euclaise/mathqa_programs huggingface dataset:
Problem: x , a , z , and b are single digit positive integers . x = 1 / 6 a . z = 1 / 6 b . ( 10 a + b ) – ( 10 x + z ) could not equal
Options: a ) 35 , b ) 30 , c ) 43 , d ) 60 , e ) 65
Rationale: "a = 6 x , b = 6 z therefore ( 6 x . 10 + 6 z ) - ( 10 x + z ) = ( 6 - 1 ) ( 10 x + z ) = 5 . ( 10 x + z ) number should be divisible by 5 c"
Answer: c
Python program:
a = 6 * 6
b = 6 * 10
c = a + b 
d = 6 * 10
e = d + 6 
f = c - e
g = f + 10 
h = g + 3
Problem: rs . 200 amounts to rs . 800 in 8 years at simple interest . if the interest is increased by 5 % , it would amount to how much ?
Options: a ) 520 , b ) 440 , c ) 260 , d ) 280 , e ) 120
Rationale: "( 200 * 5 * 8 ) / 100 = 80 200 + 80 = 280 answer : d"
Answer: d
Python program:
a = 5 / 100
b = 1 + a 
c = b ** 8
d = c * 200
Problem: the product of three consecutive numbers is 336 . then the sum of the smallest two numbers is ?
Options: a ) 13 , b ) 15 , c ) 20 , d ) 38 , e ) 56
Rationale: "product of three numbers = 336 336 = 6 * 7 * 8 . so , the three numbers are 6 , 7 and 8 . and sum of smallest of these two = 6 + 7 = 13 . answer : option a"
Answer: a
Python program:
a = 2 ** 336
b = math.factorial(336)
c = a * b
Problem: a , b , c are positive numbers such that they are in increasing geometric progression then how many such numbers are there in ( loga + logb + logc ) / 6 = log 6
Options: a ) 1 , b ) 2 , c ) 3 , d ) 4 , e ) 5
Rationale: given that a , b , c are in gp so b / a = c / b = > b ^ 2 = ac ( loga + logb + logc ) / 6 = log 6 = > log ( abc ) = 6 * log 6 = > log ( ac * b ) = log ( 6 ^ 6 ) = > log ( b ^ 3 ) = log ( 6 ^ 6 ) = > b ^ 3 = 6 ^ 6 = > b ^ 3 = ( 6 ^ 2 ) ^ 3 = > b = 6 ^ 2 = 36 it means a = 2 , c = 18 or a = 3 c = 12 or a = 4 c = 9 or a = 6 c = 6 . hence there are four such numbers answer : d
Answer: d
Python program:
a = math.log(6)
b = a + 2 
c = 1 / 2
d = b - c
Problem: calculate the l . c . m of 2 / 5 , 4 / 7 , 3 / 7 , 6 / 13 is :
Options: a ) 15 , b ) 14 , c ) 13 , d ) 12 , e ) 11
Rationale: "required l . c . m = l . c . m . of 2 , 4 , 3 , 6 / h . c . f . of 5 , 7 , 7 , 13 = 12 / 1 = 12 answer is d"
Answer: d
Python program:
a = 2 * 4
b = 3 * 6
c = a * b
Problem: the length of the rectangular field is double its width . inside the field there is square shaped pond 8 m long . if the area of the pond is 1 / 18 of the area of the field . what is the length of the field ?
Options: a ) 23 , b ) 32 , c ) 34 , d ) 43 , e ) 48
Rationale: "explanation : a / 18 = 8 * 8 = > a = 8 * 8 * 18 x * 2 x = 8 * 8 * 18 x = 24 = > 2 x = 48 answer : option e"
Answer: e
Python program:
a = square_area * (
b = a / 18
c = 1/(2)
d = math.sqrt(b)
Problem: if jake loses 8 pounds , he will weigh twice as much as his sister . together they now weigh 290 pounds . what is jake ’ s present weight , in pounds ?
Options: a ) 131 , b ) 135 , c ) 169 , d ) 196 , e ) 212
Rationale: "lets say j is the weight of jack and s is the wt of his sister . if he loses 8 pounds , he s twice as heavy as his sister . j - 8 = 2 * s also , together they weight 290 pounds j + s = 290 solvong the 2 equation , we get j = 196 pounds ! d"
Answer: d
Python program:
a = 290 - 8
b = a / 3
c = b * 2
d = c + 8
Problem: how many integers from 0 to 59 , inclusive , have a remainder of 1 when divided by 3 ?
Options: a ) 15 , b ) 16 , c ) 17 , d ) 18 , e ) 20
Rationale: "my ans is also c . 17 . explanation : 1 also gives 1 remainder when divided by 3 , another number is 4 , then 7 and so on . hence we have an arithmetic progression : 1 , 4 , 7 , 10 , . . . . . 58 , which are in the form 3 n + 1 . now we have to find out number of terms . tn = a + ( n - 1 ) d , where tn is the nth term of an ap , a is the first term and d is the common difference . so , 58 = 1 + ( n - 1 ) 3 or , ( n - 1 ) 3 = 57 or , n - 1 = 19 or , n = 20 e"
Answer: e
Python program:
a = 59 / 10
Problem: david works at a science lab that conducts experiments on bacteria . the population of the bacteria multiplies at a constant rate , and his job is to notate the population of a certain group of bacteria each hour . at 1 p . m . on a certain day , he noted that the population was 2,500 and then he left the lab . he returned in time to take a reading at 4 p . m . , by which point the population had grown to 160,000 . now he has to fill in the missing data for 2 p . m . and 3 p . m . what was the population at 3 p . m . ?
Options: a ) 45,000 , b ) 40,000 , c ) 50,000 , d ) 55,000 , e ) 60,000
Rationale: "let the rate be x , then population of the bacteria after each hour can be given as 2500 , 2500 x , 2500 ( x ^ 2 ) , 2500 ( x ^ 3 ) now population at 4 pm = 160,000 thus we have 2500 ( x ^ 3 ) = 160,000 = 64 thus x = 4 therefore population at 3 pm = 2500 ( 16 ) = 40,000 answer : b"
Answer: b
Python program:
a = 2 * 4
b = a * 2
c = b / 2
d = c ** const_0_33
e = d * 2
f = 2 * 4
g = f * 2
h = g / 2
i = h ** const_0_33
j = e * i
Problem: the manager of a produce market purchased a quantity of tomatoes for $ 0.80 per pound . due to improper handling , 15 percent of the tomatoes , by weight , were ruined and discarded . at what price per pound should the manager sell the remaining tomatoes if she wishes to make a profit on the sale of the tomatoes equal to 8 percent of the cost of the tomatoes .
Options: a ) $ 0.94 , b ) $ 0.96 , c ) $ 0.98 , d ) $ 1.02 , e ) $ 1.20
Rationale: "assume the manager bought 100 tomatoes . cost price = 80 given : 15 % are damaged - - > available tomatoes to sell = 85 85 * x - 80 = 0.08 * 80 85 x - 80 = 6.4 85 x = 86.64 x = 86.64 / 85 = 87 / 85 ( approx ) = 1.023 x is slightly under 1.023 = 1.02 answer : d"
Answer: d
Python program:
a = 8 / 100
b = 1 + a 
c = 100 - 15
d = c / 100
e = 0 / 80
f = b * e
Problem: the greatest number which on dividing 1642 and 1856 leaves remainders 6 and 4 respectively , is :
Options: a ) 123 , b ) 127 , c ) 235 , d ) 4 , e ) 505
Rationale: "explanation : required number = h . c . f . of ( 1642 - 6 ) and ( 1856 - 4 ) = h . c . f . of 1636 and 1852 = 4 . answer : d"
Answer: d
Python program:
a = 1856 - 4
b = 1642 - 6
c = math.gcd(a, b)
Problem: marcella has 27 pairs of shoes . if she loses 9 individual shoes , what is the greatest number of matching pairs she could have left ?
Options: a ) 22 , b ) 20 , c ) 19 , d ) 16 , e ) 15
Rationale: "marcella has 27 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 27 pairs of shoes minus the 5 ' destroyed ' pairs yields 22 pairs that still fulfill the requirements . answer : a"
Answer: a
Python program:
a = 9 / 2
b = math.floor(a)
c = b + 1 
d = 27 - c
Problem: how many 3 - digit numbers can be formed from the digits 2 , 3 , 5 , 6 , 7 and 9 , which are divisible by 5 and none of the digits is repeated ?
Options: a ) 5 , b ) 4 , c ) 20 , d ) 25 , e ) 30
Rationale: since each desired number is divisible by 5 , so we must have 5 at the unit place . so , there is 1 way of doing it . the tens place can now be filled by any of the remaining 5 digits ( 2 , 3 , 6 , 7 , 9 ) . so , there are 5 ways of filling the tens place . the hundreds place can now be filled by any of the remaining 4 digits . so , there are 4 ways of filling it . required number of numbers = ( 1 x 5 x 4 ) = 20 . answer c
Answer: c
Python program:
a = 5 * 4
Problem: a man invests some money partly in 12 % stock at 105 and partly in 8 % stock at 88 . to obtain equal dividends from both , he must invest the money in the ratio .
Options: a ) 35 : 44 , b ) 34 : 44 , c ) 22 : 44 , d ) 20 : 40 , e ) 50 : 45
Rationale: in case of stock 1 , if he invest rs . 105 , he will get a dividend of rs . 12 ( assume face value = 100 ) in case of stock 2 , if he invest rs . 88 , he will get a dividend of rs . 8 ( assume face value = 100 ) ie , if he invest rs . ( 88 * 12 ) / 8 , he will get a dividend of rs . 12 required ratio = 105 : ( 88 × 12 ) / 8 = 105 : ( 11 × 12 ) = 35 : ( 11 × 4 ) = 35 : 44 answer is a .
Answer: a
Python program:
a = 105 * 2
b = 88 * 3
c = a / b
Problem: a woman invested $ 1,000 , part at 5 % and the rest at 6 % . her total investment with interest at the end of the year was $ 1,055 . how much did she invest at 5 % ?
Options: a ) $ 500 , b ) $ 600 , c ) $ 700 , d ) $ 900 , e ) $ 950
Rationale: "et x be the portion invested at 5 % and let ( 1 - x ) be the rest which is invested at 6 % the question states that the return after 1 year is ( 1055 / 1000 ) - 1 = 0.055 = 5.5 % we want to find the dollar amount invested in x using our defined variables , put together the equation and solve for x ( the percentage of 1000 invested at 5 % ) 0.05 x + 0.06 ( 1 - x ) = 0.055 ( 0.05 ) x + 0.06 - ( 0.06 ) x = 0.055 - 0.01 x = - 0.005 x = - 0.005 / - 0.01 = 5 / 10 = 50 % so x = 50 % of the 1000 which is 500 answer : a"
Answer: a
Python program:
a = 5 * 2
b = a * 100
c = 5 * 2
d = c * 100
e = 5 * 2
f = e * 5
g = f + 4 
h = d + g 
i = 5 * 2
j = i * 100
k = h - j
l = k * 100
m = 5 * 2
n = m * 100
o = 5 * n
p = l - o
q = b - p
Problem: three numbers are in the ratio of 2 : 3 : 4 and their l . c . m . is 288 . what is their h . c . f . ?
Options: a ) 18 , b ) 24 , c ) 36 , d ) 42 , e ) 48
Rationale: "let the numbers be 2 x , 3 x , and 4 x . lcm of 2 x , 3 x and 4 x is 12 x . 12 x = 288 x = 24 hcf of 2 x , 3 x and 4 x = x = 24 the answer is b ."
Answer: b
Python program:
a = 2 * 4
Problem: a merchant sells an item at a 10 % discount , but still makes a gross profit of 20 percent of the cost . what percent of the cost would the gross profit on the item have been if it had been sold without the discount ?
Options: a ) 30 % , b ) 40 % , c ) 50 % , d ) 60 % , e ) 75 %
Rationale: original sp = x cost = c current selling price = . 9 x ( 10 % discount ) . 9 x = 1.2 c ( 20 % profit ) x = 1.2 / . 9 * c x = 4 / 3 c original selling price is 1.3 c which is 30 % profit answer a
Answer: a
Python program:
a = 100 - 10
b = a - 20
c = 100 - b
Problem: what decimal fraction is 70 ml of a litre ?
Options: a ) . 7 , b ) . 07 , c ) . 05 , d ) 0.07 , e ) none of these
Rationale: "answer required fraction = 70 / 1000 = 7 / 100 = . 07 correct option : b"
Answer: b
Python program:
a = 70 / 1000
Problem: the average age of applicants for a new job is 20 , with a standard deviation of 8 . the hiring manager is only willing to accept applicants whose age is within one standard deviation of the average age . assuming that all applicants ' ages are integers and that the endpoints of the range are included , what is the maximum number of different ages of the applicants ?
Options: a ) 8 , b ) 16 , c ) 17 , d ) 18 , e ) 34
Rationale: "minimum age = average - 1 standard deviation = 20 - 8 = 12 maximum age = average + 1 standard deviation = 20 + 8 = 28 maximum number of different ages of the applicants = 28 - 12 + 1 = 17 answer c"
Answer: c
Python program:
a = 20 + 8 
b = 20 - 8
c = a - b
d = c + 1
Problem: p , q and r have $ 7000 among themselves . r has two - thirds of the total amount with p and q . find the amount with r ?
Options: a ) 2800 , b ) 2403 , c ) 3998 , d ) 2539 , e ) 1930
Rationale: a 2800 let the amount with r be $ r r = 2 / 3 ( total amount with p and q ) r = 2 / 3 ( 7000 - r ) = > 3 r = 14000 - 2 r = > 5 r = 14000 = > r = 2800 .
Answer: a
Python program:
a = 2 * 2
b = 7000 * a
c = 2 * 2
d = c / 3
e = d * 3
f = 1 * 3
g = e + f 
h = 1 * 3
i = g + h 
j = b / i
Problem: unit size cubes are stacked inside a big rectangular box having dimensions corresponding to three consecutive multiples of 5 . choose exact number of cubes that can completely fill the box .
Options: a ) 750
b ) 850
c ) 950
d ) 1050
e ) none of the above
Rationale: let the dimensions of the box be , length = 5 * a , breadth = 5 * ( a + 1 ) , height = 5 * ( a + 2 ) hence , volume = 5 * 5 * 5 * a * ( a + 1 ) * ( a + 2 ) among any 3 consecutive positive integers , we will either have ( a number that is divisible by both 23 ) or ( a number divisible by 2 and another number divisible by 3 ) . volume = multiple of ( 125 * 2 * 3 ) 750 = 125 * 2 * 3 answer : a
Answer: a
Python program:
a = 5 * 2
b = 5 * 3
c = volume_rectangular_prism / (
Problem: p and q started a business investing rs 85000 and rs 15000 resp . in what ratio the profit earned after 2 years be divided between p and q respectively .
Options: a ) 17 : 5 , b ) 17 : 3 , c ) 17 : 6 , d ) 17 : 7 , e ) 17 : 8
Rationale: "explanation : in this type of question as time frame for both investors is equal then just get the ratio of their investments . p : q = 85000 : 15000 = 85 : 15 = 17 : 3 option b"
Answer: b
Python program:
a = 85000 / 15000
Problem: in one alloy there is 15 % chromium while in another alloy it is 8 % . 15 kg of the first alloy was melted together with 35 kg of the second one to form a third alloy . find the percentage of chromium in the new alloy .
Options: a ) 8.8 % , b ) 9 % , c ) 10.1 % , d ) 8.6 % , e ) 8.4 %
Rationale: "the amount of chromium in the new 15 + 35 = 50 kg alloy is 0.15 * 15 + 0.08 * 35 = 5.05 kg , so the percentage is 5.05 / 50 * 100 = 10.1 % . answer : c ."
Answer: c
Python program:
a = 15 * 15
b = a / 100
c = 8 * 35
d = c / 100
e = b + d 
f = 15 + 35 
g = e / f
h = g * 100
Problem: working alone , sawyer finishes cleaning half the house in a third of the time it takes nick to clean the entire house alone . sawyer alone cleans the entire house in 6 hours . how many hours will it take nick and sawyer to clean the entire house if they work together ?
Options: a ) 1.5 , b ) 2 , c ) 2.4 , d ) 3 , e ) 3.6
Rationale: answer is 3.6 hours . sawyer does the complete house in 6 hours while nick does it in 9 hours . 1 / ( 1 / 6 + 1 / 9 ) = 3.6 answer is e
Answer: e
Python program:
a = 1 / 6
b = 6 / 2
c = b * 3
d = 1 / c
e = a + d 
f = 1/(e)
Problem: if x is 30 percent greater than 88 , then x =
Options: a ) 68 , b ) 70.4 , c ) 86 , d ) 114.4 , e ) 108
Rationale: "x = 88 * 1.3 = 114.4 so the answer is d ."
Answer: d
Python program:
a = 30 / 100
b = a * 88
c = 88 + b
Problem: find value for x from below equation ? x + 1 = 5
Options: a ) - 5 , b ) - 4 , c ) 4 , d ) 3 , e ) 2
Rationale: 1 . subtract 1 from both sides : x + 1 - 1 = 5 - 1 2 . simplify both sides : x = 4 c
Answer: c
Python program:
a = 5 - 1
Problem: what least number should be added to 1015 , so that the sum is completely divisible by 25 ?
Options: a ) 4 , b ) 3 , c ) 2 , d ) 10 , e ) 5
Rationale: "1015 ã · 25 = 40 with remainder = 15 15 + 10 = 25 . hence 10 should be added to 1015 so that the sum will be divisible by 25 answer : option d"
Answer: d
Python program:
a = 25 - reminder
Problem: the population of a city increases @ 4 % p . a . there is an additional annual increase of 4 % of the population due to the influx of job seekers , find the % increase in population after 2 years ?
Options: a ) 14.64 % , b ) 15.64 % , c ) 16.64 % , d ) 17.64 % , e ) 18.64 %
Rationale: total annual increament in population = 4 + 4 = 8 % let the population be x population after 2 years = 1.08 x + . 0864 x population increase = 1.08 x + . 0864 x - x % increase = ( ( 1.08 x + . 0864 x - x ) / x ) * 100 = ( 1.08 + . 0864 - 1 ) * 100 = . 1664 * 100 = 16.64 % answer : c
Answer: c
Python program:
a = 4 + 4 
b = a * 2
Problem: the sum of even numbers between 1 and 31 is :
Options: a ) 240 , b ) 789 , c ) 520 , d ) 879 , e ) 456
Rationale: explanation : let sn = ( 2 + 4 + 6 + . . . + 30 ) . this is an a . p . in which a = 2 , d = 2 and l = 30 let the number of terms be n . then a + ( n - 1 ) d = 30 = > 2 + ( n - 1 ) x 2 = 30 n = 15 . sn = n / 2 ( a + l ) = 15 / 2 x ( 2 + 30 ) = ( 15 x 16 ) = 240 . answer : a
Answer: a
Python program:
a = 31 + 1 
b = 31 / 2
c = math.floor(b)
d = c / 2
e = a * d
Problem: a whale goes on a feeding frenzy that lasts for 9 hours . for the first hour he catches and eats x kilos of plankton . in every hour after the first , it consumes 3 kilos of plankton more than it consumed in the previous hour . if by the end of the frenzy the whale will have consumed a whopping accumulated total 450 kilos of plankton , how many kilos did he consume on the sixth hour ?
Options: a ) 38 , b ) 47 , c ) 50 , d ) 53 , e ) 62
Rationale: "suppose food eaten in first hour : x the ap is : x , x + 3 , x + 6 , . . . . [ number of terms ' n ' = 9 ] therefore , 9 / 2 [ 2 x + ( 9 - 1 ) * 3 ] = 450 . solving for x , x = 38 . now , 6 th term will be : x + ( 6 - 1 ) * d = 38 + 5 * 3 = 53 . hence d ! !"
Answer: d
Python program:
a = 450 / 9
b = a + 3
Problem: the average weight of 8 person ' s increases by 2.5 kg when a new person comes in place of one of them weighing 55 kg . what might be the weight of the new person ?
Options: a ) 56 kg , b ) 90 kg , c ) 75 kg , d ) data inadequate , e ) none of these
Rationale: "c 75 kg total weight increased = ( 8 x 2.5 ) kg = 20 kg . weight of new person = ( 55 + 20 ) kg = 75 kg ."
Answer: c
Python program:
a = 8 * 2
b = a + 55
Problem: income and expenditure of a person are in the ratio 5 : 4 . if the income of the person is rs . 17000 , then find his savings ?
Options: a ) 3600 , b ) 3400 , c ) 3608 , d ) 3602 , e ) 3603
Rationale: "let the income and the expenditure of the person be rs . 5 x and rs . 4 x respectively . income , 5 x = 17000 = > x = 3400 savings = income - expenditure = 5 x - 4 x = x so , savings = rs . 3400 . answer : b"
Answer: b
Python program:
a = 4 / 5
b = a * 17000
c = 17000 - b
Problem: a store reduced the price of all items in the store by 8 % on the first day and by another 10 % on the second day . the price of items on the second day was what percent of the price before the first reduction took place ?
Options: a ) 80.0 , b ) 80.9 , c ) 81.0 , d ) 81.1 , e ) 82.8
Rationale: consider price of the all items as $ 100 after a initial reduction of 8 % price becomes = 0.92 * 100 = $ 92 after the final reduction of 10 % price becomes = 0.9 * 92 = $ 82.8 price of all items on second day is 82.8 % of price on first day correct answer option e
Answer: e
Python program:
a = 100 - 8
b = a / 100
c = 100 - 10
d = c / 100
e = b * d
f = e * 100
Problem: out of 470 students of a school , 325 play football , 175 play cricket and 50 neither play football nor cricket . how many students play both football and cricket ?
Options: a ) 80 , b ) 150 , c ) 100 , d ) 180 , e ) 220
Rationale: "n ( a ) = 325 , n ( b ) = 175 , n ( aub ) = 470 - 50 = 420 . required number = n ( anb ) = n ( a ) + n ( b ) - n ( aub ) = 325 + 175 - 420 = 80 . answer is a"
Answer: a
Python program:
a = 175 + 325 
b = 470 - 50
c = a - b
Problem: in a class of 60 students 41 are taking french , 22 are taking german . of the students taking french or german , 9 are taking both courses . how many students are not enrolled in either course ?
Options: a ) 6 , b ) 15 , c ) 24 , d ) 33 , e ) 54
Rationale: "formula for calculating two overlapping sets : a + b - both + not ( a or b ) = total so in our task we have equation : 41 ( french ) + 22 ( german ) - 9 ( both ) + not = 60 54 + not = 60 not = 60 - 54 = 6 so answer is a"
Answer: a
Python program:
a = 41 + 22 
b = a - 9
c = 60 - b
Problem: tom and linda stand at point a . linda begins to walk in a straight line away from tom at a constant rate of 4 miles per hour . one hour later , tom begins to jog in a straight line in the exact opposite direction at a constant rate of 9 miles per hour . if both tom and linda travel indefinitely , what is the positive difference , in minutes , between the amount of time it takes tom to cover half of the distance that linda has covered and the amount of time it takes tom to cover twice the distance that linda has covered ?
Options: a ) 60 , b ) 72 , c ) 84 , d ) 90 , e ) 216
Rationale: e is the answer . . . . d = ts where d = distance , t = time and s = speed to travel half distance , ( 2 + 4 t ) = 9 t = = > t = 2 / 5 = = > 24 minutes to travel double distance , 2 ( 2 + 4 t ) = 9 t = = > 4 = = > 240 minutes difference , 216 minutes e
Answer: e
Python program:
a = 2 * 2
b = 2 * 4
c = 9 - b
d = a / c
e = 9 - 4
f = 2 / e
g = d - f
h = g * const_60
Problem: in 1998 the profits of company n were 10 percent of revenues . in 1999 , the revenues of company n fell by 30 percent , but profits were 10 percent of revenues . the profits in 1999 were what percent of the profits in 1998 ?
Options: a ) 70 % , b ) 105 % , c ) 120 % , d ) 124.2 % , e ) 138 %
Rationale: "0,07 r = x / 100 * 0.1 r answer a"
Answer: a
Python program:
a = 30 / 100
b = 1 - a
c = 10 / 100
d = b * c
e = 10 / 100
f = d / e
g = f * 100
Problem: p is able to do a piece of work in 15 days and q can do the same work in 20 days . if they can work together for 4 days , what is the fraction of work left ?
Options: a ) 8 / 15 , b ) 7 / 15 , c ) 1 / 15 , d ) 3 / 15 , e ) none of these
Rationale: explanation : p ' s 1 - day work = 1 / 15 q ' s 1 - day work = 1 / 20 work done by ( p + q ) in 1 day = 1 / 15 + 1 / 20 = 7 / 60 . work done by them in 4 days = ( 7 / 60 ) * 4 = 7 / 15 . work left = 1 - ( 7 / 15 ) = 8 / 15 . answer is a
Answer: a
Python program:
a = 1 / 20
b = 1 / 15
c = a + b 
d = c * 4
e = 1 - d
Problem: of the five - digit positive integers that have no digits equal to zero , how many have two digits that are equal to each other and the remaining digit different from the other two ?
Options: a ) 24440 , b ) 36440 , c ) 72440 , d ) 181440 , e ) 216440
Rationale: "of the five - digit positive integers that have no digits equal to zero , how many have two digits that are equal to each other and the remaining digit different from the other two ? a . 24 b . 36 c . 72 d . 144 e . 216 choosing the digit for p - 9 ways ; choosing the digit for q - 8 ways ; choosing the digit for r - 7 ways ; choosing the digit for s - 6 ways ; # of permutations of 3 digits in ppqrs - 5 ! / 2 ! total : 9 * 8 * 7 * 6 * 5 ! / 2 ! = 181440 . answer : d ."
Answer: d
Python program:
a = 10 - 1
b = 10 - 2
c = a * b
d = c * 1
Problem: when processing flower - nectar into honey bees ' extract , a considerable amount of water gets reduced . how much flower - nectar must be processed to yield 1 kg of honey , if nectar contains 50 % water , and the honey obtained from this nectar contains 30 % water ?
Options: a ) 1.2 kg , b ) 1.5 kg , c ) 1.4 kg , d ) 1.9 kg , e ) none of these
Rationale: "explanation : flower - nectar contains 50 % of non - water part . in honey this non - water part constitutes 70 % ( 100 - 30 ) . therefore 0.5 x amount of flower - nectar = 0.70 x amount of honey = 0.70 x 1 kg therefore amount of flower - nectar needed = ( 0.70 / 0.51 ) kg = 1.4 kgs answer : c"
Answer: c
Python program:
a = 100 - 30
b = a / 100
c = 50 / 100
d = b / c
Problem: for any integer m greater than 1 , $ m denotes the product of all the integers from 1 to m , inclusive . how many prime numbers are there between $ 7 + 2 and $ 7 + 10 , inclusive ?
Options: a ) none , b ) one , c ) two , d ) three , e ) four
Rationale: $ is basically a factorial of a number . so , we are asked to find the number of primes between 7 ! + 2 and 7 ! + 10 , inclusive . from each number 7 ! + k were 2 ≤ k ≤ 102 ≤ k ≤ 10 we can factor out k , thus there are no pries in the given range . for example : 7 ! + 2 = 2 ( 3 * 4 * 5 * 6 * 7 + 1 ) - - > a multiple of 2 , thus not a prime ; 7 ! + 3 = 3 ( 2 * 4 * 5 * 6 * 7 + 1 ) - - > a multiple of 3 , thus not a prime ; . . . 7 ! + 10 = 10 ( 3 * 4 * 6 * 7 + 1 ) - - > a multiple of 10 , thus not a prime . answer : a .
Answer: a
Python program:
a = 1 + 1 
b = a + 2 
c = b + 10 
d = 7 + 7 
e = c - d
f = e + 2
Problem: excluding stoppages , the speed of a train is 50 kmph and including stoppages it is 30 kmph . of how many minutes does the train stop per hour ?
Options: a ) 82 , b ) 17 , c ) 12 , d ) 24 , e ) 18
Rationale: "explanation : t = 20 / 50 * 60 = 24 answer : option d"
Answer: d
Python program:
a = 30 / 50
b = const_60 * a
c = const_60 - b
Problem: find the constant k so that : - x 2 - ( k + 9 ) x - 8 = - ( x - 2 ) ( x - 4 )
Options: a ) 11 , b ) 12 , c ) 15 , d ) 14 , e ) 19
Rationale: - x 2 - ( k + 9 ) x - 8 = - ( x - 2 ) ( x - 4 ) : given - x 2 - ( k + 9 ) x - 8 = - x 2 + 6 x - 8 - ( k + 9 ) = 6 : two polynomials are equal if their corresponding coefficients are equal . k = - 15 : solve the above for k correct answer c
Answer: c
Python program:
a = 4 + 2 
b = 9 + a