euclaise/mathqa_programs huggingface dataset:
Problem: at the opening of a trading day at a certain stock exchange , the price per share of stock k was $ 28 . if the price per share of stock k was $ 29 at the closing of the day , what was the percent increase in the price per share of stock k for that day ?
Options: a ) 3.57 % , b ) 5.9 % , c ) 11.1 % , d ) 12.5 % , e ) 23.6 %
Rationale: "opening = 28 closing = 29 rise in price = 1 so , percent increase = 1 / 28 * 100 = 3.57 answer : a"
Answer: a
Python program:
a = 29 / 28
b = a - 1
c = b * 100
Problem: the population of a town is 20000 . it increases annually at the rate of 20 % p . a . what will be its population after 2 years ?
Options: a ) 24440 , b ) 24800 , c ) 28400 , d ) 28800 , e ) 28600
Rationale: "explanation : formula : ( after = 100 denominator ago = 100 numerator ) 20000 * 120 / 100 * 120 / 100 = 120 * 120 * 2 = 28800 answer : option d"
Answer: d
Python program:
a = 20000 * 20
b = a / 100
c = b * 2
d = 20000 + c
Problem: bookman purchased 55 copies of a new book released recently , 10 of which are hardback and sold for $ 20 each , and rest are paperback and sold for $ 10 each . if 14 copies were sold and the total value of the remaining books was 360 , how many paperback copies were sold ?
Options: a ) 8 , b ) 10 , c ) 12 , d ) 19 , e ) 16
Rationale: the bookman had 10 hardback ad 55 - 10 = 45 paperback copies ; 14 copies were sold , hence 55 - 14 = 41 copies were left . let # of paperback copies left be p then 10 p + 20 ( 41 - p ) = 560 - - > 10 p = 260 - - > p = 26 # of paperback copies sold is 45 - 26 = 19 answer : d
Answer: d
Python program:
a = 55 - 10
b = a * 10
c = 10 * 20
d = b + c 
e = d - 360
f = math.gcd(55, 10)
g = f * 20
h = e - g
i = h / 10
Problem: in a company with 48 employees , some part - time and some full - time , exactly ( 1 / 3 ) of the part - time employees and ( 1 / 4 ) of the full - time employees take the subway to work . what is the greatest possible number r of employees who take the subway to work ?
Options: a ) 12 , b ) 13 , c ) 14 , d ) 15 , e ) 16
Rationale: "p / 3 + f / 4 = p / 3 + ( 48 - p ) / 4 = 12 + p / 2 p / 3 + f / 3 = ( p + f ) / 3 = 48 / 3 = 16 p / 4 + f / 4 = 12 p / 3 + f / 3 > p / 3 + f / 4 > p / 4 + f / 4 - - > 16 > 12 + p / 12 > 12 greatest possible r : 12 + p / 12 = 15 - - > p = 36 ( integer - - > good ) 15 or d is the answer"
Answer: d
Python program:
a = 48 * 3
b = 3 * 4
c = a / b
d = 3 * 4
e = 48 - d
f = 48 * 3
g = 3 * 4
h = f / g
i = e / h
j = c + i
Problem: in an electric circuit , three resistors with resistances 2 ohms , 5 ohms and 6 ohms are connected in parallel . in this case , if r is the combined resistance of these three resistors , then the reciprocal of r is equal to the sum of the reciprocals resistors . what is r value ?
Options: a ) 13 / 15 ohms
b ) 15 / 13 ohms
c ) 5 / 8 ohms
d ) 3 / 7 ohms
e ) 45 / 18 ohms
Rationale: the wording is a bit confusing , though basically we are told that 1 / r = 1 / 2 + 1 / 5 + 1 / 6 , from which it follows that r = 13 / 15 ohms option : a
Answer: a
Python program:
a = 1 / 6
b = 1 / 2
c = 1 / 5
d = b + c 
e = a + d
Problem: if the weight of 13 meters long rod is 23.4 kg . what is the weight of 6 meters long rod ?
Options: a ) 7.2 kg . , b ) 10.8 kg . , c ) 12.4 kg . , d ) 18.0 kg , e ) none
Rationale: "answer ∵ weight of 13 m long rod = 23.4 kg ∴ weight of 1 m long rod = 23.4 / 13 kg ∴ weight of 6 m long rod = 23.4 x 6 / 13 = 10.8 kg option : b"
Answer: b
Python program:
a = 6 * 23
b = a / 13
Problem: if the simple interest on a certain sum of money for 7 years is one – fifth of the sum , then the rate of interest per annum is
Options: a ) 4 % , b ) 2.50 % , c ) 6.20 % , d ) 5 % , e ) 2.85 %
Rationale: "explanation : let the principal ( p ) be x then , simple interest ( si ) = x / 5 time ( t ) = 7 years rate of interest per annum ( r ) = ( 100 × si ) / pt = ( 100 × ( x / 5 ) / ( x × 7 ) = 20 / 7 = 2.85 % answer : option e"
Answer: e
Python program:
a = 1 + 4 
b = 100 / a
c = b / 7
Problem: how many positive integers less than 60 are equal to the product of a positive multiple of 5 and an even number ?
Options: a ) 4 , b ) 5 , c ) 9 , d ) 10 , e ) 11
Rationale: "number of positive multiples of 5 less than 60 = 11 5 * 1 = 5 5 * 2 = 10 5 * 3 = 15 5 * 4 = 20 5 * 5 = 25 5 * 6 = 30 5 * 7 = 35 5 * 8 = 40 5 * 9 = 45 5 * 10 = 50 5 * 11 = 55 only 5 of the above are a product of a positive multiple of 5 and an even number - 10 , 20,30 , 40,50 answer b"
Answer: b
Python program:
a = 4 + 5 
b = a - 1
c = math.factorial(b)
d = math.factorial(5)
e = 4 - 1
f = math.factorial(e)
g = d * f
h = c / g
Problem: alex has to take a quiz , which has 10 true false - type question each carry 1 mark . what is the probability that alex ' s can score more than 8 mark in the quiz . given that he decides to guess randomly on the quiz .
Options: a ) 12 / 1024 , b ) 11 / 1024 , c ) 11 / 256 , d ) 12 / 256 , e ) 14 / 256
Rationale: each question has 2 options ( true or false ) . total number of ways of answering all 10 questions = ( 2 ) 10 ( 2 ) 10 more than 8 correct means either 9 correct or all correct . number of ways such that 9 correct = 10 ! / 9 ! = 10 number of ways of all correct = 1 therefore , probability of more than 8 correct = 11 / ( 2 ) 1011 / ( 2 ) 10 = 11 / 1024 answer : b
Answer: b
Python program:
a = 2 ** 10
b = 1 / a
c = 2 ** 10
d = 10 / c
e = b + d
Problem: if x and y are the two digits of the number 653 xy such that this number is divisible by 80 , then x + y = ?
Options: a ) 6 , b ) 4 , c ) 8 , d ) 8 , e ) none of these
Rationale: "80 = 2 x 5 x 8 since 653 xy is divisible by 2 and 5 both , so y = 0 . now , 653 x is divisible by 8 , so 13 x should be divisible by 8 . this happens when x = 6 . x + y = ( 6 + 0 ) = 6 . answer : a"
Answer: a
Python program:
a = 653 * 100
b = reminder / (
Problem: if x and y are integers , what is the least positive number of 24 x + 9 y ?
Options: a ) 1 , b ) 3 , c ) 4 , d ) 6 , e ) 9
Rationale: "24 x + 9 y = 3 ( 8 x + 3 y ) which will be a minimum positive number when 8 x + 3 y = 1 . 8 ( - 1 ) + 3 ( 3 ) = 1 then 3 ( 8 x + 3 y ) can have a minimum positive value of 3 . the answer is b ."
Answer: b
Python program:
a = 24 - 9
Problem: the average earning of a mechanic for the first - 4 days of a week is rs . 18 and for the last 4 days is rs . 22 . if he earns rs . 13 on the fourth day , his average earning for the whole week is ?
Options: a ) rs . 18.95 , b ) rs 16 , c ) rs . 21 , d ) rs . 25.71 , e ) none of these
Rationale: answer total earning for the week = sum of earning of first four days + sum of earning of last four days - earning of 4 th day = 4 x 18 + 4 x 22 - 13 = rs . 147 â ˆ ´ average earning = 147 / 7 = rs . 21 correct option : c
Answer: c
Python program:
a = 4 * 18
b = 4 * 22
c = a + b 
d = c - 13
e = 3 + 4 
f = d / e
Problem: six bells commence tolling together and toll at intervals of 4 , 6 , 8 , 10 , 12 and 14 seconds respectively . in 70 minutes , how many times do they toll together ?
Options: a ) 2 , b ) 3 , c ) 4 , d ) 5 , e ) 6
Rationale: "lcm of 4 , 6 , 8 10 , 12 and 14 is 840 . so , after each 840 seconds , they would toll together . hence , in 70 minutes , they would toll 70 * 60 seconds / 840 seconds = 5 times but then the question says they commence tolling together . so , they basically also toll at thebeginning ( 0 second ) . so , total tolls together = 5 + 1 = 6 answer : e"
Answer: e
Python program:
a = 4 + 3 
b = a * 4
c = b * 3
d = 4 * c
e = d * 4
f = e / 12
g = 12 / f
Problem: can you please walk me through how to best approach this problem ? thanks if # p # = ap ^ 3 + bp – 1 where a and b are constants , and # - 5 # = 10 , what is the value of # 5 # ?
Options: a ) 5 , b ) - 12 , c ) - 2 , d ) - 3 , e ) - 5
Rationale: # p # = ap ^ 3 + bp - 1 # - 5 # = 10 putting p = - 5 in above equation - 125 a - ( 5 b + 1 ) = 10 or # - 5 # = ( 125 a + 5 b + 1 ) = - 10 therefore 125 a + 5 b = - 11 . . . . . ( 1 now putting p = 5 # 5 # = 125 a + 5 b - 1 using equation 1 ( 125 a + 5 b = - 11 ) # 5 # = - 11 - 1 = - 12 hence b
Answer: b
Python program:
a = negate - (
Problem: what is the unit digit in the product ( 3 ^ 68 x 6 ^ 59 x 7 ^ 71 ) ?
Options: a ) 1 , b ) 2 , c ) 4 , d ) 6 , e ) none of them
Rationale: "unit digit in 3 ^ 4 = 1 = > unit digit in ( 3 ^ 4 ) ^ 16 = 1 therefore , unit digit in 3 ^ 65 = unit digit in [ ( 3 ^ 4 ) ^ 16 x 3 ] = ( 1 x 3 ) = 3 unit digit in 6 ^ 59 = 6 unit digit in 7 ^ 4 = 1 = > unit digit in ( 7 ^ 4 ) ^ 17 is 1 unit digit in 7 ^ 71 = unit digit in [ ( 7 ^ 4 ) ^ 17 x 7 ^ 3 ] = ( ( 1 x 3 ) = 3 therefore , required digit = unit digit in ( 3 x 6 x 3 ) = 4 answer is c"
Answer: c
Python program:
a = 3 * 6
b = a * 3
c = 3 * 6
d = c * 3
e = d - 4
f = b - e
Problem: two goods trains each 500 m long are running in opposite directions on parallel tracks . their speeds are 45 km / hr and 15 km / hr respectively . find the time taken by the slower train to pass the driver of the faster one ?
Options: a ) 78 , b ) 60 , c ) 26 , d ) 23 , e ) 12
Rationale: "relative speed = 45 + 15 = 60 km / hr . 60 * 5 / 18 = 50 / 3 m / sec . distance covered = 500 + 500 = 1000 m . required time = 1000 * 3 / 50 = 60 sec . answer : b"
Answer: b
Python program:
a = 45 + 15
Problem: if two integers x , y ( x > y ) are selected from - 10 to 11 ( inclusive ) , how many possible cases are there ?
Options: a ) 150 , b ) 180 , c ) 190 , d ) 210 , e ) 231
Rationale: "if two integers x , y ( x > y ) are selected from - 10 to 9 ( inclusive ) , how many possible cases are there ? a . 150 b . 180 c . 190 d . 210 e . 240 - - > 22 c 2 = 22 * 21 / 2 = 231 . therefore , the answer is e ."
Answer: e
Python program:
a = 11 + 10 
b = 11 + 2 
c = a + b 
d = 11 + 1 
e = c + d 
f = e + 11 
g = f + 10 
h = g + 2 
i = h + 1
Problem: an empty fuel tank with a capacity of 200 gallons was filled partially with fuel a and then to capacity with fuel b . fuel a contains 12 % ethanol by volume and fuel b contains 16 % ethanol by volume . if the full fuel tank contains 24 gallons of ethanol , how many gallons of fuel a were added ?
Options: a ) 160 , b ) 150 , c ) 100 , d ) 80 , e ) 200
Rationale: "say there are a gallons of fuel a in the tank , then there would be 200 - a gallons of fuel b . the amount of ethanol in a gallons of fuel a is 0.12 a ; the amount of ethanol in 200 - a gallons of fuel b is 0.16 ( 200 - a ) ; since the total amount of ethanol is 24 gallons then 0.12 a + 0.16 ( 200 - a ) = 24 - - > a = 200 . answer : e ."
Answer: e
Python program:
a = 16 / 100
b = 200 * a
c = b - 24
d = 16 / 100
e = 12 / 100
f = d - e
g = c / f
Problem: a take twice as much time as b or thrice as much time to finish a piece of work . working together , they can finish the work in 2 days . b can do the work alone in ?
Options: a ) 3 hours , b ) 6 hours , c ) 7 hours , d ) 4 hours , e ) 8 hours
Rationale: "b 6 hours suppose a , b and c take x , x / 2 and x / 3 respectively to finish the work . then , ( 1 / x + 2 / x + 3 / x ) = 1 / 2 6 / x = 1 / 2 = > x = 12 so , b takes 6 hours to finish the work ."
Answer: b
Python program:
a = 1 + 2 
b = a + 3 
c = b * 2
Problem: a certain candy manufacturer reduced the weight of candy bar m by 10 percent buy left the price unchanged . what was the resulting percent increase in the price per ounce of candy bar m ?
Options: a ) 10 , b ) 11 , c ) 12 , d ) 14 , e ) 9
Rationale: "assume 1 oz candy cost $ 1 before . now price remain same $ 1 but weight of candy reduces to 0.9 oz new price of candy = 1 / 0.9 = 1.11 price increase 11 % b"
Answer: b
Python program:
a = 10 / 100
b = 1 - a
c = 1 / b
d = c * 100
e = d - 100
Problem: a cyclist traveled for two days . on the second day the cyclist traveled 6 hours longer and at an average speed 10 mile per hour slower than she traveled on the first day . if during the two days she traveled a total of 280 miles and spent a total of 12 hours traveling , what was her average speed on the second day ?
Options: a ) 5 mph , b ) 10 mph , c ) 20 mph , d ) 30 mph , e ) 40 mph
Rationale: "solution : d = 280 mi t = 12 hrs đ â y 1 time = t 1 d â y 2 time = t 2 t 2 - t 1 = 4 hrs - - - - - ( i ) t 1 + t 2 = 12 hrs - - - - - ( ii ) adding i and ii , t 2 = 8 hrs and t 1 = 4 hrs d à y 1 rate = r 1 d â y 2 rate = r 2 r 1 - r 2 = 10 mph í . ẹ . r 1 = 10 + r 2 280 = 8 r 2 + 4 r 1 í . ẹ . 280 = 8 r 2 + 4 ( 10 + r 2 ) í . ẹ . r 2 = 20 mph answer : a"
Answer: a
Python program:
a = 12 - 6
b = a / 2
c = b * 10
d = 280 - c
e = 12 - 6
f = e / 2
g = 12 - 6
h = g / 2
i = h + 6 
j = f + i 
k = d / j
Problem: a person buys an article at rs . 500 . at what price should he sell the article so as to make a profit of 60 % ?
Options: a ) 800 , b ) 882 , c ) 772 , d ) 652 , e ) 271
Rationale: "cost price = rs . 500 profit = 60 % of 500 = rs . 300 selling price = cost price + profit = 500 + 300 = 800 answer : a"
Answer: a
Python program:
a = 60 / 100
b = 500 * a
c = 500 + b
Problem: a man purchased 2 blankets @ rs . 100 each , 5 blankets @ rs . 150 each and two blankets at a certain rate which is now slipped off from his memory . but he remembers that the average price of the blankets was rs . 150 . find the unknown rate of two blankets ?
Options: a ) 278 , b ) 277 , c ) 278 , d ) 450 , e ) 550
Rationale: "10 * 150 = 1500 2 * 100 + 5 * 150 = 950 1500 – 1050 = 550 answer : e"
Answer: e
Python program:
a = 10 * 150
b = 2 * 100
c = 5 * 150
d = b + c 
e = a - d
Problem: a trader bought a car at 5 % discount on its original price . he sold it at a 40 % increase on the price he bought it . what percent of profit did he make on the original price ?
Options: a ) 118 , b ) 133 , c ) 112 , d ) 113 , e ) 115
Rationale: "original price = 100 cp = 95 s = 95 * ( 140 / 100 ) = 133 100 - 133 = 5 % answer : b"
Answer: b
Python program:
a = 100 - 5
b = 100 + 40 
c = a * b
d = c / 100
e = d / 100
f = e - 1
g = f * 100
Problem: what will be the difference between simple and compound interest at 6 % per annum on a sum of rs . 1000 after 4 years ?
Options: a ) 24.19 , b ) 24.12 , c ) 22.1 , d ) 24.1 , e ) 22.5
Rationale: "s . i . = ( 1000 * 6 * 4 ) / 100 = rs . 240 c . i . = [ 1000 * ( 1 + 6 / 100 ) 4 - 1000 ] = rs . 262.5 difference = ( 262.5 - 240 ) = rs . 22.5 answer : e"
Answer: e
Python program:
a = 6 / 100
b = a + 1 
c = b ** 4
d = 1000 * c
e = d - 1000
f = 6 / 100
g = 1000 * f
h = g * 4
i = e - h
Problem: zinc and copper are melted together in the ratio 9 : 11 . what is the weight of melted mixture , if 28.8 kg of zinc has been consumed in it ?
Options: a ) 58 kg , b ) 60 kg , c ) 64 kg , d ) 70 kg , e ) none
Rationale: sol . for 9 kg zinc , mixture melted = ( 9 + 11 ) kg . for 28.8 kg zinc , mixture , melted = [ 20 / 9 x 28.8 ] kg = 64 kg . answer c
Answer: c
Python program:
a = 11 / 9
b = a * 28
c = b + 28
Problem: what is the speed of the stream if a canoe rows upstream at 9 km / hr and downstream at 12 km / hr
Options: a ) 1 kmph , b ) 4 kmph , c ) 3 kmph , d ) 2 kmph , e ) 1.5 kmph
Rationale: "sol . speed of stream = 1 / 2 ( 12 - 9 ) kmph = 1.5 kmph . answer e"
Answer: e
Python program:
a = 12 - 9
b = a / 2
Problem: . a car covers a distance of 495 km in 5 hours . find its speed ?
Options: a ) 99 , b ) 100 , c ) 102 , d ) 288 , e ) 2761
Rationale: "495 / 5 = 99 kmph answer : a"
Answer: a
Python program:
a = 495 / 5
Problem: if a number p is prime , and 2 p + 1 = q , where q is also prime , then the decimal expansion of 1 / q will produce a decimal with q - 1 digits . if this method produces a decimal with 166 digits , what is the units digit of the product of p and q
Options: a ) 1 , b ) 3 , c ) 5 , d ) 7 , e ) 9
Rationale: "3 / 7 = 0.428571 . . . ( a repeating pattern one digit long ) b"
Answer: b
Python program:
a = 166 + 1 
b = a - 1
c = b / 2
d = 166 + 1 
e = d - 1
f = e / 2
g = f - 1
h = c - g
Problem: the average weight of 5 person ' s increases by 5.5 kg when a new person comes in place of one of them weighing 68 kg . what might be the weight of the new person ?
Options: a ) 60 kg , b ) 95.5 kg , c ) 80 kg , d ) 85 kg , e ) 90 kg
Rationale: "total weight increased = ( 5 x 5.5 ) kg = 27.5 kg . weight of new person = ( 68 + 27.5 ) kg = 95.5 kg option b"
Answer: b
Python program:
a = 5 * 5
b = a + 68
Problem: in the first 10 overs of a cricket game , the run rate was only 3.2 . what should be the rate in the remaining 40 overs to reach the target of 292 runs ?
Options: a ) 6.5 , b ) 6.22 , c ) 6.29 , d ) 6.39 , e ) 6.13
Rationale: "required run rate = [ 292 - ( 3.2 * 10 ) ] / 40 = 260 / 40 = 6.5 answer : a"
Answer: a
Python program:
a = 10 * 3
b = 292 - a
c = b / 40
Problem: the radius of a semi circle is 5.2 cm then its perimeter is ?
Options: a ) 32.52 , b ) 32.48 , c ) 26.74 , d ) 32.9 , e ) 32.31
Rationale: "36 / 7 r = 5.2 = 26.74 answer : c"
Answer: c
Python program:
a = circumface / (
b = a + 2
Problem: p and q invested in a business . they earned some profit which they divided in the ratio of 2 : 3 . if p invested rs . 50 , 000 , the amount invested by q is :
Options: a ) rs . 65,000 , b ) rs . 70,000 , c ) rs . 75,000 , d ) rs . 90,000 , e ) rs . 60,000
Rationale: q invested = 50000 / 2 * 3 = 75000 answer : c
Answer: c
Python program:
a = 3 + 2 
b = a + 2 
c = 3 + 2 
d = b * c
e = d * 2
Problem: eden drove an average speed of 15 miles per hour for the first 20 miles of a tripthen at a average speed of 30 miles / hr for the remaining 20 miles of the trip if she made no stops during the trip what was eden ' s avg speed in miles / hr for the entire trip
Options: a ) 35 , b ) 20 , c ) 45 , d ) 50 , e ) 55
Rationale: avg . speed = total distance / total time total distance = 40 miles total time = 20 / 15 + 15 / 30 = 2 avg . speed = 20 . answer - b
Answer: b
Python program:
a = 20 + 20 
b = 20 / 15
c = 20 / 30
d = b + c 
e = a / d
Problem: the average temperature for monday , tuesday , wednesday and thursday was 48 degrees and for tuesday , wednesday , thursday and friday was 46 degrees . if the temperature on monday was 44 degrees . find the temperature on friday ?
Options: a ) 65 degrees , b ) 73 degrees , c ) 36 degrees , d ) 34 degrees , e ) 74 degrees
Rationale: "m + tu + w + th = 4 * 48 = 192 tu + w + th + f = 4 * 46 = 184 m = 44 tu + w + th = 192 - 44 = 148 f = 184 – 148 = 36 answer : c"
Answer: c
Python program:
a = 48 * 4
b = 46 * 4
c = a - b
d = 44 - c
Problem: if w is the set of all the integers between 49 and 88 , inclusive , that are either multiples of 3 or multiples of 2 or multiples of both , then w contains how many numbers ?
Options: a ) 11 , b ) 44 , c ) 48 , d ) 28 , e ) 26
Rationale: "official solution : number of multiples of 3 step 1 . subtract the extreme multiples of 3 within the range ( the greatest is 87 , the smallest is 51 ) : 87 - 51 = 36 step 2 . divide by 3 : 36 / 3 = 12 step 3 . add 1 : 12 + 1 = 13 . so there are 13 multiples of 3 within the range : examples are 51 , 54 , 57 , 60 , etc . number of multiples of 2 step 1 . subtract the extreme multiples of 2 within the range ( the greatest is 88 , the smallest is 50 ) : 88 - 50 = 38 step 2 . divide by 2 : 38 / 2 = 19 step 3 . add 1 : 19 + 1 = 20 . so there are 19 multiples of 2 within the range : examples are 50 , 52 , 54 , 56 , 58 , 60 etc . add the 13 multiples of 3 and the 19 multiples of 2 : 13 + 19 = 32 . however , by adding the multiples of 2 and the multiples of 3 , we are effectively counting several numbers twice : for example , 54 and 60 are parts of both the lists above . so we ca n ' t just take 13 + 19 = 32 . find the number of multiples of 6 ( which are the double counted , as 6 is divisible by both 2 and 3 ) , and subtract it from 32 : step 1 . subtract the extreme multiples of 6 within the range ( the greatest is 72 , the smallest is 54 ) : 84 - 54 = 30 step 2 . divide by 6 : 30 / 6 = 5 step 3 . add 1 : 5 + 1 = 6 . so there are 6 multiples of 6 within the range : we counted 6 numbers twice . subtract the 6 multiples of 6 from the sum of the multiples of 2 and 3 : = 13 + 19 - 6 = 32 - 6 = 26 therefore , the final number of multiples of 2 , 3 or 6 is 26 . hence , this is the correct answer . ( e )"
Answer: e
Python program:
a = 88 - 49
b = a / 3
c = math.floor(b)
d = 88 - 49
e = d / 2
f = c + e 
g = 88 - 49
h = 2 * 3
i = g / h
j = math.floor(i)
k = f - j
Problem: in the xy - coordinate plane , the graph of y = - x ^ 2 + 9 intersects line l at ( p , - 5 ) and ( t , - 7 ) . what is the least possible value of the slope of line l ?
Options: a ) 6 , b ) - 1 , c ) - 2 , d ) - 6 , e ) - 10
Rationale: we need to find out the value of p and l to get to the slope . line l and graph y intersect at point ( p , - 5 ) . hence , x = p and y = - 5 should sactisfy the graph . soliving 5 = - p 2 + 9 p 2 = 4 p = + or - 2 simillarly point ( t , - 7 ) should satisfy the equation . hence x = t and y = - 7 . - 7 = - t 2 + 9 t = + or - 4 considering p = - 2 and t = 4 , the least slope is ( - 7 + 5 ) / ( 4 - 2 ) = - 1 imo option b is correct answer .
Answer: b
Python program:
a = 7 - 5
b = 9 + 7 
c = math.sqrt(b)
d = 5 + 9 
e = math.sqrt(d)
f = c - e
g = a / f
Problem: two numbers n and 16 have lcm = 52 and gcf = 8 . find n .
Options: a ) 35 , b ) 26 , c ) 76 , d ) 87 , e ) 24
Rationale: "the product of two integers is equal to the product of their lcm and gcf . hence . 16 * n = 52 * 8 n = 52 * 8 / 16 = 26 correct answer b"
Answer: b
Python program:
a = 52 * 8
b = a / 16
Problem: an ant walks an average of 1000 meters in 30 minutes . a beetle walks 10 % less distance at the same time on the average . assuming the beetle walks at her regular rate , what is its speed in km / h ?
Options: a ) 1.8 , b ) 1.6 , c ) 2.775 . , d ) 1.9 , e ) 3.5 .
Rationale: the ant walks an average of 1000 meters in 30 minutes 1000 meters in 1 / 2 hours the beetle walks 10 % less distance = 1000 - 10 = 900 meters in 30 minutes 0.900 km in 30 / 60 = 1 / 2 hours speed = 0.900 * 2 = 1.8 km / h i guess option a should be 1.8
Answer: a
Python program:
a = 1000 / 1000
b = 30 / const_60
c = a / b
d = 10 / 100
e = 1 - d
f = c * e
Problem: two trains 151 meters and 165 meters in length respectively are running in opposite directions , one at the rate of 80 km and the other at the rate of 65 kmph . in what time will they be completely clear of each other from the moment they meet ?
Options: a ) 7.19 , b ) 7.18 , c ) 7.16 , d ) 7.84 , e ) 7.12
Rationale: "t = ( 151 + 165 ) / ( 80 + 65 ) * 18 / 5 t = 7.84 answer : d"
Answer: d
Python program:
a = 151 + 165 
b = 80 + 65 
c = b * const_0_2778
d = a / c
Problem: joe has candys on his pocket , 4 of those candies have lemon flavor , and 3 have caramel flavor . if joe take one , what is the probability that he picks one caramel flavor ?
Options: a ) 1 , b ) 2 , c ) none , d ) 3 / 7 , e ) 3 / 4
Rationale: the total number of candies is 7 and the number of candies with lemon flavor is 3 then , in one chance the probability to pick one candie with lemon flavor is 3 / 7 answer d
Answer: d
Python program:
a = 4 + 3 
b = 3 / a
Problem: john bought a total of 24 mangoes and oranges . each mango costs 80 cents and each orange costs 60 cents . if the average price of the 24 mangoes and oranges that john originally purchased was 65 cents , then how many oranges needs to return to raise the average price of his purchase to 72 cents ?
Options: a ) 4 , b ) 5 , c ) 6 , d ) 7 , e ) 14
Rationale: "let number of mangoes be x , number of oranges be 24 - x 0.80 x + ( 24 - x ) 0.60 / 24 = 0.65 solving for x , we get x = 6 - - > mangoes 6 , oranges 18 now , number of oranges to be returned be y 0.80 * 6 + ( 18 - y ) * 0.60 / 24 - y = 0.72 solving for y , y = 14 ans : e"
Answer: e
Python program:
a = 65 / 100
b = a * 24
Problem: the difference between the ages of two persons is 10 years . fifteen years ago , the elder one was twice as old as the younger one . the present age of the elder person is
Options: a ) 25 years , b ) 30 years , c ) 35 years , d ) 40 years , e ) none
Rationale: "sol . let their ages of x years and ( x + 10 ) years respectively . then , ( x + 10 ) - 15 = 2 ( x - 15 ) ⇔ x - 5 = 2 x - 30 ⇔ x = 25 . ∴ present age of the elder person = ( x + 10 ) = 35 years . answer c"
Answer: c
Python program:
a = 3 + 2 
b = 10 - a
c = 10 - b
d = 3 + 2 
e = 10 - d
f = e * 2
g = c + f