euclaise/mathqa_programs huggingface dataset:
Problem: there are 500 employees in a room . 99 % are managers . how many managers must leave the room to bring down the percentage of managers to 98 % ?
Options: a ) 150 , b ) 200 , c ) 250 , d ) 350 , e ) 400
Rationale: "there are 495 managers and 5 others . the 5 others would compose 2 % of the total number of people if there were 250 people in the room . thus 250 managers must leave . the answer is c ."
Answer: c
Python program:
a = 99 / 100
b = 500 * a
c = 98 / 100
d = 500 * c
e = b - d
f = 98 / 100
g = 1 - f
h = e / g
Problem: the speed at which a woman can row a boat in still water is 30 kmph . if he rows downstream , where the speed of current is 6 kmph , what time will he take to cover 100 metres ?
Options: a ) 8 , b ) 9 , c ) 10 , d ) 11 , e ) 12
Rationale: "speed of the boat downstream = 30 + 6 = 36 kmph = 36 * 5 / 18 = 10 m / s hence time taken to cover 100 m = 100 / 10 = 10 seconds . answer : c"
Answer: c
Python program:
a = 30 + 6 
b = a * const_0_2778
c = 100 / b
Problem: a company decreased the price of its main product by 30 % . subsequently , the number of units sold increased such that the total revenue remained unchanged . what was the ratio of the percent increase in the units sold to the percent decrease of the original price for this product ?
Options: a ) 1.26 , b ) 2.54 , c ) 5.23 , d ) 4.23 , e ) 3.33
Rationale: for the total revenue to remain the same when the price is 3 / 10 , the number of products sold must 3 / 10 times . therefore increase in the number of products sold is 100 % = > the required ratio = 100 % / 30 % = 3.33 answer : e
Answer: e
Python program:
a = 100 / 30
Problem: a train 110 m long is running with a speed of 80 km / h . in how many seconds will the train pass a man who is running at 8 km / h in the direction opposite to that in which the train is going ?
Options: a ) 3.5 , b ) 4.5 , c ) 5.5 , d ) 6.5 , e ) 7.5
Rationale: "the speed of the train relative to the man = 80 + 8 = 88 km / h . 88000 m / h * 1 h / 3600 s = ( 880 / 36 ) m / s ( 110 m ) / ( 880 / 36 m / s ) = ( 110 * 36 ) / 880 = 36 / 8 = 4.5 seconds the answer is b ."
Answer: b
Python program:
a = 80 + 8 
b = a / const_3_6
c = 110 / b
Problem: after 10 % of the inhabitants of a village disappeared , a panic set in during which 25 % of the remaining inhabitants left the village . at that time , the population was reduced to 5265 . what was the number of original inhabitants ?
Options: a ) 7500 , b ) 7800 , c ) 8100 , d ) 8400 , e ) 8700
Rationale: "let the total number of original inhabitants be x . ( 75 / 100 ) * ( 90 / 100 ) * x = 5265 ( 27 / 40 ) * x = 5265 x = 5265 * 40 / 27 = 7800 the answer is b ."
Answer: b
Python program:
a = 10 / 100
b = 1 - a
c = 10 / 100
d = 1 - c
e = 25 / 100
f = d * e
g = b - f
h = 5265 / g
Problem: a merchant has 1000 kg of sugar part of which he sells at 8 % profit and the rest at 18 % profit . he gains 14 % on the whole . the quantity sold at 18 % profit is ?
Options: a ) 700 kg , b ) 500 kg , c ) 600 kg , d ) 800 kg , e ) 900 kg
Rationale: "by the rule of alligation : profit of first part profit of second part so , ratio of 1 st and 2 nd parts = 4 : 6 = 2 : 3 . quantity of 2 nd kind = ( 3 / 5 x 1000 ) kg = 600 kg answer : c"
Answer: c
Python program:
a = 2 + 3 
b = a * 2
c = 14 / 100
d = c + 1 
e = 8 / 100
f = 1 + e 
g = d - f
h = g * 1000
i = b * h
Problem: a rower whose speed is 8 km / hr in still water rows to a certain point upstream and back to the starting point in a river which flows at 4 km / hr . what is the rower ' s average speed ( in km / hr ) for the total journey ?
Options: a ) 5 , b ) 6 , c ) 7 , d ) 8 , e ) 9
Rationale: "time upstream = d / 4 time downstream = d / 12 total time = d / 4 + d / 12 = d / 3 average speed = 2 d / ( d / 3 ) = 6 km / hr the answer is b ."
Answer: b
Python program:
a = 8 - 0
b = 8 + 4 
c = a + b 
d = c / 2
Problem: how many pounds of salt at 50 cents / lb must be mixed with 40 lbs of salt that costs 25 cents / lb so that a merchant will get 20 % profit by selling the mixture at 48 cents / lb ?
Options: a ) 20 , b ) 15 , c ) 40 , d ) 60 , e ) 25
Rationale: "selling price is 48 cents / lb for a 20 % profit , cost price should be 40 cents / lb ( cp * 6 / 5 = 48 ) basically , you need to mix 25 cents / lb ( salt 1 ) with 50 cents / lb ( salt 2 ) to get a mixture costing 40 cents / lb ( salt avg ) weight of salt 1 / weight of salt 2 = ( salt 2 - saltavg ) / ( saltavg - salt 1 ) = ( 50 - 40 ) / ( 40 - 25 ) = 2 / 3 we know that weight of salt 1 is 40 lbs . weight of salt 2 must be 60 lbs . answer ( d )"
Answer: d
Python program:
a = 48 * 40
b = 100 + 20 
c = b / 100
d = 25 * 40
e = c * d
f = a - e
g = 100 + 20 
h = g / 100
i = 50 * h
j = i - 48
k = f / j
Problem: if 10 gallons of grape juice are added to 40 gallons of a mixture , which contains 10 percent grape juice then what percent of the resulting mixture is grape juice ?
Options: a ) 14 % , b ) 25 % , c ) 28 % , d ) 34 % , e ) 50 %
Rationale: "mixture contains 4 gallons of grape juice out of 40 gallons after addition : 14 gallons of grape juice out of 50 gallons = = > 28 % answer c"
Answer: c
Python program:
a = 10 / 100
b = a * 40
c = b + 10 
d = 40 + 10 
e = c / d
f = e * 100
Problem: 18 men can complete a piece of work in 30 days . in how many days can 15 men complete that piece of work ?
Options: a ) 23 days , b ) 36 days , c ) 22 days , d ) 29 days , e ) 20 days
Rationale: "b 36 days 18 * 30 = 15 * x = > x = 36 days"
Answer: b
Python program:
a = 30 * 18
b = a / 15
Problem: if the sales tax be reduced from 4 ( 1 / 4 ) % to 1 ( 1 / 2 ) % , then what difference does it make to a person who purchases a bag with marked price of rs . 4500 ?
Options: a ) rs . 156.66 , b ) rs . 150.23 , c ) rs . 123.75 , d ) rs . 135.06 , e ) none of these
Rationale: explanation : required difference = ( 4 ( 1 / 4 ) of rs . 4500 ) - ( 1 ( 1 / 2 ) of rs . 4500 ) = ( 17 / 4 – 3 / 2 ) % of rs . 4500 = ( 11 / 4 ) x ( 1 / 100 ) x 4500 = rs . 123.75 answer c
Answer: c
Python program:
a = 1 / 4
b = 4 + a 
c = b / 100
d = c + 1 
e = 1 / 2
f = e + 1 
g = f / 100
h = g + 1 
i = 4500 / h
j = d * i
k = j - 4500
Problem: two , trains , one from howrah to patna and the other from patna to howrah , start simultaneously . after they meet , the trains reach their destinations after 9 hours and 16 hours respectively . the ratio of their speeds is :
Options: a ) 2 : 3 , b ) 4 : 3 , c ) 6 : 7 , d ) 9 : 16 , e ) 9 : 14
Rationale: let the slower train have speed of 1 unit and faster train a speed of r units of speed . let t = time to when the trains meet . rt 1 t howrah | - - - - - - - - - - - - - - - - - - - - - - - | - - - - - - - - - - | patna meet they meet rt units from howrah and 1 t units from patna for the second part of the journey the fast train at speed r has 1 t unit of distance and 9 hours to do it so 1 t / r = 9 slow train has rt units of distance at speed of 1 unit and 16 hours to do it . rt / 1 = 16 so rt / 1 16 - - - - - = - - - - giving r ^ 2 = 16 / 9 1 t / r 9 r = 4 / 3 answer : b
Answer: b
Python program:
a = 16 / 9
b = math.sqrt(a)
Problem: in a colony of 70 resident s , the ratio of the number of men and women is 4 : 3 . among the women , the ratio of the educated to the uneducated is 1 : 4 . if the ratio of the number of education to uneducated persons is 8 : 27 , then find the ratio of the number of educated and uneducated men in the colony ?
Options: a ) 1 : 9 , b ) 1 : 6 , c ) 1 : 3 , d ) 1 : 1 , e ) 1 ratio 3
Rationale: number of men in the colony = 4 / 7 ( 70 ) = 40 number of women in the colony = 3 / 7 ( 70 ) = 30 number of educated women in the colony = 1 / 5 ( 30 ) = 6 number of uneducated women in the colony = 4 / 5 ( 30 ) = 24 number of educated persons in the colony = 8 / 35 ( 70 ) = 16 as 6 females are educated , remaining 10 educated persons must be men . number of uneducated men in the colony = 40 - 10 = 30 number of educated men and uneducated men are in the ratio 10 : 30 = > 1 : 3 answer : e
Answer: e
Python program:
a = 8 + 27 
b = 8 / a
c = b * 70
d = 1 + 4 
e = 1 / d
f = 4 + 3 
g = 3 / f
h = g * 70
i = e * h
j = c - i
k = 4 + 3 
l = 4 / k
m = l * 70
n = 8 + 27 
o = 8 / n
p = o * 70
q = 1 + 4 
r = 1 / q
s = 4 + 3 
t = 3 / s
u = t * 70
v = r * u
w = p - v
x = m - w
y = j / x
Problem: what is the average ( arithmetic mean ) of all multiples of 10 from 10 to 300 inclusive ?
Options: a ) 155 , b ) 195 , c ) 200 , d ) 205 , e ) 210
Rationale: "this question can be solved with the average formula and ' bunching . ' we ' re asked for the average of all of the multiples of 10 from 10 to 300 , inclusive . to start , we can figure out the total number of terms rather easily : 1 ( 10 ) = 10 2 ( 10 ) = 20 . . . 30 ( 10 ) = 300 so we know that there are 30 total numbers . we can now figure out the sum of those numbers with ' bunching ' : 10 + 300 = 310 20 + 290 = 310 30 + 280 = 310 etc . since there are 30 total terms , this pattern will create 15 ' pairs ' of 310 . thus , since the average = ( sum of terms ) / ( number of terms ) , we have . . . ( 15 ) ( 310 ) / ( 30 ) = 155 answer : a"
Answer: a
Python program:
a = 10 + 300 
b = 300 - 10
c = b / 10
d = c + 1 
e = a * d
f = e / 2
g = 300 - 10
h = g / 10
i = h + 1 
j = f / i
Problem: if 0.75 : x : : 5 : 8 , then x is equal to
Options: a ) 1.12 , b ) 1.25 , c ) 1.20 , d ) 1.3 , e ) none
Rationale: "sol . ( x × 5 ) = ( 0.75 × 8 ) ⇒ x = 6 / 5 = 1.20 . answer c"
Answer: c
Python program:
a = 0 * 75
b = a / 5
Problem: the reciprocal of the hcf and lcm of two are 1 / 13 and 1 / 312 . if one of the number is 24 then other no . is
Options: a ) 126 , b ) 136 , c ) 146 , d ) 156 , e ) 169
Rationale: reciprocal of the hcf and lcm of two are 1 / 13 and 1 / 312 so , hcf = 13 , lcm = 312 lcm * hcf = product of two numbers = a * b = > b = lcm * hcf / a so , other = 13 * 312 / 24 = 169 answer : e
Answer: e
Python program:
a = 13 * 312
b = a / 24
Problem: the ratio of two no . addition and subtraction be 4 : 3 . the what is the ratio of numbers ?
Options: a ) 3 : 2 , b ) 4 : 3 , c ) 5 : 1 , d ) 6 : 5 , e ) 7 : 1
Rationale: ( x + y ) / ( x - y ) = 4 / 3 dividing numerator and denominator by y ( x / y ) + 1 / ( x / y ) - 1 = 4 / 3 let x / y be z z + 1 / z - 1 = 4 / 3 3 z + 3 = 4 z - 4 z = 7 x / y = 7 answer e
Answer: e
Python program:
a = 4 + 3
Problem: among 300 students , 56 % study sociology , 44 % study mathematics and 40 % study biology . if 30 % of students study both mathematics and sociology , what is the largest possible number of students who study biology but do not study either mathematics or sociology ?
Options: a ) 30 , b ) 90 , c ) 120 , d ) 172 , e ) 188
Rationale: "i would just like to add a bit of explanation after the step where you calculate that the number of students studying both m and s = 90 using your analysis : we see that the total number of students who study either maths or sociology = 132 + 168 - 90 = 210 so , in the image we know that the number of students in the zone with the black boundary = 210 let ' s assume the number of students who studyonlybiology to beb ( this is the number that we have to maximize ) and , let ' s assume the number of students who study none of the three subjects , that is the number of students in the white space = w since the total number of students = 300 , we can write : 210 + b + w = 300 or , b + w = 300 - 210 = 90 that is , b = 90 - w so , the maximum value ofbwill happen forw = 0 this is how we get , the maximum value ofb = 90 b"
Answer: b
Python program:
a = 300 / 100
b = a * 56
c = 300 / 100
d = c * 44
e = b + d 
f = 300 / 100
g = f * 30
h = e - g
i = 300 - h
Problem: 6 / [ ( 1 / 0.03 ) + ( 1 / 0.37 ) ] = ?
Options: a ) 0.004 , b ) 0.16666 , c ) 2.775 , d ) 3.6036 , e ) 36.036
Rationale: "approximate . 1 / . 03 = 100 / 3 = 33 1 / . 37 = 100 / 37 = 3 denominator becomes 33 + 3 = 36 6 / 36 = . 16666 answer ( b )"
Answer: b
Python program:
a = 6 / 0
b = 6 / 0
c = a + b 
d = 1/(c)
Problem: a marketing survey of anytown found that the ratio of trucks to sedans to motorcycles was 3 : 7 : 2 , respectively . given that there are 9,800 sedans in anytown , how many motorcycles are there ?
Options: a ) 2800 , b ) 2100 , c ) 3600 , d ) 4200 , e ) 5200
Rationale: "let the total number of trucks = 3 x total number of sedans = 7 x total number of motorcycles = 2 x total number of sedans = 9800 = > 7 x = 9800 = > x = 1400 total number of motorcycles = 2 x = 2 * 1400 = 2800 answer a"
Answer: a
Python program:
a = 3 * 3
b = a * 1000
c = b + 100 
d = c / 7
e = d * 2
Problem: in a can , there is a mixture of milk and water in the ratio 1 : 5 . if it is filled with an additional 2 litres of milk the can would be full and ratio of milk and water would become 2.00001 : 5.00001 . find the capacity of the can ?
Options: a ) 14 , b ) 44 , c ) 48 , d ) 50 , e ) 56
Rationale: let the capacity of the can be t litres . quantity of milk in the mixture before adding milk = 1 / 6 ( t - 2 ) after adding milk , quantity of milk in the mixture = 2 / 7 t . 2 t / 7 - 2 = 1 / 6 ( t - 2 ) 5 t = 84 - 14 = > t = 14 . answer : a
Answer: a
Python program:
a = 2 / 1
b = a * 5
c = b - 1
d = 2 / c
e = 5 * d
f = 2 / 1
g = f * 5
h = g - 1
i = 2 / h
j = e + i 
k = j + 2
Problem: the speed of a car increases by 2 kms after every one hour . if the distance travelling in the first one hour was 55 kms . what was the total distance travelled in 12 hours ?
Options: a ) 252 kms , b ) 152 kms , c ) 552 kms , d ) 792 kms , e ) 152 kms
Rationale: "explanation : total distance travelled in 12 hours = ( 55 + 57 + 59 + . . . . . upto 12 terms ) this is an a . p with first term , a = 55 , number of terms , n = 12 , d = 2 . required distance = 12 / 2 [ 2 x 55 + { 12 - 1 ) x 2 ] = 6 ( 132 ) = 792 kms . answer : d"
Answer: d
Python program:
a = 2 * 55
b = 12 - 1
c = b * 2
d = a + c 
e = 12 / 2
f = d * e
Problem: 45 x ? = 35 % of 900
Options: a ) 16.2 , b ) 7 , c ) 5 , d ) 500 , e ) none
Rationale: "answer let 45 x a = ( 35 x 900 ) / 100 ∴ a = ( 35 x 9 ) / 45 = 7 correct option : b"
Answer: b
Python program:
a = 35 / 100
b = a * 900
c = b / 45
Problem: the ratio of radius of a circle and the side of a square is 2 : 13 . find the ratio of their areas :
Options: a ) 2 : 1
b ) 4 : 7
c ) 8 : 77
d ) 4 : 169
e ) none
Rationale: radius / side = 2 / 13 â ‡ ’ area of circle / area of square = 4 / 169 answer : d
Answer: d
Python program:
a = 2 / 13
b = a ** 2
Problem: if the average of 54 , 55 , 57 , 58 , 59 , 62 , 62 , 63 , 65 and x is 60 , what is the value of x ?
Options: a ) 60 , b ) 62 , c ) 64 , d ) 65 , e ) 66
Rationale: "sum of the deviations of the numbers in the set from the mean is always zero 54 , 55 , 57 , 58 , 59 , 62 , 62 , 63 , 65 mean is 60 so the list is - 6 - 5 - 3 - 2 - 1 + 2 + 2 + 3 + 5 . . . this shud total to zero but this is - 5 , hence we need a number that is 5 more than the mean to get a + 5 and make it zero hence the answer is 60 + 5 = 65 d"
Answer: d
Python program:
a = 60 * 10
b = 54 + 55 
c = b + 57 
d = c + 58 
e = d + 59 
f = e + 62 
g = f + 62 
h = g + 63 
i = h + 65 
j = a - i
Problem: a ranch has both horses and ponies . exactly 5 / 6 of the ponies have horseshoes , and exactly 2 / 3 of the ponies with horseshoes are from iceland . if there are 4 more horses than ponies , what is the minimum possible combined number of horses and ponies on the ranch ?
Options: a ) 18 , b ) 21 , c ) 38 , d ) 40 , e ) 57
Rationale: "5 / 6 * p have horseshoes , so p is a multiple of 6 . 2 / 3 * 5 / 6 * p = 5 / 9 * p are icelandic ponies with horseshoes , so p is a multiple of 9 . the minimum value of p is 18 . then h = p + 4 = 22 . the minimum number of horses and ponies is 40 . the answer is d ."
Answer: d
Python program:
a = 6 / 2
b = a * 3
c = math.lcm(6, b)
d = c + 4 
e = 6 / 2
f = e * 3
g = math.lcm(6, f)
h = d + g
Problem: 20 , 22 , 26 , 34 , 41 , 46 , 56 , 67 , __ ?
Options: a ) 72 , b ) 80 , c ) 88 , d ) 68 , e ) 78
Rationale: "next no . = previous + ( sum of digits ) 20 + ( 2 + 0 ) = 22 22 + ( 2 + 2 ) = 26 26 + ( 2 + 6 ) = 34 - - - - - - - - 56 + ( 5 + 6 ) = 67 67 + ( 6 + 7 ) = 80 answer : b"
Answer: b
Python program:
a = negate - (
Problem: the sale price sarees listed for rs . 278 after successive discount is 18 % and 19 % is ?
Options: a ) 321 , b ) 276 , c ) 342 , d ) 265 , e ) 198
Rationale: "explanation : 278 * ( 88 / 100 ) * ( 81 / 100 ) = 198 answer : e"
Answer: e
Python program:
a = 278 * 18
b = a / 100
c = 278 - b
d = 278 * 18
e = d / 100
f = 278 - e
g = f * 19
h = g / 100
i = c - h
Problem: in a group of 90 students , 36 are taking history , and 30 are taking statistics . if 59 students are taking history or statistics or both , then how many students are taking history but not statistics ?
Options: a ) 9 , b ) 19 , c ) 23 , d ) 27 , e ) 29
Rationale: "number of students taking history = h = 36 number of students taking statistics = s = 30 total number of students = t = 90 number of students taking history or statistics or both = b = 59 number of students taking neither history nor statistics = n = 90 - 59 = 31 letxbe the number of students taking both history and statistics . then t = h + s + n - x or 90 = 36 + 30 + 31 - x or x = 7 now , number of students taking only history will be h - x or 36 - 7 = 29 answer : - e"
Answer: e
Python program:
a = 36 + 30 
b = a - 59
c = 36 - b
Problem: what least number must be subtracted from 427398 so that remaining no . is divisible by 14
Options: a ) 3 , b ) 5 , c ) 6 , d ) 7 , e ) 8
Rationale: "explanation : on dividing 427398 by 14 we get the remainder 6 , so 6 should be subtracted answer : option c"
Answer: c
Python program:
a = 427398 / 14
b = math.floor(a)
c = b * 14
d = 427398 - c
Problem: if the average ( arithmetic mean ) of a and b is 20 , and c – a = 30 , what is the average of b and c ?
Options: a ) 25 , b ) 30 , c ) 40 , d ) 35 , e ) 45
Rationale: "a + b / 2 = 20 = > a + b = 40 a = c - 30 . . . sub this value c - 30 + b = 40 = > c + b = 70 = > c + b / 2 = 35 answer : d"
Answer: d
Python program:
a = 30 * 2
b = 20 * 2
c = a - b
Problem: the average monthly salary of laborers and supervisors in a factory is rs . 1250 per month ; where as the average monthly salary of 6 supervisors is rs . 2450 . if the average monthly salary of the laborers is rs . 950 find the number of laborers ?
Options: a ) 87 , b ) 42 , c ) 78 , d ) 76 , e ) 26
Rationale: 5 x 6 x 2 x 50 25 100 250 x + 150 x + 200 x = 4200 600 x = 4200 x = 7 = > 6 x = 42 answer : b
Answer: b
Python program:
a = 2450 * 6
b = 1250 * 6
c = a - b
d = 1250 - 950
e = c / d
f = e * 2
g = f - 4
h = g - 2
Problem: the output of a factory is increased by 10 % to keep up with rising demand . to handle the holiday rush , this new output is increased by 40 % . by approximately what percent would the output of the factory now have to be decreased in order to restore the original output ?
Options: a ) 20 % , b ) 24 % , c ) 30 % , d ) 35 % , e ) 79 %
Rationale: "take it as original output = 100 . to meet demand increase by 10 % , then output = 110 . to meet holiday demand , new output increase by 40 % then output equals 154 to restore new holidy demand output to original 100 . final - initial / final * 100 = 54 / 154 * 100 = 35 % approxiamately . option d is correct ."
Answer: d
Python program:
a = 100 + 10 
b = a / 100
c = 100 + 40 
d = c / 100
e = b * d
f = e - 1
g = 100 + 10 
h = g / 100
i = 100 + 40 
j = i / 100
k = h * j
l = f / k
m = l * 100
Problem: balls of equal size are arranged in rows to form an equilateral triangle . the top most row consists of one ball , the 2 nd row of two balls and so on . if 424 balls are added , then all the balls can be arranged in the shape of square and each of the sides of the square contain 8 balls less than the each side of the triangle did . how many balls made up the triangle ?
Options: a ) 1176 , b ) 2209 , c ) 2878 , d ) 1210 , e ) 1560
Rationale: as expected , this question boils down to 2 equation , consider total number of balls in triangle = t and number of balls in last row = x . 1 + 2 + 3 + . . . + x = t x ( x + 1 ) / 2 = t - - - - ( a ) as mentioned in the question , side of a square will be ( x - 8 ) and total number of balls in square will be ( t + 424 ) ( x - 8 ) ^ 2 = t + 424 - - - - - ( b ) now the hardest part of the question will be to solve these 2 equations and this looks like time consuming but the easy way will be plug and play . also , we ' ve to find a value of t ( from 5 optiosn given below ) which can make a square of a a number . one we know this , it will be a cake walk . we can see that option a fits this criteria in eq ( b ) . add - 1176 + 424 = 1600 = 40 ^ 2 = ( x - 8 ) ^ 2 hence , x = 48 . cross check by putting in eq ( a ) = x ( x + 1 ) / 2 = t = > 48 * 49 / 2 = 1176 hence , answer is a .
Answer: a
Python program:
a = 4 * 100
b = 424 - a
c = 4 * 100
d = 424 - c
e = d * 2
f = e + 1 
g = b * f
Problem: a wholesaler wishes to sell 100 pounds of mixed nuts at $ 2.50 a pound . she mixes peanuts worth $ 1.50 a pound with cashews worth $ 4.00 a pound . how many pounds of cashews must she use ?
Options: a ) 40 , b ) 45 , c ) 50 , d ) 55 , e ) 60
Rationale: "cashews / peanuts = ( mean price - peanuts price ) / ( cashew price - mean price ) = ( 2.5 - 1.5 ) / ( 4 - 2.5 ) = 2 / 3 cashew = ( 2 / 5 ) * 100 = 40 kg answer is a ."
Answer: a
Python program:
a = 4 - 0
b = a * 100
c = b / 2
Problem: each week , harry is paid x dollars per hour for the first 30 hours and 1.5 x dollars for each additional hour worked that week . each week , annie is paid x dollars per hour for the first 40 hours and 2 x dollars for each additional hour worked that week . last week annie worked a total of 44 hours . if harry and annie were paid the same amount last week , how many hours did harry work last week ?
Options: a ) 40 , b ) 42 , c ) 44 , d ) 46 , e ) 48
Rationale: "annie earned 40 x + 4 ( 2 x ) = 48 x let h be the number of hours that harry worked . harry earned 30 x + 1.5 x ( h - 30 ) = 48 x ( 1.5 x ) ( h ) = 63 x h = 42 hours the answer is b ."
Answer: b
Python program:
a = 40 + 2 
b = a - 30
c = b / 1
d = c + 30
Problem: two pipes a and b can fill a cistern in 9 and 18 minutes respectively , and a third pipe c can empty it in 24 minutes . how long will it take to fill the cistern if all the three are opened at the same time ?
Options: a ) 6 min , b ) 7 min , c ) 8 min , d ) 10 min , e ) 17 min
Rationale: "1 / 9 + 1 / 18 - 1 / 24 = 1 / 8 8 / 1 = 8 answer : c"
Answer: c
Python program:
a = 1/(9)
b = 1/(18)
c = a + b 
d = c * 24
e = 1 - d
f = 9 * e
g = f + 24
Problem: laura took out a charge account at the general store and agreed to pay 5 % simple annual interest . if she charges $ 35 on her account in january , how much will she owe a year later , assuming she does not make any additional charges or payments ?
Options: a ) $ 2.10 , b ) $ 36.75 , c ) $ 37.16 , d ) $ 38.10 , e ) $ 38.80
Rationale: "principal that is amount taken by laura at year beginning = 35 $ rate of interest = 5 % interest = ( 5 / 100 ) * 35 = 1.75 $ total amount that laura owes a year later = 35 + 1.75 = 36.75 $ answer b"
Answer: b
Python program:
a = 5 / 100
b = a * 35
c = b + 35
Problem: a pharmaceutical company received $ 3 million in royalties on the first $ 20 million in sales of the generic equivalent of one of its products and then $ 9 million in royalties on the next $ 108 million in sales . by approximately what percent did the ratio of royalties to sales decrease from the first $ 20 million in sales to the next $ 108 million in sales ?
Options: a ) 8 % , b ) 15 % , c ) 45 % , d ) 52 % , e ) 56 %
Rationale: "first $ 20 million : royalties / sales ratio = 3 / 20 = 36 / 240 next $ 108 million : royalties / sales ratio = 9 / 108 = 1 / 12 = 20 / 240 answer : c"
Answer: c
Python program:
a = 3 / 20
b = a * 100
c = 9 / 108
d = c * 100
e = b - d
f = 3 / 20
g = f * 100
h = e / g
i = h * 100
Problem: what is the sum of the integers from - 194 to 195 inclusive ?
Options: a ) 0 , b ) 5 , c ) 195 , d ) 875 , e ) 965
Rationale: "sum / n = average . sum = ( average ) ( n ) average = a + b / 2 = 194 + 195 / 2 = 0.5 number of items ( n ) = b - a + 1 = 195 - ( - 194 ) + 1 = 195 + 195 = 390 . sum = average * n = 0.5 * 390 = 195 . answer is c"
Answer: c
Python program:
a = 194 * 195
b = a / 4