euclaise/mathqa_programs huggingface dataset:
Problem: in cliff ’ s impressive rock collection , there are half as many igneous rocks as sedimentary rocks . of the igneous rocks , 3 / 5 are shiny and the rest are matte , while 1 / 5 of the sedimentary rocks are shiny . if there are 30 shiny igneous rocks , how many total rocks does cliff have ?
Options: a ) 30 , b ) 45 , c ) 60 , d ) 150 , e ) 135
Rationale: "we can start with the known quantity and then go on to find the others . shiny igneous ricks are 30 . these are ( 3 / 5 ) of total igneous rocks . ( 3 / 5 ) * total igneous rocks = 30 total igneous rocks = 30 * ( 5 / 3 ) = 50 total sedimentary rocks = 2 * total igneous rocks = 2 * 50 = 100 total number of rocks = 50 + 100 = 150 answer ( d )"
Answer: d
Python program:
a = 3 * 5
b = a * 30
c = b / 3
d = c * 5
e = d / 3
Problem: there are 20 poles with a constant distance between each pole . a car takes 22 second to reach the 12 th pole . how much will it take to reach the last pole .
Options: a ) 38 , b ) 41 , c ) 28 , d ) 88 , e ) 22
Rationale: "assuming the car starts at the first pole . to reach the 12 th pole , the car need to travel 11 poles ( the first pole does n ' t count , as the car is already there ) . 11 poles 22 seconds 1 pole ( 22 / 11 ) seconds to reach the last ( 20 th ) pole , the car needs to travel 19 poles . 19 pole 19 x ( 22 / 11 ) seconds = 38 seconds answer : a"
Answer: a
Python program:
a = 22 / 12
b = a * 20
Problem: meena wrote all the numbers from 1 to 39,999 inclusive . how many digits did she write in total ?
Options: a ) 156,789 , b ) 188,889 , c ) 192,389 , d ) 241,689 , e ) 275,889
Rationale: 1 - 9 = > 1 * 9 digits 10 - 99 = > 2 * 90 = 180 ( numbers between 10 - 99 is 90 where each has 2 digits ) 100 - 999 = > 3 * 900 = 2700 1000 - 9999 = > 4 * 9000 = 36,000 10000 - 39999 = > 5 * 30,000 = 150,000 the answer is 188,889 the answer is b .
Answer: b
Python program:
a = 10 - 1
b = 100 - 10
c = b * 2
d = a + c 
e = 100 - 10
f = e * 3
g = d + f 
h = 100 - 10
i = h * 4
j = g + i
Problem: solution a is 20 % salt and solution b is 70 % salt . if you have 30 ounces of solution a and 60 ounces of solution b , in what ratio could you mix solution a with solution b to produce 50 ounces of a 50 % salt solution ?
Options: a ) 6 : 4 , b ) 6 : 14 , c ) 2 : 3 , d ) 4 : 6 , e ) 3 : 7
Rationale: "forget the volumes for the time being . you have to mix 20 % and 80 % solutions to get 50 % . this is very straight forward since 50 is int he middle of 20 and 80 so we need both solutions in equal quantities . if this does n ' t strike , use w 1 / w 2 = ( a 2 - aavg ) / ( aavg - a 1 ) w 1 / w 2 = ( 70 - 50 ) / ( 50 - 20 ) = 2 / 3 so the volume of the two solutions will be equal . answer has to be 2 : 3 c"
Answer: c
Python program:
a = 70 / 100
b = 50 * a
c = 50 / 100
d = 50 * c
e = b - d
f = 70 / 100
g = 20 / 100
h = f - g
i = e / h
j = 70 / 100
k = 50 * j
l = 50 / 100
m = 50 * l
n = k - m
o = 70 / 100
p = 20 / 100
q = o - p
r = n / q
s = 50 - r
t = i / s
Problem: what is the smallest integer that satisfies the inequality ( x - 3 ) / ( x ^ 2 - 8 x - 20 ) > 0 > 0 ?
Options: a ) - 2 , b ) 10 , c ) 3 , d ) - 1 , e ) 0
Rationale: "explanatory answer let us factorize the denominator and rewrite the expression as x − 3 / ( x − 10 ) ( x + 2 ) > 0 equate each of the terms of the expression to zero to identify the values of x that are relevant to test whether the inequality holds good . the values that are relevant to us are x = 3 , x = 10 and x = - 2 . let us arrange these values in ascending order : - 2 , 3 and 10 . the quickest way to solve inequalities questions after arriving at these values is verifying whether the inequality holds good at the following intervals . interval 1 : x < - 2 . pick a value in that range and check whether the inequality holds good . let us take x = - 10 . when x = - 10 , x − 3 / ( x − 10 ) ( x + 2 ) < 0 ; the inequality does not hold good in this interval . interval 2 : - 2 < x < 3 . let us take x = 0 . when x = 0 , x − 3 / ( x − 10 ) ( x + 2 ) = 0 − 3 / ( 0 − 10 ) ( 0 + 2 ) > 0 ; the inequality holds good in this interval . the least integer value that x can take if x > - 2 is x = - 1 . so , the correct answer is - 1 . choice d . remember : we have to find out the least integer value . and we have arrived at - 1 . do , not waste time computing the entire range of values of x that satisfy the inequality . note : in any inequality question , when the question asks us to determine the intervals in which the inequality holds good , we have to eliminate values of x that will result in the denominator becoming zero . choice d"
Answer: d
Python program:
a = negate - (
b = a / 3
Problem: in a 100 m race , a covers the distance in 36 seconds and b in 45 second . in this race a beats b by :
Options: a ) 20 m , b ) 25 m , c ) 22.5 m , d ) 9 m , e ) none of these
Rationale: "solution distance covered by b in 9 sec . = ( 100 / 45 x 9 ) m = 20 m . ∴ a beats b by 20 metres . answer a"
Answer: a
Python program:
a = 100 / 45
b = 45 - 36
c = a * b
Problem: a owner of a mart earns an income of re 1 on the first day of his business . on every subsequent day , he earns an income which is just double of that made on the previous day . on the 10 th day of business , he earns an income of :
Options: a ) 18 , b ) 21 , c ) 22 , d ) 20 , e ) 30
Rationale: 2 nd day he earns = 2 ( 2 – 1 ) 3 rd day he earns = 2 ( 3 – 1 ) on 10 th day he earns 2 ( 10 - 1 ) = 18 rupees answer : a
Answer: a
Python program:
a = 4 * 2
b = 10 + a
Problem: if p = 125 × 243 × 16 / 405 , how many digits are in p ?
Options: a ) 1 , b ) 2 , c ) 3 , d ) 4 , e ) 5
Rationale: p = 125 * 243 * 16 / 405 p = 5 ^ 3 * 3 * 9 ^ 2 * 4 ^ 2 / ( 5 * 9 ^ 2 ) p = 5 ^ 2 * 3 * 4 ^ 2 p = 20 ^ 2 * 3 = 1200 answer d
Answer: d
Python program:
a = 4 + 1 
b = 405 / a
c = 243 / b
d = c * 16
e = 4 + 1 
f = 125 / e
g = d * f
h = 100 * 3
i = g / h
Problem: jane started baby - sitting when she was 18 years old . whenever she baby - sat for a child , that child was no more than half her age at the time . jane is currently 34 years old , and she stopped baby - sitting 10 years ago . what is the current age of the oldest person for whom jane could have baby - sat ?
Options: a ) 20 , b ) 21 , c ) 22 , d ) 23 , e ) 25
Rationale: "check two extreme cases : jane = 18 , child = 9 , years ago = 34 - 18 = 16 - - > child ' s age now = 9 + 16 = 25 ; jane = 24 , child = 12 , years ago = 34 - 24 = 10 - - > child ' s age now = 12 + 10 = 22 . answer : e ."
Answer: e
Python program:
a = 18 / 2
b = 34 - 18
c = a + b
Problem: from the sale of sleeping bags , a retailer made a gross profit of 17 % of the wholesale cost . if each sleeping bag was sold for $ 28 , what was the wholesale cost per bag ?
Options: a ) 3.0 , b ) 3.36 , c ) 23.93 , d ) 25.0 , e ) 31.36
Rationale: "cost price * 1.17 = selling price - - > cost price * 1.17 = $ 28 - - > cost price = $ 23.93 . answer : c ."
Answer: c
Python program:
a = 28 * 100
b = 100 + 17 
c = a / b
Problem: mixture contains alcohol and water in the ratio 4 : 3 . if 6.5 liters of water is added to the mixture , the ratio becomes 4 : 5 . find the quantity of alcohol in the given mixture .
Options: a ) 10 , b ) 99 , c ) 27 , d ) 22 , e ) 5.6
Rationale: let the quantity of alcohol and water be 4 x litres and 3 x litres respectively 26 x = 4 ( 3 x + 5 ) 14 x = 20 x = 1.4 quantity of alcohol = ( 4 x 1.4 ) litres = 5.6 litres . answer : e
Answer: e
Python program:
a = 4 * 5
b = 6 * 5
c = 3 * 4
d = b - c
e = a / d
f = e * 4
Problem: the cost of carpeting a room 18 m long with a carpet 75 cm wide at 4.50 per metre is 810 . the breadth of the room is :
Options: a ) 7 m , b ) 7.5 m , c ) 8 m , d ) 8.5 m , e ) none of these
Rationale: length of the carpet = totalcost / rate / m = ( 8100 ⁄ 45 ) m = 180 m . area of the room = area of the carpet = ( 180 × 75 ⁄ 100 ) m 2 = 135 m 2 ∴ breadth of the room = arealength = 135 / 18 m = 7.5 m answer b
Answer: b
Python program:
a = 810 / 4
b = 75 / 100
c = a * b
d = c / 18
Problem: a farmer with 1350 acres of land had planted his fields with corn , sugar cane , and tobacco in the ratio of 5 : 2 : 2 , respectively , but he wanted to make more money , so he shifted the ratio to 2 : 2 : 5 , respectively . how many more acres of land were planted with tobacco under the new system ?
Options: a ) 90 , b ) 150 , c ) 270 , d ) 300 , e ) 450
Rationale: originally ( 2 / 9 ) * 1350 = 300 acres were planted with tobacco . in the new system ( 5 / 9 ) * 1350 = 750 acres were planted with tobacco . thus 750 - 300 = 450 more acres were planted with tobacco . the answer is e .
Answer: e
Python program:
a = 1350 * 3
b = 5 + 2 
c = b + 2 
d = a / c
Problem: the area of a square field 3136 sq m , if the length of cost of drawing barbed wire 3 m around the field at the rate of rs . 3.00 per meter . two gates of 1 m width each are to be left for entrance . what is the total cost ?
Options: a ) s . 1014 , b ) s . 1140 , c ) s . 1998 , d ) s . 1085 , e ) s . 1020
Rationale: "a 2 = 3136 = > a = 56 56 * 4 * 3 = 672 – 6 = 666 * 3.0 = 1998 answer : c"
Answer: c
Python program:
a = math.sqrt(3136)
b = a * 4
c = 2 * 1
d = b - c
e = d * 3
f = e * 3
Problem: the ratio by weight , measured in pounds , of books to clothes to electronics in a suitcase initially stands at 5 : 4 : 2 . someone removes 9 pounds of clothing from the suitcase , thereby doubling the ratio of books to clothes . how many pounds do the electronics in the suitcase weigh ?
Options: a ) 7 , b ) 8 , c ) 9 , d ) 10 , e ) 11
Rationale: "the weights of the items in the suitcase are 5 k , 4 k , and 2 k . if removing 9 pounds of clothes doubles the ratio of books to clothes , then 9 pounds represents half the weight of the clothes . 2 k = 9 pounds and then k = 4.5 pounds . the electronics weigh 2 ( 4.5 ) = 9 pounds . the answer is c ."
Answer: c
Python program:
a = 5 + 4 
b = a + 2 
c = b * 9
d = negate / (
e = 5 + 4 
f = e + 2 
g = f * 2
h = 5 + 4 
i = h + 2 
j = i * 4
k = g - j
l = 2 * d
Problem: for a race a distance of 224 meters can be covered by p in 7 seconds and q in 32 seconds . by what distance does p defeat q eventually ?
Options: a ) 800 m , b ) 838 m , c ) 834 m , d ) 831 m , e ) 836 m
Rationale: "explanation : this is a simple speed time problem . given conditions : = > speed of p = 224 / 7 = 32 m / s = > speed of q = 224 / 32 = 7 m / s = > difference in time taken = 25 seconds therefore , distance covered by p in that time = 32 m / s x 25 seconds = 800 metres answer : a"
Answer: a
Python program:
a = 7 * speed
b = 224 - a
Problem: in a particular state , 70 % of the counties received some rain on monday , and 55 % of the counties received some rain on tuesday . no rain fell either day in 35 % of the counties in the state . what percent of the counties received some rain on monday and tuesday ?
Options: a ) 20 % , b ) 40 % , c ) 50 % , d ) 60 % , e ) 70 %
Rationale: 70 + 55 + 35 = 160 % the number is 60 % above 100 % because 60 % of the counties were counted twice . the answer is d .
Answer: d
Python program:
a = 70 + 55 
b = 100 - 35
c = a - b
Problem: the present worth of a certain bill due sometime hence is rs . 400 and the true discount is rs . 20 . what is the banker ' s discount ?
Options: a ) rs . 19 , b ) rs . 22 , c ) rs . 20 , d ) rs . 21 , e ) none of these
Rationale: "explanation : bg = ( td ) 2 / pw = 202 / 400 = rs . 1 bg = bd – td = > 1 = bd - 20 = > bd = 1 + 20 = rs . 21 answer : option d"
Answer: d
Python program:
a = 20 ** 2
b = a / 400
c = 20 + b
Problem: the true discount on a bill of rs . 2660 is rs . 360 . what is the banker ' s discount ?
Options: a ) rs . 432 , b ) rs . 422 , c ) rs . 416 , d ) rs . 442 , e ) none of these
Rationale: "explanation : f = rs . 2660 td = rs . 360 pw = f - td = 2660 - 360 = rs . 2300 true discount is the simple interest on the present value for unexpired time = > simple interest on rs . 2300 for unexpired time = rs . 360 banker ' s discount is the simple interest on the face value of the bill for unexpired time = simple interest on rs . 2160 for unexpired time = 360 / 2300 × 2660 = 0.16 × 2660 = rs . 416 answer : option c"
Answer: c
Python program:
a = 2660 - 360
b = 360 / a
c = b * 2660
Problem: a train covered half of the distance between stations a and b at the speed of 48 km / hr , but then it had to stop for 15 min . to make up for the delay , it increased its speed by 53 m / sec and it arrived to station b on time . find the distance between the two stations and the speed of the train after the stop .
Options: a ) 206 , b ) 216 , c ) 226 , d ) 256 , e ) 246
Rationale: first let us determine the speed of the train after the stop . the speed was increased by 53 m / sec = 5 ⋅ 60 ⋅ 6031000 km / hr = 6 km / hr . therefore , the new speed is 48 + 6 = 54 km / hr . if it took x hours to cover the first half of the distance , then it took x − 1560 = x − 0.25 hr to cover the second part . so the equation is : 48 ⋅ x = 54 ⋅ ( x − 0.25 ) 48 ⋅ x = 54 ⋅ x − 54 ⋅ 0.25 48 ⋅ x − 54 ⋅ x = − 13.5 − 6 x = − 13.5 x = 2.25 h . the whole distance is 2 × 48 × 2.25 = 216 km . answer is b .
Answer: b
Python program:
a = 3 * 2
b = 48 + a 
c = 15 / const_60
d = b * c
e = 3 * 2
f = d / e
g = f * 48
h = g * 2
Problem: a certain city with a population of 84,000 is to be divided into 11 voting districts , and no district is to have a population that is more than 10 percent greater than the population of any other district what is the minimum possible population that the least populated district could have ?
Options: a ) a ) 10,700 , b ) b ) 10,800 , c ) c ) 7,000 , d ) d ) 11,000 , e ) e ) 11,100
Rationale: "let x = number of people in smallest district x * 1.1 = number of people in largest district x will be minimised when the number of people in largest district is maximised 10 * x * 1.1 = 11 x = total number of people in other districts so we have 11 x + x = 84 k x = 7,000 answer : c"
Answer: c
Python program:
a = 4 * 2
b = a * 100
Problem: if the number 892 , 132,27 x is divisible by 11 , what must be the value of x ?
Options: a ) 1 , b ) 2 , c ) 3 , d ) 4 , e ) 5
Rationale: "multiplication rule of 11 : ( sum of digits at odd places - sum of digits at even places ) should be divisible by 11 given number : 892 , 132,27 x sum of digits at odd places = 8 + 2 + 3 + 2 + x = 15 + x ( i ) sum of digits at even places = 9 + 1 + 2 + 7 = 19 ( ii ) ( i ) - ( ii ) = 15 + x - 19 = x - 4 hence x should be = 4 to make this a multiple of 11 ( 0 ) option d"
Answer: d
Python program:
a = 3 * 10
b = a + 1 
c = b * 2
d = c * 4
e = d * 11
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 , 8.0 , 9.0 , 6.0 , and 8.8 , what was the point value of the dive ?
Options: a ) 68.8 , b ) 73.6 , c ) 75.2 , d ) 76.8 , e ) 77.76
Rationale: "degree of difficulty of dive = 3.2 scores are 6.0 , 7.5 , 8.0 , 8.8 and 9.0 we can drop 6.0 and 9.0 sum of the remaining scores = ( 7.5 + 8 + 8.8 ) = 24.3 point of value of the dive = 24 * 3.2 = 77.76 answer e"
Answer: e
Python program:
a = 7 + 5 
b = a + 8 
c = b * 3
Problem: square p is inscribed in circle q . if the perimeter of p is 40 , what is the circumference of q ?
Options: a ) 11 √ 2 π
b ) 10 √ 2 π
c ) 9 √ 2 π
d ) 8 √ 2 π
e ) 7 √ 2 π
Rationale: square forms two right angled triangles . any time we have a right angle triangle inside a circle , the hypotenuse is the diameter . hypotenuse here = diagonal of the square = 10 sqrt ( 2 ) = diameter = > radius = 5 sqrt ( 2 ) circumference of the circle = 2 pi r = 10 pi sqrt ( 2 ) answer is b .
Answer: b
Python program:
a = 2 * math.pi
b = 40 / 4
c = b ** 2
d = 40 / 4
e = d ** 2
f = c + e 
g = math.sqrt(f)
h = g / 2
i = a * h
Problem: the sum of the first n positive perfect squares , where n is a positive integer , is given by the formula n ^ 3 / 3 + c * n ^ 2 + n / 6 , where c is a constant . what is the sum of the first 19 positive perfect squares ?
Options: a ) 1,010 , b ) 1,164 , c ) 1,240 , d ) 1,316 , e ) 2,470
Rationale: "first we need to find the constant ' c ' . the easiest way to find this is for the sum of the first two perfect squares for 1 and 2 = 1 and 4 respectively . hence lhs = 1 + 4 and plug n = 2 for rhs and simplify to get c = 1 / 2 . plug values of n = 19 and c = 1 / 2 into the equation and simplify to get the answer 2470 . option e ."
Answer: e
Python program:
a = 19 + 1 
b = 19 * a
c = 19 * 2
d = c + 1 
e = b * d
f = e / 6
g = 19 + 1 
h = 19 * g
i = 19 * 2
j = i + 1 
k = h * j
l = k / 6
m = f / l
Problem: a shopkeeper sells his goods at cost price but uses a faulty meter that weighs 800 grams . find the profit percent .
Options: a ) 20 , b ) 15 , c ) 25 , d ) 18 , e ) 19
Rationale: "explanation : ( 100 + g ) / ( 100 + x ) = true measure / faulty measure x = 0 true measure = 1000 faulty measure = 800 100 + g / 100 + 0 = 1000 / 800 100 + g = 5 / 4 * 100 g = 25 answer : c"
Answer: c
Python program:
a = 4 + 1 
b = 4 + 1 
c = a + b 
d = c * 100
e = d - 800
f = e / 800
g = f * 100
Problem: the unit digit in the product ( 293 * 567 * 917 * 343 ) is :
Options: a ) 2 , b ) 1 , c ) 6 , d ) 8 , e ) 10
Rationale: "explanation : unit digit in the given product = unit digit in ( 3 * 7 * 7 * 4 ) = 1 answer : b"
Answer: b
Python program:
a = 293 * 567
b = a * 917
c = b * 343
d = 293 * 567
e = d * 917
f = e * 343
g = 4 + 4 
h = f - g
i = c - h
Problem: what percent is 120 of 80 ?
Options: a ) 150 % , b ) 134 1 / 3 % , c ) 135 1 / 3 % , d ) 140 1 / 3 % , e ) 143 1 / 3 %
Rationale: "120 / 80 = 3 / 2 3 / 2 × 100 = 300 / 2 = 150 % a"
Answer: a
Python program:
a = 120 / 80
b = a * 100
Problem: a box has exactly 100 balls , and each ball is either red , blue , or white . if the box has 20 more blue balls than white balls , and thrice as many red balls as blue balls , how many white balls does the box has ?
Options: a ) 4 , b ) 10 , c ) 12 , d ) 14 , e ) 16
Rationale: "x = the number of red balls y = the number of blue balls z = the number of white balls from the first sentence we have equation # 1 : x + y + z = 100 . . . the box has 20 more blue balls than white balls . . . equation # 2 : y = 20 + z . . . thrice as many red balls as blue balls . . . equation # 3 : x = 3 y solve equation # 2 for z : z = y - 20 now , we can replace both x and z with y in equation # 1 3 y + y + ( y - 20 ) = 100 5 y - 20 = 100 5 y = 120 y = 24 there are 24 blue balls . this is 20 more than the number of white balls , so z = 4 . that ' s the answer . just as a check , x = 72 , and 72 + 24 + 4 = 100 . answer = 4 , ( a )"
Answer: a
Python program:
a = 20 * 3
b = 100 - a
c = b / 4
Problem: the cost of 2 chairs and 3 tables is rs . 1600 . the cost of 3 chairs and 2 tables is rs . 1200 . the cost of each table is more than that of each chair by ?
Options: a ) 228 , b ) 287 , c ) 277 , d ) 188 , e ) 400
Rationale: explanation : 2 c + 3 t = 1600 - - - ( 1 ) 3 c + 3 t = 1200 - - - ( 2 ) subtracting 2 nd from 1 st , we get - c + t = 400 = > t - c = 400 answer : e
Answer: e
Python program:
a = 3 * 1600
b = 2 * 1200
c = a - b
d = 3 * 3
e = 2 * 2
f = d - e
g = c / f
h = 3 * 1600
i = 2 * 1200
j = h - i
k = 3 * 3
l = 2 * 2
m = k - l
n = j / m
o = 2 * n
p = 1200 - o
q = p / 3
r = g - q
Problem: fox jeans regularly sell for $ 15 a pair and pony jeans regularly sell for $ 18 a pair . during a sale these regular unit prices are discounted at different rates so that a total of $ 6 is saved by purchasing 5 pairs of jeans : 3 pairs of fox jeans and 2 pairs of pony jeans . if the sum of the two discounts rates is 18 percent , what is the discount rate on pony jeans ?
Options: a ) 9 % , b ) 10 % , c ) 11 % , d ) 35 % , e ) 15 %
Rationale: "you know that fox jeans costs $ 15 , and pony jeans costs $ 18 , you also know that 3 pairs of fox jeans and 2 pairs of pony jeans were purchased . so 3 ( 15 ) = 45 - fox 2 ( 18 ) = 36 - pony the total discount discount is $ 6 and you are asked to find the percent discount of pony jeans , so 45 ( 18 - x ) / 100 + 36 ( x ) / 100 = 6 or 45 * 18 - 45 * x + 36 * x = 6 * 100 or 9 x = - 6 * 100 + 45 * 18 x = 210 / 6 = 35 % d"
Answer: d
Python program:
a = 18 / 100
b = 18 / 100
c = 18 * 2
d = b * c
e = 6 - d
f = 15 * 3
g = 18 * 2
h = f - g
i = e / h
j = a - i
k = j * 100
Problem: 90 students represent x percent of the boys at jones elementary school . if the boys at jones elementary make up 20 % of the total school population of x students , what is x ?
Options: a ) 125 , b ) 150 , c ) 212 , d ) 250 , e ) 500
Rationale: 90 = x / 100 * 20 / 100 * x = > x ^ 2 = 9 * 10000 / 2 = > x = 212 c
Answer: c
Python program:
a = 90 * 100
b = 20 / 100
c = a / b
d = math.sqrt(c)
Problem: a sells a bicycle to b and makes a profit of 20 % . b sells the same bicycle to c at a profit of 25 % . if the final s . p . of the bicycle was rs . 225 , find out the cost price of the bicycle for a .
Options: a ) 237 , b ) 126 , c ) 971 , d ) 611 , e ) 150
Rationale: "explanation : answer : e"
Answer: e
Python program:
a = 100 + 25 
b = a / 100
c = 225 / b
d = 20 + 100 
e = d / 100
f = c / e
Problem: 16 men take 21 days of 8 hours each to do a piece of work . how many days of 6 hours each would 21 women take to do the same . if 3 women do as much work as 2 men ?
Options: a ) 32 , b ) 87 , c ) 30 , d ) 99 , e ) 77
Rationale: "3 w = 2 m 16 m - - - - - - 21 * 8 hours 21 w - - - - - - x * 6 hours 14 m - - - - - - x * 6 16 * 21 * 8 = 14 * x * 6 x = 32 answer : a"
Answer: a
Python program:
a = 21 * 8
b = 16 * 3
c = a * b
d = 21 * 2
e = d * 6
f = c / e
g = math.floor(f)
h = g + 1
Problem: a and b complete a work in 4 days . a alone can do it in 6 days . if both together can do the work in how many days ?
Options: a ) 3.75 days , b ) 3.7 days , c ) 3.6 days , d ) 2.4 days , e ) 5.75 days
Rationale: "1 / 4 + 1 / 6 = 5 / 12 12 / 5 = 2.4 days answer : d"
Answer: d
Python program:
a = 1/(4)
b = 1/(6)
c = a + b 
d = 1/(c)
Problem: a 5 digit number divisible by 3 is to be formed using the digits 0 , 1 , 2 , 3 , 4 and 5 without repetitions . that total no of ways it can be done is ?
Options: a ) 122 , b ) 210 , c ) 216 , d ) 217 , e ) 220
Rationale: first step : we should determine which 5 digits from given 6 , would form the 5 digit number divisible by 3 . we have six digits : 0,1 , 2,3 , 4,5 . their sum = 15 . for a number to be divisible by 3 the sum of the digits must be divisible by 3 . as the sum of the six given numbers is 15 ( divisible by 3 ) only 5 digits good to form our 5 digit number would be 15 - 0 = ( 1 , 2,3 , 4,5 ) and 15 - 3 = ( 0 , 1,2 , 4,5 ) . meaning that no other 5 from given six will total the number divisible by 3 . second step : we have two set of numbers : 1 , 2,3 , 4,5 and 0 , 1,2 , 4,5 . how many 5 digit numbers can be formed using this two sets : 1 , 2,3 , 4,5 - - > 5 ! as any combination of these digits would give us 5 digit number divisible by 3 . 5 ! = 120 . 0 , 1,2 , 4,5 - - > here we can not use 0 as the first digit , otherwise number wo n ' t be any more 5 digit and become 4 digit . so , total combinations 5 ! , minus combinations with 0 as the first digit ( combination of 4 ) 4 ! - - > 5 ! - 4 ! = 96 120 + 96 = 216 answer : c .
Answer: c
Python program:
a = math.factorial(5)
b = 5 - 1
c = math.factorial(b)
d = 5 - 1
e = c * d
f = a + e
Problem: solution y is 30 percent liquid x and 70 percent water . if 2 kilograms of water evaporate from 8 kilograms of solutions y and 2 kilograms of solution y are added to the remaining 6 kilograms of liquid , what percent of this new liquid solution is liquid x ?
Options: a ) 30 % , b ) 33 1 / 3 % , c ) 37 1 / 2 % , d ) 40 % , e ) 50 %
Rationale: "at the beginning , you have 8 kg of solution y , i . e . 70 % * 8 kg = 5,6 kg of water 30 % * 8 kg = 2,4 kg of x 2 kg of water evaporate : 5,6 kg - 2 kg = 3,6 kg of water 2,4 kg of x 2 kg of liquid are added : 3,6 kg + 2 * 0,70 = 5 kg of water 2,4 kg + 2 * 0,30 = 3 kg of x so you have 3 kg of x in 8 kg ( 3 + 5 ) solution . therefore x concentration is 3 / 8 = 37,5 % answer : c"
Answer: c
Python program:
a = 30 / 100
b = 8 * a
c = 30 / 100
d = 2 * c
e = b + d 
f = 30 / 100
g = 8 * f
h = 30 / 100
i = 2 * h
j = g + i 
k = 70 / 100
l = 8 * k
m = l - 2
n = 70 / 100
o = 2 * n
p = m + o 
q = j + p 
r = e / q
s = 100 * r