euclaise/mathqa_programs huggingface dataset:
Problem: 3 pumps , working 8 hours a day , can empty a tank in 2 days . how many hours a day must 8 pumps work to empty the tank in 1 day ?
Options: a ) 6 , b ) 10 , c ) 11 , d ) 12 , e ) 13
Rationale: "3 pumps take 16 hrs total ( 8 hrs a day ) if 1 pump will be working then , it will need 16 * 3 = 48 hrs 1 pump need 48 hrs if i contribute 8 pumps then 48 / 8 = 6 hrs . answer : a"
Answer: a
Python program:
a = 3 * 8
b = a * 2
c = b / 8
Problem: a , b and c can do a piece of work in 4 days , 6 days and 8 days respectively . how long will they taken , if all the three work together ?
Options: a ) 2 , b ) 4 , c ) 5 , d ) 1 11 / 13 , e ) 9
Rationale: "1 / 4 + 1 / 6 + 1 / 8 = 13 / 24 = > 24 / 13 = > 1 11 / 13 days answer : d"
Answer: d
Python program:
a = 1/(8)
b = 1/(4)
c = 1/(6)
d = b + c 
e = a + d 
f = 1/(e)
Problem: a student has to obtain 45 % of the total marks to pass . he got 150 marks and failed by 30 marks . the maximum marks are ?
Options: a ) 300 , b ) 250 , c ) 280 , d ) 320 , e ) 400
Rationale: "let the maximum marks be x then , 45 % of x = 150 + 30 45 x / 100 = 180 45 x = 180 * 100 = 18000 x = 400 answer is e"
Answer: e
Python program:
a = 150 + 30 
b = 45 / 100
c = a / b
Problem: the units digit of ( 35 ) ^ ( 87 ) + ( 93 ) ^ ( 46 ) is :
Options: a ) 2 , b ) 4 , c ) 6 , d ) 8 , e ) 0
Rationale: "step 1 : ( 35 ) ^ ( 87 ) can be broken up into ( 5 ) ^ 87 x ( 7 ) ^ 87 . each power of 7 ends in a units digit of either a 7 , 9,3 or 1 . each power of 5 ends in a 5 . when you multiply 5 by any odd number you will end up with a units digit of 5 . step 2 : ( 93 ) ^ ( 46 ) can be broken up into ( 3 ) ^ 46 x ( 31 ) ^ 46 . each power of 31 ends in a units digit of 1 . each power of 3 ends in a units digit of either 3 , 9,7 and 1 . since there is a pattern here where every 4 th power of 3 ends in a units digit of 3 , the 46 th power of 3 would end in a units digit of 9 . when you multiply 1 by 9 you end up with a units digit of 9 . therefore , the units digit we are looking for is 5 + 9 = 14 . units digit will be 4 . answer b ."
Answer: b
Python program:
a = reminder * (
b = reminder + (
Problem: a survey of employers found that during 1993 employment costs rose 3.5 percent , where employment costs consist of salary costs and fringe - benefit costs . if salary costs rose 3 percent and fringe - benefit costs rose 5.5 percent during 1993 , then fringe - benefit costs represented what percent of employment costs at the beginning of 1993 ?
Options: a ) 16.5 % , b ) 20 % , c ) 35 % , d ) 55 % , e ) 65 %
Rationale: "in my view easiest method would be , eliminating the percentage sign let 3.5 be 35 5.5 be 55 and 3 be 30 then first eq : s + f = e 130 s + 155 f = 135 e 5 s = 20 f therefore , s = 4 f and then e = 5 f f / e = f / 5 f = 20 % therefore , answer is b"
Answer: b
Python program:
a = 3 - 5
b = 5 - 5
c = a / b
d = c * 100
Problem: if f ( x ) = 2 x ^ 2 + y , and f ( 2 ) = 30 , what is the value of f ( 10 ) ?
Options: a ) 104 , b ) 60 , c ) 52 , d ) 50 , e ) 222
Rationale: f ( x ) = 2 x ^ 2 + y f ( 2 ) = 30 = > 2 * ( 2 ) ^ 2 + y = 30 = > 8 + y = 30 = > y = 22 f ( 10 ) = 2 * ( 10 ) ^ 2 + 22 = 222 answer e
Answer: e
Python program:
a = 2 ** 2
b = a * 2
c = 30 - b
d = 10 ** 2
e = 2 * d
f = c + e
Problem: if a certain coin is flipped , the probability that the coin will land heads is 1 / 2 . if the coin is flipped 5 times , what is the probability that it will land heads up on the first 2 flips but not on the last 3 flips ?
Options: a ) 1 / 2 , b ) 1 / 4 , c ) 1 / 8 , d ) 1 / 16 , e ) 1 / 32
Rationale: "p ( hhttt ) = 1 / 2 * 1 / 2 * 1 / 2 * 1 / 2 * 1 / 2 = 1 / 32 the answer is e ."
Answer: e
Python program:
a = 1 / 2
b = a ** 5
Problem: by weight , liquid x makes up 0.5 percent of solution p and 1.5 percent of solution q . if 200 grams of solution p are mixed with 800 grams of solution q , then liquid x accounts for what percent of the weight of the resulting solution ?
Options: a ) 1.3 % , b ) 1.2 % , c ) 1.1 % , d ) 1.0 % , e ) 0.9 %
Rationale: the number of grams of liquid x is 0.5 ( 200 ) / 100 + 1.5 ( 800 ) / 100 = 1 + 12 = 13 grams . 13 / 1000 = 1.3 % the answer is a .
Answer: a
Python program:
a = 1 * 5
b = a / 100
c = 1 + b 
d = c / 1000
e = d * 100
Problem: there 3 kinds of books in the library physics , chemistry and biology . ratio of physics to chemistry is 3 to 2 ; ratio of chemistry to biology is 4 to 3 , and the total of the books is more than 3000 . which one of following can be the total q of the book ?
Options: a ) 3003 , b ) 3027 , c ) 3024 , d ) 3021 , e ) 3018
Rationale: first , you have to find the common ratio for all 3 books . you have : p : c : b 3 : 2 - - > multiply by 2 ( gives you row 3 ) 4 : 6 6 : 4 : 3 hence : p : c : b : t ( total ) = q 6 : 4 : 3 : 13 - - - - > this means , the total number must be a multiple of 13 . answer a is correct since 299 is divisible by 13 , hence is 2990 and so is 3003 ( 2990 + 13 ) .
Answer: a
Python program:
a = 3000 + 3
Problem: the difference between the place values of 6 and 1 in the number 527631 is
Options: a ) 596 , b ) 587 , c ) 533 , d ) 568 , e ) 599
Rationale: sol . = ( place value of 6 ) – ( place value of 1 ) = ( 600 - 1 ) = 599 answer e
Answer: e
Python program:
a = 10 * 6
b = a - 6
Problem: when tossed , a certain coin has equal probability of landing on either side . if the coin is tossed 3 times , what is the probability that it will land twice on heads and once on tails ?
Options: a ) 1 / 16 , b ) 1 / 3 , c ) 1 / 6 , d ) 1 / 2 , e ) 1 / 8
Rationale: "must be once on twice and once on tails 1 / 2 * 1 / 2 * 1 / 2 = 1 / 8 answer : e"
Answer: e
Python program:
a = 2 ** 3
b = 1 / a
Problem: the cost of a one - family home was $ 120,000 in 1980 . in 1988 , the price had increased to $ 186,000 . what was the percent increase in the cost of the home ?
Options: a ) 60 % , b ) 50 % , c ) 55 % , d ) 40 % , e ) 33.3 %
Rationale: "increase = 186000 - 120000 = 66000 % increase = 66000 * 100 / 120000 = 55 % answer : option c"
Answer: c
Python program:
a = 4 * 4
b = 12 * a
c = b * 1000
d = 12 * 1000
e = d * 10
f = c - e
g = 12 * 1000
h = g * 10
i = f / h
j = i * 100
Problem: [ ( 5 / 2 ÷ 1 / 2 × 5 / 2 ) ] / [ ( 5 / 2 × 1 / 2 ÷ 5 / 2 ) ] = ?
Options: a ) 25 , b ) 20 , c ) 18 , d ) 16 , e ) 14
Rationale: explanation : [ ( 5 / 2 ÷ 1 / 2 × 5 / 2 ) ] / [ ( 5 / 2 × 1 / 2 ÷ 5 / 2 ) ] = [ 5 / 2 × 2 / 1 × 5 / 2 ] / [ 5 / 2 × 1 / 2 × 2 / 5 ] = 25 / 2 / 1 / 2 = 25 / 2 x 2 / 1 = 25 answer : option a
Answer: a
Python program:
a = 5 / 2
b = 1 / 2
c = a / b
d = 5 / 2
e = c * d
f = 5 / 2
g = 1 / 2
h = f * g
i = 5 / 2
j = h / i
k = e / j
Problem: the length of a room is 5.5 m and width is 3.75 m . what is the cost of paying the floor by slabs at the rate of $ 700 per sq . metre .
Options: a ) $ 12537.50 , b ) $ 13537.50 , c ) $ 14437.50 , d ) $ 16437.50 , e ) $ 18537.50
Rationale: "c area = 5.5 × 3.75 sq . metre . cost for 1 sq . metre . = $ 700 hence , total cost = 5.5 × 3.75 × 700 = $ 14437.50"
Answer: c
Python program:
a = 5 * 5
b = 700 * a
Problem: the h . c . f . of two numbers is 12 and their l . c . m . is 600 . if one of the numbers is 480 , then the other is :
Options: a ) 11 , b ) 10 , c ) 8 , d ) 15 , e ) 12
Rationale: "other number = ( 12 x 600 ) / 480 = 15 . answer : d"
Answer: d
Python program:
a = 12 * 480
Problem: find the value of ( 85 + 32 / 113 ) × 113
Options: a ) 9263 , b ) 9244 , c ) 9636 , d ) 9623 , e ) 9637
Rationale: "= ( 85 + 32 / 113 ) × 113 = ( 9605 + 32 ) / 113 × 113 = 9637 / 113 × 113 = 9637 answer is e ."
Answer: e
Python program:
a = 32 / 113
b = a + 85 
c = b * 113
Problem: you collect baseball cards . suppose you start out with 19 . maria takes half of one more than the number of baseball cards you have . since you ' re nice , you give peter 1 baseball card . since his father makes baseball cards , paul decides to triple your baseball cards . how many baseball cards do you have at the end ?
Options: a ) 17 , b ) 18 , c ) 19 , d ) 20 , e ) 24
Rationale: "solution start with 19 baseball cards . maria takes half of one more than the number of baseball cards you have . so maria takes half of 19 + 1 which is 10 , so you ' re left with 19 - 10 = 9 . peter takes 1 baseball card from you : 9 - 1 = 8 baseball cards . paul triples the number of baseball cards you have : 8 ã — 3 = 24 baseball cards . so you have 24 at the end . correct answer : e"
Answer: e
Python program:
a = 19 - 4
b = a - 4
c = b - 1
d = c * 3
Problem: in township k , 1 / 5 of the housing units are equiped with cable tv . if 1 / 12 of the housing units , including 1 / 3 of those that are equiped with cable tv , are equipped with videocassette recorders , what fraction of the housing units have neither cable tv nor videocassette recorders ?
Options: a ) 23 / 30 , b ) 11 / 15 , c ) 47 / 60 , d ) 1 / 6 , e ) 2 / 15
Rationale: "1 / 5 - - cable tv ( this includes some data from video cassette recorder ) 1 / 10 - - video cassette recorder including 1 / 3 ( equiped with cable tv ) i . e . 1 / 3 ( 1 / 5 ) = 1 / 15 therefore only video cassette recorder = 1 / 12 - 1 / 15 = 1 / 60 total = 1 / 5 + 1 / 60 + neither cable tv nor videocassette recorders 1 = 13 / 60 + neither cable tv nor videocassette recorders therefore neither cable tv nor videocassette recorders = 1 - 13 / 60 = 47 / 60 hence c ."
Answer: c
Python program:
a = 12 + 5 
b = 12 * 2
c = a / b
Problem: the average salary of all the workers in a workshop is rs . 8000 . the average salary of 7 technicians is rs . 20000 and the average salary of the rest is rs . 6000 . the total number of workers in the workshop is :
Options: a ) 23 , b ) 49 , c ) 22 , d ) 20 , e ) 21
Rationale: "let the total number of workers be x . then , 8000 x = ( 20000 * 7 ) + 6000 ( x - 7 ) = 2000 x = 98000 = x = 49 . answer : b"
Answer: b
Python program:
a = 20000 - 8000
b = 7 * a
c = 8000 - 6000
d = b / c
e = 7 + d
Problem: the two lines y = x and x = - 4 intersect on the coordinate plane . if z represents the area of the figure formed by the intersecting lines and the x - axis , what is the side length t of a cube whose surface area is equal to 6 z ?
Options: a ) t = 16 , b ) t = 8 √ 2 , c ) t = 8 , d ) t = 2 √ 2 , e ) ( √ 2 ) / 3
Rationale: "800 score official solution : the first step to solving this problem is to actually graph the two lines . the lines intersect at the point ( - 4 , - 4 ) and form a right triangle whose base length and height are both equal to 4 . as you know , the area of a triangle is equal to one half the product of its base length and height : a = ( 1 / 2 ) bh = ( 1 / 2 ) ( 4 × 4 ) = 8 ; so z = 8 . the next step requires us to find the length of a side of a cube that has a face area equal to 8 . as you know the 6 faces of a cube are squares . so , we can reduce the problem to finding the length of the side of a square that has an area of 8 . since the area of a square is equal to s ² , where s is the length of one of its side , we can write and solve the equation s ² = 8 . clearly s = √ 8 = 2 √ 2 , oranswer choice ( d ) ."
Answer: d
Python program:
a = 4 * 4
b = a / 2
c = math.sqrt(b)
Problem: find the value of x from the below equation ? : 3 x ^ 2 + 5 x + 2 = 0
Options: a ) - 1 , b ) - 2 , c ) 1 , d ) 2 , e ) 3
Rationale: "a = 3 , b = 5 , c = 2 x 1,2 = ( - 5 ± √ ( 52 - 4 × 3 × 2 ) ) / ( 2 × 3 ) = ( - 5 ± √ ( 25 - 24 ) ) / 6 = ( - 5 ± 1 ) / 6 x 1 = ( - 5 + 1 ) / 6 = - 4 / 6 = - 2 / 3 x 2 = ( - 5 - 1 ) / 6 = - 6 / 6 = - 1 a"
Answer: a
Python program:
a = 2 ** 3
b = 5 * 5
c = a - b
d = math.sqrt(c)
e = 2 - d
f = e / 3
Problem: the h . c . f of two numbers is 23 and the other two factors of their l . c . m are 12 and 13 . the larger of the two numbers is :
Options: a ) 299 , b ) 278 , c ) 322 , d ) 231 , e ) 121
Rationale: "clearly , the numbers are ( 23 * 12 ) and ( 23 * 13 ) . larger number = ( 23 * 13 ) = 299 . answer : a"
Answer: a
Python program:
a = 23 * 13
Problem: two sides of a triangle have lengths x and t and meet at a right angle . if the perimeter of the triangle is 4 x , what is the ratio of x to t ?
Options: a ) a ) 2 : 3
b ) b ) 3 : 4
c ) c ) 4 : 3
d ) d ) 3 : 2
e ) e ) 2 : 1
Rationale: ahhhh . . . . my bad . thank you , you ' re correct . 8 x = 6 t - - > x / t = 3 / 4 . actually b is the right answer .
Answer: b
Python program:
a = 3 / 4
Problem: in 70 liters of a mixture of milk and water , the quantity of water is 10 % . how much water should be added so that new mixture may 25 % water .
Options: a ) 14 , b ) 15 , c ) 16 , d ) 17 , e ) 18
Rationale: there are 10 % of water in 70 l - - > there are 7 l of waters ; after x liters of water is added amount of water becomes ( 7 + x ) liters , which on the other hand is 1 / 4 th ( 25 % ) of new ( 70 + x ) liters of mixture : 7 + x = 1 / 4 * ( 70 + x ) - - > 28 + 4 x = 70 + x - - > x = 14 answer : a
Answer: a
Python program:
a = 100 - 25
b = 25 - 10
c = a / b
d = 70 / c
Problem: an athlete runs 150 metres race in 24 seconds . what is his speed ?
Options: a ) 27 , b ) 38 , c ) 37 , d ) 30 , e ) 28
Rationale: "speed = distance / time = 150 / 20 = 7.5 m / s = 7.5 * 18 / 5 = 27 km / hr answer : a"
Answer: a
Python program:
a = 150 / 24
b = a * const_3_6
Problem: a can contains a mixture of liquids a and b is the ratio 7 : 5 . when 15 litres of mixture are drawn off and the can is filled with b , the ratio of a and b becomes 7 : 9 . how many liter of liquid a was contained by the can initially ?
Options: a ) 30 , b ) 35 , c ) 40 , d ) 45 , e ) 50
Rationale: "ci * vi = cf * vf ( 7 / 12 ) * ( v 1 - 15 ) = ( 7 / 16 ) * v 1 ( v 1 - 15 ) / v 1 = 3 / 4 15 accounts for the difference of 1 on ratio scale so initial volume = v 1 = 4 * 15 = 60 litres . 7 / 12 of the initial mixture was liquid a so liquid a was ( 7 / 12 ) * 60 = 35 litres . answer : b"
Answer: b
Python program:
a = 7 + 15 
b = 7 + 5 
c = 5 / b
d = c * 15
e = 15 - d
f = a * e
g = 15 * 7
h = 7 * 5
i = g - h
j = f / i
k = 7 * j
Problem: find the smallest number that must be added to 1780 to make it a perfect square .
Options: a ) 17 , b ) 42 , c ) 69 , d ) 47 , e ) 52
Rationale: "4 1780 ( 42 16 82 180 164 16 number to be added = ( 43 ) 2 - 1780 = 1849 - 1780 = 69 . answer c"
Answer: c
Python program:
a = 1780 / 1000
b = a / 3
c = b / 3
d = c / 3
e = 1780 / 1000
f = e / 3
g = f / 3
h = g / 3
i = d * h
Problem: two trains , one from howrah to patna and the other from patna to howrah , start simultaneously . after they meet , the trains reach their destinations after 9 hours and 25 hours respectively . the ratio of their speeds is ?
Options: a ) 4 : 5 , b ) 5 : 3 , c ) 4 : 4 , d ) 4 : 8 , e ) 4 : 1
Rationale: "let us name the trains a and b . then , ( a ' s speed ) : ( b ' s speed ) = √ b : √ a = √ 25 : √ 9 = 5 : 3 answer : b"
Answer: b
Python program:
a = math.sqrt(25)
b = math.sqrt(9)
c = a / b
Problem: a thief goes away with a santro car at a speed of 40 kmph . the theft has been discovered after half an hour and the owner sets off in a bike at 55 kmph when will the owner over take the thief from the start ?
Options: a ) a ) 1.33 , b ) b ) 5 , c ) c ) 7 , d ) d ) 5 , e ) e ) 8
Rationale: "explanation : | - - - - - - - - - - - 20 - - - - - - - - - - - - - - - - - - - - | 55 40 d = 20 rs = 55 – 40 = 15 t = 20 / 15 = 1.33 hours answer : option a"
Answer: a
Python program:
a = 1 / 2
b = a * 40
c = 55 - 40
d = b / c
e = 1 / 2
f = d - e
Problem: a newspaper manufacturer produces 800 units of a certain model each month at a cost to the manufacturer of £ 50 per unit and all of the produced units are sold each month . what is the minimum selling price per unit that will ensure that the monthly profit ( revenue from sales minus production costs ) on the sales of these units will be at least £ 80000 ?
Options: a ) 115 , b ) 520 , c ) 550 , d ) 750 , e ) 796
Rationale: 800 ( x - 50 ) ≥ 80000 x - 50 ≥ 800 x ≥ 750 answer : option d
Answer: d
Python program:
a = 80000 / 800
b = 50 + a
Problem: p and q started a business investing rs . 85,000 and rs . 20,000 respectively . in what ratio the profit earned after 2 years be divided between p and q respectively ?
Options: a ) 17 : 6 , b ) 17 : 0 , c ) 17 : 4 , d ) 17 : 2 , e ) 17 : 3
Rationale: "p : q = 85000 : 20000 = 17 : 4 . answer : c"
Answer: c
Python program:
a = 2 + 3 
b = a + 3 
c = 2 + 3 
d = c * 2
e = b * d
f = 2 + 3 
g = e + f 
h = 2 + 3 
i = h * 2
j = 3 * i
k = 2 + 3 
l = j + k 
m = g / l
Problem: x does a work in 10 days . y does the same work in 15 days . in how many days they together will do the same work ?
Options: a ) 10 , b ) 15 , c ) 3 , d ) 6 , e ) 12
Rationale: "x ' s 1 day ' s work = 1 / 10 y ' s 1 day ' s work = 1 / 15 ( x + y ) ' s 1 day ' s work = ( 1 / 10 + 1 / 15 ) = 1 / 6 both together will finish the work in 6 days . correct option is d"
Answer: d
Python program:
a = 1 / 10
b = 1 / 15
c = a + b 
d = 1/(c)
Problem: a rectangular lawn of length 200 m by 120 m has two roads running along its center , one along the length and the other along the width . if the width of the roads is 5 m what is the area y covered by the two roads ?
Options: a ) 400 , b ) 1550 , c ) 1575 , d ) 1600 , e ) 1625
Rationale: "area covered by road along the length = 5 * 200 = 1000 square meter area covered by road along the width = 5 * 120 = 600 square meter common area in both roads ( where the roads intersect ) = square with side 5 meter = 5 * 5 = 25 total area of the roads y = 1000 + 600 - 25 = 1575 answer : option c"
Answer: c
Python program:
a = rectangle_area + (
Problem: which expression has the greatest value ?
Options: a ) 1977452 / 1977455 , b ) 1982466 / 1982469 , c ) 1982487 / 1982490 , d ) 1982456 / 1982459 , e ) 1982465 / 1982468
Rationale: "the difference between each numerator / denominator pair is three . the largest expression ( which in this case will also be the closest to one ) is the expression where ' 3 ' is the smallest fraction of the numerator ( or the denominator ) . the largest numerator is 1982487 , or c , and this will give an expression with a value closest to one . we can also demonstrate that this approach works with some simple logic . taking numerator / denominator pairs that differ by three . . . 1 / 4 = 0.25 2 / 5 = 0.4 3 / 6 = 0.5 . . . 27 / 30 = 0.9 . . . 1982487 / 1982490 = 0.999998486 . . . answer : c"
Answer: c
Python program:
a = 3 * 3
b = 3600 - a
c = 3600 - 4
d = b / c
Problem: a train 108 m long moving at a speed of 50 kmph crosses a train 112 m long coming from opp direction in 6 seconds . the speed of the second train is
Options: a ) 48 kmph , b ) 54 kmph , c ) 66 kmph , d ) 82 kmph , e ) 69 kmph
Rationale: both trains are moving in opposite direction means we need to add their speeds . i . e : 1 st train speed is = 50 kmph let the 2 nd train speed = x kmph relative speed = ( 50 + x ) kmph = ( 50 + x ) * 5 / 18 = ( 250 + 5 x ) / 18 m / sec distance covered by two trains = 108 + 112 = 220 m therefore , 220 / ( ( 250 + 5 x ) / 18 ) = 6 = > 250 + 5 x = 660 = > x = 82 km / hr . answer : d
Answer: d
Python program:
a = 108 + 112 
b = a / 6
c = const_3_6 * b
d = c - 50
Problem: what is the greatest prime factor of 4 ^ 17 - 2 ^ 29 ?
Options: a ) 2 , b ) 3 , c ) 5 , d ) 7 , e ) 31
Rationale: i ' m happy to help with this . we know 4 = 2 ^ 2 , so 4 ^ 17 = ( 2 ^ 2 ) ^ 17 = 2 ^ ( 2 * 17 ) = 2 ^ 34 that takes advantage of a law of exponents that says ( a ^ n ) ^ m = a ^ ( n * m ) so , 4 ^ 17 - 2 ^ 29 = 2 ^ 34 - 2 ^ 29 = 2 ^ ( 29 + 5 ) - 2 ^ 29 = ( 2 ^ 29 ) * ( 2 * 6 ) - 2 ^ 29 = ( 2 ^ 6 - 1 ) * ( 2 ^ 29 ) = ( 32 - 1 ) * ( 2 ^ 29 ) = 31 * ( 2 ^ 29 ) the prime factors of 31 are 31 , so the largest prime factor is 31 , answer choice d . here ' s a blog you may find helpful . http : / / magoosh . com / gmat / 2012 / gmat - math - factors / does all that make sense ? please let me know if you have any further questions . mike wow . i am floored by how great of an explanation you provided . posts like that make me really think that doing thousands of practice problems with good explanations beats out reading books on math every day of the week . e
Answer: e
Python program:
a = 2 + 29
Problem: jo ' s collection contains us , indian and british stamps . if the ratio of us to indian stamps is 5 to 2 and the ratio of indian to british stamps is 4 to 1 , what is the ratio of us to british stamps ?
Options: a ) 5 : 1 , b ) 10 : 5 , c ) 15 : 2 , d ) 20 : 2 , e ) 25 : 2
Rationale: "u / i = 5 / 2 i / b = 4 / 1 since i is multiple of both 2 ( as per first ratio ) and 5 ( as per second ratio ) so let ' s assume that i = 10 i . e . multiplying teh first ratio by 5 and second ration by 2 in each numerator and denominator then , u : i : b = 20 : 8 : 2 i . e . u : b = 20 : 2 answer : option d"
Answer: d
Python program:
a = 5 * 4
b = 1 * 2
c = a / b
Problem: by investing in 16 % stock at 64 , one earns rs . 1500 . the investment made is ?
Options: a ) 2288 , b ) 2877 , c ) 5760 , d ) 7636 , e ) 5728
Rationale: "to earn rs . , investment = rs . 64 . to earn rs . 1500 , investment = = rs . 5760 . answer : c"
Answer: c
Python program:
a = 4 * 2
b = 4 * 2
c = a * b
d = c * 3
e = 100 / 2
f = d / e
g = 4 * 100
h = 1500 - g
i = f * h
Problem: a student , after his teacher ' s question , chose a number , multiplied it by 2 , then subtracted 138 from the result and got 102 . what was the number he chose ?
Options: a ) 344 , b ) 251 , c ) 411 , d ) 212 , e ) 120
Rationale: let x be the number he chose , then 2 ⋅ x − 138 = 102 2 x = 240 x = 120 correct answer is e ) 120
Answer: e
Python program:
a = 138 + 102 
b = a / 2
Problem: what is the sum of the greatest common factor and the lowest common multiple of 36 and 16 ?
Options: a ) 148 , b ) 210 , c ) 314 , d ) 320 , e ) 344
Rationale: prime factorization of 36 = 2 x 2 x 3 x 3 prime factorization of 16 = 2 x 2 x 2 x 2 gcf = 4 lcm = 144 sum = 148 . answer a .
Answer: a
Python program:
a = 36 * 16
b = a / 4
Problem: lisa and robert have taken the same number of photos on their school trip . lisa has taken 3 times as many photos as claire and robert has taken 28 more photos than claire . how many photos has claire taken ?
Options: a ) 6 , b ) 8 , c ) 10 , d ) 12 , e ) 14
Rationale: "l = r l = 3 c r = c + 28 3 c = c + 28 c = 14 the answer is e ."
Answer: e
Python program:
a = 3 - 1
b = 28 / a
Problem: a fruit seller sells mangoes at the rate of rs . 5 per kg and thereby loses 20 % . at what price per kg , he should have sold them to make a profit of 5 %
Options: a ) rs 6.56 , b ) rs 9.56 , c ) rs 10.56 , d ) rs 11.56 , e ) none of these
Rationale: "explanation : 80 : 5 = 105 : x x = ( 5 × 105 / 80 ) = rs 6.56 option a"
Answer: a
Python program:
a = 100 + 5 
b = 5 * a
c = 100 - 20
d = b / c
Problem: a train covers a distance of 15 km in 10 min . if it takes 6 sec to pass a telegraph post , then the length of the train is ?
Options: a ) m , b ) m , c ) m , d ) m , e ) m
Rationale: "speed = ( 15 / 10 * 60 ) km / hr = ( 90 * 5 / 18 ) m / sec = 25 m / sec . length of the train = 25 * 6 = 150 m . answer : c"
Answer: c
Python program:
a = 15 / 10
b = a - 6
c = 15 / b
Problem: a special municipal payroll tax charges not tax on a payroll less than $ 200,000 and only 0.1 % on a company ’ s payroll above $ 200,000 . if belfried industries paid $ 400 in this special municipal payroll tax , then they must have had a payroll of ?
Options: a ) $ 180,000 , b ) $ 202,000 , c ) $ 220,000 , d ) $ 400,000 , e ) $ 600,000
Rationale: "answer : e , ( with different approach ) : the 400 paid is 0.1 % of the additional amount above 200,000 . let it be x now 0.1 % of x = 400 therefore x = 400,000 total = 200,000 + x = 600,000"
Answer: e
Python program:
a = 400 * 100
b = a * 10
Problem: there are 7 red shoes & 3 green shoes . if two of red shoes are drawn what is the probability of getting red shoes
Options: a ) 1 / 13 , b ) 1 / 14 , c ) 1 / 15 , d ) 7 / 15 , e ) 7 / 16
Rationale: "taking 2 red shoe the probablity is 7 c 2 from 10 shoes probablity of taking 2 red shoe is 7 c 2 / 10 c 2 = 7 / 15 answer : d"
Answer: d
Python program:
a = math.comb(7, 2)
b = 7 + 3 
c = math.comb(b, 2)
d = a / c
Problem: a can do a piece of work in 8 days . b can do it in 16 days . with the assistance of c they completed the work in 4 days . find in how many days can c alone do it ?
Options: a ) 87 days , b ) 20 days , c ) 26 days , d ) 19 days , e ) 16 days
Rationale: "c = 1 / 4 - 1 / 8 - 1 / 16 = 1 / 16 = > 16 days answer : e"
Answer: e
Python program:
a = 8 * 16
b = 8 * 16
c = 8 * 16
d = c / 8
e = 8 * 16
f = e / 16
g = d + f 
h = g * 4
i = b - h
j = i / 4
k = a / j