euclaise/mathqa_programs huggingface dataset:
Problem: on a certain day , tim invested $ 500 at 10 percent annual interest , compounded annually , and lana invested 900 at 5 percent annual interest , compounded annually . the total amount of interest earned by tim ’ s investment in the first 2 years was how much greater than the total amount of interest earned by lana ’ s investment in the first 2 years ?
Options: a ) $ 5 , b ) $ 12.75 , c ) $ 51.75 , d ) $ 100.75 , e ) $ 105
Rationale: "compounded annually means that the interest is applied once per year . one can have 10 % annual interest compounded monthly - in this case 10 % / 12 would be applied each month , or 10 % annual interest compounded daily etc . with respect to the problem at hand , at the end of two years , tim would have 500 ( 1.10 ) ^ 2 = 500 ( 1.21 ) = 605 and lana would have 900 ( 1.05 ) ^ 2 = 900 ( 1.1025 ) = 992.25 thus , tim earned 105 dollars , while lana earned 92.25 dollars the difference is $ 12.75 and the answer is b ."
Answer: b
Python program:
a = 10 / 100
b = 1 + a 
c = b ** 2
d = 500 * c
e = d - 500
f = 5 / 100
g = 1 + f 
h = g ** 2
i = h * 900
j = i - 900
k = e - j
Problem: a cube of sides 9 is first painted red and then cut into smaller cubes of side 3 . how many of the smaller cube have painted on exactly 2 sides ?
Options: a ) 30
b ) 24
c ) 12
d ) 8
e ) 9
Rationale: n = side of big cube / side of small cube and no . of smaller cubes with two surfaces painted is ( n - 2 ) * 12 ( 3 - 2 ) * 12 = 12 ans answer : c
Answer: c
Python program:
a = 9 * 3
b = 3 + 4 
c = a - b
d = 4 * 2
e = c - d
Problem: sam invested rs . 5000 @ 10 % per annum for one year . if the interest is compounded half - yearly , then the amount received by sam at the end of the year will be ?
Options: a ) 500.2 , b ) 320.0 , c ) 220.5 , d ) 100.1 , e ) 230.2
Rationale: "p = rs . 5000 ; r = 10 % p . a . = 5 % per half - year ; t = 1 year = 2 half - year amount = [ 5000 * ( 1 + 5 / 100 ) 2 ] = ( 5000 * 21 / 20 * 21 / 20 ) = rs . 220.50 answer : c"
Answer: c
Python program:
a = 10 / 2
b = a / 100
c = b + 1 
d = c ** 2
e = d * 5000
Problem: a person incurs 20 % loss by selling a watch for $ 1000 . at what price should the watch be sold to earn 20 % profit ?
Options: a ) $ 1000 , b ) $ 950 , c ) $ 1500 , d ) $ 1150 , e ) $ 1250
Rationale: "let the new selling price be $ x ( 100 - loss % ) : ( 1 st s . p . ) = ( 100 + gain % ) : ( 2 nd s . p . ) ( 100 - 20 ) / 1000 = ( 100 + 20 ) / x x = 120 * 1000 / 80 = 1500 answer is c"
Answer: c
Python program:
a = 20 / 100
b = 1 - a
c = 1000 / b
Problem: a , b and c can complete a piece of work in 24 , 6 and 12 days respectively . working together , they will complete the same work in :
Options: a ) 33 / 7 , b ) 43 / 7 , c ) 24 / 7 , d ) 19 / 7 , e ) none
Rationale: if a can do a piece of work in n days , then a ' s 1 day ' s work = 1 / n ( a + b + c ) ' s 1 day ' s work = 1 / 24 + 1 / 6 + 1 / 12 = 7 / 24 so , all the three together will complete the job in = 24 / 7 days answer : c
Answer: c
Python program:
a = 1/(12)
b = 1/(24)
c = 1/(6)
d = b + c 
e = a + d 
f = 1/(e)
Problem: a man covered a certain distance at some speed . had he moved 3 kmph faster , he would have taken 40 minutes less . if he had moved 2 kmph slower , he would have taken 40 minutes more . the distance ( in km ) is :
Options: a ) 35 , b ) 36 , c ) 37 , d ) 40 , e ) 45
Rationale: "according to given condition vt = ( v + 3 ) ( t - 2 / 3 ) vt = ( v - 2 ) ( t + 2 / 3 ) here v is velocity in kmph , t is time in hours and 2 / 3 is value of 40 min in hour on solving we will get t = 10 / 3 and and v = 12 so distance = ( 10 / 3 ) * 12 = 40 kms answer : d"
Answer: d
Python program:
a = 2 * 3
b = a * 2
c = 3 - 2
d = b / c
e = 40 / const_60
f = d * e
g = 2 * 3
h = g * 2
i = 3 - 2
j = h / i
k = j / 3
l = 1 + k 
m = f * l
Problem: two pipes a and b can fill a cistern in 20 and 30 minutes respectively , and a third pipe c can empty it in 60 minutes . how long will it take to fill the cistern if all the three are opened at the same time ?
Options: a ) 15 min , b ) 15 1 / 7 min , c ) 17 1 / 7 min , d ) 7 1 / 7 min , e ) 7 2 / 7 min
Rationale: "1 / 20 + 1 / 30 - 1 / 60 = 4 / 60 60 / 4 = 15 answer : a"
Answer: a
Python program:
a = 1/(20)
b = 1/(30)
c = a + b 
d = c * 3
e = 1 - d
f = 20 * e
g = f + 60
Problem: a shoe merchant has declared a 10 % rebate in prices . how much rebate would one get if he purchases 5 pairs of shoes at rs . 28 each ?
Options: a ) 11 , b ) 12 , c ) 13 , d ) 14 , e ) 15
Rationale: explanation : 5 shirts * rs . 28 = rs . 140 rebate = 10 % * 140 = 14 correct option : d
Answer: d
Python program:
a = 10 / 100
b = 5 * 28
c = a * b
Problem: if the average of 8 digits is 20 and the average of 5 of them is 12 , calculate the average of the remaining 3 numbers ?
Options: a ) 13.3 , b ) 38.3 , c ) 35.3 , d ) 31.3 , e ) 33.3
Rationale: "explanation : total of the 8 digits - 8 * 20 = 160 total of the 5 digits - 5 * 12 = 60 total of the remaining 3 digits - 160 - 60 = 100 average of the remaining 3 numbers = 100 / 3 = 33.3 answer : e"
Answer: e
Python program:
a = 8 * 20
b = 5 * 12
c = a - b
d = c / 3
Problem: in a restaurant , the profit is 120 % of the cost . if the cost increases by 12 % but the selling price remains constant , approximately what percentage of the selling price is the profit ?
Options: a ) 30 % , b ) 49 % , c ) 90 % , d ) 100 % , e ) none of these
Rationale: "explanation : let c . p . = rs . 100 . then , profit = rs . 120 , s . p . = rs . 220 . new c . p . = 112 % of rs . 100 = rs . 112 new s . p . = rs . 220 . profit = rs . ( 220 - 112 ) = rs . 108 . required percentage = ( 108 / 220 * 100 ) % = 49 % appox answer : b"
Answer: b
Python program:
a = 120 / 100
b = 100 * a
c = b + 100 
d = 12 / 100
e = 1 + d 
f = 100 * e
g = c - f
h = 120 / 100
i = 100 * h
j = i + 100 
k = g / j
l = 100 * k
Problem: a man purchased 3 blankets @ rs . 100 each , 5 blankets @ rs . 150 each and two blankets at a certain rate which is now slipped off from his memory . but he remembers that the average price of the blankets was rs . 150 . find the unknown rate of two blankets ?
Options: a ) 278 , b ) 277 , c ) 278 , d ) 450 , e ) 272
Rationale: "10 * 150 = 1500 3 * 100 + 5 * 150 = 1050 1500 – 1050 = 450 answer : d"
Answer: d
Python program:
a = 10 * 150
b = 3 * 100
c = 5 * 150
d = b + c 
e = a - d
Problem: a shop owner sells 30 mtr of cloth and gains sp of 10 mtrs . find the gain % ?
Options: a ) 30 % , b ) 40 % , c ) 50 % , d ) 60 % , e ) 70 %
Rationale: "here , selling price of 10 m cloth is obtained as profit . profit of 10 m cloth = ( s . p . of 30 m cloth ) – ( c . p . of 30 m cloth ) selling price of 20 m cloth = selling price of 30 m of cloth let cost of each metre be rs . 100 . therefore , cost price of 20 m cloth = rs . 2000 and s . p . of 20 m cloth = rs . rs . 3000 profit % = 10 × 100 = 50 % 20 profit of 50 % was made by the merchant . c"
Answer: c
Python program:
a = 30 - 10
b = 10 / a
c = b * 100
Problem: a certain dark blue paint contains 40 percent blue pigment and 60 percent red pigment by weight . a certain green paint contains 40 percent blue pigment and 60 percent yellow pigment . when these paints are mixed to produce a brown paint , the brown paint contains 40 percent blue pigment . if the brown paint weighs 10 grams , then the red pigment contributes how many grams of that weight ?
Options: a ) 3.5 , b ) 4 , c ) 4.5 , d ) 3 , e ) 5
Rationale: 10 grams of combined mixture and 40 % blue pigment means that the mixtures were mixed 50 % each . thus 5 grams a piece . out of the 5 grams of the dark blue paint , 60 % is red . therefore , 5 * . 6 = 3 grams of red pigment
Answer: d
Python program:
a = 10 * 40
b = a / 100
c = b / 2
d = 60 / 40
e = c * d
Problem: in goshawk - eurasian nature reserve 30 percent of the birds are hawks , and 40 percent of the non - hawks are paddyfield - warblers . if there are 25 percent as many kingfishers as paddyfield - warblers in the reserve , then what percent of the birds x in the nature reserve are not hawks , paddyfield - warblers , or kingfishers ?
Options: a ) 25 % , b ) 35 % , c ) 45 % , d ) 70 % , e ) 80 %
Rationale: "1 . we are given the following percentages : 30 ( 70 ) , 40 ( 60 ) , 25 ( 75 ) . there are two threads from here . first starts at 30 % and finishes there . second one starts at 70 , then 40 , and then 25 . we need a value that is divisible by 7 , 2 , and 5 at least once . lets pick a number now , say 700 . so say if non hawks are 700 ( this is 70 % of the total , so total = 1000 ) , then paddy warbs are 2 / 5 x 700 = 1400 / 5 = 280 . kingfishers , therefore , are 280 / 4 = 70 . lets add them up . 300 hawks + 280 peddy warbs + 70 kingsifhers = 650 . so all others are 1000 - 650 = 350 or 35 % of total birds . the main job here to to identify the smart number to start the question with . this can be time consuming , but once identified , this question can be solved fairly quickly . 2 . another method : if x is total - - > non hawks = 0.7 x - - > warbs = 0.4 ( 0.7 x ) - - > kfs = 0.25 ( 0.4 ( 0.7 x ) ) . our job is to find out x : ( 0.3 x + 0.28 x + 0.07 x ) / x . or 0.65 x / x = 0.65 . we need to find 1 - 0.65 = 0.35 or 35 % . b"
Answer: b
Python program:
a = 25 + 25 
b = a / 2
c = 10 + b
Problem: if ( a – b ) is 13 more than ( c + d ) and ( a + b ) is 3 less than ( c – d ) , then ( a – c ) is :
Options: a ) 6 , b ) 2 , c ) 3 , d ) 4 , e ) 5
Rationale: "( a – b ) – ( c + d ) = 13 and ( c – d ) – ( a + b ) = 3 = > ( a – c ) – ( b + d ) = 13 and ( c – a ) – ( b + d ) = 3 = > ( b + d ) = ( a – c ) – 13 and ( b + d ) = ( c – a ) – 3 = > ( a – c ) – 13 = ( c – a ) – 3 = > 2 ( a – c ) = 10 = > ( a – c ) = 5 answer : e"
Answer: e
Python program:
a = 13 / 3
Problem: how many integers between 1 and 1,400 are divisible by 25 , and 35 ?
Options: a ) 4 , b ) 5 , c ) 6 , d ) 7 , e ) 8
Rationale: "lcm of the given numbers = 175 therefore , number of integers = 1400 / 175 = 8 answer is option e"
Answer: e
Python program:
a = 2 * 100
b = 3 + 4 
c = b * 10
d = a + c 
e = d + 2 
f = 1 - 400
Problem: rahul can done a work in 5 days and meena can done a work in 10 days . in how many days that both are work together ?
Options: a ) 3 / 10 , b ) 10 / 3 , c ) 1 / 3 , d ) 5 , e ) 6 / 3
Rationale: a ' s one day work = 1 / 5 b ' s one day work = 1 / 10 a + b = 1 / 5 + 1 / 10 = 10 + 5 / 50 = 10 / 3 days ans : option b
Answer: b
Python program:
a = 1 / 5
b = 1 / 10
c = a + b 
d = 1/(c)
Problem: a bicycle wheel has a diameter of 0.75 m . how many complete revolutions does it make in 1 km ?
Options: a ) 424 , b ) 448 , c ) 1408 , d ) 710 , e ) 223
Rationale: "1 revolution = 3.14 * diameter . number of revolutions in 1 km = 1000 m / ( 3.14 * 0.75 m ) = 424.6 . hence 424 complete revolutions . answer a"
Answer: a
Python program:
a = 1000 * 1
b = 3 * 4
c = b + 2 
d = 4 * 2
e = d + 2 
f = e ** 2
g = c / f
h = 3 + g 
i = h * 0
j = a / i
Problem: country x taxes each of its citizens an amount equal to 15 percent of the first $ 40,000 of income , plus 20 percent of all income in excess of $ 40,000 . if a citizen of country x is taxed a total of $ 8,000 , what is her income ?
Options: a ) $ 40,000 , b ) $ 50,000 , c ) $ 64,000 , d ) $ 66,667 , e ) $ 80,000
Rationale: equation is correct , so math must be a problem . 0.15 * 40,000 + 0.2 * ( x - 40,000 ) = 8,000 - - > 6,000 + 0.2 x - 8,000 = 8,000 - - > 0.2 x = 10,000 - - > x = 50,000 . answer : b .
Answer: b
Python program:
a = 4 * 10
b = a * 1000
c = 4 * 2
d = c * 1000
e = 15 / 100
f = 4 * 10
g = f * 1000
h = e * g
i = d - h
j = 20 / 100
k = i / j
l = b + k
Problem: if a ^ 2 + b ^ 2 = 10 and ab = 10 , what is the value of the expression ( a - b ) ^ 2 + ( a + b ) ^ 2 ?
Options: a ) 10 , b ) 20 , c ) 30 , d ) 60 , e ) 70
Rationale: "( a - b ) ^ 2 = a ^ 2 + b ^ 2 - 2 ab = 10 - 20 = - 10 ( a + b ) ^ 2 = a ^ 2 + b ^ 2 + 2 ab = 10 + 20 = 30 so ( a + b ) ^ 2 + ( a - b ) ^ 2 = 30 - 10 = 20 b"
Answer: b
Python program:
a = math.sqrt(10)
b = a * 10
c = b + 3
Problem: a , b , c , d and e are 5 consecutive points on a straight line . if bc = 2 cd , de = 8 , ab = 5 and ac = 11 , what is the length of ae ?
Options: a ) 18 , b ) 20 , c ) 22 , d ) 24 , e ) 26
Rationale: "ac = 11 and ab = 5 , so bc = 6 . bc = 2 cd so cd = 3 . the length of ae is ab + bc + cd + de = 5 + 6 + 3 + 8 = 22 the answer is c ."
Answer: c
Python program:
a = 11 - 5
b = a / 2
c = 11 + b 
d = c + 8
Problem: on a windy day , out of every 3 sand dunes formed , only 1 remains . out of 5 blown - out sand - dunes , 1 has treasure and only 2 out of 3 sand dunes formed have lucky coupons . find the probability that the blown - out sand dune will contain both the things .
Options: a ) 2 / 25 , b ) 4 / 75 , c ) 7 / 75 , d ) 3 / 5 , e ) 4 / 45
Rationale: probability of sand dune blown out = 2 / 3 probability that it has treasure = 1 / 5 probability that it has lucky coupon = 2 / 3 total probability = 2 / 3 * 1 / 5 * 2 / 3 = 4 / 45 answer : e
Answer: e
Python program:
a = 1 / 3
b = 1 - a
c = 2 / 3
d = 1 / 5
e = c * d
f = b * e
Problem: in the faculty of reverse - engineering , 250 second year students study numeric methods , 423 second year students study automatic control of airborne vehicles and 134 second year students study them both . how many students are there in the faculty if the second year students are approximately 80 % of the total ?
Options: a ) 515 . , b ) 545 . , c ) 618 . , d ) 674 . , e ) 666 .
Rationale: "answer is d : 674 solution : total number of students studying both are 423 + 250 - 134 = 539 ( subtracting the 134 since they were included in the both the other numbers already ) . so 80 % of total is 539 , so 100 % is approx . 674 ."
Answer: d
Python program:
a = 250 + 423
Problem: what is the measure of the radius of the circle that circumscribes a triangle whose sides measure 2 , 3 and 5 ?
Options: a ) 2.5 , b ) 3 , c ) 4 , d ) 4.5 , e ) 5
Rationale: "some of pyhtagron triplets we need to keep it in mind . like { ( 2 , 3,5 ) , ( 5 , 12,13 ) , ( 7 , 24,25 ) , ( 11 , 60,61 ) . so now we know the triangle is an right angle triangle . the circle circumscribes the triangle . the circumraduis of the circle that circumscribes the right angle triangle = hypotanse / 2 = 5 / 2 = 2.5 ans . a"
Answer: a
Python program:
a = triangle_area_three_edges / (
Problem: the price of 10 chairs is equal to that of 4 tables . the price of 15 chairs and 2 tables together is rs . 4000 . the total price of 12 chairs and 3 tables is
Options: a ) rs . 3800 , b ) rs . 3900 , c ) rs . 4000 , d ) rs . 4200 , e ) rs . 4400
Rationale: "let the cost of a chair and that of a table be rs . x and rs . y respectively . then , 10 x = 4 y or y = 5 x . 2 15 x + 2 y = 4000 15 x + 2 x 5 x = 4000 2 20 x = 4000 x = 200 . so , y = 5 x 200 = 500 . 2 hence , the cost of 12 chairs and 3 tables = 12 x + 3 y = rs . ( 2400 + 1500 ) = rs . 3900 . b"
Answer: b
Python program:
a = 4 / 10
b = 15 * a
c = b + 2 
d = 4000 / c
e = d * 3
f = 4 / 10
g = 4 / 10
h = 15 * g
i = h + 2 
j = 4000 / i
k = f * j
l = k * 12
m = e + l
Problem: if there is an equal probability of a child being born a boy or a girl , what is the probability that a couple who have 7 children have two children of the same sex and one of the opposite sex ?
Options: a ) 1 / 3 , b ) 2 / 3 , c ) 1 / 4 , d ) 7 / 64 , e ) 3 / 5
Rationale: "no of ways of selecting a gender - 2 c 1 no of ways of selecting any 2 children out of 7 = 7 c 2 total possible outcomes - 2 ^ 7 ( each child can be either a girl or a boy ) probability = 2 c 1 * 7 c 2 / 2 ^ 7 = 2 * 7 / 2 * 2 * 2 * 2 * 2 * 2 * 2 = 7 / 64 ans = d"
Answer: d
Python program:
a = 2 / 7
Problem: instead of multiplying a number by 2 , the number is divided by 10 . what is the percentage of error obtained ?
Options: a ) 94 % , b ) 92 % , c ) 95 % , d ) 93 % , e ) 97 %
Rationale: let the number be x the right number is 2 x the wrong number is x / 10 error is ( 2 x - x / 10 ) = 19 x / 10 percentage of error is ( ( 19 x / 10 ) / 2 x ) * 100 = 95 % answer : c
Answer: c
Python program:
a = 10 / 10
b = 2 * 10
c = a / b
d = c * 100
e = 100 - d
Problem: for the past n days , the average ( arithmetic mean ) daily production at a company was 50 units . if today ' s production of 90 units raises the average to 54 units per day , what is the value of n ?
Options: a ) 30 , b ) 18 , c ) 10 , d ) 9 , e ) 7
Rationale: "( average production for n days ) * n = ( total production for n days ) - - > 50 n = ( total production for n days ) ; ( total production for n days ) + 90 = ( average production for n + 1 days ) * ( n + 1 ) - - > 50 n + 90 = 54 * ( n + 1 ) - - > n = 9 . or as 40 extra units increased the average for n + 1 days by 4 units per day then 40 / ( n + 1 ) = 4 - - > n = 9 . answer d ."
Answer: d
Python program:
a = 90 - 50
b = 54 - 50
c = a / b
d = c - 1
Problem: the cash difference between the selling prices of an article at a profit of 2 % and 4 % is rs 3 . the ratio of two selling prices is
Options: a ) 51 : 52 , b ) 52 : 53 , c ) 53 : 54 , d ) 54 : 55 , e ) 51 : 52
Rationale: "explanation : let the cost price of article is rs . x required ratio = ( 102 % of x ) / ( 104 % of x ) = 102 / 104 = 51 / 52 = 51 : 52 . answer : e"
Answer: e
Python program:
a = 100 + 2 
b = 100 + 4 
c = a / b
Problem: jose completes a piece of work in 10 days , raju completes the same work in 40 days . if both of them work together , then the number of days required to complete the work is
Options: a ) 5 days , b ) 6 days , c ) 8 days , d ) 10 days , e ) 12 days
Rationale: if a can complete a work in x days and b can complete the same work in y days , then , both of them together can complete the work in x y / x + y days . that is , the required no . of days = 10 × 40 / 50 = 8 days . c )
Answer: c
Python program:
a = 1/(40)
b = 1/(10)
c = a + b 
d = 1/(c)
Problem: 5 men and 12 boys finish a piece of work in 4 days , 7 men and 6 boys do it in 5 days . the ratio between the efficiencies of a man and boy is ?
Options: a ) 6 : 8 , b ) 6 : 4 , c ) 6 : 2 , d ) 6 : 5 , e ) 6 : 2
Rationale: 5 m + 12 b - - - - - 4 days 7 m + 6 b - - - - - - - 5 days 20 m + 48 b = 35 m + 30 b 18 b = 15 m = > 5 m = 6 b m : b = 6 : 5 answer : d
Answer: d
Python program:
a = 12 * 4
b = 6 * 5
c = a - b
d = 7 * 5
e = 5 * 4
f = d - e
g = c / f
Problem: the volume of the largest right circular cone that can be cut out of a cube of edge 7 cm is :
Options: a ) 89.8 cm ³
b ) 92.5 cm ³
c ) 132.8 cm ³
d ) 144.5 cm ³
e ) none
Rationale: sol . volume of the block = ( 10 * 5 * 2 ) cm ³ . volume of the cone carved out = [ 1 / 3 * 22 / 7 * 3 * 3 * 7 ] cm ³ = 66 cm ³ ∴ wood wasted = ( 100 - 66 ) % = 34 % . answer a
Answer: a
Python program:
a = 7 * 3
b = a + 1 
c = 1 * b
d = 7 / 2
e = c * d
f = 7 / 2
g = e * f
h = g * 7
i = 3 * 7
j = h / i
Problem: two trains of length 100 meters and 200 meters are 140 meters apart . they are moving towards each other on parallel tracks , at speeds of 54 km / h and 72 km / h . after how many seconds will the trains meet ?
Options: a ) 2 , b ) 4 , c ) 6 , d ) 8 , e ) 10
Rationale: "the speeds are 54000 / 3600 = 15 m / s and 72000 / 3600 = 20 m / s the relative speed is 35 m / s . time = 140 / 35 = 4 seconds the answer is b ."
Answer: b
Python program:
a = 54 + 72 
b = a * const_0_2778
c = 140 / b
Problem: two trains start simultaneously from opposite ends of a 140 - km route and travel toward each other on parallel tracks . train x , traveling at a constant rate , completes the 140 - km trip in 4 hours . train y , travelling at a constant rate , completes the 140 - km trip in 3 hours . how many kilometers had train x traveled when it met train y ?
Options: a ) 60 , b ) 64 , c ) 68 , d ) 72 , e ) 76
Rationale: "if the two trains cover a total distance d , then train x travels ( 3 / 7 ) * d while train y travels ( 4 / 7 ) * d . if the trains travel 140 km to the meeting point , then train x travels ( 3 / 7 ) * 140 = 60 km . the answer is a ."
Answer: a
Python program:
a = 140 / 4
b = 140 / 4
c = 140 / 3
d = b + c 
e = 140 / d
f = a * e
Problem: the year next to 1991 having the same calendar as that of 1990 is –
Options: a ) 1998 , b ) 2001 , c ) 2002 , d ) 2003 , e ) none of these
Rationale: we go on counting the odd days from 1991 onward still the sum is divisible by 7 . the number of such days are 14 upto the year 2001 . so , the calender for 1991 will be repeated in the year 2002 . answer c
Answer: c
Python program:
a = 1991 - 1990
b = 1991 + a
Problem: find ( 7 x + 6 y ) / ( x - 2 y ) if x / 2 y = 3 / 2 ?
Options: a ) 24 , b ) 25 , c ) 26 , d ) 27 , e ) 29
Rationale: "x / 2 y = 3 / 2 = > x = 6 y / 2 = 3 y = > ( 7 x + 6 y ) / ( x - 2 y ) = ( ( 7 * ( 3 y ) ) + 6 y ) / ( 3 y - 2 y ) = > 27 y / y = 27 answer : d"
Answer: d
Python program:
a = 3 / 2
b = a * 2
c = b * 7
d = c + 6 
e = 3 / 2
f = e * 2
g = f - 2
h = d / g
Problem: a car was driving at 72 km / h for 20 minutes , and then at 81 km / h for another 40 minutes . what was its average speed ?
Options: a ) 76 . , b ) 77 . , c ) 78 . , d ) 79 . , e ) 80 .
Rationale: driving at 72 km / h for 20 minutes , distance covered = 72 * 1 / 3 = 24 km driving at 90 km / h for 40 minutes , distance covered = 81 * 2 / 3 = 54 km average speed = total distance / total time = 78 / 1 = 78 km / h answer : a
Answer: a
Python program:
a = 20 + 40 
b = 20 / a
c = b * 72
d = 20 + 40 
e = 40 / d
f = e * 81
g = c + f 
h = 20 + 40 
i = h / const_60
j = g / i
Problem: a , b and c can do a piece of work in 24 days , 30 days and 40 days respectively . they began the work together but c left 4 days before the completion of the work . in how many days was the work completed ?
Options: a ) 33 , b ) 77 , c ) 66 , d ) 11 , e ) 99
Rationale: "one day work of a , b and c = 1 / 24 + 1 / 30 + 1 / 40 = 1 / 10 work done by a and b together in the last 4 days = 4 * ( 1 / 24 + 1 / 30 ) = 3 / 10 remaining work = 7 / 10 the number of days required for this initial work = 7 days . the total number of days required = 4 + 7 = 11 days . answer : d"
Answer: d
Python program:
a = 1 / 24
b = 1 / 30
c = a + b 
d = c * 4
e = 1 - d
f = 2 + 3 
g = 2 * 4
h = f * g
i = 1 / h
j = 1 / 24
k = 1 / 30
l = j + k 
m = i + l 
n = e / m
o = n + 4
Problem: nicky and cristina are running a race . since cristina is faster than nicky , she gives him a 36 meter head start . if cristina runs at a pace of 4 meters per second and nicky runs at a pace of only 3 meters per second , how many seconds will nicky have run before cristina catches up to him ?
Options: a ) 15 seconds , b ) 18 seconds , c ) 25 seconds , d ) 36 seconds , e ) 45 seconds
Rationale: used pluging in method say t is the time for cristina to catch up with nicky , the equation will be as under : for nicky = n = 3 * t + 36 for cristina = c = 5 * t @ t = 36 , n = 144 c = 144 right answer ans : d
Answer: d
Python program:
a = 4 - 3
b = 36 / a
Problem: what is the largest integral value of ' k ' for which the quadratic equation x 2 - 6 x + k = 0 will have two real and distinct roots ?
Options: a ) 9 , b ) 7 , c ) 3 , d ) 8 , e ) 12
Rationale: explanatory answer any quadratic equation will have real and distinct roots if the discriminant d > 0 the discriminant ' d ' of a quadratic equation ax 2 + bx + c = 0 is given by b 2 - 4 ac in this question , the value of d = 62 - 4 * 1 * k if d > 0 , then 36 > 4 k or k < 9 . therefore , the highest integral value that k can take is 8 . correct choice is ( d )
Answer: d
Python program:
a = 6 ** 2
b = 2 ** 2
c = a / b
d = c - 1
Problem: a certain sum of money is divided among a , b and c such that a gets one - third of what b and c together get and b gets two - seventh of what a and c together get . if the amount received by a is $ 20 more than that received by b , find the total amount shared by a , b and c .
Options: a ) $ 320 , b ) $ 420 , c ) $ 720 , d ) $ 220 , e ) $ 200
Rationale: "a = 1 / 3 ( b + c ) = > c = 3 a - b - - - ( 1 ) b = 2 / 7 ( a + c ) = > c = 3.5 b - a - - ( b ) a - b = $ 20 a = 20 + b ( 1 ) = = = > c = 60 + 3 b - b = 2 b + 60 = = > 2 b - c = - 60 - - - ( 3 ) ( 2 ) = = = > c = 3.5 b - b - 20 = 2.5 b - 20 = = > 2.5 b - c = 20 - - - ( 4 ) from ( 4 ) and ( 3 ) 0.5 b = 80 b = $ 160 a = $ 180 c = 540 - 160 = $ 380 total amount = 180 + 160 + 380 = $ 720 answer : c"
Answer: c
Python program:
a = 3 * 20
b = a * 2
c = 2 * 20
d = b + c 
e = 3 * 20
f = e * 2
g = 2 * 20
h = f + g 
i = h + 20 
j = d + i 
k = 3 * 20
l = k * 2
m = 2 * 20
n = l + m 
o = n + 20 
p = o * 3
q = 3 * 20
r = q * 2
s = 2 * 20
t = r + s 
u = p - t
v = j + u