euclaise/mathqa_programs huggingface dataset:
Problem: a horse is tethered to one corner of a rectangular grassy field 45 m by 25 m with a rope 22 m long . over how much area of the field can it graze ?
Options: a ) 354 cm 2 , b ) 380 m 2 , c ) 350 m 2 , d ) 407 m 2 , e ) none of these
Rationale: "area of the shaded portion = 1 ⁄ 4 × π × ( 22 ) 2 = 380 m 2 answer b"
Answer: b
Python program:
a = 22 ** 2
b = a * math.pi
c = b / 4
Problem: p and q started a business investing rs . 85,000 and rs . 35,000 respectively . in what ratio the profit earned after 2 years be divided between p and q respectively ?
Options: a ) 17 : 6 , b ) 17 : 0 , c ) 17 : 7 , d ) 17 : 2 , e ) 17 : 3
Rationale: p : q = 85000 : 35000 = 17 : 7 . answer : c
Answer: c
Python program:
a = 2 + 3 
b = a + 3 
c = 2 + 3 
d = c * 2
e = b * d
f = 2 + 3 
g = e + f 
h = 2 + 3 
i = h * 2
j = 3 * i
k = 2 + 3 
l = j + k 
m = g / l
Problem: a can complete a project in 30 days and b can complete the same project in 30 days . if a and b start working on the project together and a quits 10 days before the project is completed , in how many days will the project be completed ?
Options: a ) 18 days , b ) 27 days , c ) 26.67 days , d ) 5 days , e ) 12 days
Rationale: "let x = the number of days taken to complete the project . the amount of work done by a is ( x - 10 ) * ( 1 / 20 ) . the amount of work done by b is ( x ) * ( 1 / 30 ) . ( 1 / 30 ) * ( x - 10 ) + ( 1 / 30 ) * ( x ) = 1 ( x / 30 ) + ( x / 30 ) - ( 10 / 30 ) = 1 2 x / 30 = 1 / 3 x = 5 therefore , the answer is d : 5 ."
Answer: d
Python program:
a = 1 / 30
b = a * 10
c = 1 - b
d = 1 / 30
e = 1 / 30
f = d + e 
g = c / f
h = g + 10
Problem: express a speed of 42 kmph in meters per second ?
Options: a ) 10 mps , b ) 18 mps , c ) 19 mps , d ) 17 mps , e ) 12 mps
Rationale: "42 * 5 / 18 = 12 mps answer : e"
Answer: e
Python program:
a = const_0_2778 * 42
Problem: a box has exactly 100 balls , and each ball is either red , blue , or white . if the box has 5 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 ) 8 , 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 5 more blue balls than white balls . . . equation # 2 : y = 5 + z . . . thrice as many red balls as blue balls . . . equation # 3 : x = 3 y solve equation # 2 for z : z = y - 5 now , we can replace both x and z with y in equation # 1 3 y + y + ( y - 5 ) = 100 5 y - 5 = 100 5 y = 105 y = 21 there are 21 blue balls . this is 5 more than the number of white balls , so z = 16 . that ' s the answer . just as a check , x = 63 , and 63 + 21 + 16 = 100 . answer = 16 , ( e )"
Answer: e
Python program:
a = 5 * 3
b = 100 - a
c = b / 4
Problem: mahesh marks an article 15 % above the cost price of rs . 540 . what must be his discount percentage if he sells it at rs . 459 ?
Options: a ) 18 % , b ) 21 % , c ) 20 % , d ) 26.1 % , e ) none of these
Rationale: "cp = rs . 540 , mp = 540 + 15 % of 540 = rs . 621 sp = rs . 459 , discount = 621 - 459 = 162 discount % = 162 / 621 * 100 = 26.1 % answer : d"
Answer: d
Python program:
a = 100 + 15 
b = a / 100
c = 540 * b
d = c - 459
e = d * 100
f = 100 + 15 
g = f / 100
h = 540 * g
i = e / h
Problem: income and expenditure of a person are in the ratio 7 : 6 . if the income of the person is rs . 21000 , then find his savings ?
Options: a ) rs . 3600 , b ) rs . 3603 , c ) rs . 3639 , d ) rs . 3000 , e ) rs . 3602
Rationale: "let the income and the expenditure of the person be rs . 7 x and rs . 6 x respectively . income , 7 x = 21000 = > x = 3000 savings = income - expenditure = 7 x - 6 x = x so , savings = rs . 3000 answer : d"
Answer: d
Python program:
a = 6 / 7
b = a * 21000
c = 21000 - b
Problem: a man spends 1 / 3 rd of his salary on food . he spends 1 / 4 th on rent and 1 / 5 th on cloths . if he is left with 1760 , then who much salary does he earn
Options: a ) 8223 , b ) 8123 , c ) 8323 , d ) 8423 , e ) 8523
Rationale: let total salary be x a / q = > x = ( x / 3 ) + ( x / 4 ) + ( x / 5 ) + 1760 = > x - 47 x / 60 = 1760 = > 13 x / 60 = 1760 = > x = 1760 * 60 / 13 = > x = 8123 ( approax ) answer : b
Answer: b
Python program:
a = 1 / 3
b = 1 / 4
c = a + b 
d = 1 / 5
e = c + d 
f = 1 - e
g = 1760 / f
Problem: what is the largest 4 digit number exactly divisible by 48 ?
Options: a ) 4676 , b ) 4678 , c ) 9984 , d ) 9504 , e ) 9936
Rationale: largest 4 digit number = 9999 9999 ÷ 48 = 208 , remainder = 15 hence largest 4 digit number exactly divisible by 48 = 9999 - 15 = 9984 answer : c
Answer: c
Python program:
a = 10 ** 4
b = a / 48
c = math.floor(b)
d = c * 48
Problem: the ratio of length of two refill is 9 : 8.2 nd refill got damaged when only half length of 2 nd refill get used . the ratio of total no . of pages written by both refill .
Options: a ) 8 : 3 , b ) 6 : 5 , c ) 9 : 8 , d ) 9 : 4 , e ) 5 : 4
Rationale: the no . of page written is directly proportional to length of refill . so , initial no . of page to be write = 9 x , 8 x . now , 2 nd refill only can write 4 x page so new ratio of page written = 9 x / 4 x = 9 : 4 . answer d
Answer: d
Python program:
a = 9 - 1
b = a / 2
c = 9 / b
Problem: a train running at the speed of 45 km / hr crosses a pole in 16 seconds . find the length of the train .
Options: a ) 200 , b ) 188 , c ) 204 , d ) 288 , e ) 500
Rationale: "speed = 45 * ( 5 / 18 ) m / sec = 25 / 2 m / sec length of train ( distance ) = speed * time ( 25 / 2 ) * 16 = 200 meter answer : a"
Answer: a
Python program:
a = 45 * 1000
b = a / 3600
c = b * 16
Problem: he number of times a bucket of capacity 4 liters to be used to fill up a tank is less than number of ties another bucket of capacity 3 liters used for the same purpose by 4 . what is the capacity of the tank ?
Options: a ) 360 liters , b ) 256 , c ) 48 , d ) 525 , e ) 425
Rationale: 4 x = 3 ( x + 4 ) , where x may be number of times 4 l bucket is used . 4 x = 3 ( x + 4 ) - - > 1 . x = 12 , substitute x to lhs or rhs of 1 , which gets you the capacity , and it is 48 . answer : c
Answer: c
Python program:
a = 3 * 4
b = 4 * a
Problem: a and b start a business , with a investing the total capital of rs . 5000 , on the condition that b pays a interest @ 10 % per annum on his half of the capital . a is a working partner and receives rs . 500 per month from the total profit and any profit remaining is equally shared by both of them . at the end of the year , it was found that the income of a is twice that of b . find the total profit for the year ?
Options: a ) a ) 2500 , b ) b ) 3500 , c ) c ) 5000 , d ) d ) 6000 , e ) e ) 8000
Rationale: interest received by a from b = 10 % of half of rs . 5000 = 10 % * 2500 = 250 . amount received by a per annum for being a working partner = 500 * 12 = rs . 1000 . let ' p ' be the part of the remaining profit that a receives as his share . total income of a = ( 250 + 1000 + p ) total income of b = only his share from the remaining profit = ' p ' , as a and b share the remaining profit equally . income of a = twice the income of b ( 250 + 1000 + p ) = 2 ( p ) p = 1250 total profit = 2 p + 1000 = 2 * 1250 + 1000 = 3500 answer : b
Answer: b
Python program:
a = 5000 / 2
b = a / 10
c = b * 3
d = c * 4
e = d + 500
Problem: two mba admissions committees are to be formed randomly from 6 second year mbas with 3 members each . what is the probability w that jane will be on the same committee as albert ?
Options: a ) 12 % , b ) 20 % , c ) 33 % , d ) 40 % , e ) 50 %
Rationale: "total number of ways to choose 3 member committee - 6 c 3 = ( 6 ! / 3 ! 3 ! ) = 20 no . of ways albert n jane are in same committee : - ( 4 c 1 * 2 ) = 8 probability w = ( 8 / 20 ) * 100 = 40 % . + 1 for me . . : d"
Answer: d
Python program:
a = math.comb(4, 1)
b = a * 2
c = math.comb(6, 3)
d = b / c
e = 5 * 5
f = e * 4
g = d * f
Problem: how many plants will be there in a circular bed whose outer edge measure 35 cms , allowing 4 cm 2 for each plant ?
Options: a ) 18 , b ) 750 , c ) 24 , d ) 19 , e ) none of these
Rationale: "circumference of circular bed = 35 cm area of circular bed = ( 35 ) 2 â  „ 4 ï € space for each plant = 4 cm 2 â ˆ ´ required number of plants = ( 35 ) 2 â  „ 4 ï € ã · 4 = 24.36 = 24 ( approx ) answer c"
Answer: c
Python program:
a = 2 * math.pi
b = 35 / a
c = circle_area / (
Problem: the weights of one liter vegetable ghee packet of two brands ‘ a ’ and ‘ b ’ are 900 gm and 700 gm respectively . if they are mixed in the ratio of 3 : 2 by volumes to form a mixture of 4 liters , what is the weight ( in kg ) of the mixture ?
Options: a ) 3.84 , b ) 1.75 , c ) 3.28 , d ) 2.72 , e ) none of these
Rationale: "here ' s how i did it . my notes from reading the problem were : 1 l a = 900 gm 1 l b = 700 gm we are mixing five parts ( 3 parts a plus 2 parts b , 5 parts total ) to get 4 l , so 5 x = 4 - - - > x = 4 / 5 . each part is 4 / 5 of a liter . so if we have 3 parts a , we have 900 * 3 * ( 4 / 5 ) = 2160 if we have 2 parts b , we have 700 * 2 * ( 4 / 5 ) = 1120 2160 + 1120 = 3280 solving for units gives us 3.28 so the answer is c"
Answer: c
Python program:
a = 3 * 900
b = 2 * 700
c = a + b 
d = 4 * c
e = 3 + 2 
f = d / e
g = f / 1000
Problem: the average of 11 numbers is 60 . out of 11 numbers the average of first 6 no . is 78 , and last 6 numbers is 75 then find 6 th number ?
Options: a ) a ) 258 , b ) b ) 65 , c ) c ) 58 , d ) d ) 62 , e ) e ) 48
Rationale: "6 th number = sum of 1 st 6 no . s + sum of last 6 no . s - sum of 11 no . s answer = 6 * 78 + 6 * 75 - 11 * 60 = 258 answer is a"
Answer: a
Python program:
a = 6 * 78
b = 6 * 75
c = a + b 
d = 11 * 60
e = c - d
Problem: a train running at the speed of 120 km / hr crosses a pole in 9 seconds . find the length of the train .
Options: a ) 100 meter , b ) 150 meter , c ) 200 meter , d ) 250 meter , e ) 300 meter
Rationale: "speed = 120 * ( 5 / 18 ) m / sec = 200 / 6 m / sec length of train ( distance ) = speed * time ( 200 / 6 ) * 9 = 300 meter answer : e"
Answer: e
Python program:
a = 120 * 1000
b = a / 3600
c = b * 9
Problem: marts income is 60 percent more than tims income and tims income is 50 percent less than juans income . what percentage of juans income is marts income
Options: a ) 124 % , b ) b ) 120 % , c ) c ) 96 % , d ) d ) 80 % , e ) e ) 64 %
Rationale: "m = ( 160 / 100 ) t t = ( 50 / 100 ) j = > m = ( 80 / 100 ) j answer d ."
Answer: d
Python program:
a = 100 + 60 
b = 100 - 50
c = 100 / b
d = c * 100
e = a / d
f = e * 100
Problem: 155 liters of a mixture of milk and water contains in the ratio 3 : 2 . how much water should now be added so that the ratio of milk and water becomes 3 : 4 ?
Options: a ) 12 liters , b ) 62 liters , c ) 41 liters , d ) 50 liters , e ) 34 liters
Rationale: milk = 3 / 5 * 155 = 93 liters water = 62 liters 93 : ( 62 + p ) = 3 : 4 186 + 3 p = 372 = > p = 62 62 liters of water are to be added for the ratio become 3 : 4 . answer : b
Answer: b
Python program:
a = 3 + 2 
b = 155 / a
c = b * 2
Problem: the center of a circle lies on the origin of the coordinate plane . if a point ( x , y ) is randomly selected inside of the circle , what is the probability that y > 0 and y > x ?
Options: a ) 1 / 8 , b ) 1 / 6 , c ) 3 / 8 , d ) 1 / 2 , e ) 3 / 4
Rationale: the line y = x divides the circle into two equal areas . all the points above the line y = x satisfy the condition that y > x . all the points above the x - axis satisfy the condition that y > 0 . the intersection of these two areas is 3 / 8 of the circle . the answer is c .
Answer: c
Python program:
a = 2 * 4
b = 3 / a
Problem: how many different positive integers are factors of 196 ?
Options: a ) 1 , b ) 2 , c ) 3 , d ) 49 , e ) 36
Rationale: "15 , 14 × 15 , 14 = 7 ^ 2 × 2 ^ 2 so total factors = ( 6 + 1 ) ( 6 + 1 ) = 49 answer : d"
Answer: d
Python program:
a = 2 ** 2
b = a + 2
Problem: the product of two numbers is 266 and their difference is 5 . what is the bigger number ?
Options: a ) 13 , b ) 15 , c ) 19 , d ) 24 , e ) none of these
Rationale: "explanation : let the two numbers be a and b , here a > b ab = 266 b = 266 / a - - - - - - - - - - - - - - - - - ( i ) given , a – b = 5 - - - - - - - - - - - ( ii ) substitute from ( i ) in ( ii ) , we get a – 266 / a = 5 a 2 – 5 a + 266 = 0 ( a – 19 ) ( a – 14 ) = 0 therefore , a = 19 or a = 14 hence , bigger number = a = 19 answer : c"
Answer: c
Python program:
a = 2 * 266
b = 5 - a
c = math.sqrt(b)
d = c ** 2
e = 4 * 266
f = d + e 
g = math.sqrt(f)
Problem: if 821562 is to be divisible by 5 , what is the least whole number that should be added to it ?
Options: a ) 6 , b ) 4 , c ) 5 , d ) 2 , e ) 3
Rationale: a number is divisible by 8 if the number formed by the last three digits is divisible by 8 . here , 821562 = 562 , the next multiple of 9 is 568 . 6 must be added to 821562 to make it divisible by 8 a
Answer: a
Python program:
a = math.floor(5)
b = a + 1
Problem: in 2008 , the profits of company n were 10 percent of revenues . in 2009 , the revenues of company n fell by 20 percent , but profits were 16 percent of revenues . the profits in 2009 were what percent of the profits in 2008 ?
Options: a ) 80 % , b ) 105 % , c ) 120 % , d ) 124.2 % , e ) 128 %
Rationale: "x = profits r = revenue x / r = 0,1 x = 10 r = 100 2009 : r = 80 x / 80 = 0,16 = 16 / 100 x = 80 * 16 / 100 x = 12.8 12.8 / 10 = 1,28 = 128 % , answer e"
Answer: e
Python program:
a = 20 / 100
b = 1 - a
c = 16 * b
d = c / 10
e = d * 100
Problem: the difference between the place values of 8 and 3 in the number 587435 is
Options: a ) 75200 , b ) 79970 , c ) 75460 , d ) 24580 , e ) none
Rationale: sol . = ( place value of 8 ) – ( place value of 3 ) = ( 80000 - 30 ) = 79970 answer b
Answer: b
Python program:
a = 10 * 8
b = a - 8
Problem: if the average ( arithmetic mean ) of a and b is 35 and the average of b and c is 80 , what is the value of c − a ?
Options: a ) 25 , b ) 50 , c ) 90 , d ) 140 , e ) it can not be determined from the information given .
Rationale: "- ( a + b = 70 ) b + c = 160 c - a = 90 c . 90"
Answer: c
Python program:
a = 80 * 2
b = 35 * 2
c = a - b
Problem: a group of men decided to do a work in 17 days , but 8 of them became absent . if the rest of the group did the work in 21 days , find the original number of men ?
Options: a ) 15 , b ) 20 , c ) 42 , d ) 25 , e ) 18
Rationale: "original number of men = 8 * 21 / ( 21 - 17 ) = 42 answer is c"
Answer: c
Python program:
a = 8 * 21
b = 21 - 17
c = a / b
Problem: arun purchased 30 kg of wheat at the rate of rs . 11.50 per kg and 20 kg of wheat at the rate of 14.25 per kg . he mixed the two and sold the mixture . approximately what price per kg should be sell the mixture to make 10 % profit ?
Options: a ) 13.86 , b ) 16.33 , c ) 16.35 , d ) 16.3 , e ) 16.32
Rationale: "c . p . of 50 kg wheat = ( 30 * 11.50 + 20 * 14.25 ) = rs . 630 . s . p . of 50 kg wheat = 110 % of rs . 630 = 110 / 100 * 630 = rs . 693 s . p . per kg = 693 / 50 = rs . 13.86 answer : a"
Answer: a
Python program:
a = 30 * 11
b = 20 * 14
c = a + b 
d = 30 * 11
e = 20 * 14
f = d + e 
g = f / 100
h = g * 10
i = c + h 
j = 30 + 20 
k = i / j
Problem: in an apartment building that has 490 units , 4 out of every 7 units are currently rented , including 1 / 6 of the one - bedroom units . if , of the rented apartments , there is a 6 : 1 ratio of two - bedroom units to one - bedroom units , and the building only consists of two - bedroom and one - bedroom units , how many two - bedroom units are not rented ?
Options: a ) 50 , b ) 70 , c ) 10 , d ) 105 , e ) 140
Rationale: rented = 4 / 7 * 490 = 280 . rented two - bedroom = 6 / 7 * 280 = 240 ; rented one - bedroom = 1 / 7 * 280 = 40 ( or 280 - 240 = 40 ) . rented one - bedroom units are 1 / 5 of all one - bedroom : 1 / 6 * { all one bedroom } = 40 - - > { all one - bedroom } = 240 . { all two - bedroom } = 490 - 240 = 250 . two - bedroom not rented = 250 - 240 = 10 . answer : c .
Answer: c
Python program:
a = 490 / 7
b = 4 * a
c = 490 / 7
d = 4 * c
e = 6 + 1 
f = d / e
g = 6 * f
h = b - g
i = 1 / 6
j = h / i
k = 490 - j
l = 490 / 7
m = 4 * l
n = 6 + 1 
o = m / n
p = 6 * o
q = k - p
Problem: a certain bus driver is paid a regular rate of $ 16 per hour for any number of hours that does not exceed 40 hours per week . for any overtime hours worked in excess of 40 hours per week , the bus driver is paid a rate that is 75 % higher than his regular rate . if last week the bus driver earned $ 976 in total compensation , how many total hours did he work that week ?
Options: a ) 51 , b ) 52 , c ) 59 , d ) 55 , e ) 56
Rationale: "for 40 hrs = 40 * 16 = 640 excess = 976 - 640 = 336 for extra hours = . 75 ( 16 ) = 12 + 16 = 28 number of extra hrs = 336 / 28 = 12 total hrs = 40 + 12 = 52 answer b"
Answer: b
Python program:
a = 16 * 40
b = 976 - a
c = 100 + 75 
d = 16 * c
e = d / 100
f = b / e
g = 40 + f
Problem: a works twice as fast as b . if b can complete a work in 18 days independently , the number of days in which a and b can together finish the work is :
Options: a ) 4 days , b ) 6 days , c ) 8 days , d ) 10 days , e ) 12 days
Rationale: "explanation : ratio of rates of working of a and b = 2 : 1 . so , ratio of times taken = 1 : 2 a ' s 1 day ' s work = 1 / 9 b ' s 1 day ' s work = 1 / 18 ( a + b ) ' s 1 day ' s work = ( 1 / 9 + 1 / 18 ) = 3 / 18 = 1 / 6 so , a and b together can finish the work in 6 days answer is b"
Answer: b
Python program:
a = 1 / 18
b = 1 / 18
c = 2 * b
d = a + c 
e = 1/(d)
Problem: he average weight of 8 persons increases by 2.5 kg when a new person comes in place of one of them weighing 65 kg . what might be the weight of the new person ?
Options: a ) 75 kg , b ) 55 kg , c ) 45 kg , d ) 85 kg , e ) 25 kg
Rationale: explanation : total weight increased = ( 8 x 2.5 ) kg = 20 kg . weight of new person = ( 65 + 20 ) kg = 85 kg . answer : d
Answer: d
Python program:
a = 2 * 5
b = a + 65
Problem: a , band c enter into partnership . a invests 3 times as much as b and b invests two - third of what c invests . at the end of the year , the profit earned is rs . 8800 . what is the share of b ?
Options: a ) 1100 , b ) 800 , c ) 1400 , d ) 1200 , e ) 1600
Rationale: "let c ' s capital = rs . x . then , b ' s capital = rs . ( 2 / 3 ) x a ’ s capital = rs . ( 3 x ( 2 / 3 ) . x ) = rs . 2 x . ratio of their capitals = 2 x : ( 2 / 3 ) x : x = 6 : 2 : 3 . hence , b ' s share = rs . ( 8800 x ( 2 / 11 ) ) = rs . 1600 . answer is e"
Answer: e
Python program:
a = 2 * 3
b = 2 / 3
c = b * 3
d = a + c 
e = d + 3 
f = 2 / e
g = 8800 * f
Problem: how many numbers are divisible by 4 between 1 and 100 ?
Options: a ) 25 , b ) 24 , c ) 23 , d ) 22 , e ) 20
Rationale: "numbers divisible by 4 till 100 = ( 100 / 4 ) = 25 but we should not consider 100 as we are asked to find the numbers between 1 and 100 which are divisible by 4 . so answer is 24 numbers . answer is option b"
Answer: b
Python program:
a = 4 * 1
b = 100 / a
Problem: a certain city with a population of 120,000 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 ) 10,000 , c ) c ) 10,900 , 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 = 120 k x = 10,000 answer : b"
Answer: b
Python program:
a = 4 * 2
b = a * 100
Problem: two trains of length 100 m and 200 m are 100 m apart . they start moving towards each other on parallel tracks , at speeds 54 kmph and 72 kmph . after how much time will the trains meet ?
Options: a ) 20 / 8 sec , b ) 20 / 4 sec , c ) 20 / 7 sec , d ) 22 / 7 sec , e ) 60 / 7 sec
Rationale: "they are moving in opposite directions , relative speed is equal to the sum of their speeds . relative speed = ( 54 + 72 ) * 5 / 18 = 7 * 5 = 35 mps . the time required = d / s = 100 / 35 = 20 / 7 sec . answer : c"
Answer: c
Python program:
a = 54 + 72 
b = a * const_0_2778
c = 100 / b
Problem: an oil cylinder was 3 / 4 th full . when 4 bottles of oil is poured into it , it is 4 / 5 th full . how many bottles of oil can the full cylinder hold ?
Options: a ) 90 , b ) 75 , c ) 70 , d ) 80 , e ) 85
Rationale: ( 4 / 5 - 3 / 4 ) cylinder is filled by 4 bottles 0.8 - 0.75 = 0.05 cylinder is filled by 4 bottles 1 cylinder is filled by 4 / 0.05 = 80 bottles answer : d
Answer: d
Python program:
a = 4 / 5
b = 3 / 4
c = a - b
d = c / 4
e = 1 / d
Problem: if f ( f ( n ) ) + f ( n ) = 2 n + 3 , f ( 0 ) = 1 then f ( 2013 ) = ?
Options: a ) 2014 , b ) 2088 , c ) 270 , d ) 1881 , e ) 1781
Rationale: "f ( f ( 0 ) ) + f ( 0 ) = 2 ( 0 ) + 3 ⇒ ⇒ f ( 1 ) = 3 - 1 = 2 , f ( 1 ) = 2 f ( f ( 1 ) ) + f ( 1 ) = 2 ( 1 ) + 3 ⇒ ⇒ f ( 2 ) = 5 - 2 = 3 , f ( 2 ) = 3 f ( f ( 2 ) ) + f ( 2 ) = 2 ( 2 ) + 3 ⇒ ⇒ f ( 3 ) = 7 - 3 = 4 , f ( 3 ) = 4 . . . . . . . . . . . . . . f ( 2013 ) = 2014 ans : a"
Answer: a
Python program:
a = 1 + 2013
Problem: last year manfred received 26 paychecks . each of his first 6 paychecks was $ 750 ; each of his remaining paychecks was $ 50 more than each of his first 6 paychecks . to the nearest dollar , what was the average ( arithmetic mean ) amount of his pay checks for the year ?
Options: a ) $ 752 , b ) $ 755 , c ) $ 765 , d ) $ 788 , e ) $ 775
Rationale: "= ( 750 * 6 + 800 * 20 ) / 26 = 788 answer is d . posted from my mobile device"
Answer: d
Python program:
a = 750 + 50 
b = a * 50
c = 6 * 750
d = b + c 
e = d / 26
Problem: a certain no . when divided by 110 leaves a remainder 25 , what is the remainder if the same no . be divided by 15 ?
Options: a ) 2 , b ) 4 , c ) 7 , d ) 8 , e ) 9
Rationale: "explanation : 110 + 25 = 135 / 15 = 9 ( remainder ) e"
Answer: e
Python program:
a = 110 - 25
b = a - 4
c = b - 2
Problem: of the final grades received by the students in a certain math course , 1 / 5 are a ' s , 1 / 4 are b ' s , 1 / 2 are c ' s , and the remaining 30 grades are d ' s . what is the number of students in the course ?
Options: a ) 80 , b ) 110 , c ) 160 , d ) 600 , e ) 400
Rationale: "we start by creating a variable for the total number of students in the math course . we can say : t = total number of students in the math course next , we can use variable t in an equation that we translate from the given information . we are given that , of the final grades received by the students in a certain math course , 1 / 5 are a ' s , 1 / 4 are b ' s , 1 / 2 are c ' s , and the remaining 30 grades are d ' s . since this represents all the grades in the class , it represents all the students in the class . thus we know : # a ’ s + # b ’ s + # c ’ s + # d ’ s = total number of students in the class 1 / 5 ( t ) + ¼ ( t ) + ½ ( t ) + 30 = t we can multiply the entire equation by 20 to cancel out the denominators of the fractions and we have : 4 t + 5 t + 10 t + 600 = 20 t 19 t + 600 = 20 t 600 = t there are a total of 600 students in the math class . answer is d ."
Answer: d
Python program:
a = 1 / 5
b = 1 / 4
c = a + b 
d = 1 / 2
e = c + d 
f = 1 - e
g = 30 / f
Problem: a man can row 3 kmph in still water . when the river is running at 1.2 kmph , it takes him 1 hour to row to a place and black . what is the total distance traveled by the man ?
Options: a ) 2.9 , b ) 2.8 , c ) 2.4 , d ) 2.8 , e ) 2.2
Rationale: "m = 3 s = 1.2 ds = 3.6 us = 1.8 x / 3.6 + x / 1.8 = 1 x = 1.2 d = 1.2 * 2 = 2.4 answer : c"
Answer: c
Python program:
a = 3 + 1 
b = 3 - 1
c = a * b
d = 3 + 1 
e = 3 - 1
f = d + e 
g = c / f
h = g * 2
Problem: lloyd normally works 7.5 hours per day and earns $ 4.50 per hour . for each hour he works in excess of 7.5 hours on a given day , he is paid 2.5 times his regular rate . if lloyd works 10.5 hours on a given day , how much does he earn for that day ?
Options: a ) $ 33.75 , b ) $ 47.25 , c ) $ 51.75 , d ) $ 54.00 , e ) $ 67.50
Rationale: "daily working hour * regular rate + overtime * increased rate 7.5 * 4.5 + 3 * 4.5 * 2.5 = 67.5 answer e"
Answer: e
Python program:
a = 7 * 5
b = 10 - 5
c = b * 2
d = c * 4
e = a + d