euclaise/mathqa_programs huggingface dataset:
Problem: a basketball player is shooting hoops . he shoots a free throw , a high school 3 - pointer , and then a professional 3 - pointer . the probability that he makes the free throw is 4 / 5 , the probability that he makes the high school 3 - pointer is 1 / 2 , and the probability that he makes the professional 3 - pointer is 1 / 3 . what is the probability that he makes at least one of the 3 shots ?
Options: a ) 14 / 15 , b ) 15 / 16 , c ) 17 / 18 , d ) 9 / 10 , e ) 5 / 6
Rationale: the probability that he makes at least one of the three shots = 1 - ( the probability that he misses all of the shots ) the probability that he misses all shots = ( prob that he misses free throw ) * ( prob that he misses 3 - pointer ) * ( prob that he misses the professional 3 - pointer ) prob that he misses the free throw = 1 - 4 / 5 = 1 / 5 ; prob that he misses the 3 - pointer = 1 - 1 / 2 = 1 / 2 ; prob that he misses the professional 3 - pointer = 1 - 1 / 3 = 2 / 3 thus the probability that he misses all shots = ( 1 / 5 ) * ( 1 / 2 ) * ( 2 / 3 ) = 1 / 15 answer : 1 - 1 / 15 = 14 / 15 a
Answer: a
Python program:
a = 10 + 4 
b = 5 * 3
c = a / b
Problem: a confectioner decides to sell all of his pastry due to the coming holiday . his pastry goods are equally divided among a group of 28 regular customers . if only 49 customers come to the bakery , each one will receive 6 less pastry goods . how much pastry does the confectioner needs to sell ?
Options: a ) 392 , b ) 412 . , c ) 432 . , d ) 502 , e ) 522
Rationale: "solution 1 : given that number of pastries are equally divided in to 28 groups , so the answer should be a multiple of 28 . and in the given choices , only 392 is divisible by 28 with remainder 0 ( make sure others are no multiples of 28 ) . so this is good enough to stop here , but to verify , 392 / 28 = 14 and 392 / 49 = 8 , which confirms the second part of question , 14 - 8 , 6 pastry short of each customer . solution 2 : going mathematical , expressing in the equation form , let x be the number of pastries and , n be the number of customers in 28 groups . so , x = 28 * n , as per second statement , x = 49 * ( n - 6 ) solve the above 2 for n and then we get x as 392 . answer is a : 392 ."
Answer: a
Python program:
a = 49 * 6
b = 49 - 28
c = a / b
d = c * 28
Problem: what decimal of an hour is a second
Options: a ) . 0028 , b ) . 0027 , c ) . 0026 , d ) . 0025 , e ) none of these
Rationale: explanation : 1 / ( 60 * 60 ) = 1 / 3600 = . 0027 option b
Answer: b
Python program:
a = 1 / const_60
b = a / const_60
Problem: a train of 24 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 , d ) 9 , e ) 2
Rationale: "d = 25 * 60 + 1500 = 3000 m t = 3000 / 60 * 18 / 5 = 180 sec = 3 mins answer : b"
Answer: b
Python program:
a = 24 + 1 
b = a * 60
c = b / 1000
d = c + 1
Problem: the total cost of 100 paper plates and 200 paper cups is $ 7.50 at the same rates what is the total cost of 20 of the plates and 40 of the cups ?
Options: a ) $ . 90 , b ) $ 1.00 , c ) $ 1.20 , d ) $ 1.50 , e ) $ 1.60
Rationale: "u dont need to go through all this what u have with u is 100 p + 200 c = $ 7.50 just divide the equation by 5 and you will get what u are looking for 20 p + 40 c = $ 1.50 therefore oa is d"
Answer: d
Python program:
a = 20 / 100
b = a * 7
Problem: the average age of 20 students in a class is 15 years . if the age of teacher is also included , the average becomes 16 years , find the age of the teacher .
Options: a ) 35 , b ) 38 , c ) 45 , d ) 36 , e ) 60
Rationale: "explanation : if teacher ' s age is 15 years , there is no change in the average . but teacher has contributed 1 year to all the students along with maintaining his age at 16 . age of teacher = average age of all + total increase in age = 16 + ( 1 x 20 ) = 36 years answer : d"
Answer: d
Python program:
a = 20 * 15
b = a + 16 
c = b + 20 
d = 20 * 15
e = c - d
Problem: in how many t ways can 4 white and 3 black chess pieces be arranged in a row such that they occupy alternate places ? assume that the pieces are distinct .
Options: a ) t = 288 , b ) t = 144 , c ) t = 12 , d ) 48 , e ) 96
Rationale: 4 white chess pieces can be arranged in 4 ! ways and 4 black pieces can be arranged in 3 ! ways . w _ w _ w _ w number of ways = 4 ! * 3 ! = 24 * 6 = 144 answer b
Answer: b
Python program:
a = math.factorial(3)
b = math.factorial(4)
c = a * b
Problem: a baseball card decreased in value 20 % in its first year and 10 % in its second year . what was the total percent decrease of the card ' s value over the two years ?
Options: a ) 28 % , b ) 30 % , c ) 32 % , d ) 36 % , e ) 72 %
Rationale: "let the initial value of baseball card = 100 after first year , value of baseball card = ( 1 - 20 / 100 ) * 100 = 80 after second year , value of baseball card = ( 1 - 10 / 100 ) * 80 = 72 total percent decrease of the card ' s value over the two years = ( 100 - 72 ) / 100 * 100 % = 28 % answer a"
Answer: a
Python program:
a = 10 / 100
b = 1 - a
c = 20 / 100
d = 1 - c
e = b * d
f = e * 100
g = 100 - f
Problem: 1393 x 1393 = ?
Options: a ) a ) 1951609 , b ) b ) 1951601 , c ) c ) 1940449 , d ) d ) 1951603 , e ) e ) 1951604
Rationale: "1393 x 1393 = ( 1393 ) 2 = ( 1400 - 7 ) 2 = ( 1400 ) 2 + ( 7 ) 2 - ( 2 x 1400 x 7 ) = 1960000 + 49 - 19600 = 1960049 - 19600 = 1940449 . answer : c"
Answer: c
Python program:
a = 1393 / 1393
b = a * 100
Problem: two alloys a and b are composed of two basic elements . the ratios of the compositions of the two basic elements in the two alloys are 5 : 3 and 5 : 1 , respectively . a new alloy x is formed by mixing the two alloys a and b in the ratio 4 : 3 . what is the ratio of the composition of the two basic elements in alloy x ?
Options: a ) 1 : 1 , b ) 2 : 3 , c ) 5 : 2 , d ) 4 : 3 , e ) 7 : 9
Rationale: "mixture a has a total of 5 + 3 = 8 parts . if in the final mixture this represents 4 parts , then the total number of parts in mixture b should be ( 8 / 4 ) * 3 = 6 . so , we should take of mixture b a quantity with 5 and 1 parts , respectively . this will give us in the final mixture ( 5 + 5 ) : ( 3 + 1 ) , which means 10 : 4 , or 5 : 2 . answer c ."
Answer: c
Python program:
a = 4 * 5
b = 5 + 3 
c = b / 2
d = 3 * c
e = a + d 
f = 4 * 3
g = 5 + 3 
h = g / 2
i = 3 * h
j = f + i 
k = e / j
Problem: how many liters of pure alcohol must be added to a 100 - liter solution that is 20 percent alcohol in order to produce a solution that is 24 percent alcohol ?
Options: a ) 7 / 2 , b ) 5 , c ) 20 / 3 , d ) 100 / 19 , e ) 39 / 4
Rationale: "20 % alcohol solution means ; in the 100 liter solution , 20 liters of solution is alcohol and 80 liters other solvents . if we addxliters of alcohol to the solution , the solution becomes 100 + xliters and alcohol , which was 20 liters , becomes 20 + x liters . according to the statement ; 20 + x = 24 % of ( 100 + x ) or 20 + x = ( 100 + x ) 6 / 25 500 + 25 x = 600 + 6 x 19 x = 100 x = 100 / 19 ans : d"
Answer: d
Python program:
a = 4 + 3 
b = 100 / a
Problem: a room 8 m 47 cm long and 7 m 77 cm broad is to be paved with square tiles . find the least number of square tiles required to cover the floor .
Options: a ) 13636 , b ) 13440 , c ) 13647 , d ) 13431 , e ) 13675
Rationale: "explanation : area of the room = ( 847 x 777 ) cm 2 . size of largest square tile = h . c . f . of 847 cm and 777 cm = 7 cm . area of 1 tile = ( 7 x 7 ) cm 2 . number of tiles required = ( 847 × 777 ) / ( 7 × 7 ) = 13431 answer : option d"
Answer: d
Python program:
a = 8 * 100
b = a + 47 
c = 7 * 100
d = c + 77 
e = b * d
f = 2 * 4
g = f + 2 
h = 47 - g
i = 2 * 4
j = i + 2 
k = 47 - j
l = h * k
m = e / l
Problem: if x and y are numbers such that ( x + 8 ) ( y - 8 ) = 0 , what is the smallest possible value of x ^ 2 + y ^ 2
Options: a ) 4 , b ) 24 , c ) 54 , d ) 64 , e ) 94
Rationale: "from ( x + 8 ) ( y - 8 ) = 0 it follows that either , x = - 8 or y = 8 . thus either x ^ 2 = 64 or y ^ 2 = 64 . now , if x ^ 2 = 64 , then the least value of y ^ 2 is 0 , so the least value of x ^ 2 + y ^ 2 = 64 + 0 = 64 . similarly if y ^ 2 = 64 , then the least value of x ^ 2 is 0 , so the least value of x ^ 2 + y ^ 2 = 0 + 64 = 64 . answer : d ."
Answer: d
Python program:
a = 8 ** 2
Problem: what will be the compound interest on rs . 50000 after 3 years at the rate of 12 % per annum
Options: a ) rs 20123.20 , b ) rs 20246.4 , c ) rs 20123.40 , d ) rs 20123.50 , e ) none of these
Rationale: "explanation : ( 50000 × ( 1 + 12 / 100 ) 3 ) = > 50000 × 28 / 25 × 28 / 25 × 28 / 25 = > 70246.4 so compound interest will be 70246.4 - 50000 = rs 20246.4 option b"
Answer: b
Python program:
a = 4 * 100
b = a * 100
c = 12 / 100
d = 1 + c 
e = d ** 3
f = b * e
g = 4 * 100
h = g * 100
i = f - h
Problem: dick and jane each saved $ 1000 in 1989 . in 1990 dick saved 15 percent more than in 1989 , and together he and jane saved a total of $ 2000 . approximately what percent less did jane save in 1990 than in 1989 ?
Options: a ) 3 % , b ) 5 % , c ) 10 % , d ) 15 % , e ) 18 %
Rationale: 1990 dick saved = $ 1150 jane saved = $ 850 ( jane saved $ 150 less than she did the prior year ) jane saved approximately $ 150 / 1000 $ ( 15 % ) less in 1990 answer : d
Answer: d
Python program:
a = 15 / 100
b = a * 1000
c = b + 1000 
d = 2000 - c
e = 1000 - d
f = 1000 / 100
g = e / f
Problem: calculate the share of y , if rs . 2690 is divided among x , y and z in the ratio 5 : 7 : 9 ?
Options: a ) 890.7 , b ) 826.7 , c ) 895.7 , d ) 896.7 , e ) 816.7
Rationale: "5 + 7 + 9 = 21 2690 / 21 = 128.1 y ' s share = 7 * 128.1 = 896.7 answer : d"
Answer: d
Python program:
a = 5 + 7 
b = a + 9 
c = 2690 / b
d = c * 5
Problem: the perimeter of an equilateral triangle is 45 . if one of the side is the side of an isoceles triangle of perimeter 40 then what is the lenght of base of isoceles triangle .
Options: a ) 10 units , b ) 20 units , c ) 30 units , d ) 40 units , e ) 15 units
Rationale: "base of isoceles triangle is 40 - 15 - 15 = 10 units . answer : a"
Answer: a
Python program:
a = 45 / 3
b = 40 - a
c = 45 / 3
d = b - c
Problem: a lemonade stand sold only small and large cups of lemonade on tuesday . 3 / 5 of the cups sold were small and the rest were large . if the large cups were sold for 5 / 6 as much as the small cups , what fraction of tuesday ' s total revenue was from the sale of large cups ?
Options: a ) 7 / 16 , b ) 7 / 15 , c ) 10 / 21 , d ) 17 / 35 , e ) 5 / 14
Rationale: "let the total # of cups be 10 . # of small cups sold 3 / 5 * 10 = 6 ; # of large cups sold 10 - 6 = 4 ; let the price of small cup be $ 6 , then the price of larges cup would be 5 / 6 * 6 = $ 5 ; revenue from small cups : 6 * $ 6 = $ 36 ; revenue from large cups cups : 4 * $ 5 = $ 20 ; fraction of total revenue from large cups : 20 / ( 36 + 20 ) = 5 / 14 . answer : e"
Answer: e
Python program:
a = 3 / 5
b = a * 10
c = 10 - b
d = 5 / 6
e = 3 / 5
f = e * 10
g = d * f
h = c * g
i = 3 / 5
j = i * 10
k = 3 / 5
l = k * 10
m = j * l
n = 3 / 5
o = n * 10
p = 10 - o
q = 5 / 6
r = 3 / 5
s = r * 10
t = q * s
u = p * t
v = m + u 
w = h / v
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 4860 . what was the number of original inhabitants ?
Options: a ) 7000 , b ) 7200 , c ) 7400 , d ) 7600 , e ) 7800
Rationale: let the total number of original inhabitants be x . ( 75 / 100 ) * ( 90 / 100 ) * x = 4860 ( 27 / 40 ) * x = 4860 x = 4860 * 40 / 27 = 7200 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 = 4860 / g
Problem: worker a takes 7 hours to do a job . worker b takes 10 hours to do the same job . how long it take both a & b , working together but independently , to do the same job ?
Options: a ) 70 / 17 , b ) 40 / 9 , c ) 50 / 9 , d ) 60 / 9 , e ) 80 / 9
Rationale: "one day work of a = 1 / 7 one day work of b = 1 / 10 so one day work of a and b together = 1 / 7 + 1 / 10 = 17 / 70 so total days required = 70 / 17 answer : a"
Answer: a
Python program:
a = 1 / 7
b = 1 / 10
c = a + b 
d = 1 / c
Problem: in what time will a train 200 meters long cross an electric pole , if its speed is 128 km / hr
Options: a ) 5 seconds , b ) 5.7 seconds , c ) 3 seconds , d ) 2.5 seconds , e ) none of these
Rationale: "explanation : first convert speed into m / sec speed = 128 * ( 5 / 18 ) = 35 m / sec time = distance / speed = 200 / 35 = 5.7 seconds option b"
Answer: b
Python program:
a = 128 * const_0_2778
b = 200 / a
Problem: 4 , 12 , 48 , 240 , 1440 , 10080,80640 , 725760 ( . . . )
Options: a ) 7257600 , b ) 10080 , c ) 6200 , d ) 10020 , e ) 12500
Rationale: "explanation : go on multiplying the given numbers by 3 , 4 , 5 , 6 , 7,8 , 9,10 answer : option a"
Answer: a
Python program:
a = negate - (
Problem: if rs . 10 be allowed as true discount on a bill of rs . 110 at the end of a certain time , then the discount allowed on the same sum due at the end of double the time is ?
Options: a ) 68.33 , b ) 18.33 , c ) 28.33 , d ) 48.33 , e ) 98.33
Rationale: explanation : present worth = amount - truediscount = 110 - 10 = rs . 100 si on rs . 100 for a certain time = rs . 10 si on rs . 100 for doube the time = rs . 20 truediscount on rs . 120 = 120 - 100 = rs . 20 truediscount on rs . 110 = = rs . 18.33 answer : b
Answer: b
Python program:
a = 10 + 110 
b = a - 100
c = 10 + 110 
d = b / c
e = 110 * d
Problem: a train 120 m long running at 60 kmph crosses a platform in 20 sec . what is the length of the platform ?
Options: a ) 213 , b ) 298 , c ) 350 , d ) 726 , e ) 267
Rationale: "d = 60 * 5 / 18 = 20 = 333 â € “ 120 = 213 answer : a"
Answer: a
Python program:
a = 60 * const_0_2778
b = 20 * a
c = b - 120
Problem: two pipes a and b can fill a tank in 12 hours and 15 hours respectively . if both pipe open together in tank , then how much time it take to fill the tank ?
Options: a ) 15 , b ) 18 , c ) 20 / 3 , d ) 19 / 4 , e ) 25 / 4
Rationale: in 1 hour pipe a fill = 1 / 12 in 1 hour pipe b fill = 1 / 15 pipe ( a + b ) in 1 hour = [ 1 / 12 + 1 / 15 ] = 3 / 20 total time taken to fill the tank = 20 / 3 hour answer c
Answer: c
Python program:
a = 1 / 12
b = 1 / 15
c = a + b 
d = 1 / c
Problem: when a number is divided by 13 , the remainder is 6 . when the same number is divided by 7 , then remainder is 1 . what is the number ?
Options: a ) 243 , b ) 253 , c ) 312 , d ) 432 , e ) none of these
Rationale: "explanation : take 243 243 ÷ 7 = 34 , remainder = 5 hence this is not the answer take 312 312 ÷ 7 = 44 , remainder = 4 hence this is not the answer take 253 253 ÷ 7 = 36 , remainder = 1 . 253 ÷ 13 = 19 , remainder = 6 this satisfies both the conditions given in the question . hence it is the answer . answer : b"
Answer: b
Python program:
a = 10 + 12 
b = a + 4 
c = 13 * b
d = c + 6
Problem: for the past n days , the average ( arithmetic mean ) daily production at a company was 60 units . if today ' s production of 90 units raises the average to 62 units per day , what is the value of n ?
Options: a ) 30 , b ) 14 , c ) 10 , d ) 9 , e ) 7
Rationale: "( average production for n days ) * n = ( total production for n days ) - - > 60 n = ( total production for n days ) ; ( total production for n days ) + 90 = ( average production for n + 1 days ) * ( n + 1 ) - - > 60 n + 90 = 62 * ( n + 1 ) - - > n = 14 . or as 30 extra units increased the average for n + 1 days by 2 units per day then 30 / ( n + 1 ) = 2 - - > n = 14 . answer : b ."
Answer: b
Python program:
a = 90 - 60
b = 62 - 60
c = a / b
d = c - 1
Problem: james took a 3 - hour bike ride . in the second hour he travlled 24 miles , which was 20 percent farther than he traveled the first hour . if he traveled 25 percent farther in the third hour than he did in the second hour , how many miles did jose travel during the entire ride ?
Options: a ) 74.0 , b ) 54.9 , c ) 55.5 , d ) 57.0 , e ) 63.0
Rationale: "let the distance travelled in the first hour be x . thus , 1.2 x = 24 , x = 20 . now , the distance travelled in the 3 rd hour = 24 + 1 / 4 â ˆ — 24 = 30 . = 24 + 20 + 30 = 74 answer : a"
Answer: a
Python program:
a = 1 * 100
b = a * 24
c = 1 * 100
d = c + 20 
e = b / d
f = 25 * 24
g = f / 20
h = e + g 
i = h + 24
Problem: a rectangular block 6 cm by 12 cm by 15 cm is cut up into an exact number of equal cubes . find the least possible number of cubes .
Options: a ) 30 , b ) 40 , c ) 10 , d ) 20 , e ) 50
Rationale: "explanation : volume of the block = ( 6 x 12 x 15 ) cm 3 = 1080 cm 3 side of the largest cube = h . c . f . of 6 cm , 12 cm , 15 cm = 3 cm . volume of this cube = ( 3 x 3 x 3 ) cm 3 = 27 cm 3 number of cubes = ( 1080 / 27 ) = 40 . answer : b"
Answer: b
Python program:
a = rectangle_area / (
b = a - 10
c = 3 * 2
d = 1000 * c
e = b + d 
f = 3 * 1000
g = 15 * 10
h = f + g 
i = e / h
Problem: a train 360 m long is running at a speed of 45 km / hr . in what time will it pass a bridge 390 m long ?
Options: a ) 40 sec , b ) 60 sec , c ) 45 sec , d ) 48 sec , e ) 50 sec
Rationale: "speed = 45 * 5 / 18 = 25 / 2 m / sec total distance covered = 360 + 140 = 750 m required time = 750 * 2 / 25 = 40 sec answer : b"
Answer: b
Python program:
a = 45 - 390
b = a * const_0_2778
c = 360 / b
Problem: an empty fuel tank with a capacity of 200 gallons was filled partially with fuel a and then to capacity with fuel b . fuel a contains 12 % ethanol by volume and fuel b contains 16 % ethanol by volume . if the full fuel tank contains 20 gallons of ethanol , how many gallons of fuel a were added ?
Options: a ) 300 , b ) 150 , c ) 100 , d ) 80 , e ) 50
Rationale: "say there are a gallons of fuel a in the tank , then there would be 200 - a gallons of fuel b . the amount of ethanol in a gallons of fuel a is 0.12 a ; the amount of ethanol in 200 - a gallons of fuel b is 0.16 ( 200 - a ) ; since the total amount of ethanol is 20 gallons then 0.12 a + 0.16 ( 200 - a ) = 20 - - > a = 300 . answer : a ."
Answer: a
Python program:
a = 16 / 100
b = 200 * a
c = b - 20
d = 16 / 100
e = 12 / 100
f = d - e
g = c / f
Problem: the circus sells two kinds of tickets : lower seats for $ 30 and upper seats for $ 20 . on a certain night , the circus sells 80 tickets and gets $ 2100 in revenue from the sales . how many tickets for lower seats did they sell ?
Options: a ) 40
b ) 45
c ) 50
d ) 55
e ) 60
Rationale: let l be the number of lower seat tickets . let u be the number of upper seat tickets . l + u = 80 and u = 80 - l . 30 l + 20 u = 2100 . 30 l + 20 ( 80 - l ) = 2100 10 l + 1600 = 2100 . 10 l = 500 . l = 50 . the answer is c .
Answer: c
Python program:
a = 30 * 80
b = a - 2100
c = 30 - 20
d = b / c
e = 80 - d
Problem: the average weight of 8 persons increases by 1.5 kg . if a person weighing 65 kg is replaced by a new person , what could be the weight of the new person ?
Options: a ) 76 kg , b ) 77 kg , c ) 76.5 kg , d ) data inadequate , e ) none of these
Rationale: "total weight increases = 8 × 1.5 = 12 kg so the weight of new person = 65 + 12 = 77 kg answer b"
Answer: b
Python program:
a = 8 * 1
b = 65 + a
Problem: the speed at which a man can row a boat in still water is 26 kmph . if he rows downstream , where the speed of current is 4 kmph , what time will he take to cover 150 metres ?
Options: a ) 18 , b ) 27 , c ) 28 , d ) 12 , e ) 25
Rationale: speed of the boat downstream = 26 + 4 = 30 kmph = 30 * 5 / 18 = 8.33 m / s hence time taken to cover 150 m = 150 / 8.33 = 18 seconds . answer : a
Answer: a
Python program:
a = 26 + 4 
b = a * const_0_2778
c = 150 / b
Problem: a mathematics teacher tabulated the marks secured by 35 students of 8 th class . the average of their marks was 72 . if the marks secured by reema was written as 35 instead of 99 then find the correct average marks up to two decimal places .
Options: a ) 73.41 , b ) 74.31 , c ) 72.43 , d ) 73.43 , e ) 73.82
Rationale: "total marks = 35 x 72 = 2520 corrected total marks = 2520 - 35 + 99 = 2584 correct average = 2584 / 35 = 73.82 answer : e"
Answer: e
Python program:
a = 35 * 72
b = 99 - 35
c = a - b
d = c / 35
Problem: two employees m and n are paid a total of $ 572 per week by their employer . if m is paid 120 percent of the salary paid to n , how much is n paid per week ?
Options: a ) $ 220 , b ) $ 240 , c ) $ 260 , d ) $ 300 , e ) $ 320
Rationale: "1.2 n + n = 572 2.2 n = 572 n = 260 the answer is c ."
Answer: c
Python program:
a = 120 / 100
b = a + 1 
c = 572 / b
Problem: if rs . 527 be divided among a , b , c in such a way that a gets 2 / 3 of what b gets and b gets 1 / 4 of what c gets , then their shares are respectively ?
Options: a ) s . 300 , b ) s . 360 , c ) s . 389 , d ) s . 368 , e ) s . 372
Rationale: ( a = 2 / 3 b and b = 1 / 4 c ) = a / b = 2 / 3 and b / c = 1 / 4 a : b = 2 : 3 and b : c = 1 : 4 = 3 : 12 a : b : c = 2 : 3 : 12 a ; s share = 527 * 2 / 17 = rs . 62 b ' s share = 527 * 3 / 17 = rs . 93 c ' s share = 527 * 12 / 17 = rs . 372 . answer : e
Answer: e
Python program:
a = 2 / 3
b = 1 / 4
c = a * b
d = 1 / 4
e = c + d 
f = e + 1 
g = 527 / f
Problem: the annual interest rate earned by an investment increased by 10 percent from last year to this year . if the annual interest rate earned by the investment this year was 9 percent , what was the annual interest rate last year ?
Options: a ) 1 % , b ) 1.1 % , c ) 8.18 % , d ) 10 % , e ) 10.8 %
Rationale: "9 = 1.1 * x x = 8.18 % answer c )"
Answer: c
Python program:
a = 9 * 100
b = 9 + 100 
c = a / b
Problem: in what ratio should a variety of rice costing rs . 6 per kg be mixed with another variety of rice costing rs . 8.75 per kg to obtain a mixture costing rs . 7.50 per kg ?
Options: a ) 1 / 68 , b ) 62 / 89 , c ) 12 / 68 , d ) 11 / 84 , e ) 5 / 6
Rationale: "explanation : let us say the ratio of the quantities of cheaper and dearer varieties = x : y by the rule of allegation , x / y = ( 87.5 - 7.50 ) / ( 7.50 - 6 ) = 5 / 6 answer : e"
Answer: e
Python program:
a = 8 - 75
b = 8 - 75
c = a / b
d = 8 - 75
e = 8 - 75
f = d / e
g = 1 - f
h = c / g
Problem: a driver goes on a trip of 60 kilometers , the first 30 kilometers at 60 kilometers per hour and the remaining distance at 30 kilometers per hour . what is the average speed of the entire trip in kilometers per hour ?
Options: a ) 35 , b ) 36 , c ) 40 , d ) 42 , e ) 45
Rationale: "the time for the first part of the trip was 30 / 60 = 1 / 2 hours . the time for the second part of the trip was 30 / 30 = 1 hour . the total time for the trip was 3 / 2 hours . the average speed for the trip was 60 / ( 3 / 2 ) = 40 kph the answer is c ."
Answer: c
Python program:
a = 30 / 60
b = 60 - 30
c = b / 30
d = a + c 
e = 60 / d
Problem: a certain meter records voltage between 0 and 10 volts inclusive . if the average value of 3 recordings on the meter was 7 volts , what was the smallest possible recording in volts ?
Options: a ) 2 , b ) 3 , c ) 4 , d ) 5 , e ) 6
Rationale: "if average of 3 is 7 so sum of 3 should be 21 3 recording can be from 0 - 10 inclusive to find one smallest other two should be highest so , lets assume three var are a , b , c say a is smallest and give b and c greatest readings say 9 and 9 so a has to be 3 b"
Answer: b
Python program:
a = 3 * 7
b = a - 10
Problem: the perimeter of one square is 48 cm and that of another is 28 cm . find the perimeter and the diagonal of a square which is equal in area to these two combined ?
Options: a ) 13 √ 4 , b ) 13 √ 2 , c ) 23 √ 2 , d ) 13.9 √ 2 , e ) 13 √ 9
Rationale: "4 a = 48 4 a = 28 a = 12 a = 7 a 2 = 144 a 2 = 49 combined area = a 2 = 193 = > a = 13.9 d = 13.9 √ 2 answer : d"
Answer: d
Python program:
a = 48 / 4
b = a ** 2
c = 28 / 4
d = c ** 2
e = b + d 
f = e * 2
g = math.sqrt(f)
Problem: two bullet train s 140 m and 160 m long run at the speed of 60 km / hr and 40 km / hr respectively in opposite directions on parallel tracks . the time ( in seconds ) which they take to cross each other , is :
Options: a ) 15.8 sec . , b ) 12.8 sec . , c ) 11.8 sec . , d ) 10.8 sec . , e ) 08.8 sec .
Rationale: "d 10.8 sec . relative speed = ( 60 + 40 ) km / hr = 100 x 5 / 18 = 250 / 9 m / sec . distance covered in crossing each other = ( 140 + 160 ) m = 300 m . required time = 300 x 9 / 250 = 54 / 5 = 10.8 sec ."
Answer: d
Python program:
a = 140 + 160 
b = 60 + 40 
c = b * const_0_2778
d = a / c