euclaise/mathqa_programs huggingface dataset:
Problem: mr . kramer , the losing candidate in a two - candidate election , received 942568 votes , which was exactly 30 percent of all votes cast . approximately what percent of the remaining votes would he need to have received in order to have won at least 50 percent of all the votes cast ?
Options: a ) 10 % , b ) 12 % , c ) 15 % , d ) 29 % , e ) 20 %
Rationale: let me try a simpler one . lets assume that candidate got 30 % votes and total votes is 100 . candidate won = 30 remaining = 70 to get 50 % , candidate requires 20 votes from 100 which is 20 % and 20 votes from 70 . 20 / 70 = 2 / 7 = . 285 = 28.5 % which is approx 29 % . hence the answer is d .
Answer: d
Python program:
a = 942568 * 100
b = a / 30
c = 50 / 100
d = b * c
e = d - 942568
f = 942568 * 100
g = f / 30
h = g - 942568
i = e / h
j = i * 100
Problem: how many pieces of 0.40 meteres can be cut from a rod 47.5 meteres long
Options: a ) 100 , b ) 118 , c ) 120 , d ) 125 , e ) 70
Rationale: "explanation : we need so simple divide 47.5 / 0.40 , = ( 4750 / 40 ) = 118 option b"
Answer: b
Python program:
a = 47 / 5
Problem: y = x ^ 2 + bx + 128 cuts the x axis at ( h , 0 ) and ( k , 0 ) . if h and k are integers , what is the least value of b ?
Options: a ) - 129 , b ) - 132 , c ) 32 , d ) 64 , e ) 128
Rationale: "as the curve cuts the x - axis at ( h , 0 ) and ( k , 0 ) . therefore h , k are the roots of the quadratic equation . for the quadratic equation is in the form of ax ^ 2 + bx + c = 0 , the product of the roots = c / a = 128 / 1 = 64 and the sum of the roots = - b / a = - b / 1 128 can be expressed as product of two numbers in the following ways : 1 * 128 2 * 64 4 * 32 8 * 16 the sum of the roots is maximum when the roots are 1 and 128 and the maximum sum is 1 + 128 = 129 . the least value possible for b is therefore - 129 . a"
Answer: a
Python program:
a = negate - (
Problem: 3 years ago , the average age of a family of 5 members was 17 . a baby having been born , the average age of the family is the same today . what is the age of the child ?
Options: a ) 3 , b ) 2 , c ) 4 , d ) 1 , e ) 5
Rationale: present age of 5 members = 5 x 17 + 3 x 5 = 100 years also , present ages of 5 members + age of the baby = 6 x 17 = 102 years age of the baby = 102 – 100 = 2 years . answer : b
Answer: b
Python program:
a = 3 * 5
b = 17 - a
Problem: car a runs at the speed of 33 km / hr & reaches its destination in 7 hr . car b runs at the speed of 44 km / h & reaches its destination in 5 h . what is the respective ratio of distances covered by car a & car b ?
Options: a ) 20 : 23 , b ) 25 : 27 , c ) 21 : 20 , d ) 29 : 23 , e ) 24 : 25
Rationale: "sol . distance travelled by car a = 33 × 7 = 231 km distance travelled by car b = 44 × 5 = 220 km ratio = 231 / 220 = 21 : 20 c"
Answer: c
Python program:
a = 33 * 7
b = 44 * 5
c = a / b
Problem: a and b undertake to do a piece of work for $ 120 . a alone can do it in 4 days while b alone can do it in 6 days . with the help of c , they finish it in 2 days . find the share of b ?
Options: a ) $ 150 , b ) $ 100 , c ) $ 200 , d ) $ 50 , e ) $ 40
Rationale: "c ' s 1 day work = ( 1 / 2 ) - ( 1 / 4 + 1 / 6 ) = 1 / 12 a : b : c = 1 / 4 : 1 / 6 : 1 / 12 = 3 : 2 : 1 b ' s share = 120 * 2 / 6 = $ 40 answer is e"
Answer: e
Python program:
a = 2 * 6
b = 1/(4)
c = a * b
d = 2 * 6
e = 1/(2)
f = 1/(4)
g = 1/(6)
h = f + g 
i = e - h
j = d * i
k = 2 * 6
l = 1/(4)
m = k * l
n = j + m 
o = 2 * 6
p = 1/(6)
q = o * p
r = n + q 
s = c / r
t = s * 120
Problem: a , b , and c were to be paid in proportion to the part of work they did while working on the same piece of work . a and b individually can finish the piece of work in 12 days and 15 days respectively . they worked together for 5 days and then c completed the remaining work all alone . if $ 810 was the net sum to be paid for the entire work , what was the average daily wage of b ?
Options: a ) $ 144 , b ) $ 90 , c ) $ 60 , d ) $ 54 , e ) $ 48
Rationale: the correct answer is d .
Answer: d
Python program:
a = 1 / 15
b = a * 5
c = b * 810
d = c / 5
Problem: an aeroplane covers a certain distance at a speed of 240 kmph in 4 hours . to cover the same distance in 1 2 / 3 hours , it must travel at a speed of :
Options: a ) 520 , b ) 620 , c ) 576 , d ) 740 , e ) 720
Rationale: "distance = ( 240 x 4 ) = 960 km . speed = distance / time speed = 960 / ( 5 / 3 ) km / hr . [ we can write 1 2 / 3 hours as 5 / 3 hours ] required speed = ( 960 x 3 / 5 ) km / hr = 576 km / hr answer c ) 576 km / hr"
Answer: c
Python program:
a = 240 * 4
b = 2 / 3
c = 1 + b 
d = a / c
e = d / 2
Problem: how many numbers from 29 to 79 are exactly divisible by 11 ?
Options: a ) 5 , b ) 7 , c ) 9 , d ) 11 , e ) 12
Rationale: "option ' a ' 29 / 11 = 2 and 79 / 11 = 7 = = > 7 - 2 = 5 numbers"
Answer: a
Python program:
a = 79 / 11
b = math.floor(a)
c = b * 11
d = 29 / 11
e = math.floor(d)
f = e + 1 
g = f * 11
h = c - g
i = h / 11
j = i + 1
Problem: the racing magic takes 60 seconds to circle the racing track once . the charging bull makes 40 rounds of the track in an hour . if they left the starting point together , how many minutes will it take for them to meet at the starting point for the second time ?
Options: a ) 3 , b ) 6 , c ) 9 , d ) 12 , e ) 15
Rationale: time taken by racing magic to make one circle = 60 seconds time taken bycharging bullto make one circle = 60 mins / 40 = 1.5 mins = 90 seconds lcm of 90 and 60 seconds = 180 seconds time taken for them to meet at the starting point for the second time = 180 * 2 = 360 seconds = 6 mins answer b
Answer: b
Python program:
a = 60 / 40
b = const_60 * a
c = b * 2
d = c / const_60
e = d * 2
Problem: how many liters of water must be evaporated from 50 liters of a 2 - percent sugar solution to get a 10 - percent solution ?
Options: a ) 25 , b ) 30 , c ) 35 , d ) 40 , e ) 45
Rationale: "2 % of a 50 liter solution is 1 l which is 10 % of the solution at the end . the solution at the end must be 1 l . we need to evaporate 40 liters . the answer is d ."
Answer: d
Python program:
a = 50 / 100
b = a * 10
c = 50 - b
Problem: what is the probability of always having x + y > 0 , where y < 0
Options: a ) 1 / 2 , b ) 1 / 8 , c ) 3 / 4 , d ) 1 / 4 , e ) none
Rationale: "total value of x can be : 1 . x < 0 ; 2 . x = 0 ; 3 . x > 0 but less than y in magnitude 4 . x > 0 as well as | y | so probability of having x + y > 0 would be 1 / 4 answer : d"
Answer: d
Python program:
a = 3 + 3 
b = math.comb(a, 3)
c = 2 / b
Problem: the surface area of a sphere is 4 π r 2 , where r is the radius of the sphere . if the area of the base of a hemisphere is 3 , what is the surface area w of that hemisphere ?
Options: a ) 6 / π , b ) 9 / π , c ) 6 , d ) 9 , e ) 12
Rationale: "given area of the base of a hemisphere is 3 = pi * r ^ 2 thus r = sqrt ( 3 / pi ) . surface area of whole sphere = 4 * pi * r ^ 2 . = 4 * pi * 3 / pi = 12 . since the hemisphere is half of a sphere the surface area of the hemisphere = 12 / 2 = 6 ( curved part , not including the flat rounded base ) . but the total surface area = 6 + area of the base of a hemisphere . = 6 + 3 = 9 . answer is d ! !"
Answer: d
Python program:
a = 4 * math.pi
b = 3 / math.pi
c = a * b
d = c / 2
e = 3 / math.pi
f = math.pi * e
g = d + f
Problem: factory x ' s bulbs work for over 5000 hours in 37 % of cases , whereas factory y ' s bulbs work for over 5000 hours in 75 % of cases . it is known that factory x supplies 40 % of the total bulbs available . what is the chance that a purchased bulb will work for longer than 5000 hours ?
Options: a ) 56.4 % , b ) 58 % , c ) 57.4 % , d ) 55 % , e ) 59.8 %
Rationale: "for x , 40 % of 37 % will work . for y , 60 % of 75 % will work . * 60 % is the rest of the bulb supply in the market . so , the probability that a purchased bulb will work is : 0.40 ( 0.37 ) = . 148 0.60 ( 0.75 ) = 0.45 the combined probability then is 14.8 + 45 = 59.8 % ans e"
Answer: e
Python program:
a = 37 + 75 
b = a / 2
Problem: a certain shade of gray paint is obtained by mixing 3 parts of white paint with 5 parts of black paint . if 2 gallons of the mixture is needed and the individual colors can be purchased only in one gallon or half gallon cans , what is the least amount of paint e , in gallons , that must be purchased in order to measure out the portions needed for the mixture ?
Options: a ) 2 , b ) 2 1 / 2 , c ) 3 , d ) 3 1 / 2 , e ) 4
Rationale: "given w : b = 3 : 5 that means say 3 gallons of white paint + 5 gallons of black paint = 8 gallons of paint mixture . but we want least amount of whiteblack paints for minimum of 2 gallons of mixture , so lets reduce keeping same ratio , 1.5 : 2.5 gives 1.5 + 2.5 = 4 gallons of mixture , but we want only 2 gallons , lets further reduce 0.75 : 1.25 gives 1 + 1.5 = 2.5 gallons of mixture . this looks ok , but lets reduce further just to be sure 0.375 : 0.625 gives 0.5 + 1 = 1.5 gallons of mixture , thats less than 2 gallons of mixture , so not acceptable . so correct ans is 2.5 gallons . b"
Answer: b
Python program:
a = const_0_25 * 2
b = 2 * 5
c = a + b
Problem: a and b complete a work in 4 days . a alone can do it in 8 days . if both together can do the work in how many days ?
Options: a ) 3.75 days , b ) 3.99 days , c ) 2.67 days , d ) 2.98 days , e ) 2.44 days
Rationale: "1 / 4 + 1 / 8 = 3 / 8 8 / 3 = 2.67 days answer : c"
Answer: c
Python program:
a = 1/(4)
b = 1/(8)
c = a + b 
d = 1/(c)
Problem: roja and pooja start moving in the opposite directions from a pole . they are moving at the speeds of 8 km / hr and 3 km / hr respectively . after 4 hours what will be the distance between them ?
Options: a ) 22 km , b ) 20 km , c ) 44 km , d ) 18 km , e ) 16 km
Rationale: "distance = relative speed * time = ( 8 + 3 ) * 4 = 44 km [ they are travelling in the opposite direction , relative speed = sum of the speeds ] . answer : c"
Answer: c
Python program:
a = 8 + 3 
b = a * 4
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 q 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 q : 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: how many multiples of 8 are there between 100 and 200 ( both are inclusive ) ?
Options: a ) 27 , b ) 4 , c ) 6 , d ) 13.5 , e ) 8
Rationale: "the answer is ( 200 - 100 ) / 8 + 1 = 13.5 answer is d"
Answer: d
Python program:
a = 200 - 100
b = a / 8
c = b + 1
Problem: the salary of a typist was at first raised by 10 % and then the same was reduced by 5 % . if he presently draws rs . 1045 . what was his original salary ?
Options: a ) 1009 , b ) 1018 , c ) 1000 , d ) 1082 , e ) 1029
Rationale: "x * ( 110 / 100 ) * ( 95 / 100 ) = 1045 x * ( 11 / 10 ) * ( 1 / 100 ) = 11 x = 1000 answer : c"
Answer: c
Python program:
a = 10 / 100
b = 1 + a 
c = 5 / 100
d = 1 - c
e = b * d
f = 1045 / e
Problem: how many pounds of salt at 50 cents / lb must be mixed with 45 lbs of salt that costs 35 cents / lb so that a merchant will get 20 % profit by selling the mixture at 48 cents / lb ?
Options: a ) 20 , b ) 15 , c ) 40 , d ) 50 , e ) 90
Rationale: "selling price is 48 cents / lb for a 20 % profit , cost price should be 40 cents / lb ( cp * 6 / 5 = 48 ) basically , you need to mix 35 cents / lb ( salt 1 ) with 50 cents / lb ( salt 2 ) to get a mixture costing 45 cents / lb ( salt avg ) weight of salt 1 / weight of salt 2 = ( salt 2 - saltavg ) / ( saltavg - salt 1 ) = ( 50 - 45 ) / ( 45 - 35 ) = 1 / 2 we know that weight of salt 1 is 45 lbs . weight of salt 2 must be 90 lbs . answer ( e )"
Answer: e
Python program:
a = 48 * 45
b = 100 + 20 
c = b / 100
d = 35 * 45
e = c * d
f = a - e
g = 100 + 20 
h = g / 100
i = 50 * h
j = i - 48
k = f / j
Problem: if the sum of a number and its square is 132 , then what is the number ?
Options: a ) 10 , b ) 11 , c ) 12 , d ) 13 , e ) 14
Rationale: "explanation : let the number be x . then , x 2 + x = 132 = > x 2 + x - 132 = 0 = > ( x + 12 ) ( x - 11 ) = 0 = > x = 11 answer : option b"
Answer: b
Python program:
a = math.sqrt(132)
b = math.floor(a)
Problem: 0.363 * 0.522 + 0.363 * 0.478 = ?
Options: a ) 0.522 , b ) 0.845 , c ) 0.363 , d ) 0.985 , e ) 0.885
Rationale: "given expression = 0.363 * ( 0.522 + 0.478 ) = 0.363 * 1 = 0.363 answer : c"
Answer: c
Python program:
a = 0 * 363
Problem: lilly has 10 fish and rosy has 8 fish . in total , how many fish do they have in all ?
Options: a ) 12 , b ) 14 , c ) 16 , d ) 18 , e ) 20
Rationale: "10 + 8 = 18 the answer is d ."
Answer: d
Python program:
a = 10 + 8
Problem: a certain clock marks every hour by striking a number of times equal to the hour , and the time required for a stroke is exactly equal to the time interval between strokes . at 6 : 00 the time lapse between the beginning of the first stroke and the end of the last stroke is 55 seconds . at 12 : 00 , how many seconds elapse between the beginning of the first stroke and the end of the last stroke ?
Options: a ) a . 72 , b ) b . 115 , c ) c . 48 , d ) d . 46 , e ) e . 44
Rationale: "at 6 : 00 it ' ll chime 6 times . if we assume that the time taken to chime is x , then time between chimes is also x . so you have 6 chimes , which is 6 x and 5 time intervals between chimes . this means that 11 x = 55 seconds . thus x = 5 seconds . by a similar logic , at 12 : 00 , there are 12 chimes and 11 intervals so the total time is ( 12 + 11 ) x = 23 x = 115 seconds . answer b"
Answer: b
Python program:
a = 1 + 4 
b = 6 + a 
c = 55 / b
d = 1 + 4 
e = 6 + d 
f = 12 + e 
g = c * f
Problem: two numbers n and 10 have lcm = 36 and gcf = 5 . find n .
Options: a ) 35 , b ) 56 , c ) 76 , d ) 18 , e ) 24
Rationale: "the product of two integers is equal to the product of their lcm and gcf . hence . 10 * n = 36 * 5 n = 36 * 5 / 10 = 18 correct answer d"
Answer: d
Python program:
a = 36 * 5
b = a / 10
Problem: the difference between c . i . and s . i . on an amount of rs . 15,000 for 2 years is rs . 216 . what is the rate of interest per annum ?
Options: a ) 8 , b ) 2 , c ) 9 , d ) 4 , e ) 12
Rationale: "explanation : [ 15000 * ( 1 + r / 100 ) 2 - 15000 ] - ( 15000 * r * 2 ) / 100 = 216 15000 [ ( 1 + r / 100 ) 2 - 1 - 2 r / 100 ] = 216 15000 [ ( 100 + r ) 2 - 10000 - 200 r ] / 10000 = 216 r 2 = ( 216 * 2 ) / 3 = 144 = > r = 12 rate = 12 % answer : option e"
Answer: e
Python program:
a = math.sqrt(216)
Problem: employees of a certain company are each to receive a unique 7 - digit identification code consisting of the digits 0 , 1 , 2 , 3 , 4 , 5 , and 6 such that no digit is used more than once in any given code . in valid codes , the second digit in the code is exactly twice the first digit . how many valid codes are there ?
Options: a ) 42 , b ) 120 , c ) 210 , d ) 360 , e ) 840
Rationale: "one can use slot method to solve this . 7 digit identification code has 7 slots to fill . for the first slot there are three possible options . ( 1,2 and 3 because first digit has to be half of second ) for the second slot there are three possible options . ( 2,4 and 6 because second digit has to be twice the second ) to fill the first two slots there are only three possible ways . because if the , if the first is 1 the second has to be 2 ( only 1 way ) if the first is 2 the second has to be 4 ( only 1 way ) if the first is 3 the second has to be 6 ( only 1 way ) . so total ways to fill first two slots = 3 ways you are now left with 5 digits and 5 slots to fill , which can be filled in 5 ! ways i . e . 120 ways . total no : of valid codes will be therefore : 120 * 3 = 360 ways . answer : d"
Answer: d
Python program:
a = 2 * 3
b = a * 2
Problem: it is the new year and mandy has made a resolution to lose weight this year . she plans to exercise and do yoga . for exercise she plans to workout at the gym and ride her bicycle in the ratio of 2 : 3 everyday . she will also do yoga in the ratio , yoga : exercise = 2 : 3 . if she rides her bike for 20 minutes , how much time will she spend doing yoga ? ( rounded to minutes )
Options: a ) 10 min . , b ) 33 min . , c ) 17 min . , d ) 23 min . , e ) 25 min .
Rationale: "the ratio is 2 : 3 = gym : ride , so ( 20 ) ( 3 / 2 ) = 30 minutes at the gym , and 30 + 20 = 50 minutes exercise , so ( 2 / 3 ) ( 50 ) = 33 minutes yoga . answer : b"
Answer: b
Python program:
a = 2 + 3 
b = 3 / a
c = 20 * b
d = 2 + 3 
e = 3 / d
f = 2 + 3 
g = 3 / f
h = e * g
i = c / h
Problem: two whales are moving in the same direction at 18 mps and 15 mps . the faster whale crosses the slow whale in 15 seconds . what is the length of the slower whale in meters ?
Options: a ) 45 m , b ) 56 m , c ) 39 m , d ) 33 m , e ) 62 m
Rationale: relative speed = ( 18 - 15 ) = 3 mps . distance covered in 15 sec = 15 * 3 = 45 m . the length of the faster train = 45 m . answer : a
Answer: a
Python program:
a = 18 - 15
b = a * 15
Problem: a circular path of 16 m radius has marginal walk 3 m wide all round it . find the cost of leveling the walk at rs . 2 per m 2 ?
Options: a ) rs . 660
b ) rs . 40
c ) rs . 44
d ) rs . 42
e ) rs . 43
Rationale: explanation : π ( 19 ^ 2 - 16 ^ 2 ) = 22 / 7 * ( 361 - 256 ) = 330 330 * 2 = rs . 660 answer : option a
Answer: a
Python program:
a = 16 + 3 
b = circle_area - (
c = 2 * b
Problem: speed of a boat in standing water is 14 kmph and the speed of the stream is 1.2 kmph . a man rows to a place at a distance of 4864 km and comes back to the starting point . the total time taken by him is
Options: a ) 700 hours , b ) 350 hours , c ) 1400 hours , d ) 1010 hours , e ) none of these
Rationale: explanation : speed downstream = ( 14 + 1.2 ) = 15.2 kmph speed upstream = ( 14 - 1.2 ) = 12.8 kmph total time taken = ( 4864 / 15.2 ) + ( 4864 / 12.8 ) = 320 + 380 = 700 hours . answer : option a
Answer: a
Python program:
a = 14 + 1 
b = 4864 / a
c = 14 - 1
d = 4864 / c
e = b + d
Problem: the avearge score of a cricketer for 10 matches is 38.9 runs . if the average for the first 6 matches is 41 . then find the average for the last 4 matches ?
Options: a ) 33.25 , b ) 35.75 , c ) 34.25 , d ) 35 , e ) none
Rationale: solution required average = ( 38.9 x 10 ) - ( 41 x 6 ) / 4 = 143 / 4 . = 35.75 answer b
Answer: b
Python program:
a = 10 * 38
b = 6 * 41
c = a - b
d = c / 4
Problem: noelle walks from point a to point b at an average speed of 6 kilometers per hour . at what speed , in kilometers per hour , must noelle walk from point b to point a so that her average speed for the entire trip is 7 kilometers per hour ?
Options: a ) 6.75 , b ) 7 , c ) 7.25 , d ) 7.5 , e ) 8.4
Rationale: "let ' s suppose that speed while returning was xkm / h since the distance is same , we can apply the formula of avg speed avg speed = 2 s 1 s 2 / s 1 + s 2 7 = 2 * 6 * x / 6 + x x = 8.4 e is the answer"
Answer: e
Python program:
a = 7 * 6
b = 2 * 6
c = b - 7
d = a / c
Problem: 6 x 0.6 x 0.06 x 0.006 x 60 = ?
Options: a ) 77.76 , b ) 7.776 , c ) 0.7776 , d ) 0.07776 , e ) none otf these
Rationale: "explanation : ? = 6 x 6 / 10 x 6 / 100 x 6 / 1000 x 60 = 77760 / 1000000 = 7776 / 100000 = 0.07776 answer : option d"
Answer: d
Python program:
a = 6 * 0
b = 0 * 6
c = a - b
d = c / 60
Problem: 0.009 / x = 0.02 . find the value of x
Options: a ) 0.045 , b ) 0.09 , c ) 0.9 , d ) 9 , e ) 90
Rationale: "x = 0.009 / 0.045 = 0.9 answer : a"
Answer: a
Python program:
a = 0 / 9
Problem: if two projectiles are launched at the same moment from 2520 km apart and travel directly towards each other at 432 km per hour and 576 km per hour respectively , how many minutes will it take for them to meet ?
Options: a ) 130 , b ) 135 , c ) 140 , d ) 145 , e ) 150
Rationale: "the projectiles travel a total of 1008 km per hour . the time to meet is 2520 / 1008 = 2.5 hours = 150 minutes the answer is e ."
Answer: e
Python program:
a = 432 + 576 
b = 2520 / a
c = b * const_60
Problem: what is the smallest number by which 3600 be divided to make it a perfect cube ?
Options: a ) 9
b ) 50
c ) 300
d ) 450
e ) 550
Rationale: solution 3600 = 23 * 52 * 32 * 2 . to make it a perfect cube , it must be divided by 52 * 32 * 2 i . e . , 450 . answer d
Answer: d
Python program:
a = 2 ** 3
b = 3600 / a
Problem: radius of a circle is 5 cm , if we draw a rectangle of maximum size , what is the area of rectangle ?
Options: a ) 30
b ) 40
c ) 50
d ) 60
e ) 70
Rationale: area of rectangle of max size inside circle will be a square with diagonal equal to 10 cms . then side of square = root ( 100 / 2 ) = root 50 area of square = root 50 * root 50 = 50 sq cms . answer : c
Answer: c
Python program:
a = 5 * 2
b = 5 * 2
c = a * b
d = c / 2
Problem: each week , harry is paid x dollars per hour for the first 30 hours and 1.5 x dollars for each additional hour worked that week . each week , james is paid x dollars per hour for the first 40 hours and 2 x dollars for each additional hour worked that week . last week james worked a total of 47 hours . if harry and james were paid the same amount last week , how many hours did harry work last week ?
Options: a ) 35 , b ) 36 , c ) 37 , d ) 38 , e ) 46
Rationale: "amount earned by james = 40 * x + 7 * 2 x = 54 x therefore , amount earned by harry = 54 x but we know the amount harry earned assuming working y hours ( y > 30 ) is 30 * x + ( y - 30 ) * 1.5 x [ [ we know y > 30 because in 30 h the most harry could earn is 30 x , but he has earned 54 x ] ] so x * ( 1.5 y - 45 + 30 ) = 54 x or x * ( 1.5 y - 15 ) = 54 x so 1.5 y - 15 = 54 so 1.5 y = 69 so y = 46 answer is e"
Answer: e
Python program:
a = 40 + 2 
b = a - 30
c = b / 1
d = c + 30
Problem: the greatest number that divides 60 and 190 leaving remainder 6 and 10 respectively is :
Options: a ) 15 , b ) 18 , c ) 19 , d ) 22 , e ) 23
Rationale: explanation : 60 - 6 = 54 , 190 - 10 = 180 highest number that divides 54 and 180 is hcf of numbers hcf of 54 nad 180 = 18 answer : b
Answer: b
Python program:
a = 190 - 10
b = math.gcd(60, 190)
c = a / b
Problem: 5 bells begin to toll together at 12 : 00 noon and toll respectively at intervals of 3 , 4 , 5 , 6 , and 7 seconds . not including the toll at 12 : 00 noon , how many more times will all 5 bells toll together before 1 : 00 pm ( i . e . one hour later ) ?
Options: a ) 6 , b ) 8 , c ) 10 , d ) 12 , e ) 14
Rationale: the least common multiple is 2 * 2 * 3 * 5 * 7 = 420 . 3600 seconds / 420 = 8 + remainder . the answer is b .
Answer: b
Python program:
a = 3 * 4
b = a * 5
c = b * 7
d = 3600 / c
e = math.floor(d)
Problem: 9 students bought burgers for $ 143 dollars . if the bill has to be divided among these students , how much amount should be added to the amound to make it divided amoung them equally in dollars ( in whole number of dollars )
Options: a ) $ 1 , b ) $ 2 , c ) $ 3 , d ) $ 4 , e ) $ 5
Rationale: in order to divide the sum in 9 parts , the amount must be divisible by 9 divisibility rule of 9 : the sum of the digits must be divisible by 9 sum of digits of 143 = 8 and 9 is divisible by 9 . hence , we need to add 1 to this number for it to be divisible by 9 correct option : a
Answer: a
Python program:
a = 9 - reminder
Problem: amit and ananthu can do a work in 15 days and 25 days respectively . amit started the work and left after 3 days . ananthu took over and completed the work . in how many days was the total work completed ?
Options: a ) 28 days , b ) 20 days , c ) 23 days , d ) 25 days , e ) 27 days
Rationale: "amit ’ s one day ’ s work = 1 / 15 amit ’ s 3 day ’ s work = 1 / 15 * 3 = 1 / 5 work left = 1 - 1 / 5 = 4 / 5 ananthu ’ s one day ’ s work = 1 / 25 ananthu can do work in = 4 / 5 * 25 = 20 / 1 days so total days = 25 + 3 = 28 days answer : a"
Answer: a
Python program:
a = 1/(15)
b = a * 3
c = 1 - b
d = 1/(25)
e = c / d
f = e + 3