euclaise/mathqa_programs huggingface dataset:
Problem: a company produces 120000 bottles of water everyday . if a case can hold 12 bottles of water . how many cases are required by the company to hold its one day production
Options: a ) 2000 , b ) 4500 , c ) 5000 , d ) 8000 , e ) 10000
Rationale: number of bottles that can be held in a case = 12 number of cases required to hold 120000 bottles = 120000 / 12 = 10000 cases . so the answer is e = 10000
Answer: e
Python program:
a = 120000 / 12
Problem: at a garage sale , all of the items were sold at different prices . if the price of a radio sold at the garage sale was both the 15 th highest price and the 22 nd lowest price among the prices of the items sold , how many items were sold at the garage sale ?
Options: a ) 34 , b ) 35 , c ) 36 , d ) 37 , e ) 38
Rationale: "there were 14 items sold at a higher price than the radio and 21 items sold at a lower price than the radio . including the radio , there were 14 + 21 + 1 = 36 items sold . the answer is c ."
Answer: c
Python program:
a = 22 + 15 
b = a - 1
Problem: the cash difference between the selling prices of an book at a profit of 4 % and 6 % is $ 3 . the ratio of the two selling prices is :
Options: a ) 50 : 53 , b ) 58 : 53 , c ) 52 : 53 , d ) 42 : 36 , e ) 38 : 53
Rationale: "c 52 : 53 let c . p . of the book be $ x . then , required ratio = 104 % of x / 106 % of x = 104 / 106 = 52 / 53 = 52 : 53"
Answer: c
Python program:
a = 100 + 4 
b = 100 + 6 
c = a / b
Problem: in town x , 120 percent of the population are employed , and 80 percent of the population are employed males . what percent of the employed people in town x are females ?
Options: a ) 16 % , b ) 25 % , c ) 33 % , d ) 40 % , e ) 52 %
Rationale: "total employed people 12 % , out of which 80 are employed males , hence 40 % are employed females . ( employed females ) / ( total employed people ) = 40 / 120 = 1 / 3 = 33 % answer : c ."
Answer: c
Python program:
a = 120 - 80
b = a / 120
c = b * 100
Problem: if an average hard drive had a capacity of 0.1 tb in 2000 , and average hard drive capacities double every 5 years , what will be the average hard drive capacity in 2050 ?
Options: a ) 256 , b ) 512 , c ) 768 , d ) 1024 , e ) 1536
Rationale: "0.1 * 2 ^ 10 = 0.1 * 1024 = 102.4 the answer is d ."
Answer: d
Python program:
a = 0 * 1
b = a * 2
c = b * 2
d = c * 2
e = d * 2
f = e * 2
g = f * 2
h = g * 2
i = h * 2
j = i * 2
k = j + 0 
l = k * 10
Problem: ( x + 3 ) is a factor in x ^ 2 - mx - 15 . what is the value of m ?
Options: a ) 1 , b ) 2 , c ) 3 , d ) 4 , e ) 5
Rationale: "i solved the second degree equation and found it like this : x ^ 2 - mx - 15 = 0 ( x - 5 ) ( x + 3 ) = 0 x = 5 or x = - 3 substituting both values for x in the equation we find : x ^ 2 - mx - 15 = > ( - 3 ) ^ 2 - m ( - 3 ) = 15 = > 9 + 3 m = 15 = > 3 m = 15 - 9 = 6 = > m = 2 and with 5 , using a similar process we end up with : ( 5 ) ^ 2 - m ( 5 ) = 15 - 5 m = 15 - 25 = - 10 m = 2 ao , ans b"
Answer: b
Python program:
a = 15 / 3
b = a - 3
Problem: a small water pump would take 3 hours to fill an empty tank . a larger pump would take 1 / 4 hour to fill the same tank . how many hours would it take both pumps , working at their respective constant rates , to fill the empty tank if they began pumping at the same time ?
Options: a ) 3 / 13 , b ) 1 / 5 , c ) 1 / 10 , d ) 1 / 3 , e ) 1 / 7
Rationale: rate of the small pump is 1 / 3 tank / hour rate of the larger pump is 1 / ( 1 / 4 ) or 4 tank / hour ; combined rate of the two pumps is 1 / 3 + 4 = 13 / 3 tank / hour , together they will fill the empty tank in 1 / ( 13 / 3 ) = 3 / 13 hours ( time = job / rate ) . answer : a
Answer: a
Python program:
a = 1/(3)
b = a + 4 
c = 1/(b)
Problem: by approximately what percent is x greater than 4 / 7 if ( 1 / 7 ) ( x ) = 1 ?
Options: a ) 1125 % , b ) 956 % , c ) 417 % , d ) 3788 % , e ) 219 %
Rationale: what percent is x greater than 4 / 7 if ( 1 / 7 ) ( x ) = 1 ? = > x = 7 % change = [ ( 7 - 4 / 7 ) / ( 4 / 7 ) ] * 100 = ( 49 / 4 - 1 ) * 100 = 45 * 25 = 1125 % ans , a
Answer: a
Python program:
a = 4 / 7
b = 7 - a
c = 4 / 7
d = b / c
e = d * 100
Problem: when 1 / 10 percent of 3,000 is subtracted from 1 / 10 of 3,000 , the difference is
Options: a ) 0 , b ) 50 , c ) 450 , d ) 397 , e ) 500
Rationale: "we can break this problem into two parts : 1 ) what is 1 / 10 percent of 3,000 ? 2 ) what is 1 / 10 of 3,000 ? to calculate 1 / 10 percent of 3,000 we must first remember to divide 1 / 10 by 100 . so we have : ( 1 / 10 ) / ( 100 ) to divide a number by 100 means to multiply it by 1 / 100 , so we have : 1 / 10 x 1 / 100 = 1 / 1,000 thus , 1 / 10 percent of 3,000 = 1 / 1,000 x 3,000 = 3 . now let ' s concentrate on part 2 . we need to calculate 1 / 10 of 3,000 . to do this we simply multiply 1 / 10 by 3,000 . 1 / 10 x 3,000 = 300 the answer to part 1 is 3 , and the answer to part 2 is 300 . their difference is 300 – 3 = 397 . answer d ."
Answer: d
Python program:
a = 3 + 4 
b = a * 1000
c = 1 / 10
d = b * c
e = 1 / 10
f = e / 100
g = 3 + 4 
h = g * 1000
i = f * h
j = d - i
Problem: how many multiples of 5 are there between 10 and 89 , 10 and 89 inclusive ?
Options: a ) 17 , b ) 16 , c ) 18 , d ) 19 , e ) 20
Rationale: "5 multiples are . . . 10,15 , 20,25 , 30,35 , 40,45 , 50,55 , 60,65 , 70,75 , 80,85 , . . . , . . . , the answer is = 16 answer is b"
Answer: b
Python program:
a = 89 - 10
b = a / 5
c = b + 1
Problem: a worker can load one truck in 5 hours . a second worker can load the same truck in 8 hours . if both workers load one truck simultaneously while maintaining their constant rates , approximately how long , in hours , will it take them to fill one truck ?
Options: a ) 2.5 , b ) 2.7 , c ) 2.9 , d ) 3.1 , e ) 3.3
Rationale: "the workers fill the truck at a rate of 1 / 5 + 1 / 8 = 13 / 40 of the truck per hour . then the time to fill one truck is 40 / 13 which is about 3.1 hours . the answer is d ."
Answer: d
Python program:
a = 1 / 5
b = 1 / 8
c = a + b 
d = 1/(c)
Problem: if 4 a = 5 b and ab ≠ 0 , what is the ratio of a / 5 to b / 4 ?
Options: a ) 125 / 64 , b ) 25 / 16 , c ) 1 , d ) 4 / 5 , e ) 64 / 125
Rationale: a nice fast approach is the first find a pair of numbers that satisfy the given equation : 4 a = 5 b here ' s one pair : a = 5 and b = 4 what is the ratio of a / 5 to b / 4 ? in other words , what is the value of ( a / 5 ) / ( b / 4 ) ? plug in values to get : ( a / 5 ) / ( b / 4 ) = ( 5 / 5 ) / ( 4 / 4 ) = 1 / 1 = 1 c
Answer: c
Python program:
a = 4 * 5
b = 5 * 4
c = a / b
Problem: what number is that , to which if 1 , 5 , and 13 , be severally added , the first sum shall be to the second , as the second to the third ?
Options: a ) 1 , b ) 2 , c ) 3 , d ) 4 , e ) 5
Rationale: solution let x = the number required . by the conditions , x + 1 : x + 5 = a + 5 : x + 13 subtracting terms , ( art . 385,2 . ) x + 1 : 4 = x + 5 : 8 therefore 8 x + 8 = 4 x + 20 . and x = 3 . answer c
Answer: c
Python program:
a = 13 + 5 
b = a + 1 
c = b + 1 
d = 13 - 5
e = c - d
f = 5 - 1
g = e / f
Problem: the price of a cycle is reduced by 25 per cent . the new price is reduced by a further 40 per cent . the two reductions together are equal to a single reduction of
Options: a ) 45 % , b ) 55 % , c ) 35 % , d ) 32.5 % , e ) 30 %
Rationale: "price = p initially price reduced by 25 % which means new price is 3 / 4 p now on this new price further 40 percent is reduced which means the new price is merely 60 percent of 3 / 4 p = = > ( 3 / 4 ) x ( 3 / 5 ) p = 9 / 20 p is the new price after both deduction which is 45 percent of the original value p . this implies this entire series of deduction is worth having discounted 55 % of p . so answer is b = 55 %"
Answer: b
Python program:
a = 100 - 40
b = a / 100
c = 100 - 25
d = b * c
e = 100 - d
Problem: 2.505 / 10.02 =
Options: a ) 0.35 , b ) 0.3505 , c ) 0.25 , d ) 0.351 , e ) 0.3527
Rationale: "2.505 / 10.02 2505 / 1002 = 2.5 move the comma two places to the left as we have 2 decimal places from the divisor : 0.25 . answer : c"
Answer: c
Python program:
a = 2 / 505
b = a * 100
Problem: 1000 boys have provisions for 15 days . if 200 more men join them , for how many days will the provisions last now ?
Options: a ) 12 , b ) 12.5 , c ) 13 , d ) 13.5 , e ) 14
Rationale: explanation : 1000 * 15 = 1200 * x x = 12.5 b
Answer: b
Python program:
a = 1000 * 15
b = 1000 + 200 
c = a / b
Problem: in a certain neighborhood , there are half as many beige houses as white houses , and 6 times as many white houses as brown houses . what is the ratio of the number of brown houses to the number of beige houses ?
Options: a ) 1 : 3 , b ) 1 : 9 , c ) 2 : 5 , d ) 5 : 3 , e ) 6 : 1
Rationale: the ratio of beige : white : brown = 3 : 6 : 1 the answer is a .
Answer: a
Python program:
a = 2 / 6
Problem: the surface area of a sphere is 4 π r ^ 2 , where r is the radius of the sphere . if the surface area of sphere a is eight times as large as the surface area of sphere b , then the radius of sphere a is how many times the radius of sphere b ?
Options: a ) 2
b ) 2 √ 2
c ) 4
d ) 2 π
e ) π · √ 8
Rationale: r 1 : radius of sphere a r 2 : radius of sphere b as per question , 4 π r 1 ^ 2 = 8 ∗ 4 π r 2 ^ 2 or r 12 = 8 ∗ r 2 ^ 2 or r 1 = 2 √ 2 r 2 . hence , b
Answer: b
Python program:
a = 4 * 2
b = math.sqrt(a)
Problem: a man buy a book in rs 50 & sale it rs 50 . what is the rate of profit ? ? ?
Options: a ) 10 % , b ) 0 % , c ) 30 % , d ) 25 % , e ) 28 %
Rationale: "cp = 50 sp = 50 profit = 50 - 50 = 0 % = 0 / 50 * 100 = 0 % answer : b"
Answer: b
Python program:
a = 50 - 50
b = a / 50
c = b * 100
Problem: a train passes a station platform in 50 sec and a man standing on the platform in 20 sec . if the speed of the train is 72 km / hr . what is the length of the platform ?
Options: a ) 550 , b ) 400 , c ) 700 , d ) 600 , e ) 850
Rationale: "speed = 72 * 5 / 18 = 20 m / sec . length of the train = 20 * 20 = 400 m . let the length of the platform be x m . then , ( x + 400 ) / 50 = 20 = > x = 600 m . answer : d"
Answer: d
Python program:
a = 72 * const_0_2778
b = 20 * a
Problem: certain stocks in january were 40 % less than they were in february and 15 % greater than they were in march . what was the percentage decrease in the stocks from february to march ?
Options: a ) 50.81 % , b ) 15.11 % , c ) 20.7 % , d ) 48.8 % , e ) 40 %
Rationale: "let stocks value in feb = 100 = > in jan = 60 and march = 60 * 100 / 115 = 51.2 % thus , percent decrease in stocks from feb to march = 100 - 51.2 = 48.8 % hence answer is d"
Answer: d
Python program:
a = 100 - 40
b = a / 100
c = 100 / b
d = 100 + 15 
e = d / 100
f = 100 / e
g = c - f
h = 100 - 40
i = h / 100
j = 100 / i
k = g / j
l = k * 100
Problem: fresh grapes contain 85 % water by weight and raisins obtained by drying fresh grapes contain 25 % water by weight . how many kgs of fresh grapes are needed to get 20 kgs of raisins ?
Options: a ) 75 kgs , b ) 64 kgs , c ) 100 kgs , d ) 65 kgs , e ) 70 kgs
Rationale: the weight of non - water in 20 kg of dried grapes ( which is 100 - 25 = 75 % of whole weight ) will be the same as the weight of non - water in x kg of fresh grapes ( which is 100 - 85 = 15 % of whole weight ) , so 20 * 0.75 = x * 0.15 - - > x = 100 . answer : c
Answer: c
Python program:
a = 100 - 25
b = 20 * a
c = b / 100
d = c + 85
Problem: the average age of a family of 6 members is 24 years . if the age of the youngest member is 8 years , what was the average age of the family at the birth of the youngest member ?
Options: a ) 15 , b ) 16 , c ) 21 , d ) 12 , e ) 19
Rationale: "present age of total members = 6 x 24 = 144 8 yrs back their ages were = 6 x 8 = 48 ages at the birth of youngest member = 144 - 48 = 96 therefore , avg age at the birth of youngest member = 96 / 6 = 16 . answer : b"
Answer: b
Python program:
a = 6 * 24
b = a - 8
c = b / 4
d = c - 8
Problem: tickets to a certain concert sell for $ 20 each . the first 10 people to show up at the ticket booth received a 40 % discount , and the next 20 received a 15 % discount . if 45 people bought tickets to the concert , what was the total revenue from ticket sales ?
Options: a ) $ 600 , b ) $ 760 , c ) $ 850 , d ) $ 980 , e ) $ 1,140
Rationale: price of 1 ticket = 20 $ revenue generated from sales of first 10 tickets = 10 * ( 60 / 100 * 20 ) = 10 * 12 = 120 revenue generated from sales of next 20 tickets = 20 * ( 85 / 100 * 20 ) = 20 * 17 = 340 revenue generated from sales of last 15 tickets = 20 * 15 = 300 revenue generated from sales of 45 tickets = 120 + 340 + 300 = 760 $ answer b
Answer: b
Python program:
a = 45 - 20
b = a - 10
c = 40 / 100
d = 1 - c
e = d * 10
f = b + e 
g = 15 / 100
h = 1 - g
i = h * 20
j = f + i 
k = j * 20
Problem: a car averages 35 miles per hour for the first 4 hours of a trip and averages 44 miles per hour for each additional hour of travel time . if the average speed for the entire trip is 38 miles per hour , how many hours long is the trip ?
Options: a ) 6 , b ) 8 , c ) 10 , d ) 12 , e ) 14
Rationale: "let t be the total time of the trip . 35 * 4 + 44 ( t - 4 ) = 38 t 6 t = 176 - 140 t = 6 the answer is a ."
Answer: a
Python program:
a = 38 * 4
b = 35 * 4
c = a - b
d = 44 - 38
e = c / d
f = e + 4
Problem: a 300 m long train crosses a platform in 39 sec while it crosses a signal pole in 18 sec . what is the length of the platform ?
Options: a ) 288 , b ) 350 , c ) 889 , d ) 276 , e ) 234
Rationale: "speed = 300 / 18 = 50 / 3 m / sec . let the length of the platform be x meters . then , ( x + 300 ) / 39 = 50 / 3 3 x + 900 = 1950 = > x = 350 m . answer : b"
Answer: b
Python program:
a = speed * (
b = a - 39
Problem: what is the decimal equivalent of ( 1 / 4 ) ^ 5 ?
Options: a ) 0.0016 , b ) 0.0625 , c ) 0.0001 , d ) 0.25 , e ) 0.5
Rationale: "( 1 / 4 ) ^ 5 = 1 / 1024 = 0.0001 answer : c"
Answer: c
Python program:
a = 1 / 4
b = a ** 5
Problem: a palindrome is a number that reads the same front - to - back as it does back - to - front ( e . g . 202 , 575 , 1991 , etc . ) p is the smallest integer greater than 800 that is both a prime and a palindrome . what is the sum of the digits of p ?
Options: a ) 3 , b ) 4 , c ) 5 , d ) 6 , e ) 7
Rationale: "given that p is smallest integer greater than 800 - assume there is a 3 - digit that satisfies the above conditions . let the number be xyx ; question asks us the values of 2 x + y we can straight away cross out options a ) and d ) - sum of digits 3 or 6 implies it is divisible by 3 - - - > we know that p is a prime number coming to option b ) 2 x + y = 4 - - > only x = 2 and y = 0 satisfy this equation ( x > 2 will never give sum of digits = 4 ) ; but 202 is divisible by 2 ; we know that p is a prime number similarly option c ) 2 x + y = 5 - - > only x = 2 and y = 1 satisfy this equation ( x > 2 will never give sum of digits = 5 ) ; but 212 is divisible by 2 ; we know that p is a prime number therefore answer option should be e - - - > can be verified by taking 2 x + y = 7 - - - > x = 3 and y = 1 ; gives 313 e"
Answer: e
Python program:
a = 3 + 3
Problem: a reduction of 35 % in the price of apples would enable a man to obtain 42 more for rs . 20 , what is reduced price per dozen ?
Options: a ) 1.7 , b ) 3.5 , c ) 6.3 , d ) 7.1 , e ) 10.4
Rationale: "a 20 * ( 35 / 100 ) = 6 - - - 42 ? - - - 12 = > rs . 1.7"
Answer: a
Python program:
a = 35 * 20
b = a / 100
c = b / 42
d = c * 12
Problem: what is the units digit of ( 52 ^ 5 ) ( 37 ^ 3 ) ( 71 ^ 9 ) ?
Options: a ) 3 , b ) 4 , c ) 6 , d ) 7 , e ) 8
Rationale: "the units digit of 52 ^ 5 is the units digit of 2 ^ 5 which is 2 . the units digit of 37 ^ 3 is the units digit of 7 ^ 3 which is 3 . the units digit of 71 ^ 9 is the units digit of 1 ^ 9 which is 1 . the units digit of 2 * 3 * 1 is 6 . the answer is c ."
Answer: c
Python program:
a = math.factorial(52)
b = math.factorial(5)
c = a * b
d = math.factorial(52)
e = math.factorial(3)
f = d * e
g = c + f 
h = g / 52
Problem: how many seconds will a 220 metre long train take to cross a man running with a speed of 8 km / hr in the direction of the moving train if the speed of the train is 80 km / hr ?
Options: a ) 25 , b ) 30 , c ) 40 , d ) 11 , e ) 60
Rationale: "explanation : speed of train relatively to man = ( 80 - 8 ) km / hr = 72 km / hr = ( 72 x 5 / 18 ) m / sec = 20 m / sec time taken to pass the man = ( 220 / 20 ) sec = 11 sec . answer : d"
Answer: d
Python program:
a = 80 - 8
b = const_0_2778 * a
c = 220 / b
Problem: pipe a can fill a tank in 16 minutes and pipe b cam empty it in 24 minutes . if both the pipes are opened together after how many minutes should pipe b be closed , so that the tank is filled in 30 minutes ?
Options: a ) 18 , b ) 27 , c ) 98 , d ) 27 , e ) 21
Rationale: "let the pipe b be closed after x minutes . 30 / 16 - x / 24 = 1 = > x / 24 = 30 / 16 - 1 = 14 / 16 = > x = 14 / 16 * 24 = 21 . answer : e"
Answer: e
Python program:
a = 30 / 16
b = a - 1
c = b * 24
Problem: what is the units digit of ( 147 ^ 25 ) ^ 50 ?
Options: a ) 1 , b ) 3 , c ) 5 , d ) 7 , e ) 9
Rationale: the units digit of the exponents of 7 repeat in a cycle of four , which is { 7,9 , 3,1 } . the number 25 has the form 4 n + 1 so the units digit is 7 inside the bracket . the exponent 50 has the form 4 n + 2 , so the units digit is 9 . the answer is e .
Answer: e
Python program:
a = 4 + 3 
b = a + 2
Problem: fox jeans regularly sell for $ 15 a pair and pony jeans regularly sell for $ 18 a pair . during a sale these regular unit prices are discounted at different rates so that a total of $ 9 is saved by purchasing 5 pairs of jeans : 3 pairs of fox jeans and 2 pairs of pony jeans . if the sum of the two discounts rates is 33 percent , what is the discount rate on pony jeans ?
Options: a ) 9 % , b ) 10 % , c ) 11 % , d ) 12 % , e ) 65 %
Rationale: "x discount on pony jeans , ( 0.33 - x ) discount on fox jeans . set the equation : 3 * 15 ( 0.33 - x ) + 2 * 18 x = 9 - - > x = 0.65 = 65 % answer : e ."
Answer: e
Python program:
a = 33 / 100
b = 33 / 100
c = 18 * 2
d = b * c
e = 9 - d
f = 15 * 3
g = 18 * 2
h = f - g
i = e / h
j = a - i
k = j * 100
Problem: a train travelling at a speed of 75 mph enters a tunnel 31 / 2 miles long . the train is 1 / 4 mile long . how long does it take for the train to pass through the tunnel from the moment the front enters to the moment the rear emerges ?
Options: a ) 2.5 min , b ) 3 min , c ) 3.2 min , d ) 3.5 min , e ) 4 min
Rationale: total distance = ( 7 / 2 + 1 / 4 ) miles = 15 / 4 miles time taken = 15 / 4 * 75 hrs = 1 / 20 hrs = 3 min answer b
Answer: b
Python program:
a = 1 / 4
b = 3 + 4 
c = b / 2
d = a + c 
e = d / 75
f = e * const_60
Problem: the value of log 343 7 is
Options: a ) 1 / 3 , b ) - 3 , c ) - 1 / 3 , d ) 3 , e ) 0.3
Rationale: "solution let log 3437 = n . then , 343 n = 7 = ( 73 ) n = 7 . ‹ = › 3 n = 1 ‹ = › n = 1 / 3 . log 343 7 = 1 / 3 . answer a"
Answer: a
Python program:
a = 4 + 1 
b = a * 1000
c = 7 - b
d = math.log(c)
e = 4 + 1 
f = math.log(e)
g = d / f
h = math.log(g)
Problem: a watch was sold at a loss of 16 % . if it was sold for rs . 140 more , there would have been a gain of 4 % . what is the cost price ?
Options: a ) 700 , b ) 882 , c ) 799 , d ) 778 , e ) 901
Rationale: "84 % 104 % - - - - - - - - 20 % - - - - 140 100 % - - - - ? = > rs . 700 answer : a"
Answer: a
Python program:
a = 140 * 100
b = 100 + 4 
c = 100 - 16
d = b - c
e = a / d
Problem: robin ' s average ( arithmetic mean ) test score on 9 tests is 82 . what must be robin ' s score on a 10 th test for his average score on the 10 tests to be 83 ?
Options: a ) 92 , b ) 82 , c ) 72 , d ) 62 , e ) 52
Rationale: ( 9 * 82 + x ) / 10 = 83 x = ( 10 * 83 ) - ( 9 * 82 ) x = 830 - 738 total score required 830 - 738 = 92 correct answer is a
Answer: a
Python program:
a = 10 * 83
b = 9 * 82
c = a - b
Problem: the simple form of the ratio 9 / 8 : 3 / 4 is ?
Options: a ) 5 : 8 , b ) 5 : 5 , c ) 5 : 9 , d ) 3 : 2 , e ) 5 : 1
Rationale: "9 / 8 : 3 / 4 = 3 : 2 answer : d"
Answer: d
Python program:
a = 3 / 4
Problem: a goods train runs at the speed of 72 km / hr and crosses a 210 m long platform in 26 sec . what is the length of the goods train ?
Options: a ) 382 , b ) 782 , c ) 278 , d ) 310 , e ) 881
Rationale: "speed = 72 * 5 / 18 = 20 m / sec . time = 26 sec . let the length of the train be x meters . then , ( x + 210 ) / 26 = 20 x = 310 m . answer : d"
Answer: d
Python program:
a = 72 / 3600
b = a * 1000
c = b * 26
d = c - 210
Problem: linda spent 3 / 4 of her savings on furniture and the rest on a tv . if the tv cost her $ 220 , what were her original savings ?
Options: a ) $ 900 , b ) $ 880 , c ) $ 1000 , d ) $ 700 , e ) $ 1500
Rationale: "if linda spent 3 / 4 of her savings on furnitute , the rest 4 / 4 - 3 / 4 = 1 / 4 on a tv but the tv cost her $ 220 . so 1 / 4 of her savings is $ 220 . so her original savings are 4 times $ 220 = $ 880 correct answer b"
Answer: b
Python program:
a = 3 / 4
b = 1 - a
c = 220 / b
Problem: i have only 1 $ and 2 $ note . i want to give 95 $ to john . how many maximum number of 2 $ note i need ?
Options: a ) 39 , b ) 95 , c ) 47 , d ) 55 , e ) 76
Rationale: check whether 95 is divisible by 2 then that is maximum no of 2 $ note else check next maximum term before 95 so 94 / 2 = 47 ans is c
Answer: c
Python program:
a = 95 / 2
Problem: if 10,000 microns = 1 decimeter , and 10,000 , 000,000 angstroms = 1 decimeter , how many angstroms equal 1 micron ?
Options: a ) 0.01 , b ) 1 , 000,000 , c ) 0.001 , d ) 1,000 , e ) 1.0 e - 05
Rationale: given that 10,000 microns = 1 decimeter = 10,000 , 000,000 angstroms so , 1 micron = 10,000 , 000,000 / 10,000 = 1 , 000,000 answer : b
Answer: b
Python program:
a = 100 * 100
b = 1 / a
c = 100 * 100
d = b * c
Problem: a train 125 m long crosses a platform 125 m long in 14 sec ; find the speed of the train ?
Options: a ) 87 kmph , b ) 64 kmph , c ) 54 kmph , d ) 16 kmph , e ) 18 kmph
Rationale: "d = 125 + 125 = 250 t = 14 s = 250 / 14 * 18 / 5 = 64 kmph answer : b"
Answer: b
Python program:
a = 125 * const_0_2778
b = 14 * a
c = b - 125
Problem: salad dressing p is made up of 30 % vinegar and 70 % oil , and salad dressing q contains 10 % vinegar and 90 % oil . if the two dressings are combined to produce a salad dressing that is 12 % vinegar , dressing p comprises what percentage of the new dressing ?
Options: a ) 50 % , b ) 40 % , c ) 30 % , d ) 20 % , e ) 10 %
Rationale: let x be the percentage of dressing p in the new dressing . 0.3 x + 0.1 ( 1 - x ) = 0.12 0.2 x = 0.02 x = 0.1 = 10 % the answer is e .
Answer: e
Python program:
a = 30 - 10
b = 12 - 10
c = a / b
Problem: what is the compound interest paid on a sum of rs . 3500 for the period of 2 years at 10 % per annum .
Options: a ) 630 , b ) 735 , c ) 825 , d ) 600 , e ) none of these
Rationale: "solution = interest % for 1 st year = 10 interest % for 2 nd year = 10 + 10 % of 10 = 10 + 10 * 10 / 100 = 11 total % of interest = 10 + 11 = 21 total interest = 21 % 3500 = 3500 * ( 21 / 100 ) = 735 answer b"
Answer: b
Python program:
a = 10 / 100
b = 1 + a 
c = b ** 2
d = 3500 * c
e = d - 3500
Problem: a grand father has 3 grand children . age difference of two children among them is 3 . eldest child age is 3 times the youngest child ’ s age and the eldest child age is two year more than the sum of age of other two children . what is the age of the eldest child ?
Options: a ) 22 , b ) 15 , c ) 28 , d ) 26 , e ) 9
Rationale: as the eldest son ' s age is 3 times that of the youngest , eldest son ' s age should be a multiple of 3 . from the given options take 15 as the eldest son ' s age . then youngest son ' s age becomes 5 . but eldest sons age is 2 more than the sum of the remaining two sons . so sum of the remaining two sons is 13 . so the age of the middle son is 13 - 5 = 8 . which satisfies another condition in the question that the difference between the two sons age is 3 . so answer is 15 . answer : b
Answer: b
Python program:
a = 3 * 3
b = a + 3 
c = b + 3
Problem: rs . 1500 is divided into two parts such that if one part is invested at 6 % and the other at 5 % the whole annual interest from both the sum is rs . 87 . how much was lent at 5 % ?
Options: a ) 228 , b ) 299 , c ) 300 , d ) 500 , e ) 188
Rationale: "( x * 5 * 1 ) / 100 + [ ( 1500 - x ) * 6 * 1 ] / 100 = 87 5 x / 100 + 90 â € “ 6 x / 100 = 87 x / 100 = 3 = > x = 300 answer : c"
Answer: c
Python program:
a = 5 + 6 
b = a * 100