euclaise/mathqa_programs huggingface dataset:
Problem: the ratio w , by volume of soap to alcohol to water in a 76 litre solution is 2 : 50 : 100 . the solution is then altered by adding more soap , alcohol and water . after this alteration the ratio , by volume of soap to water in the solution doubles whereas the ratio , by volume of soap to water remains the same as before . what could be the resulting volume .
Options: a ) 79 litres , b ) 78 litres , c ) 77 litres , d ) 152 liters , e ) 304 litres
Rationale: i guess it should be the ratio w , by volume ofsoaptowaterin the solutiondoubleswhereas the ratio , by volume ofalocoholtowaterremains thesameas before 2 : 50 : 100 = > 1 : 25 : 50 . if we add all the parts , we get 76 liters so we have 1 liters of soap , 25 liters of alcohol and 50 liters of water . now as per the question , soap : water doubles but alcohol to water remains the same . so soap becomes 2 liters , alcohol remains 25 liters and water remains at 50 liters . hence 77 liters - option c )
Answer: c
Python program:
a = 76 + 1
Problem: the sum of the numbers is 98 . if the ratio between the first and the second be 2 : 3 and that between the second and third be 5 : 8 , then find the second number ?
Options: a ) 24 , b ) 30 , c ) 36 , d ) 42 , e ) 50
Rationale: given ratios 2 : 3 5 : 8 10 : 15 : 24 the second number = 98 / ( 10 + 15 + 24 ) * 15 = 30 answer is b
Answer: b
Python program:
a = math.lcm(3, 5)
b = 98 * a
c = 8 * 3
d = 5 * 2
e = 5 * 3
f = d + e 
g = c + f 
h = b / g
Problem: jaime earned enough money by selling seashells at 35 cents each to buy several used paperback books at 55 cents each . if he spent all of the money he earned selling seashells to buy the books , what is the least number of seashells he could have sold ?
Options: a ) 5 , b ) 11 , c ) 17 , d ) 22 , e ) 30
Rationale: let ' s test answer d : 22 seashells . . . . with 22 seashells , jamie would have 22 ( 35 ) = 770 cents . this would allow him to buy 14 books for 770 cents total , with no money left over . this is an exact match for what we were told , so this must be the answer . final answer : [ reveal ] spoiler : d
Answer: d
Python program:
a = math.lcm(35, 55)
b = a / 35
c = b + 10
Problem: a manufacturer produces a certain men ' s athletic shoe in integer sizes from 8 to 17 . for this particular shoe , each unit increase in size corresponds to a 1 / 5 - inch increase in the length of the shoe . if the largest size of this shoe is 40 % longer than the smallest size , how long , in inches , is the shoe in size 15 ?
Options: a ) 5.4 , b ) 5.9 , c ) 6.3 , d ) 6.7 , e ) 7.5
Rationale: let x be the length of the size 8 shoe . then 0.4 x = 9 / 5 x = 4.5 inches the size 15 shoe has a length of 4.5 + 7 / 5 = 5.9 inches the answer is b .
Answer: b
Python program:
a = 1 / 5
b = 17 - 8
c = a * b
d = 40 / 100
e = c / d
f = 15 - 8
g = 1 / 5
h = f * g
i = e + h
Problem: the average salary / head of allthe workers in a workshop is rs . 850 , if the average salary / head of 7 technician is rs . 1000 and the average salary / head of the rest is rs . 780 , the total no . of workers in the work - shop is ?
Options: a ) 18 , b ) 20 , c ) 22 , d ) 24 , e ) 26
Rationale: "let the total number of workers be y . so sum of salary for all workers = sum of salary of 7 technician + sum of salary for other y - 7 workers . 7 x 1000 + 780 ( y - 7 ) = 850 y ⇒ 7000 + 780 y - 5460 = 850 y ⇒ 70 y = 1540 ∴ y = 22 so total number of workers = 22 c"
Answer: c
Python program:
a = 7 * 1000
b = 7 * 780
c = a - b
d = 850 - 780
e = c / d
Problem: a man buys a cycle for rs . 1600 and sells it at a loss of 20 % . what is the selling price of the cycle ?
Options: a ) 1410 , b ) 1420 , c ) 1430 , d ) 1440 , e ) 1280
Rationale: "s . p . = 80 % of rs . 1600 = 80 / 100 x 1600 = rs . 1280 answer : e"
Answer: e
Python program:
a = 100 - 20
b = a * 1600
c = b / 100
Problem: 15 people went to a hotel for combine dinner party 10 of them spent rs . 50 each on their dinner and rest spent 4 more than the average expenditure of all the 15 . what was the total money spent by them .
Options: a ) 1628.4 , b ) 1534 , c ) 780 , d ) 1496 , e ) none of these
Rationale: "solution : let average expenditure of 15 people be x . then , 15 x = 10 * 50 + 5 * ( x + 4 ) ; or , 15 x = 10 * 50 + 5 x + 20 ; or , x = 52 ; so , total money spent = 52 * 15 = rs . 780 . answer : option c"
Answer: c
Python program:
a = 10 * 50
b = 15 - 10
c = b * 4
d = a + c 
e = 15 - 10
f = 15 - e
g = d / f
h = g * 15
Problem: what is the maximum number of pieces of birthday cake of size 5 ” by 5 ” that can be cut from a cake 15 ” by 15 ” ?
Options: a ) 5 , b ) 10 , c ) 16 , d ) 20 , e ) 9
Rationale: "the prompt is essentially asking for the maximum number of 5 x 5 squares that can be cut from a larger 15 by 15 square . since each ' row ' and each ' column ' of the larger square can be sub - divided into 3 ' pieces ' each , we have ( 3 ) ( 3 ) = 9 total smaller squares ( at maximum ) . e"
Answer: e
Python program:
a = 15 * 15
b = 5 * 5
c = a / b
Problem: the width of a rectangular hall is ½ of its length . if the area of the hall is 450 sq . m , what is the difference between its length and breadth ?
Options: a ) 8 m , b ) 10 m , c ) 12 m , d ) 15 m , e ) 17 m
Rationale: "let the length of the hall be x m breadth of the hall = 1 x / 2 m area of the hall = length * breadth 450 = x * 1 x / 2 x ² = 900 x = 30 difference between the length and breadth of the hall = x - 1 x / 2 = x / 2 = 30 / 2 = 15 m answer : d"
Answer: d
Python program:
a = 1 / 2
b = 450 / a
c = math.sqrt(b)
d = c / 2
Problem: if p / q = 4 / 5 , then the value of 1 / 7 + { ( 2 q - p ) / ( 2 q + p ) } is ?
Options: a ) 4 / 7 , b ) 34 , c ) 1 , d ) 2 , e ) 3
Rationale: "answer given exp . = 4 / 7 + { ( 2 q - p ) / ( 2 q + p ) } dividing numerator as well as denominator by q , exp = 1 / 7 + { 2 - p / q ) / ( 2 + p / q ) } = 1 / 7 + { ( 2 - 4 / 5 ) / ( 2 + 4 / 5 ) } = 1 / 7 + 6 / 14 = 1 / 7 + 3 / 7 = 4 / 7 correct option : a"
Answer: a
Python program:
a = 1 / 7
b = 4 / 5
c = 2 - b
d = 4 / 5
e = 2 + d 
f = c / e
g = a + f
Problem: when a natural number n is successively divided by 1020 , 3040 . the remainders are 5060 , 7080 . what will be the sum of the remainders if the order of the division is reversed ?
Options: a ) 16 , b ) 14 , c ) 28 , d ) 11 , e ) 9
Rationale: 10 20 30 40 50 60 70 80 leave the top right - most number 8 start with bottom right - most number 5 80 * 30 + 70 = 2470 2470 * 20 + 60 = 49460 49460 * 10 + 50 = 494650 this is the number required now , do the successive division in the reverse order the sum of the remainders is 28 hence , the correct option is c
Answer: c
Python program:
a = 4 + 3 
b = 1 + 2 
c = a + b 
d = c * 2
e = 5060 / 1020
f = math.floor(e)
g = 7080 / 3040
h = math.floor(g)
i = f * h
j = d + i
Problem: in the land of oz only one or two - letter words are used . the local language has 68 different letters . the parliament decided to forbid the use of the seventh letter . how many words have the people of oz lost because of the prohibition ?
Options: a ) 65 , b ) 66 , c ) 67 , d ) 131 , e ) 136
Rationale: "the answer to the question is indeed e . the problem with above solutions is that they do not consider words like aa , bb , . . . the number of 1 letter words ( x ) that can be made from 68 letters is 68 ; the number of 2 letter words ( xx ) that can be made from 68 letters is 68 * 68 , since each x can take 68 values . total : 68 + 68 * 68 . similarly : the number of 1 letter words ( x ) that can be made from 67 letters is 67 ; the number of 2 letter words ( xx ) that can be made from 67 letters is 67 * 67 , since each x can take 67 values . total : 67 + 67 * 67 . the difference is ( 68 + 68 * 68 ) - ( 67 + 67 * 67 ) = 136 . answer : e ."
Answer: e
Python program:
a = 1 + 68 
b = a + 68
Problem: if the sales tax be reduced from 4 ( 1 / 3 ) % to 2 ( 1 / 2 ) % , then what difference does it make to a person who purchases a bag with marked price of rs . 8000 ?
Options: a ) 146.69 , b ) 146.66 , c ) 146.62 , d ) 146.61 , e ) 146.6
Rationale: "explanation : required difference = ( 4 ( 1 / 3 ) of rs . 8000 ) - ( 2 ( 1 / 2 ) of rs . 8000 ) = ( 13 / 3 – 5 / 2 ) % of rs . 8000 = ( 11 / 6 ) x ( 1 / 100 ) x 8000 = rs . 146.66 answer : b"
Answer: b
Python program:
a = 1 / 4
b = 4 + a 
c = b / 100
d = c + 1 
e = 1 / 2
f = e + 1 
g = f / 100
h = g + 1 
i = 8000 / h
j = d * i
k = j - 8000
Problem: how many positive 3 - digit integers are divisible by both 3 and 7 ?
Options: a ) 43 , b ) 45 , c ) 47 , d ) 50 , e ) 52
Rationale: a number to be divisible by both 3 and 7 should be divisible by the least common multiple of 3 and 7 so by 21 . multiples of 21 between 100 and 999 , inclusive is ( last - first ) / multiple + 1 = ( 987 - 105 ) / 21 + 1 = 42 + 1 = 43 answer : a .
Answer: a
Python program:
a = math.lcm(3, 7)
b = 1000 / a
c = math.floor(b)
d = math.lcm(3, 7)
e = 100 / d
f = math.floor(e)
g = c - f
Problem: the average of 50 numbers id 62 . if two numbers , namely 45 and 55 are discarded , the average of the remaining numbers is :
Options: a ) 22.3 , b ) 33.2 , c ) 22.2 , d ) 51.3 , e ) 62.5
Rationale: "explanation : total of 50 numbers = ( 50 × 62 ) = 3100 total of 48 numbers = ( 3100 - ( 45 + 55 ) ] = 3000 required average = 3000 / 48 = 62.5 answer : e"
Answer: e
Python program:
a = 50 * 62
b = 45 + 55 
c = a - b
d = 50 - 2
e = c / d
Problem: in what time will a train 100 meters long cross an electric pole , if its speed is 144 km / hr
Options: a ) 8.5 seconds , b ) 2.8 seconds , c ) 3.5 seconds , d ) 2.5 seconds , e ) 2.6 seconds
Rationale: "first convert speed into m / sec speed = 144 * ( 5 / 18 ) = 40 m / sec time = distance / speed = 100 / 40 = 2.5 seconds answer : d"
Answer: d
Python program:
a = 144 * const_0_2778
b = 100 / a
Problem: what is the unit digit of ( 6 ! * 6 ! / 6 ! * 3 ! ) ?
Options: a ) 0 , b ) 1 , c ) 2 , d ) 3 , e ) 4
Rationale: ( 6 ! * 6 ! / 6 ! * 3 ! ) = ( 6 ! / 3 ! ) = 720 / 6 = 120 units digit of the above product will be equal to 0 answer a
Answer: a
Python program:
a = math.factorial(6)
b = math.factorial(6)
c = a * b
d = math.factorial(6)
e = math.factorial(3)
f = d * e
g = c / f
Problem: two vessels contains equal number of mixtures milk and water in the ratio 5 : 3 and 6 : 2 . both the mixtures are now mixed thoroughly . find the ratio of milk to water in the new mixture so obtained ?
Options: a ) 11 : 5 , b ) 9 : 13 , c ) 5 : 11 , d ) 11 : 3 , e ) 15 : 4
Rationale: "the ratio of milk and water in the new vessel is = ( 5 / 8 + 6 / 8 ) : ( 3 / 8 + 2 / 8 ) = 11 / 8 : 5 / 8 = 11 : 5 answer is a"
Answer: a
Python program:
a = 6 + 2 
b = 5 + 3 
c = a / b
d = 5 * c
e = d + 6 
f = 6 + 2 
g = 5 + 3 
h = f / g
i = 3 * h
j = i + 2 
k = e / j
Problem: mona and donald fly to rome for the weekend . they take cash only in notes of $ 10 and notes of € 10 . mona carries 3 times the amount of euros donald carries . she also carries as many dollars as donald carries . the number of € 10 notes they take is double the number of $ 10 notes they take . if donald carries a total of 39 notes ( of either $ 10 or € 10 , ) then what is the total number of notes ( of either $ 10 or € 10 , ) they take ?
Options: a ) 130 , b ) 80 , c ) 100 , d ) 120 , e ) 150
Rationale: let e 10 = x no . d 10 = y no . donald is having x + y notes mona carries 3 x + y again x = 2 y or donald x + y = 39 or 3 y = 39 y = 13 ; x = 26 , total notes they carry = 104 + 26 = 130 a
Answer: a
Python program:
a = 39 * 3
b = 39 / 3
c = a + b
Problem: in a lake , there is a patch of lily pads . every day , the patch doubles in size . it takes 34 days for the patch to cover the entire lake , how many days would it take the patch to cover half of the lake ?
Options: a ) 33 , b ) 2 ^ 4 * 3 , c ) 24 , d ) 38 , e ) 47
Rationale: "working backward from the day it ' s covered : day 34 : fully covered day 33 : half covered so 33 days answer : a"
Answer: a
Python program:
a = 34 - 1
Problem: the water level in a reservoir has been dropping at the rate of 14 inches per day . exactly 5 days ago , the water level was at h inches . what will be the water level exactly 4 days from now if the rate at which the level is dropping remains the same ?
Options: a ) h − 12 , b ) h − 56 , c ) h − 14 , d ) h + 14 , e ) h - 126
Rationale: "drop = 14 inches / day 5 days ago = h , means now it ' s equal h - 70 and in 4 days = h - 70 - 56 = h - 126 answer e"
Answer: e
Python program:
a = 4 / 5
b = 14 * a
Problem: how long does a train 165 meters long running at the rate of 54 kmph take to cross a bridge 850 meters in length ?
Options: a ) 28 , b ) 27 , c ) 55 , d ) 18 , e ) 67.7
Rationale: "t = ( 850 + 165 ) / 54 * 18 / 5 t = 67.7 answer : e"
Answer: e
Python program:
a = 165 + 850 
b = 54 * const_0_2778
c = a / b
Problem: in the faculty of reverse - engineering , 350 second year students study numeric methods , 250 second year students study automatic control of airborne vehicles and 100 second year students study them both . how many students are there in the faculty if the second year students are approximately 25 % of the total ?
Options: a ) 1800 , b ) 1900 , c ) 2100 , d ) 2000 , e ) 2200
Rationale: "total number of students studying both are 350 + 250 - 100 = 500 ( subtracting the 100 since they were included in the both the other numbers already ) . so 25 % of total is 500 , so 100 % is 2000 answer is d"
Answer: d
Python program:
a = 350 + 250
Problem: how many numbers from 39 to 79 are exactly divisible by 11 ?
Options: a ) 5 , b ) 7 , c ) 4 , d ) 11 , e ) 12
Rationale: 39 / 11 = 1 and 79 / 11 = 7 = = > 7 - 3 = 4 numbers answer : c
Answer: c
Python program:
a = 79 / 11
b = math.floor(a)
c = b * 11
d = 39 / 11
e = math.floor(d)
f = e + 1 
g = f * 11
h = c - g
i = h / 11
j = i + 1
Problem: in the coordinate plane , points ( x , 1 ) and ( 12 , y ) are on line k . if line k passes through the origin and has slope 1 / 2 , then x + y =
Options: a ) 4.5 , b ) 7 , c ) 8 , d ) 11 , e ) 12
Rationale: "line k passes through the origin and has slope 1 / 2 means that its equation is y = 1 / 2 * x . thus : ( x , 1 ) = ( 2 , 1 ) and ( 12 , y ) = ( 12,6 ) - - > x + y = 2 + 6 = 8 . answer : c ."
Answer: c
Python program:
a = 12 * 2
b = 1 / 2
c = a * b
Problem: when a number is divided by 6 & then multiply by 12 the answer is 8 what is the no . ?
Options: a ) 4.5 , b ) 5 , c ) 5.5 , d ) 5.8 , e ) 4
Rationale: "if $ x $ is the number , x / 6 * 12 = 8 = > 2 x = 8 = > x = 4.0 e"
Answer: e
Python program:
a = 8 / 12
b = a * 6
Problem: in one year , the population , of a village increased by 30 % and in the next year , it decreased by 30 % . if at the end of 2 nd year , the population was 13650 , what was it in the beginning ?
Options: a ) 7787 , b ) 8000 , c ) 15000 , d ) 1277 , e ) 2081
Rationale: "x * 130 / 100 * 70 / 100 = 13650 x * 0.91 = 13650 x = 13650 / 0.91 = > 15000 answer : c"
Answer: c
Python program:
a = 30 / 100
b = 1 - a
c = 13650 / b
d = 30 / 100
e = 1 + d 
f = c / e
Problem: three table runners have a combined area of 208 square inches . by overlapping the runners to cover 80 % of a table of area 175 square inches , the area that is covered by exactly two layers of runner is 24 square inches . what is the area of the table that is covered with three layers of runner ?
Options: a ) 22 square inches
b ) 20 square inches
c ) 24 square inches
d ) 28 square inches
e ) 30 square inches
Rationale: total = a + b + c - ( sum of exactly 2 - group overlaps ) - 2 * ( all three ) + neither 80 % * 175 = 208 - 24 - 2 * ( all three ) + 0 2 * ( all three ) = 208 - 24 - 140 all three = 22 answer : a
Answer: a
Python program:
a = 208 - 24
b = 80 / 100
c = 175 * b
d = a - c
e = d / 2
Problem: calculate the amount that an investor needs to be invest to earn $ 460 in interest in 12 months if the investor plans to invest x dollars in a savings account that pays interest at an annual rate of 9 % compounded semi - annually ?
Options: a ) 7,000 , b ) 4,000 , c ) 6,000 , d ) 5,000 , e ) 8,000
Rationale: "the approach is substitution , our interest requirement is 460 after 12 months , 2 compounding period . calculate the compound interest on each option and find out the one that yields 460 in 12 months 5,000 yielded $ 460 using the formula a = p ( 1 + r / n ) nt hence answer is d"
Answer: d
Python program:
a = 100 * 460
b = a / 9
Problem: the least number , which when divided by 48,60 , 72,108 and 140 leaves 38,50 , 62,98 and 130 as remainder respectively , is :
Options: a ) 11115 , b ) 15110 , c ) 15120 , d ) 15210 , e ) 12510
Rationale: "solution here ( 48 - 38 ) = 10 , ( 60 - 50 ) = 10 , ( 72 - 62 ) = 10 , ( 108 - 98 ) = 10 & ( 140 - 130 ) = 10 . so , required number = ( l . c . m . of 48 , 60,72 , 108,140 ) - 10 = 15120 - 10 = 15110 . answer b"
Answer: b
Python program:
a = 38 * 50
Problem: company c sells a line of 25 products with an average retail price of $ 1,200 . if none of these products sells for less than $ 400 , and exactly 12 of the products sell for less than $ 1,000 , what is the greatest possible selling price of the most expensive product ?
Options: a ) 10,000 , b ) 11.0 , c ) 12,000 , d ) 13,200 , e ) 14,000
Rationale: "the average price of 25 products is $ 1,200 means that the total price of 25 products is 25 * 1,200 = $ 30,000 . next , since exactly 12 of the products sell for less than $ 1,000 , then let ' s make these 12 items to be at $ 400 each ( min possible ) . now , the remaining 12 items can not be priced less than $ 1,000 , thus the minimum possible price of each of these 12 items is $ 1,000 . thus the minimum possible value of 24 products is 12 * 400 + 12 * 1,000 = $ 16,800 . therefore , the greatest possible selling price of the most expensive product is $ 30,000 - $ 16,800 = $ 13,200 . answer : d ."
Answer: d
Python program:
a = 12 * 100
b = a * 25
c = 400 * 12
d = 25 - 12
e = d - 1
f = e * 1
g = c + f 
h = b - g
Problem: how many bricks , each measuring 80 cm x 11.25 cm x 6 cm , will be needed to build a wall of 8 m x 6 m x 22.5 cm ?
Options: a ) 6400 , b ) 2000 , c ) 5500 , d ) 7400 , e ) 3000
Rationale: "number of bricks = volume of the wall / volume of 1 brick = ( 800 x 600 x 22.5 ) / ( 80 x 11.25 x 6 ) = 2000 answer : b"
Answer: b
Python program:
a = 8 * 100
b = 6 * 100
c = a * b
d = c * 22
e = 80 * 11
f = e * 6
g = d / f
Problem: a man goes downstream at 13 kmph , and upstream 8 kmph . the speed of the stream is
Options: a ) 0 kmph , b ) 4 kmph , c ) 16 kmph , d ) 2.5 kmph , e ) 26 kmph
Rationale: "speed of the stream = 1 / 2 ( 13 - 8 ) kmph = 2.5 kmph . correct option : d"
Answer: d
Python program:
a = 13 - 8
b = a / 2
Problem: drum x is 1 / 2 full of oil and drum y , which has twice the capacity of drum x , is 1 / 2 full of oil . if all of the oil in drum x is poured into drum y , then drum y will be filled to what capacity ?
Options: a ) 2 / 3 , b ) 3 / 4 , c ) 4 / 5 , d ) 5 / 6 , e ) 7 / 8
Rationale: "( 1 / 2 ) x = ( 1 / 4 ) y ( 1 / 4 ) y + ( 1 / 2 ) y = ( 3 / 4 ) y the answer is b ."
Answer: b
Python program:
a = 1 / 2
b = a * 12
c = 12 / 2
d = 1 / 2
e = c * d
f = b + e 
g = f / 12
Problem: the average weight of 8 people increases by 2.5 kg when a new person comes in place of one of them weighing 45 kg . what is the weight of the new person ?
Options: a ) 75 kg , b ) 85 kg , c ) 95 kg , d ) 65 kg , e ) 55 kg
Rationale: the total weight increase = ( 8 x 2.5 ) kg = 20 kg weight of new person = ( 45 + 20 ) kg = 65 kg the answer is d .
Answer: d
Python program:
a = 2 * 5
b = a + 45
Problem: average of 10 matches is 32 , how many runs one should should score to increase his average by 3 runs .
Options: a ) a ) 65 , b ) b ) 76 , c ) c ) 78 , d ) d ) 80 , e ) e ) 88
Rationale: "explanation : average after 11 innings should be 35 so , required score = ( 11 * 35 ) - ( 10 * 32 ) = 385 - 320 = 65 answer : option a"
Answer: a
Python program:
a = 32 + 3 
b = 10 + 1 
c = a * b
d = 10 * 32
e = c - d
Problem: how many internal diagonals does a hexagon ( six sided polygon ) have ?
Options: a ) 5 , b ) 6 , c ) 8 , d ) 9 , e ) 10
Rationale: "number of diagonals in any polygon can be found using this formula : n ( n - 3 ) / 2 here n = 6 no . of diagonals = 6 ( 6 - 3 ) / 2 = 9 ans d"
Answer: d
Python program:
a = 2 * 4
b = a - 3
c = 2 * 4
d = c / 2
e = b * d
Problem: running at their respective constant rate , machine x takes 2 days longer to produce w widgets than machines y . at these rates , if the two machines together produce 5 w / 4 widgets in 3 days , how many days would it take machine x alone to produce 3 w widgets .
Options: a ) 4 , b ) 6 , c ) 18 , d ) 10 , e ) 12
Rationale: "i am getting 12 . e . hope havent done any calculation errors . . approach . . let y = no . of days taken by y to do w widgets . then x will take y + 2 days . 1 / ( y + 2 ) + 1 / y = 5 / 12 ( 5 / 12 is because ( 5 / 4 ) w widgets are done in 3 days . so , x widgets will be done in 12 / 5 days or 5 / 12 th of a widget in a day ) solving , we have y = 4 = > x takes 6 days to doing x widgets . so , he will take 18 days to doing 3 w widgets . answer : c"
Answer: c
Python program:
a = 3 * 2
b = a * 3
Problem: find a sum for 1 st 7 prime number ' s ?
Options: a ) 25 , b ) 28 , c ) 58 , d ) 34 , e ) 36
Rationale: "required sum = ( 2 + 3 + 5 + 7 + 11 + 13 + 17 ) = 58 note : 1 is not a prime number option c"
Answer: c
Python program:
a = 2 + 3 
b = 2 + 3 
c = a + b 
d = 2 + 3 
e = d + 2 
f = c + e 
g = 7 + 2 
h = f + g 
i = 7 + 2 
j = i + 2 
k = h + j 
l = 7 + 2 
m = l + 2 
n = m + 4 
o = k + n 
p = 7 + 2 
q = p + 2 
r = q + 4 
s = r + 2 
t = o + s 
u = 7 + 2 
v = u + 2 
w = v + 4 
x = w + 2 
y = x + 4 
z = t + y
Problem: a and b can do a piece of work in 9 days . with the help of c they finish the work in 6 days . c alone can do that piece of work in ?
Options: a ) 33 , b ) 878 , c ) 18 , d ) 88 , e ) 11
Rationale: "c = 1 / 6 â € “ 1 / 9 = 1 / 18 = > 18 days answer : c"
Answer: c
Python program:
a = 6 / 9
b = 6 - a
c = 1/(b)
Problem: the length of a rectangular garden is three times its width . if the area of the rectangular garden is 507 square meters , then what is the width of the rectangular garden ?
Options: a ) 10
b ) 11
c ) 12
d ) 13
e ) 14
Rationale: let x be the width of the garden . 3 x ^ 2 = 507 x ^ 2 = 169 x = 13 the answer is d .
Answer: d
Python program:
a = 507 / 3
b = math.sqrt(a)
Problem: due to construction , the speed limit along an 9 - mile section of highway is reduced from 55 miles per hour to 30 miles per hour . approximately how many minutes more will it take to travel along this section of highway at the new speed limit than it would have taken at the old speed limit ?
Options: a ) a ) 5.61 , b ) b ) 8 , c ) c ) 10 , d ) d ) 15 , e ) e ) 8.19
Rationale: "old time in minutes to cross 9 miles stretch = 9 * 60 / 55 = 9 * 12 / 11 = 9.81 new time in minutes to cross 9 miles stretch = 9 * 60 / 30 = 9 * 2 / 1 = 18 time difference = 8.19 ans : e"
Answer: e
Python program:
a = 55 + 9 
b = a - 1
c = 9 / 30
d = 9 / 55
e = c - d
f = b * e
g = max(f)
Problem: 220 % of a number x is 44 . what is 44 % of x .
Options: a ) 8.8 , b ) 8.9 , c ) 6.6 , d ) 7.7 , e ) none
Rationale: solution : given , 220 % of x = 44 or , x = 20 . thus , 44 % of 20 = ( 44 * 20 ) / 100 = 8.8 answer : option a
Answer: a
Python program:
a = 220 / 44
b = a + 44 
c = b + 4 
d = c - 44
Problem: what is the smallest of 6 consecutive odd integers whose average ( arithmetic mean ) is b + 2 ?
Options: a ) b - 3 , b ) b - 6 , c ) b - 1 , d ) b , e ) b + 1
Rationale: since the numbers are consecutive odd integers , mean = median = 3 rd integer + 4 th integer / 2 and 1 st integer = 3 rd integer - 4 let ' s say 3 rd integer = n and 4 th integer = n + 2 2 n + 2 / 2 = b + 2 n = b + 1 1 st integer = b + 1 - 4 = b - 3 a is the answer
Answer: a
Python program:
a = 6 - 1
b = 2 - a
Problem: a motorcyclist goes from bombay to pune , a distance of 180 kms at an average of 20 kmph speed . another man starts from bombay by car 2 â ½ hours after the first , and reaches pune â ½ hour earlier . what is the ratio of the speed of the motorcycle and the car ?
Options: a ) 1 : 2 , b ) 2 : 3 , c ) 1 : 9 , d ) 1 : 5 , e ) 1 : 1
Rationale: "t = 180 / 20 = 9 h t = 9 - 3 = 6 time ratio = 9 : 6 = 3 : 2 speed ratio = 2 : 3 answer : b"
Answer: b
Python program:
a = 180 / 20
b = 180 / a
c = 180 / 20
d = c - 3
e = 180 / d
f = b / e