euclaise/mathqa_programs huggingface dataset:
Problem: how much is 50 % of 40 is greater than 4 / 5 of 25 ?
Options: a ) 0 , b ) 67 , c ) 88 , d ) 12 , e ) 66
Rationale: "( 50 / 100 ) * 40 – ( 4 / 5 ) * 25 = 0 answer : a"
Answer: a
Python program:
a = 50 / 100
b = 40 * a
c = 4 / 5
d = c * 25
e = b - d
Problem: a certain telescope increases the visual range at a particular location from 80 kilometers to 150 kilometers . by what percent is the visual range increased by using the telescope ?
Options: a ) 30 % , b ) 33 1 / 2 % , c ) 40 % , d ) 60 % , e ) 87.5 %
Rationale: "original visual range = 80 km new visual range = 150 km percent increase in the visual range by using the telescope = ( 150 - 80 ) / 80 * 100 % = 7 / 8 * 100 % = 87.5 % answer e"
Answer: e
Python program:
a = 150 - 80
b = a / 80
c = b * 100
Problem: 34 . the side surface of a cylinder is rolled with a rectangle . if the height of a cylinder is 16 feet and the perimeter of the circular base . is 12 feet , what is the diagonal of the rectangle ?
Options: a ) 16
b ) 20
c ) 18
d ) 22
e ) 21
Rationale: think of an aluminum can can . if you took off the bottom and top and cut a slit down the length , it would flatten to a rectangle . the dimensions of the rectangle are the height of the can and the circumference of the circle . since you know both , use pythagoreans theorem or properties of 3 - 4 - 5 triangles to solve for the hypothenuse , 20 . ( correct answer b )
Answer: b
Python program:
a = 16 * 16
b = 12 * 12
c = a + b 
d = math.sqrt(c)
Problem: if ( x + yi ) / i = ( 7 + 9 i ) , where x and y are real , what is the value of ( x + yi ) ( x - yi ) ?
Options: a ) 110 , b ) 120 , c ) 130 , d ) 140 , e ) 150
Rationale: ( x + yi ) / i = ( 7 + 9 i ) ( x + yi ) = i ( 7 + 9 i ) = - 9 + 7 i ( x + yi ) ( x - yi ) = ( - 9 + 7 i ) ( - 9 - 7 i ) = 81 + 49 = 130 correct answer is c 0130
Answer: c
Python program:
a = 7 * 9
b = a * 2
Problem: how long does a train 110 m long traveling at 60 kmph takes to cross a bridge of 240 m in length ?
Options: a ) 18.9 sec , b ) 88.9 sec , c ) 22.9 sec , d ) 21.00 sec , e ) 72.0 sec
Rationale: "d = 110 + 240 = 350 m s = 60 * 5 / 18 = 50 / 3 t = 350 * 3 / 50 = 21.00 sec answer : d"
Answer: d
Python program:
a = 110 + 240 
b = 60 * const_0_2778
c = a / b
Problem: convert 250 inches into centimeter ?
Options: a ) 635 cm , b ) 620 cm , c ) 650 cm , d ) 610 cm , e ) 654 cm
Rationale: "1 inch = 2.54 cm 250 inches = 250 * 2.54 = 635 cm answer is a"
Answer: a
Python program:
a = 3 + 2 
b = a * 2
c = 3 + 2 
d = c * 2
e = b * d
f = e * 250
g = 3 + 2 
h = g * 2
i = 3 + 2 
j = i * 2
k = h * j
l = f / k
Problem: it takes 40 identical printing presses 12 hours to print 500,000 papers . how many hours would it take 30 of these printing presses to print 500,000 papers ?
Options: a ) 14 , b ) 15 , c ) 16 , d ) 18 , e ) 20
Rationale: "40 printing presses can do 1 / 12 of the job each hour . 30 printing presses can do 3 / 4 * 1 / 12 = 1 / 16 of the job each hour . the answer is c ."
Answer: c
Python program:
a = 1000 / 2
b = a * 1000
c = 1000 / 2
d = c * 1000
e = d / 40
f = e / 12
g = f * 30
h = b / g
Problem: a certain company reported that the revenue on sales increased 60 % from 2000 to 2003 , and increased 80 % from 2000 to 2005 . what was the approximate percent increase in revenue for this store from 2003 to 2005 ?
Options: a ) 50 % , b ) 40 % , c ) 35 % , d ) 32 % , e ) 13 %
Rationale: "assume the revenue in 2000 to be 100 . then in 2003 it would be 160 and and in 2005 180 , so from 2003 to 2005 it increased by ( 180 - 160 ) / 160 = 20 / 160 = 13 % answer : e ."
Answer: e
Python program:
a = 80 / 100
b = 1 + a 
c = 60 / 100
d = 1 + c 
e = b - d
f = 60 / 100
g = 1 + f 
h = e / g
i = h * 100
Problem: if the price of a book is first decreased by 25 % and then increased by 20 % , then the net change in the price will be :
Options: a ) 10 , b ) 388 , c ) 37 , d ) 29 , e ) 22
Rationale: "explanation : let the original price be rs . 100 . new final price = 120 % of ( 75 % of rs . 100 ) = rs . ( 120 / 100 * 75 / 100 * 100 ) = rs . 90 . decrease = 10 % answer : a ) 10"
Answer: a
Python program:
a = 100 * 25
b = a / 100
c = 100 - b
d = c / 100
e = 100 * 20
f = e / 100
g = 100 + f 
h = g / 100
i = d * h
j = i * 100
k = 100 - j
Problem: p runs 20 % faster than q so p gives q a 300 meter head start . if the race ends in a tie , how far ( in meters ) did p run in the race ?
Options: a ) 1500 , b ) 1600 , c ) 1700 , d ) 1800 , e ) 1900
Rationale: "let d be the race distance that p ran . let t be the time it took to complete the race . let v be q ' s speed . t = d / 1.2 v = ( d - 300 ) / v d = 1.2 d - 360 0.2 d = 360 d = 1800 meters . the answer is d ."
Answer: d
Python program:
a = 300 * 100
b = a / 20
c = b + 300
Problem: if a certain number is divided by 11 , the quotient , dividend , and divisor , added together , will amount to 71 . what is the number ?
Options: a ) 18 , b ) 28 , c ) 48 , d ) 38 , e ) 55
Rationale: "let x = the number sought . then x / 11 + x + 11 = 71 and x = 55 . e"
Answer: e
Python program:
a = 71 - 11
b = a * 11
c = 11 + 1 
d = b / c
Problem: the population of a town increases 25 % and 30 % respectively in two consecutive years . after the growth the present population of the town is 1950 . then what is the population of the town 2 years ago ?
Options: a ) a ) 800 , b ) b ) 900 , c ) c ) 1000 , d ) d ) 1100 , e ) e ) 1200
Rationale: "explanation : formula : ( after = 100 denominator ago = 100 numerator ) 1950 * 100 / 125 * 100 / 130 = 1200 answer : option e"
Answer: e
Python program:
a = 25 / 100
b = 1 + a 
c = 30 / 100
d = 1 + c 
e = b * d
f = 1950 / e
Problem: the number 0.127 is how much greater than 1 / 8 ?
Options: a ) 1 / 100 , b ) 1 / 1500 , c ) 1 / 2 , d ) 1 / 500 , e ) 1 / 600
Rationale: "explanation : 0.127 expressed as a fraction = 127 / 1000 1 / 8 can also be expressed as ( 1 x 125 ) / ( 8 x 125 ) = 125 / 1000 the difference is 2 / 1000 , which is 1 / 500 answer is d"
Answer: d
Python program:
a = 1 / 8
b = 0 - 127
Problem: a retailer purchases shirts from a wholesaler and then sells the shirts in her store at a retail price that is 80 percent greater than the wholesale price . if the retailer decreases the retail price by 25 percent this will have the same effect as increasing the wholesale price by what percent ?
Options: a ) 26 , b ) 37.5 , c ) 35 , d ) 44 , e ) 50
Rationale: "answer : c = 35 . assume rs . 100 to be the price at which the retailer buys from wholesaler . 80 % increase makes retail price = 180 . now 25 % decrease - > ( 1 - 25 / 100 ) * 180 = 135 . now compared to the wholesale price of 100 , 35 % increase is what will have the same effect as increasing the wholesale price ."
Answer: c
Python program:
a = 80 / 100
b = 1 + a 
c = 25 / 100
d = 1 - c
e = b * d
f = e - 1
g = f * 100
Problem: a cistern which could be filled in 4 hours takes one hour more to be filled owing to a leak in its bottom . if the cistern is full in what time will the leak empty it ?
Options: a ) 76 hrs , b ) 99 hrs , c ) 55 hrs , d ) 20 / 3 hrs , e ) 11 hrs
Rationale: "1 / 4 - 1 / x = 1 / 10 = > 20 / 3 hrs answer : d"
Answer: d
Python program:
a = 1 / 4
b = 1 / 10
c = a - b
d = 1/(c)
Problem: let p be a prime number . if n = 7 p , how many divisors does n have ?
Options: a ) 1 , b ) 2 , c ) 3 , d ) 4 , e ) 5
Rationale: two . n = 7 * p , and both 7 and p are prime . so the answer is b .
Answer: b
Python program:
a = 1 / 2
b = 7 / 2
c = b - 2
d = a + c
Problem: in a factory there are 3 types of machine m 1 , m 2 and m which produces 25 % , 35 % and 40 % of the total products respectively . m 1 , m 2 and m 3 produces 2 % , 4 % and 5 % defective products , respectively . what is the percentage of non - defective products ?
Options: a ) 89 % , b ) 97.1 % , c ) 96.1 % , d ) 86.1 % , e ) none of these
Rationale: solution : non - defective products , { [ ( 25 * 0.98 ) + ( 35 * 0.96 ) + ( 40 * 0.95 ) ] / 100 } * 100 = 96.1 % . answer : option c
Answer: c
Python program:
a = 2 / 100
b = a * 25
c = 4 / 100
d = c * 35
e = b + d 
f = 5 / 100
g = f * 40
h = e + g 
i = 100 - h
Problem: if a = - 1 , what is the value of – ( a ^ 2 + a ^ 3 + a ^ 4 + a ^ 5 + a ^ 6 ) ?
Options: a ) - 14 , b ) - 4 , c ) - 1 , d ) 4 , e ) 14
Rationale: if a = - 1 , then putting values in equation = - [ ( - 1 ) ^ 2 + ( - 1 ) ^ 3 + ( - 1 ^ 4 ) + ( - 1 ^ 5 ) + ( - 1 ^ 6 ) ] = - [ 1 - 1 + 1 - 1 + 1 ] = - 1 answer = c = - 1
Answer: c
Python program:
a = 1 - 2
b = a ** 6
Problem: 6 animals of a circus has to be placed inside in 6 cages one in each cage . if 4 of the cage are too small for 6 of the animal then find the number of ways of caging the animal .
Options: a ) a . 240 , b ) b . 808250 , c ) c . 502450 , d ) d . 784200 , e ) e . 302400
Rationale: ways for cages that are too small = 5 * 4 * 3 * 2 = 120 since we have 2 cages and 2 animal left therefore ways for 2 cages = 2 ! total ways = 120 * 2 ! = 604800 answer a
Answer: a
Python program:
a = 6 * 4
b = a * 10
Problem: a goods train runs at the speed of 72 kmph and crosses a 250 m long platform in 30 seconds . what is the length of the goods train ?
Options: a ) 230 m , b ) 350 m , c ) 260 m , d ) 270 m , e ) none of these
Rationale: "explanation : speed = [ 72 x ( 5 / 18 ) ] m / sec = 20 m / sec . time = 30 sec . let the length of the train be x metres . then , [ ( x + 250 ) / 30 ] = 20 = > x + 250 = 600 = > x = 350 . answer : b"
Answer: b
Python program:
a = const_0_2778 * 72
b = 250 / a
c = 30 - b
d = const_0_2778 * 72
e = c * d
Problem: in a class of 20 students , 3 students did not borrow any books from the library , 9 students each borrowed 1 book , 4 students each borrowed 2 books , and the rest borrowed at least 3 books . if the average number of books per student was 2 , what is the maximum number of books any single student could have borrowed ?
Options: a ) 13 , b ) 14 , c ) 15 , d ) 16 , e ) 17
Rationale: "the total number of books the students borrowed is 20 * 2 = 40 . the students who borrowed zero , one , or two books borrowed 9 * 1 + 4 * 2 = 17 books . the 4 students who borrowed at least three books borrowed 40 - 17 = 23 books . if 3 of these students borrowed exactly 3 books , then the maximum that one student could have borrowed is 23 - 9 = 14 books . the answer is b ."
Answer: b
Python program:
a = 20 * 2
b = 9 * 1
c = b + 4 
d = c + 3 
e = 20 - d
f = e - 1
g = f * 3
h = 9 * 1
i = 4 * 3
j = h + i 
k = g + j 
l = a - k
Problem: the speed at which a man can row a boat in still water is 6 km / hr . if he rows downstream , where the speed of current is 3 km / hr , how many seconds will he take to cover 80 meters ?
Options: a ) 28 , b ) 32 , c ) 36 , d ) 40 , e ) 44
Rationale: "the speed of the boat downstream = 6 + 3 = 9 km / hr 9 km / hr * 5 / 18 = 2.5 m / s the time taken to cover 80 meters = 80 / 2.5 = 32 seconds . the answer is b ."
Answer: b
Python program:
a = 6 + 3 
b = a * const_0_2778
c = 80 / b
Problem: a prison of 10,000 inmates has enough food to feed them all for 50 days . after 10 days some of the inmates leave and the food is now enough for the same period of 50 days as before . how many of them left ?
Options: a ) 3,000 , b ) 2,200 , c ) 2,000 , d ) 1,000 , e ) 200
Rationale: 10,000 - - - 50 10,000 - - - 40 x - - - 50 x * 50 = 10,000 * 40 x = 8,000 10,000 - - - - - - - - 2,000 answer = c
Answer: c
Python program:
a = 10 / 50
b = a * 10
Problem: a retailer buys a radio for rs 225 . his overhead expenses are rs 15 . he sellis the radio for rs 300 . the profit percent of the retailer is
Options: a ) 10 % , b ) 50 % , c ) 25 % , d ) 52 % , e ) none of these
Rationale: "explanation : cost price = ( 225 + 15 ) = 240 sell price = 300 gain = ( 60 / 240 ) * 100 = 25 % . answer : c"
Answer: c
Python program:
a = 225 + 15 
b = 300 / a
c = b * 100
d = c - 100
Problem: if teena is driving at 55 miles per hour and is currently 7.5 miles behind joe , who is driving at 40 miles per hour in the same direction then in how many minutes will teena be 52.5 miles ahead of joe ?
Options: a ) 15 , b ) 240 , c ) 75 , d ) 90 , e ) 105
Rationale: "this type of questions should be solved without any complex calculations as these questions become imperative in gaining that extra 30 - 40 seconds for a difficult one . teena covers 55 miles in 60 mins . joe covers 40 miles in 60 mins so teena gains 15 miles every 60 mins teena need to cover 7.5 + 52.5 miles . teena can cover 7.5 miles in 30 mins teena will cover 52.5 miles in 210 mins so answer 30 + 210 = 240 mins . ( answer b )"
Answer: b
Python program:
a = 55 - 40
b = a + 7 
c = 55 - 40
d = b / c
e = d * const_60
Problem: on a partly cloudy day , derek decides to walk back from work . when it is sunny , he walks at a speed of s miles / hr ( s is an integer ) and when it gets cloudy , he increases his speed to ( s + 1 ) miles / hr . if his average speed for the entire distance is 2.8 miles / hr , what fraction r of the total distance did he cover while the sun was shining on him ?
Options: a ) 1 / 4 , b ) 4 / 5 , c ) 1 / 5 , d ) 1 / 6 , e ) 1 / 7
Rationale: if s is an integer and we know that the average speed is 2.8 , s must be = 2 . that meanss + 1 = 3 . this implies that the ratio of time for s = 2 is 1 / 4 of the total time . the formula for distance / rate is d = rt . . . so the distance travelled when s = 2 is 2 t . the distance travelled for s + 1 = 3 is 3 * 4 t or 12 t . therefore , total distance covered while the sun was shining over him is r = 2 / 14 = 1 / 7 . answer : e
Answer: e
Python program:
a = math.lcm(2, 3)
b = a / 2
c = b - 2
Problem: fresh grapes contain 90 % by weight while dried grapes contain 20 % water by weight . what is the weight of dry grapes available from 5 kg of fresh grapes ?
Options: a ) 2 kg , b ) 2.4 kg , c ) 2.5 kg , d ) 10 kg , e ) 0.625
Rationale: "the weight of non - water in 5 kg of fresh grapes ( which is 100 - 90 = 10 % of whole weight ) will be the same as the weight of non - water in x kg of dried grapes ( which is 100 - 20 = 80 % of whole weight ) , so 5 â ˆ — 0.1 = x â ˆ — 0.8 - - > x = 0.625 answer : e ."
Answer: e
Python program:
a = 100 - 90
b = a * 5
c = b / 100
d = 100 - 20
e = c / d
f = e * 100
Problem: steve traveled the first 2 hours of his journey at 50 mph and the last 3 hours of his journey at 80 mph . what is his average speed of travel for the entire journey ?
Options: a ) 68 mph , b ) 56.67 mph , c ) 60 mph , d ) 64 mph , e ) 66.67 mph
Rationale: "average speed = total distance / total time = ( 50 * 2 + 80 * 3 ) / ( 2 + 3 ) = 68 ans : a"
Answer: a
Python program:
a = 80 * 3
b = 50 * 2
c = a + b 
d = 3 + 2 
e = c / d
f = 100 / 3
g = f - const_0_33
h = e + g
Problem: in a certain state , the ratio of registered republicans to registered democrats is 3 to 2 , and every registered voter is either a republican or a democrat . if 80 percent of the republicans and 25 percent of the democrats are expected to vote for candidate x , and everyone else is expected to vote for candidate y , by what percent is candidate x expected to win the election ?
Options: a ) 2 % , b ) 5 % , c ) 16 % , d ) 20 % , e ) 25 %
Rationale: "since we were expected to find a percentage figure - it thought that it might be easier to pick a ' smart number ' to represent the total number of voters ( republicans and democrats ) . therefore , i picked 100 ( as the total number of voters ) and thus 30 : 20 represents the number ratio of republicans : democrats . if 80 % of republicans ( which is ( 60 * 0.8 ) = 48 ) and 25 % of democrats ( 40 * 0.25 = 10 ) voted for candidate x , means that out of total of 100 voters ; 58 ( 48 + 10 ) voters voted for candidate x and 42 voted for candidate y . thus we can infer that candidate x is expected to win the election by 16 ( 58 - 42 ) votes . therefore candidate x is expected to win the election by ( 16 / 100 ) votes which is equivalent to 16 % . i think the answer is c ."
Answer: c
Python program:
a = 25 / 100
b = a * 2
c = 80 / 100
d = c * 3
e = b + d 
f = 80 / 100
g = f * 3
h = 3 - g
i = 25 / 100
j = i * 2
k = 2 - j
l = h + k 
m = e - l
n = 3 + 2 
o = m / n
p = o * 100
Problem: the simple interest on a certain sum of money at the rate of 5 % p . a . for 8 years is rs . 840 . at what rate of interest the same amount of interest can be received on the same sum after 5 years ?
Options: a ) 6 % , b ) 8 % , c ) 9 % , d ) 10 % , e ) none
Rationale: "solution s . i . = rs . 840 , r = 5 % , t = 8 years . principal = rs . ( 800 x 840 / 5 x 8 ) = rs . 2100 . now , p = rs . 2100 , s . i . = rs . 840 , t = 5 years . ∴ rate = ( 100 x 840 / 2100 x 5 ) = 8 % . answer b"
Answer: b
Python program:
a = 840 / 5
b = 840 / 8
c = 5 / 100
d = b / c
e = a / d
f = e * 100
Problem: what is the rate percent when the simple interest on rs . 1200 amount to rs . 400 in 4 years ?
Options: a ) 8.33 % , b ) 6 % , c ) 2 % , d ) 95 % , e ) 1 %
Rationale: "interest for 4 yrs = 400 interest for 1 yr = 100 interest rate = 100 / 1200 x 100 = 8.33 % answer : a"
Answer: a
Python program:
a = 100 * 400
b = 1200 * 4
c = a / b
Problem: the average weight of a , b and c is 45 kg . if the average weight of a and b be 40 kg and that of b and c be 43 kg , then the weight of b is ?
Options: a ) 24 kg , b ) 62 kg , c ) 34 kg , d ) 31 kg , e ) 37 kg
Rationale: "let a , b , c represent their respective weights . then , we have : a + b + c = ( 45 * 3 ) = 135 - - - ( i ) a + b = ( 40 * 2 ) = 80 - - - ( ii ) b + c = ( 43 * 2 ) = 86 - - - ( iii ) adding ( ii ) and ( iii ) , we get : a + 2 b + c = 166 - - - ( iv ) subtracting ( i ) from ( iv ) , we get : b = 31 b ' s weight = 31 kg . answer : d"
Answer: d
Python program:
a = 40 * 2
b = 43 * 2
c = a + b 
d = 45 * 3
e = c - d
Problem: what is the units digit of 17 ^ 83 × 13 ^ 82 × 11 ^ 83 ?
Options: a ) 4 , b ) 5 , c ) 6 , d ) 7 , e ) 8
Rationale: "to find : the units digit of 17 ^ 83 × 13 ^ 82 × 11 ^ 87 let ' s reduce the clutter and simplify the product ( 7 ^ 83 ) ( 3 ^ 82 ) ( 1 ^ 87 ) 7 has a cyclicity of 4 : the last digit of any positive power of 7 repeats itself after every 4 th power so 7 ^ 5 has the same last digit as 7 ^ 1 , 7 ^ 9 , 7 ^ 13 thus , 7 ^ 83 has the same last digit as 7 ^ 3 , 7 ^ 7 , 7 ^ 11 i . e . 3 3 has a cyclicity of 4 : exactly the same routine as above thus , 3 ^ 82 has the same last digit as 3 ^ 2 , 3 ^ 6 , 3 ^ 10 i . e . 9 any power of 1 will result in 1 as the last digit so , product of our last digits = 3 x 9 x 1 = 27 . . . . last digit is 5 correct option : b"
Answer: b
Python program:
a = math.factorial(17)
b = math.factorial(83)
c = a * b
d = math.factorial(17)
e = math.factorial(82)
f = d * e
g = c + f 
h = g / 17
Problem: 400 students took a mock exam in delhi , 60 % of the boys and 80 % of the girls cleared the cut off in the examination . if the total percentage of students qualifying is 65 % , how many girls appeared in the examination ?
Options: a ) 50 , b ) 100 , c ) 120 , d ) 140 , e ) 180
Rationale: 60 % * x + 80 % * ( 400 - x ) = 65 % * 400 ans = 100 answer : b
Answer: b
Python program:
a = 65 / 100
b = 400 * a
c = 60 / 100
d = 400 * c
e = b - d
f = 80 / 100
g = 60 / 100
h = f - g
i = e / h
Problem: what is the greater of the two numbers whose product is 2688 , given that the sum of the two numbers exceeds their difference by 64 ?
Options: a ) a ) 84 , b ) b ) 104 , c ) c ) 110 , d ) d ) 72 , e ) of these
Rationale: "let the greater and the smaller number be g and s respectively . gs = 2560 g + s exceeds g - s by 64 i . e . , g + s - ( g - s ) = 64 i . e . , 2 s = 64 = > s = 32 . g = 2688 / s = 84 . answer : a"
Answer: a
Python program:
a = 2 ** 4
b = a * 2
c = 2688 / b
Problem: the proportion of copper and zinc in the brass is 3 : 7 . how much zinc will there be in 100 kg of brass ?
Options: a ) 70 , b ) 50 , c ) 40 , d ) 270 , e ) 170
Rationale: "7 / 10 * 100 = 70 answer : a"
Answer: a
Python program:
a = 7 + 3 
b = 7 / a
c = b * 100
Problem: a contractor undertakes to do a job within 100 days and hires 10 people to do it . after 20 days , he realizes that one fourth of the work is done so he fires 2 people . in how many more days q will the work get over ?
Options: a ) q = 60 , b ) q = 70 , c ) q = 75 , d ) 80 , e ) 100
Rationale: we can also use the concept of man - days here 100 days - - > 10 men so the job includes 100 * 10 = 1000 man - days after 20 days 1 / 4 of job is completed so 1 / 4 x 1000 man - days = 250 man - days job is done now the balance job = 1000 - 250 = 750 man - days worth of job since 2 men are fired so b / l men = 8 therefore total no . of days of job = 750 man - day / 8 days = 375 / 4 = 94 days ( approx . ) now since this is total and ques . is asking for additional no . of days , so 94 - 20 = 74 days the nearest approx . to answer is 75 ans : c ( 75 days )
Answer: c
Python program:
a = 10 * 20
b = a / const_0_25
c = 1 - const_0_25
d = b * c
e = 10 - 2
f = d / e
Problem: find the value of c from ( 8 ) ^ 3 x 9 ^ 3 ã · 679 = c .
Options: a ) 249.7 , b ) 529.7 , c ) 549.7 , d ) 594.7 , e ) 119.7
Rationale: given exp . = ( 8 ) ^ 3 x 9 ^ 3 ã · 679 = c = 512 x 729 ã · 679 = 549.7 c
Answer: c
Python program:
a = 8 ** 3
b = 9 ** 3
c = a * b
d = c / 679
Problem: a man has $ 10,000 to invest . he invests $ 4000 at 5 % and $ 3500 at 4 % . in order to have a yearly income of $ 500 , he must invest the remainder at
Options: a ) 6 % , b ) 6.1 % , c ) 6.2 % , d ) 6.3 % , e ) 6.4 %
Rationale: income from $ 4000 at 5 % in one year = $ 4000 of 5 % . = $ 4000 × 5 / 100 . = $ 4000 × 0.05 . = $ 200 . income from $ 3500 at 4 % in one year = $ 3500 of 4 % . = $ 3500 × 4 / 100 . = $ 3500 × 0.04 . = $ 140 . total income from 4000 at 5 % and 3500 at 4 % = $ 200 + $ 140 = $ 340 . remaining income amount in order to have a yearly income of $ 500 = $ 500 - $ 340 . = $ 160 . total invested amount = $ 4000 + $ 3500 = $ 7500 . remaining invest amount = $ 10000 - $ 7500 = $ 2500 . we know that , interest = principal × rate × time interest = $ 160 , principal = $ 2500 , rate = r [ we need to find the value of r ] , time = 1 year . 160 = 2500 × r × 1 . 160 = 2500 r 160 / 2500 = 2500 r / 2500 [ divide both sides by 2500 ] 0.064 = r r = 0.064 change it to a percent by moving the decimal to the right two places r = 6.4 % therefore , he invested the remaining amount $ 2500 at 6.4 % in order to get $ 500 income every year . the answer is ( e )
Answer: e
Python program:
a = 4000 / 100
b = a * 5
c = 500 - b
d = 3500 / 100
e = d * 4
f = c - e
g = 100 * 100
h = g - 4000
i = h - 3500
j = i / 100
k = f / j
Problem: a train speeds past a pole in 11 seconds and a platform 120 m long in 22 seconds . its length is ?
Options: a ) 128 , b ) 177 , c ) 199 , d ) 120 , e ) 150
Rationale: let the length of the train be x meters and its speed be y m / sec . they , x / y = 11 = > y = x / 11 x + 120 / 22 = x / 11 x = 120 m . answer : d
Answer: d
Python program:
a = 2 - 1
b = 120 * a
Problem: a farmer has an apple orchard consisting of fuji and gala apple trees . due to high winds this year 10 % of his trees cross pollinated . the number of his trees that are pure fuji plus the cross - pollinated ones totals 180 , while 3 / 4 of all his trees are pure fuji . how many of his trees are pure gala ?
Options: a ) 31 , b ) 33 , c ) 55 , d ) 77 , e ) 88
Rationale: "let f = pure fuji , g = pure gala and c - cross pollinated . c = 10 % of x where x is total trees . c = . 1 x also 3 x / 4 = f and c + f = 180 = > . 1 x + 3 / 4 x = 180 = > x = 211 211 - 180 = pure gala = 31 . a"
Answer: a
Python program:
a = 10 / 100
b = 3 / 4
c = a + b 
d = 180 / c
e = d - 180
Problem: the banker â € ™ s gain on a sum due 3 years hence at 12 % per annum is rs . 90 . the banker â € ™ s discount is
Options: a ) rs . 340 , b ) rs . 840 , c ) rs . 1020 , d ) rs . 760 , e ) none
Rationale: "solution t . d = ( b . g x 100 / r x t ) = rs . ( 90 x 100 / 12 x 3 ) = rs . 250 . b . d = rs ( 250 + 90 ) = rs . 340 . answer a"
Answer: a
Python program:
a = 90 * 100
b = 3 * 12
c = a / b
d = c + 90
Problem: in the quadratic equation x 2 - bx + 20 = 0 , if the product of two roots is 20 , what is the sum of the two roots ?
Options: a ) 20 , b ) 12 , c ) 16 , d ) 14 , e ) 18
Rationale: explanation : the sum of the roots of the quadratic equation ax 2 + ax + c = 0 are ( - b / a ) and the product of the roots are ( c / a ) . thus , in the equation x 2 - ax + 20 = 0 , where a = 1 , b = - a and c = 20 . we get , product of the roots = 20 sum of the roots = - ( - 12 ) / 1 = 12 answer : b
Answer: b
Python program:
a = 20 / 2
b = a + 2