euclaise/mathqa_programs huggingface dataset:
Problem: a sum of rs . 2769 is lent into two parts so that the interest on the first part for 8 years at 3 % per annum may be equal to the interest on the second part for 3 years at 5 % per annum . find the second sum ?
Options: a ) 1642 , b ) 1640 , c ) 1632 , d ) 2789 , e ) 1704
Rationale: "( x * 8 * 3 ) / 100 = ( ( 2769 - x ) * 3 * 5 ) / 100 24 x / 100 = 41535 / 100 - 15 x / 100 39 x = 41535 = > x = 1065 second sum = 2769 – 1065 = 1704 answer : e"
Answer: e
Python program:
a = 3 * 5
b = a * 2769
c = 3 * 5
d = 8 * 3
e = c + d 
f = b / e
g = 2769 - f
Problem: ( 0.0077 ) ( 3.6 ) / ( 0.04 ) ( 0.1 ) ( 0.007 ) =
Options: a ) 0.099 , b ) 0.0099 , c ) 9.9 , d ) 990 , e ) 99
Rationale: "( 0.0077 ) ( 3.6 ) / ( 0.04 ) ( 0.1 ) ( 0.007 ) = 0.0077 * 360 / 4 * ( 0.1 ) ( 0.007 ) = 0.077 * 90 / 1 * 0.007 = 77 * 90 / 7 = 11 * 90 = 990 answer : d"
Answer: d
Python program:
a = 0 * 77
b = 0 * 4
c = b * 0
d = a / c
Problem: in a certain candy store , 22 % of the customers are caught sampling the candy and are charged a small fine , but 12 % of the customers who sample the candy are not caught . what is the total percent of all customers who sample candy ?
Options: a ) 22 % , b ) 23 % , c ) 24 % , d ) 25 % , e ) 34 %
Rationale: "since 12 % of the customers who sample the candy are not caught , then 88 % of the customers who sample the candy are caught : { % of customers who sample candy } * 0.88 = 0.22 ; { % of customers who sample candy } = 0.25 . answer : d ."
Answer: d
Python program:
a = 100 - 12
b = a / 100
c = 22 / b
Problem: a lent rs . 5000 to b for 2 years and rs . 3000 to c for 4 years on simple interest at the same rate of interest and received rs . 1760 in all from both of them as interest . the rate of interest per annum is ?
Options: a ) 16 % , b ) 12 % , c ) 74 % , d ) 10 % , e ) 8 %
Rationale: "let the rate be r % p . a . then , ( 5000 * r * 2 ) / 100 + ( 3000 * r * 4 ) / 100 = 1760 100 r + 120 r = 1760 r = 8 % answer : e"
Answer: e
Python program:
a = 5000 * 2
b = 3000 * 4
c = a + b 
d = 1760 / c
e = d * 100
Problem: out of 4 numbers , the average of first 3 is 20 and that of the last 3 is 15 . if the last number is 18 , the first number is :
Options: a ) 22 , b ) 33 , c ) 77 , d ) 99 , e ) 27
Rationale: explanation : let the numbers be a , b , c , d given , a + b + c = 60 , b + c + d = 45 now , d = 18 thus , b + c + 18 = 45 ⇒ b + c = 27 putting the value of b + c in a + b + c = 60 a + 27 = 60 ⇒ a = 33 answer : b
Answer: b
Python program:
a = 20 * 3
b = 15 * 3
c = b - 18
d = a - c
Problem: 4 car rental agencies a , b , c and d rented a plot for parking their cars during the night . a parked 15 cars for 12 days , b parked 12 cars for 20 days , c parked 18 cars for 18 days and d parked 16 cars for 15 days . if a paid rs . 1125 as rent for parking his cars , what is the total rent paid by all the 4 agencies ?
Options: a ) rs . 6152 , b ) rs . 6159 , c ) rs . 6156 , d ) rs . 6150 , e ) rs . 6196
Rationale: the ratio in which the four agencies will be paying the rents = 15 * 12 : 12 * 20 : 18 * 18 : 16 * 15 = 180 : 240 : 324 : 240 = 45 : 60 : 81 : 60 let us consider the four amounts to be 45 k , 60 k , 81 k and 60 k respectively . the total rent paid by the four agencies = 45 k + 60 k + 81 k + 60 k = 246 k it is given that a paid rs . 1125 45 k = 1125 = > k = 25 246 k = 246 ( 25 ) = rs . 6150 thus the total rent paid by all the four agencies is rs . 6150 . answer : d
Answer: d
Python program:
a = 16 / 15
b = a * 1125
c = 15 / 12
d = b / c
e = 18 / 18
f = e * 1125
g = 15 / 12
h = f / g
i = d + h 
j = 12 / 20
k = j * 1125
l = 15 / 12
m = k / l
n = i + m 
o = n + 1125 
p = 4 * 100
q = o - p
r = q * 2
Problem: harry started a 7 - mile hike with a full 9 - cup canteen of water and finished the hike in 2 hours with 3 cup of water remaining in the canteen . if the canteen leaked at the rate of 1 cup per hour and harry drank 2 cups of water during the last mile , how many cups did he drink per mile during the first 6 miles of the hike ?
Options: a ) 1 / 6 , b ) 2 / 6 , c ) 3 / 6 , d ) 4 / 6 , e ) 5 / 6
Rationale: "no of cups leaked during the trip = 2 cups . no of cups harry drank = 6 cups . no of cups harry drank during the first 6 miles = 4 . drink / mile = 4 / 6 answer d"
Answer: d
Python program:
a = 9 - 2
b = a - 2
c = b - 1
d = c / 6
Problem: the banker ' s gain on a sum due 6 years hence at 12 % per annum is rs . 900 . what is the banker ' s discount ?
Options: a ) 1240 , b ) 1120 , c ) 1190 , d ) 2150 , e ) none of these
Rationale: "explanation : td = ( bg × 100 ) / tr = ( 900 × 100 ) / ( 6 × 12 ) = rs . 1250 bg = bd – td = > 900 = bd - 1250 = > bd = 2150 answer : option d"
Answer: d
Python program:
a = 900 * 100
b = 12 * 6
c = a / b
d = 900 + c
Problem: 8 ^ 100 is divisible by 17 . find the remainder for this ?
Options: a ) 10 , b ) 12 , c ) 16 , d ) 17 , e ) 19
Rationale: "this is an extremely difficult problem to solve with out fermat ' s little theorem . by applying fermat ' s little theorem , we know that 816 when divided by 17 , the remainder is 1 . so divide 100 by 16 and find the remainder . remainder = 4 therefore , 100 = ( 16 × 6 ) + 4 now this problem can be written as 810017 = 816 × 6 + 417 = ( 816 ) 6 × 8417 now this problem simply boils down to ( 1 ) 6 × 8417 = 8417 84 = 82 × 82 , we need to find the remainder when 64 × 64 is divisible by 17 . or 13 × 13 = 169 . when 169 is divided by 17 , remainder is 16 . c"
Answer: c
Python program:
a = 17 - 8
Problem: a shopkeeper sold an book offering a discount of 5 % and earned a profit of 42.5 % . what would have been the percentage of profit earned if no discount was offered ?
Options: a ) 140 , b ) 120 , c ) 130 , d ) 110 , e ) 150
Rationale: "let c . p . be $ 100 . then , s . p . = $ 142.50 let marked price be $ x . then , 95 / 100 x = 142.5 x = 14250 / 95 = $ 150 now , s . p . = $ 150 , c . p . = $ 100 profit % = 50 % . e"
Answer: e
Python program:
a = 100 + 42 
b = 100 - 5
c = a / b
d = 100 * c
Problem: a driver would have reduced the time it took to drive from home to the store by 1 / 4 if the average speed had been increased by 10 miles per hour . what was the actual average speed , in miles per hour , when the driver drove from home to the store ?
Options: a ) 12 , b ) 15 , c ) 20 , d ) 25 , e ) 30
Rationale: since the distance remains the same ( we ' re just changing the rate and time ) , any increase in rate or time is met with a decrease in the other term . decreasing the time by 1 / 4 would give us : d = ( r ) ( t ) = ( 3 t / 4 ) ( x * r ) x = 4 / 3 since ( 3 t / 4 ) ( 4 r / 3 ) = ( r ) ( t ) = d 4 r / 3 = r + 10 r / 3 = 10 r = 30 the answer is e .
Answer: e
Python program:
a = 1 / 4
b = 1 - a
c = b * 10
d = 1 / 4
e = 1 - d
f = 1 - e
g = c / f
Problem: a can do a job in 15 days and b can do it in 30 days . a and b working together will finish twice the amount of work in - - - - - - - days ?
Options: a ) 14 days , b ) 16 days , c ) 20 days , d ) 11 days , e ) 19 days
Rationale: "c 1 / 15 + 1 / 30 = 1 / 10 10 * 2 = 20 days"
Answer: c
Python program:
a = 1 / 15
b = 1 / 30
c = a + b
Problem: at a supermarket , john spent 1 / 2 of his money on fresh fruits and vegetables , 1 / 3 on meat products , and 1 / 10 on bakery products . if he spent the remaining $ 10 on candy , how much did john spend at the supermarket ?
Options: a ) $ 60 , b ) $ 80 , c ) $ 90 , d ) $ 120 , e ) $ 150
Rationale: "let ' s let t = total number of dollars spent at the supermarket . with this variable we can set up an equation and determine t . we are given that john spent 1 / 2 of his money on fresh fruits and vegetables , or ( 1 / 2 ) t , 1 / 3 on meat products , or ( 1 / 3 ) t , and 1 / 10 on bakery products , or ( 1 / 10 ) t . we are also given that he spent the remaining $ 10 on candy . since we know where all his money was allocated , we can sum these values together and set the sum to t . so we have : ( 1 / 2 ) t + ( 1 / 3 ) t + ( 1 / 10 ) t + 10 = t to get rid of the fractions we can multiply the entire equation by 30 , and we obtain : 15 t + 10 t + 3 t + 300 = 30 t 28 t + 300 = 30 t 300 = 2 t t = 150 john spent $ 90 at the supermarket . answer : e"
Answer: e
Python program:
a = 1 / 10
b = 1 / 3
c = a + b 
d = 1 / 2
e = c + d 
f = 1 - e
g = 10 / f
Problem: the h . c . f . of two numbers is 12 and their l . c . m . is 600 . if one of the number is 120 , find the other ?
Options: a ) 100 , b ) 60 , c ) 120 , d ) 200 , e ) 150
Rationale: "other number = 12 * 600 / 120 = 60 answer is b"
Answer: b
Python program:
a = 12 * 120
Problem: 66.2 is what percent of 1000 ?
Options: a ) 6.62 , b ) 66.2 , c ) 662 , d ) 0.662 , e ) 0.0662
Rationale: "we assume that 1000 is 100 % assume ' x ' is value we looking for here , 1000 = 100 % and x % = 66.2 therefore , 100 / x = 1000 / 66.2 100 / x = 15.105 x = 6.62 a"
Answer: a
Python program:
a = 66 / 2
b = a * 100
Problem: if the sum and difference of two numbers are 5 and 10 respectively , then the difference of their square is :
Options: a ) 50 , b ) 28 , c ) 160 , d ) 180 , e ) 18
Rationale: "let the numbers be x and y . then , x + y = 5 and x - y = 10 x 2 - y 2 = ( x + y ) ( x - y ) = 5 * 10 = 50 . answer : a"
Answer: a
Python program:
a = 5 + 10 
b = a / 2
c = b ** 2
d = 5 + 10 
e = d / 2
f = 5 - e
g = f ** 2
h = c - g
Problem: find the least number which when divided by 56 , 78 leaves a remainder 3 but when divided by 9 leaves no remainder
Options: a ) 9632 , b ) 7896 , c ) 8741 , d ) 1683 , e ) 8523
Rationale: l . c . m of 5,6 , 7,8 = 840 required number is of the form of 840 k + 3 least value of k for which ( 840 k + 3 ) is divided by 9 is k = 2 required number = ( 840 * 2 + 3 ) = 1683 answer ( d )
Answer: d
Python program:
a = 2 + 3 
b = 3 + 3 
c = a * b
d = 3 + 4 
e = c * d
f = 4 + 4 
g = e * f
Problem: what is the average of first 21 multiples of 8 ?
Options: a ) a ) 70 , b ) b ) 77 , c ) c ) 79 , d ) d ) 81 , e ) e ) 88
Rationale: "required average = 8 ( 1 + 2 + . . . . + 21 ) / 21 ( 8 / 21 ) x ( ( 21 x 22 ) / 2 ) ( because sum of first 21 natural numbers ) = 88 e"
Answer: e
Python program:
a = 21 + 1 
b = 21 * a
c = b / 2
d = c / 21
e = d * 8
Problem: a invested $ 150 in a business after 6 months b invested $ 200 in the business . end of the year if they got $ 100 as profit . find a shares ?
Options: a ) $ 100 , b ) $ 75 , c ) $ 20 , d ) $ 120 , e ) $ 60
Rationale: "a : b = 150 * 12 : 200 * 6 a : b = 3 : 2 a ' s share = 100 * 3 / 5 = $ 60 answer is e"
Answer: e
Python program:
a = 200 / 2
b = 200 / 2
c = 150 + b 
d = a / c
e = 1 - d
f = 100 * e
Problem: for any number y , y * is defined as the greatest positive even integer less than or equal to y . what is the value of 9.2 – 9.2 * ?
Options: a ) 0.2 , b ) 1.2 , c ) 1.8 , d ) 2.2 , e ) 4.0
Rationale: "since y * is defined as the greatest positive even integer less than or equal to y , then 9.2 * = 8 ( the greatest positive even integer less than or equal to 9.2 is 4 ) . hence , 9.2 – 9.2 * = 9.2 - 8 = 1.2 answer : b ."
Answer: b
Python program:
a = math.floor(9, 2)
b = a - 1
c = 9 - 2
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 . 1.40 per meter . two gates of 1 m width each are to be left for entrance . what is the total cost ?
Options: a ) 399 , b ) 272 , c ) 932.4 , d ) 277 , e ) 311
Rationale: "answer : option c explanation : a 2 = 3136 = > a = 56 56 * 4 * 3 = 672 â € “ 6 = 666 * 1.4 = 932.4 answer : c"
Answer: c
Python program:
a = math.sqrt(3136)
b = a * 4
c = 2 * 1
d = b - c
e = d * 1
f = e * 3
Problem: $ 400 is divided amongst a , b and c so that a may get 2 / 3 as much as b and c together , b may get 6 / 9 as much as a and c together , then the share of a is
Options: a ) $ 100 , b ) $ 150 , c ) $ 160 , d ) $ 200 , e ) $ 250
Rationale: "a : ( b + c ) = 2 : 3 a ' s share = 400 * 2 / 5 = $ 160 answer is c"
Answer: c
Python program:
a = 2 / 3
b = a + 1 
c = 400 / b
d = 2 / 3
e = c * d
Problem: 2 . the value of x + x ( xx ) when x = 2 is :
Options: a ) 5 , b ) 10 , c ) 8 , d ) 15 , e ) 20
Rationale: x + x ( xx ) put the value of x = 2 in the above expression we get , 2 + 2 ( 22 ) = 2 + 2 ( 2 × 2 ) = 2 + 2 ( 4 ) = 2 + 8 = 10 answer : b
Answer: b
Python program:
a = 2 * 2
b = a * 2
c = b + 2
Problem: find the value of x from the below equation ? : x ^ 2 + 5 x + 25 = 0
Options: a ) no answer , b ) 25 , c ) 1 , d ) 0 , e ) - 2
Rationale: "a = 1 , b = 5 , c = 25 x 1,2 = ( - 5 â ± â ˆ š ( 5 ^ 2 - 4 ã — 1 ã — 25 ) ) / ( 2 ã — 1 ) = ( - 5 â ± â ˆ š ( 25 - 100 ) ) / 2 = ( - 5 â ± â ˆ š - 75 ) / 2 no real roots a"
Answer: a
Python program:
a = 5 ** 2
b = 25 * 25
c = a - b
d = math.sqrt(c)
e = 5 - d
f = e / 2
Problem: a doctor prescribed 18 cubic centimeters of a certain drug to a patient whose body weight was 75 pounds . if the typical dosage is 2 cubic centimeters per 15 pounds of the body weight , by what percent was the prescribed dosage greater than the typical dosage ?
Options: a ) 8 % , b ) 9 % , c ) 11 % , d ) 12.5 % , e ) 20 %
Rationale: "typical dosage is dose : weight : : 2 : 15 . now if weight is 75 : ( 75 / 15 ) ) then typical dosage would be 2 * 5 = 10 cc . dosage = 18 cc . dosage is greater by 2 cc . % dosage is greater : ( 2 / 10 ) * 100 = 20 % e is the answer ."
Answer: e
Python program:
a = 2 / 15
b = a * 75
c = b - 18
d = 2 / 15
e = d * 75
f = c / e
g = f * 100
Problem: if two positive numbers are in the ratio 1 / 7 : 1 / 5 , then by what percent is the second number more than the first ?
Options: a ) 70 % , b ) 90 % , c ) 60 % , d ) 40 % , e ) 65 %
Rationale: "given ratio = 1 / 7 : 1 / 5 = 5 : 7 let first number be 5 x and the second number be 7 x . the second number is more than first number by 2 x . required percentage = 2 x / 5 x * 100 = 40 % . answer : d"
Answer: d
Python program:
a = 1 / 5
b = a * 100
Problem: 30.5 % of 2000
Options: a ) 556 , b ) 612.5 , c ) 756.8 , d ) 610 , e ) 820
Rationale: 1 % of 2000 = 20 30 % of 2000 = 30 * 20 = 600 0.5 % of 2000 = 0.5 * 2000 = 10 total = 610 answer : d
Answer: d
Python program:
a = 30 / 5
b = a * 100
Problem: if the operation x is defined by a x b = ( b - a ) ^ 2 / a ^ 2 for all numbers a and b , and a ≠ 0 , then − 1 x ( 1 x − 1 ) =
Options: a ) − 1 , b ) 0 , c ) 1 , d ) 25 , e ) 29
Rationale: on solving the inner bracket we get 4 . then we get equation as - 1 x 4 where b = 4 and a = - 1 answer d
Answer: d
Python program:
a = negate - (
b = a ** 1
c = b - 2
d = c ** negate
Problem: the two lines y = x and x = - 3 intersect on the coordinate plane . if z represents the area of the figure formed by the intersecting lines and the x - axis , what is the side length of a cube whose surface area is equal to 6 z ?
Options: a ) 16 , b ) 3 / √ 2 , c ) 8 , d ) 2 √ 2 , e ) ( √ 2 ) / 3
Rationale: 800 score official solution : the first step to solving this problem is to actually graph the two lines . the lines intersect at the point ( - 3 , - 3 ) and form a right triangle whose base length and height are both equal to 4 . as you know , the area of a triangle is equal to one half the product of its base length and height : a = ( 1 / 2 ) bh = ( 1 / 2 ) ( 3 × 3 ) = 9 / 2 ; so z = 9 / 2 . the next step requires us to find the length of a side of a cube that has a face area equal to 9 / 2 . as you know the 6 faces of a cube are squares . so , we can reduce the problem to finding the length of the side of a square that has an area of 9 / 2 . since the area of a square is equal to s ² , where s is the length of one of its side , we can write and solve the equation s ² = 9 / 2 . clearly s = √ 9 / 2 = 3 / √ 2 , oranswer choice ( b ) .
Answer: b
Python program:
a = 3 * 3
b = a / 2
c = math.sqrt(b)
Problem: subtracting 4 % of a from a is equivalent to multiplying a by how much ?
Options: a ) 0.96 , b ) 9.4 , c ) 0.094 , d ) 94 , e ) none
Rationale: "answer let a - 4 % of a = ab . ⇒ ( 96 x a ) / 100 = ab ∴ b = 0.96 correct option : a"
Answer: a
Python program:
a = 100 - 4
b = a / 100
Problem: each of the integers from 0 to 9 , inclusive , is written on a separate slip of blank paper and the ten slips are dropped into a hat . if 5 of the slips are the drawn , without replacement , what is the probability that all 5 have a even number written on it ?
Options: a ) 1 / 252 , b ) 1 / 10 , c ) 1 / 8 , d ) 1 / 2 , e ) 5 / 9
Rationale: "key is that there is no replacement , so each successive choice will become more skewed towards picking a neg ( i . e . the pool of positives decreases , while the pool of negatives stay the same ) p ( + on 1 st pick ) = 5 / 10 p ( + on 2 nd pick ) = 4 / 9 p ( + on 3 rd pick ) = 3 / 8 p ( + on 4 rd pick ) = 2 / 7 p ( + on 5 rd pick ) = 1 / 6 5 / 10 * 4 / 9 * 3 / 8 * 2 / 7 * 1 / 6 = 1 / 252 a"
Answer: a
Python program:
a = 4 + 1 
b = 9 + 1 
c = a / b
d = 5 + 1 
e = d - 1
f = 9 + 1 
g = f - 1
h = e / g
i = c * h
j = 5 + 1 
k = j - 1
l = k - 1
m = 9 + 1 
n = m - 1
o = n - 1
p = l / o
q = i * p
r = 5 + 1 
s = r - 1
t = s - 1
u = t - 1
v = 9 + 1 
w = v - 1
x = w - 1
y = x - 1
z = u / y
A = q * z
Problem: if a and b are integers and ( a * b ) ^ 5 = 32 y , y could be :
Options: a ) 16 , b ) 1 , c ) 8 , d ) 12 , e ) 24
Rationale: "distribute the exponent . a ^ 5 * b ^ 5 = 32 y find the prime factorization of 32 . this is 2 ^ 5 * 1 . we need 1 the answer is b ."
Answer: b
Python program:
a = 2 ** 5
b = 32 / a
c = b * 2
Problem: it was calculated that 100 men could complete a piece of work in 20 days . when work was scheduled to commence , it was found necessary to send 50 men to another project . how much longer will it take to complete the work ?
Options: a ) 45 days . , b ) 40 days . , c ) 38 days . , d ) 35 days . , e ) 30 days .
Rationale: one day work = 1 / 20 one man ’ s one day work = 1 / ( 20 * 100 ) now : no . of workers = 50 one day work = 50 * 1 / ( 20 * 100 ) the total no . of days required to complete the work = ( 100 * 20 ) / 50 = 40 answer : b
Answer: b
Python program:
a = 100 / 50
b = 20 * a
Problem: if a is thrice as fast as b and together can do a work in 15 days . in how many days a alone can do the work ?
Options: a ) 36 , b ) 20 , c ) 28 , d ) 54 , e ) 45
Rationale: "a ’ s one day ’ s work = 1 / x b ’ s one day ’ s work = 1 / 3 x a + b ’ s one day ’ s work = 1 / x + 1 / 3 x = 1 / 15 = 3 + 1 / 3 x = 4 / 3 x = 1 / 15 x = 15 * 4 / 3 = 20 answer : b"
Answer: b
Python program:
a = 15 * 4
b = 3 / a
c = 1/(b)
Problem: average of 5 numbers is - 10 , and the sum of 3 of the numbers is 16 , wat is the average of the other 2 numbers ?
Options: a ) - 33 , b ) 33 , c ) 35 , d ) 36 , e ) - 35
Rationale: let the five numbers be a , b , c , d , e . then their average is ( a + b + c + d + e 5 ) = 10 . ( a + b + c + d + e 5 ) = 10 . now three of the numbers have a sum of 16 , say , a + b + c = 16 a + b + c = 16 . so substitute 16 for a + b + ca + b + c in the average above : ( 16 + d + e 5 ) = 10 . ( 16 + d + e 5 ) = 10 . solving this equation for d + ed + e gives d + e = − 66 d + e = − 66 . finally , dividing by 2 ( to form the average ) gives ( d + e 2 ) = − 33 . ( d + e 2 ) = − 33 . hence , the answer is a : - 33
Answer: a
Python program:
a = 5 * 10
b = a - 16
c = b / 2
Problem: if | 4 x + 6 | = 50 , what is the sum of all the possible values of x ?
Options: a ) 2 , b ) - 2 , c ) 4 , d ) - 3 , e ) 6
Rationale: "there will be two cases 4 x + 6 = 50 or 4 x + 6 = - 50 = > x = 11 or x = - 14 sum of both the values will be - 14 + 11 = - 3 answer is d"
Answer: d
Python program:
a = 50 - 6
b = a / 4
Problem: a merchant sells an item at a 20 % discount , but still makes a gross profit of 20 percent of the cost . what percent e of the cost would the gross profit on the item have been if it had been sold without the discount ?
Options: a ) 20 % , b ) 40 % , c ) 50 % , d ) 60 % , e ) 75 %
Rationale: "let the market price of the product is mp . let the original cost price of the product is cp . selling price ( discounted price ) = 100 % of mp - 20 % mp = 80 % of mp . - - - - - - - - - - - - - - - - ( 1 ) profit made by selling at discounted price = 20 % of cp - - - - - - - - - - - - - - ( 2 ) apply the formula : profit e = selling price - original cost price = > 20 % of cp = 80 % of mp - 100 % cp = > mp = 120 cp / 80 = 3 / 2 ( cp ) now if product is sold without any discount , then , profit = selling price ( without discount ) - original cost price = market price - original cost price = mp - cp = 3 / 2 cp - cp = 1 / 2 cp = 50 % of cp thus , answer should bec ."
Answer: c
Python program:
a = 100 - 20
b = a - 20
c = 100 - b
Problem: the cost price of a radio is rs . 2300 and it was sold for rs . 1800 , find the loss % ?
Options: a ) 18 , b ) 99 , c ) 27 , d ) 26 , e ) 21
Rationale: "2300 - - - - 500 100 - - - - ? = > 21 % answer : e"
Answer: e
Python program:
a = 2300 - 1800
b = a / 2300
c = b * 100
Problem: a and b can finish a work 30 days if they work together . they worked together for 20 days and then b left . a finished the remaining work in another 20 days . in how many days a alone can finish the work ?
Options: a ) 30 , b ) 60 , c ) 40 , d ) 20 , e ) 50
Rationale: amount of work done by a and b in 1 day = 1 / 30 amount of work done by a and b in 20 days = 20 × ( 1 / 30 ) = 20 / 30 = 2 / 3 remaining work – 1 – 2 / 3 = 1 / 3 a completes 1 / 3 work in 20 days amount of work a can do in 1 day = ( 1 / 3 ) / 20 = 1 / 60 = > a can complete the work in 60 days answer is b .
Answer: b
Python program:
a = 30 - 20
b = 20 / a
c = 30 * b
Problem: 0.0004 ? = 0.01
Options: a ) 4 , b ) 0.4 , c ) 0.04 , d ) 40 , e ) none of these
Rationale: "explanation : required answer = 0.0004 / 0.01 = 0.04 / 1 = 0.04 . answer : option c"
Answer: c
Python program:
a = 0 / 4
b = a * 100
Problem: 860 % of 50 + 50 % of 860 = ?
Options: a ) 430 , b ) 516 , c ) 660 , d ) 860 , e ) none
Rationale: "solution given expression = [ 860 / 100 x 50 + 50 / 100 x 860 ] = 430 + 430 = 860 . answer d"
Answer: d
Python program:
a = 860 * 50
b = a / 50
Problem: in a lake , there is a patch of lily pads . every day , the patch doubles in size . it takes 39 days for the patch to cover the entire lake , how many days would it take the patch to cover half of the lake ?
Options: a ) 36 , b ) 2 ^ 4 * 3 , c ) 24 , d ) 38 , e ) 47
Rationale: "working backward from the day it ' s covered : day 39 : fully covered day 38 : half covered so 38 days answer : d"
Answer: d
Python program:
a = 39 - 1
Problem: find the product of the localvalue and absolutevalue of 4 in 20468 ?
Options: a ) 1000 , b ) 1100 , c ) 1200 , d ) 1300 , e ) 1600
Rationale: "local value of 4 = 4 x 100 = 400 place value of 4 = 4 there fore = 4 x 400 = 1600 e"
Answer: e
Python program:
a = 4 * 1000
b = a * 4
Problem: marcella has 20 pairs of shoes . if she loses 9 individual shoes , what is the greatest number of matching pairs she could have left ?
Options: a ) 21 , b ) 20 , c ) 19 , d ) 16 , e ) 15
Rationale: "marcella has 20 pairs of shoes and loses 9 shoes . to minimize the loss of identical pairs of shoes we want marcella to lose as many identical pairs as possible . this would yield 4 identical pairs and 1 additional shoe ( destroying 5 pairs of shoes ) . the 20 pairs of shoes minus the 5 ' destroyed ' pairs yields 15 pairs that still fulfill the requirements . answer : e"
Answer: e
Python program:
a = 9 / 2
b = math.floor(a)
c = b + 1 
d = 20 - c
Problem: a miniature roulette wheel is divided into 10 equal sectors , each bearing a distinct integer from 1 to 10 , inclusive . each time the wheel is spun , a ball randomly determines the winning sector by settling in that sector . if the wheel is spun five times , approximately what is the probability that the product of the five winning sectors ’ integers will be even ?
Options: a ) 50 % , b ) 67 % , c ) 85 % , d ) 91 % , e ) 97 %
Rationale: "the only way to have an odd product is if all 5 integers are odd . p ( odd product ) = 1 / 2 * 1 / 2 * 1 / 2 * 1 / 2 * 1 / 2 = 1 / 32 p ( even product ) = 1 - 1 / 32 = 31 / 32 which is about 97 % the answer is e ."
Answer: e
Python program:
a = 10 / 2
b = a / 10
c = b ** 2
d = 1 - c
e = d * 100
Problem: on a map , 7 centimeters represents 35 kilometers . two cities 245 kilometers apart would be separated on the map by how many centimeters ?
Options: a ) 15 , b ) 37 , c ) 49 , d ) 110 , e ) 180
Rationale: 1 centimeter represents 5 kilometers ( 35 / 7 ) x = 245 / 5 = 49 answer : c
Answer: c
Python program:
a = 7 / 35
b = a * 245