g / k
m = 50 * 2
n = l * m
Problem: if the diameter of circle r is 60 % of the diameter of circle s , the area of circle r is what percent of the area of circle s ?
Options: a ) 50 %
b ) 46 %
c ) 36 %
d ) 26 %
e ) 38 %
Rationale: let diameter of circle r , dr = 60 and diameter of circle s , ds = 100 radius of circle r , rr = 30 radius of circle s , rs = 50 area of circle r / area of circle s = ( pi * rr ^ 2 ) / ( pi * rs ^ 2 ) = ( 30 / 50 ) ^ 2 = ( 6 / 10 ) ^ 2 = 36 % answer : c
Answer: c
Python program:
a = circle_area * (
b = a / 100
Problem: a small company reduced its faculty by approximately 13 percent to 263 employees . what was the original number of employees ?
Options: a ) a ) 182 , b ) b ) 208 , c ) c ) 220 , d ) d ) 224 , e ) e ) 302
Rationale: if x is the original number of employees , then after 13 % reduction in employees number is . 87 x but we are given . 87 x = 263 x = 302 so the original number of employees is 302 correct answer - e
Answer: e
Python program:
a = 100 - 13
b = a / 100
c = 263 / b
Problem: the average weight of 8 person ' s increases by 2.5 kg when a new person comes in place of one of them weighing 70 kg . what is the weight of the new person ?
Options: a ) 90 , b ) 65 , c ) 85 , d ) 95 , e ) 80
Rationale: "total increase in weight = 8 × 2.5 = 20 if x is the weight of the new person , total increase in weight = x − 70 = > 20 = x - 70 = > x = 20 + 70 = 90 answer is a ."
Answer: a
Python program:
a = 8 * 2
b = a + 70
Problem: a can contains a mixture of liquids a and b is the ratio 7 : 5 . when 9 litres of mixture are drawn off and the can is filled with b , the ratio of a and b becomes 7 : 9 . how many liter m of liquid a was contained by the can initially ?
Options: a ) 10 , b ) 20 , c ) 21 , d ) 25 , e ) 27
Rationale: "as a : b : : 7 : 5 - - - > only option c is a multiple of 7 and hence it is a good place to start . also a : b : : 7 : 5 means that , a = ( 712 ) * total and b = ( 5 / 12 ) * total if a = 21 , b = 15 - - - > remove 9 litres - - - > you remove ( 7 / 12 ) * 9 of a - - - > a remaining = 21 - ( 7 / 12 ) * 9 = 63 / 4 similarly , for b , you remove ( 5 / 12 ) * 9 - - - > b remaining = 15 - ( 5 / 12 ) * 9 = 45 / 4 and then add 9 more litres of b - - - > 9 + 45 / 4 = 81 / 4 thus a / b ( final ratio ) = ( 45 / 4 ) / ( 81 / 4 ) = 7 : 9 , the same as the final ratio mentioned in the question . hence c is the correct answer . a / b = 7 / 9 = ( 7 x - ( 7 / 12 ) * 9 ) / ( 5 x - ( 5 / 12 ) * 9 + 9 ) , where 7 x and 5 x are initial quantities of a and b respectively . thus , 7 / 9 = ( 7 x - ( 7 / 12 ) * 9 ) / ( 5 x - ( 5 / 12 ) * 9 + 9 ) - - - > giving you x = 3 . thus a ( original ) m = 7 * 3 = 21 . c"
Answer: c
Python program:
a = 7 + 9 
b = 7 + 5 
c = 5 / b
d = c * 9
e = 9 - d
f = a * e
g = 9 * 7
h = 7 * 5
i = g - h
j = f / i
k = 7 * j