euclaise/mathqa_programs huggingface dataset:
Problem: each week , harry is paid x dollars per hour for the first 12 hours and 1.5 x dollars for each additional hour worked that week . each week , james is paid x dollars per 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 41 hours if harry and james were paid the same amount last week , how many hours did harry work last week ?
Options: a ) 32 , b ) 36 , c ) 37 , d ) 38 , e ) 39
Rationale: "42 x = 12 x + 1.5 x ( h - 12 ) = = > 42 = 12 + 1.5 ( h - 12 ) = = > h - 12 = 30 / 1.5 = 20 = = > h = 32 answer is a"
Answer: a
Python program:
a = 40 + 2 
b = a - 12
c = b / 1
d = c + 12
Problem: a , b and c play a cricket match . the ratio of the runs scored by them in the match is a : b = 5 : 3 and b : c = 5 : 2 . if the total runs scored by all of them are 60 , the runs scored by b are ?
Options: a ) 20.23 , b ) 20.13 , c ) 30.93 , d ) 19.56 , e ) 10.93
Rationale: "a : b = 5 : 3 b : c = 5 : 2 a : b : c = 25 : 15 : 6 15 / 46 * 60 = 19.56 answer : d"
Answer: d
Python program:
a = 5 / 3
b = 2 / 5
c = a + b 
d = c + 5 
e = 60 / d
f = e * 2
Problem: a van takes 6 hours to cover a distance of 180 km . how much should the speed in kmph be maintained to cover the same direction in 3 / 2 th of the previous time ?
Options: a ) 50 kmph , b ) 60 kmph , c ) 70 kmph , d ) 80 kmph , e ) 20 kmph
Rationale: "time = 6 distence = 180 3 / 2 of 6 hours = 6 * 3 / 2 = 9 hours required speed = 180 / 9 = 20 kmph e"
Answer: e
Python program:
a = 3 / 2
b = a * 6
c = 180 / b
Problem: find the principal which yields a simple interest of rs . 20 and compound interest of rs . 30 in two years , at the same percent rate per annum ?
Options: a ) s . 20 , b ) s . 48 , c ) s . 42 , d ) s . 20 , e ) s . 60
Rationale: "explanation : si in 2 years = rs . 20 , si in 1 year = rs . 10 ci in 2 years = rs . 30 % rate per annum = [ ( ci – si ) / ( si in 1 year ) ] * 100 = [ ( 30 – 20 ) / 20 ] * 100 = 50 % p . a . let the principal be rs . x time = t = 2 years % rate = 50 % p . a . si = ( prt / 100 ) 20 = ( x * 50 * 2 ) / 100 x = rs . 20 answer : a"
Answer: a
Python program:
a = 30 - 20
b = a * 100
c = b / 2
Problem: a can do a work in 40 days , b in 60 days . a alone start the work after 10 days he left work . in how many days b can finish the work ?
Options: a ) 20 days , b ) 15 days , c ) 30 days , d ) 45 days , e ) 50 days
Rationale: 10 days work of a = 10 / 40 = 1 / 4 remaining work = 1 - 1 / 4 = 3 / 4 b can finish 3 / 4 work = 60 * 3 / 4 = 45 days answer is d
Answer: d
Python program:
a = 1 / 40
b = 10 * a
c = 1 - b
d = 1 / 60
e = c / d
Problem: a certain university will select 1 of 4 candidates eligible to fill a position in the mathematics department and 2 of 7 candidates eligible to fill 2 identical positions in the computer science department . if none of the candidates is eligible for a position in both departments , how many different sets of 3 candidates are there to fill the 3 positions ?
Options: a ) 81 , b ) 82 , c ) 84 , d ) 86 , e ) 88
Rationale: 1 c 4 * 2 c 7 = 4 * 21 = 84 the answer is ( c )
Answer: c
Python program:
a = 7 * 3
b = a * 4
Problem: each factor of 150 is inscribed on its own plastic ball , and all of the balls are placed in a jar . if a ball is randomly selected from the jar , what is the probability that the ball is inscribed with a multiple of 15 ?
Options: a ) 1 / 16 , b ) 5 / 42 , c ) 1 / 8 , d ) 3 / 16 , e ) 1 / 3
Rationale: "the # of factors 150 has is 12 so out of 12 factors only four are multiples of 15 : 15 , 30,75 and 150 , itself ; so , the probability is 4 / 12 = 1 / 3 . answer : c ."
Answer: c
Python program:
a = math.comb(15, 1)
b = a / 15
c = 3 ** 2
d = b / c
Problem: 15.03 ã — 0.01 = ?
Options: a ) 0.1503 , b ) 0.001503 , c ) 1.503 , d ) 0.001503 , e ) none of these
Rationale: "15.03 ã — 0.01 = ? or , ? = 0.1503 answer a"
Answer: a
Python program:
a = 15 / 3
b = a * 100
Problem: 12 men can complete a piece of work in 4 days , while 15 women can complete the same work in 4 days . 6 men start working on the job and after working for 2 days , all of them stopped working . how many women should be put on the job to complete the remaining work , if it is to be completed in 3 days .
Options: a ) 15 , b ) 18 , c ) 22 , d ) 25 , e ) 26
Rationale: one man ’ s one day ’ s work = 1 / 48 one woman ’ s one day ’ s work = 1 / 60 6 men ’ s 2 day ’ s work = ( ( 6 / 48 ) x 2 ) = 1 / 4 remaining work = 3 / 4 now , 1 / 60 work s done in 1 day by 1 woman . thus , 3 / 4 work will be done in 3 days by ( 60 x ( 3 / 4 ) x ( 1 / 3 ) ) = 15 women . answer : a
Answer: a
Python program:
a = 1 / 4
b = a / 15
c = 1 / b
d = 6 * 2
e = 1 / 4
f = e / 12
g = d * f
h = 1 - g
i = c * h
j = 1 / 3
k = i * j
Problem: mr . kramer , the losing candidate in a two - candidate election , received 942,568 votes , which was exactly 20 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 ) 27 % , e ) 37 %
Rationale: "lets assume that candidate got 20 % votes and total votes is 100 . candidate won = 20 remaining = 80 to get 50 % , candidate requires 30 votes from 100 which is 30 % and 30 votes from 80 . 30 / 80 = 37.5 % which is approx 37 % . hence the answer is e"
Answer: e
Python program:
a = 50 / 100
b = 20 / 100
c = a - b
d = 20 / 100
e = 1 - d
f = c / e
g = f * 100
Problem: in a mixture 60 litres , the ratio of milk and water 2 : 1 . if this ratio is to be 1 : 2 , then the quanity of water to be further added is :
Options: a ) 20 , b ) 30 , c ) 40 , d ) 50 , e ) 60
Rationale: quantity of milk = ( 60 x 2 / 3 ) litres = 40 litres . quantity of water in it = ( 60 - 40 ) litres = 20 litres . new ratio = 1 : 2 let quantity of water to be added further be x litres . then , milk : water = ( 40 / ( 20 + x ) ) now , ( 40 / ( 20 + x ) ) = 1 / 2 = 20 + x = 80 = x = 60 . therefore , quantity of water to be added = 60 litres . answer is e .
Answer: e
Python program:
a = 2 + 1 
b = 60 / a
c = 60 - b
d = c * 2
e = 2 + 1 
f = 60 / e
g = d - f
Problem: a tap can fill a tank in 16 hours . after half the tank is filled , 3 more similar taps are opened . what is the total time taken to fill the tank completely ?
Options: a ) 2 hrs , b ) 1 hrs , c ) 10 hrs , d ) 5 hrs , e ) 4 hrs
Rationale: explanation : a tap can fill a tank in 16 hours . therefore the tap can fill half the tank in 8 hours . one tap take time to fill half of the tank = 8 hrs 4 taps take time to fill half of the tank = 8 / 4 hrs = 2 hrs total time taken to fill the tank = 8 hr + 2 hr = 10 hrs answer : c
Answer: c
Python program:
a = 3 + 3 
b = 16 - a
Problem: the sale price sarees listed for rs . 600 after successive discount is 20 % and 5 % is ?
Options: a ) 227 , b ) 358 , c ) 456 , d ) 787 , e ) 191
Rationale: "600 * ( 80 / 100 ) * ( 95 / 100 ) = 456 answer : c"
Answer: c
Python program:
a = 600 * 20
b = a / 100
c = 600 - b
d = 600 * 20
e = d / 100
f = 600 - e
g = f * 5
h = g / 100
i = c - h
Problem: a reduction of 25 % in the price of oil enables a house wife to obtain 5 kgs more for rs . 700 , what is the reduced price for kg ?
Options: a ) 35 , b ) 60 , c ) 70 , d ) 80 , e ) 20
Rationale: "a 700 * ( 25 / 100 ) = 175 - - - - 5 ? - - - - 1 = > rs . 35"
Answer: a
Python program:
a = 700 * 25
b = a / 100
c = b / 5
Problem: robert is travelling on his cycle and has calculated to reach point a at 2 p . m . if he travels at 10 kmph , he will reach there at 12 noon if he travels at 15 kmph . at what speed must he travel to reach a at 1 p . m . ?
Options: a ) 8 , b ) 12 , c ) 11 , d ) 16 , e ) 18
Rationale: "explanation : let the distance travelled by x km . then , = > ( x / 10 ) - ( x / 15 ) = 2 = > 3 x - 2 x = 60 = > x = 60 = > time taken to travel 60 km at 10 km / hr = 60 / 10 = 6 hours . = > so , robert started 6 hours before 2 p . m . i . e . , at 8 a . m . therefore , speed required = ( 60 / 5 ) km / hr = 12 km / hr answer : b"
Answer: b
Python program:
a = 1 / 10
b = 1 / 15
c = a - b
d = 2 / c
e = 4 + 1 
f = d / e
Problem: the average of 10 consecutive integers is 16 . then , 9 is deducted from the first consecutive number , 8 is deducted from the second , 7 is deducted form the third , and so on until the last number which remains unchanged . what is the new average ?
Options: a ) 10.5 , b ) 11 , c ) 11.5 , d ) 12 , e ) 12.5
Rationale: the total subtracted is ( 9 + 8 + . . . + 1 ) = ( 9 * 10 ) / 2 = 45 on average , each number will be reduced by 45 / 10 = 4.5 therefore , the overall average will be reduced by 4.5 the answer is c .
Answer: c
Python program:
a = 10 * 16
b = 4 + 1 
c = b * 9
d = a - c
e = d / 10
Problem: after 2 games , team b had an average of 61.5 points per game . if it got only 47 points in game 3 , how many more points does it need to score to get its total above 500 ?
Options: a ) 805 , b ) 740 , c ) 670 , d ) 530 , e ) 330
Rationale: ( 2 * 61.5 ) + 47 + x > 500 123 + 47 + x > 500 170 + x > 500 = > x > 330 option e
Answer: e
Python program:
a = 2 * 61
b = a + 47 
c = 500 - b
Problem: calculate the number of bricks , each measuring 25 cm * 15 cm * 8 cm required to construct a wall of dimensions 10 m * 4 m * 5 m when 10 % of its volume is occupied by mortar ?
Options: a ) 3388 , b ) 27678 , c ) 6000 , d ) 2977 , e ) 27681
Rationale: 10 * 4 / 100 * 5 * 90 / 100 = 25 / 100 * 15 / 100 * 8 / 100 * x 10 * 20 * 90 = 15 * 2 * x = > x = 6000 answer : c
Answer: c
Python program:
a = 10 * 100
b = 4 * 100
c = a * b
d = 5 * 100
e = c * d
f = 10 - 1
g = f / 10
h = e * g
i = 25 * 15
j = i * 8
k = h / j
l = k / 10
Problem: a class has a ratio of 3 : 6 : 7 of children with red hair , blonde hair and black hair respectively . if the class has 9 kids with red hair , how many kids are in the class ?
Options: a ) 99 , b ) 48 , c ) 16 , d ) 22 , e ) 60
Rationale: since there are 9 children with red hair , and the class exists in a 3 : 6 : 7 ratio , there are 3 times more children than the unit ratio . therefore 9 red - haired children 3 * ( 6 ) blonde - haired children 3 * ( 7 ) black - haired children 9 + 18 + 21 = 48 alternatively , a part - to - whole ratio can be set up . since the whole is 3 + 6 + 7 = 16 , 9 / 3 = x / 16 3 * 16 = 48 answer : b )
Answer: b
Python program:
a = 7 + 6 
b = a + 3 
c = b * 3
Problem: a certain club has 10 members , including parry . one of the 10 members is chosen at random to be the president , one of the remaining 9 members is to be chosen at random to be the secretary , and one of the remaining 8 members is to be chosen at random to be the treasurer . what is the probability that parry will be either the member chose to be secretary or the member chose to be treasurer ?
Options: a ) 1 / 720 , b ) 1 / 80 , c ) 1 / 10 , d ) 1 / 9 , e ) 1 / 5
Rationale: in order to become a secretary the person can not be chosen as a president . this can be done in 9 / 10 ways . then to become a secretary this person ' s probability is 1 / 9 probability to become a secretary = ( 9 / 10 * 1 / 9 ) = 1 / 10 similar concept for treasurer . probability of not president = 9 / 10 , probability of not secretary = 8 / 9 , probability of treasurer 1 / 8 probability to become a treasurer = ( 9 / 10 * 8 / 9 * 1 / 8 ) = 1 / 10 since , the problem is saying parry secretary or treasurer it is addition : 1 / 10 + 1 / 10 = 1 / 5 = e
Answer: e
Python program:
a = 1 / 10
b = 1 / 10
c = a + b
Problem: a millionaire bought a job lot of hats 1 / 4 of which were brown . the millionaire sold 2 / 3 of the hats including 4 / 5 of the brown hats . what fraction of the unsold hats were brown .
Options: a ) 1 / 60 , b ) 1 / 15 , c ) 3 / 20 , d ) 3 / 5 , e ) 3 / 4
Rationale: if initially he had x hats . x / 4 were brown . sold x * 2 / 3 hats . left with x / 3 hats . sold ( x / 4 ) * ( ( 4 / 5 ) = x / 5 brown hats and left with x / 4 - x / 5 = x / 20 brown hats . fraction of brown hats in total remaining hats = ( x / 20 ) / ( x / 3 ) = 3 / 20 hats answer : c
Answer: c
Python program:
a = 4 / 5
b = 1 - a
c = 1 / 4
d = b * c
e = 2 / 3
f = 1 - e
g = d / f
Problem: if three machines working at the same rate can do 3 / 4 of a job in 30 minutes , how many minutes would it take two machines working at the same rate to do 3 / 5 of the job ?
Options: a ) 36 , b ) 60 , c ) 75 , d ) 80 , e ) 100
Rationale: "using the std formula m 1 d 1 h 1 / w 1 = m 2 d 2 h 2 / w 2 substituting the values we have 3 * 1 / 2 * 4 / 3 = 2 * 5 / 3 * x ( converted 30 min into hours = 1 / 2 ) 2 = 10 / 3 * x x = 3 / 5 hour so 36 minutes answer : a"
Answer: a
Python program:
a = 3 / 5
b = 3 / 4
c = b / 5
d = c / 30
e = d * 2
f = a / e
Problem: { ( 481 + 426 ) 2 - 4 x 481 x 426 } = ?
Options: a ) 3025 , b ) 4200 , c ) 3060 , d ) 3210 , e ) none of these
Rationale: "explanation : here , the given statement is like ( a + b ) 2 - 4 ab where a = 481 and b = 426 ( a + b ) 2 - 4 ab = ( a 2 + 2 ab + b 2 ) - 4 ab = a 2 - 2 ab + b 2 = ( a - b ) 2 hence { ( 481 + 426 ) 2 - 4 x 481 x 426 } = ( 481 - 426 ) 2 = 552 = 3025 . answer : option a"
Answer: a
Python program:
a = 481 + 426 
b = a ** 2
c = 4 * 481
d = c * 426
e = b - d
Problem: working together at their respective constant rates , machine a and machine b can produce 900 units in 8 hours . working alone , machine b would complete that same output in 50 % more time . if machine a were to work on its own for an 8 - hour shift , what percent of the 900 unit total would it produce ?
Options: a ) 30 , b ) 33 , c ) 50 , d ) 67 , e ) 75
Rationale: "1 / a + 1 / b = 1 / t 1 / a + 1 / 12 = 1 / 8 ( 50 % more of 8 is 12 ) 1 / a = 1 / 24 machine a can produce 900 units in 24 hrs , so it can produce 900 * 8 / 24 = 300 units is 8 hrs . 300 is 30 % of 900 . a is the answer"
Answer: a
Python program:
a = 4 * 4
b = a * 100
c = b / 8
d = 4 * 4
e = d * 100
f = 8 * 50
g = f / 100
h = 8 + g 
i = e / h
j = c - i
k = j * 8
l = 4 * 4
m = l * 100
n = k / m
o = n * 100
Problem: sum of the squares of 3 no . ' s is 138 and the sum of their products taken two at a time is 131 . find the sum ?
Options: a ) 20 , b ) 24 , c ) 26 , d ) 28 , e ) 30
Rationale: ( a + b + c ) 2 = a 2 + b 2 + c 2 + 2 ( ab + bc + ca ) = 138 + 2 * 131 a + b + c = √ 400 = 20 a
Answer: a
Python program:
a = 131 * 2
b = a + 138 
c = math.sqrt(b)
Problem: a not - so - good clockmaker has four clocks on display in the window . clock # 1 loses 10 minutes every hour . clock # 2 gains 15 minutes every hour relative to clock # 1 ( i . e . , as clock # 1 moves from 12 : 00 to 1 : 00 , clock # 2 moves from 12 : 00 to 1 : 15 ) . clock # 3 loses 20 minutes every hour relative to clock # 2 . finally , clock # 4 gains 20 minutes every hour relative to clock # 3 . if the clockmaker resets all four clocks to the correct time at 12 noon , what time will clock # 4 display after 6 actual hours ( when it is actually 6 : 00 pm that same day ) ?
Options: a ) 5 : 00 , b ) 5 : 34 , c ) 5 : 42 , d ) 6 : 00 , e ) 6 : 24
Rationale: "c 1 loses 15 minutes every hour . so after 60 minutes have passed , c 1 displays that 60 - 15 = 45 minutes have passed . c 2 gains 15 minutes for every 60 minutes displayed on c 1 . thus , the time displayed on c 2 is 75 / 60 = 5 / 4 the time displayed on c 1 . so after 60 minutes have passed , c 2 displays the passing of ( 5 / 4 * 45 ) minutes . c 3 loses 20 minutes for every 60 minutes displayed on c 2 . thus , the time displayed on c 3 is 40 / 60 = 2 / 3 the time displayed on c 2 . so after 60 minutes have passed , c 3 displays the passing of ( 2 / 3 * 5 / 4 * 45 ) minutes . c 4 gains 20 minutes for every 60 minutes displayed on c 3 . thus , the time displayed on c 4 is 80 / 60 = 4 / 3 the time displayed on clock 3 . so after 60 minutes have passed , c 4 displays the passing of 4 / 3 * 2 / 3 * 5 / 4 * 45 = 50 minutes . c 4 loses 10 minutes every hour . in 6 hours , c 4 will lose 6 * 10 = 60 minutes = 1 hour . since the correct time after 6 hours will be 6 pm , c 4 will show a time of 6 - 1 = 6 pm . the correct answer is d ."
Answer: d
Python program:
a = 6 * 10
b = const_60 + 15 
c = b / const_60
d = const_60 - 20
e = d / const_60
f = c * e
g = const_60 + 20 
h = g / const_60
i = f * h
j = const_60 - 10
k = i * j
l = a - k
Problem: if x and y are positive integers and 11 + x + y + xy = 25 , what is the value of x + y ?
Options: a ) 3 , b ) 5 , c ) 6 , d ) 8 , e ) 9
Rationale: "try each answer choices . for a : 11 + 3 + xy = 25 ; xy = 11 ( impossible , 11 prime number . 1 + 11 does n ' t equal 3 ) for b : 11 + 5 + xy = 25 ; xy = 9 ( no combination of xy = 9 and x + y = 5 ) for c : 11 + 6 + xy = 25 ; xy = 8 ( x + y = 6 ; x = 2 , y = 4 or x = 4 , y = 2 ) for d : 11 + 8 + xy = 25 ; xy = 6 ( no combination of xy = 6 and x + y = 8 ) for e : 11 + 9 + xy = 25 ; xy = 5 ( impossible , 5 prime number . 1 + 5 does n ' t equal 9 ) therefore , answer c ."
Answer: c
Python program:
a = 25 + 1
Problem: a 6000 liter tank , half - full of water is being filled from a pipe with a flow rate of 1 kiloliter every 2 minutes . at the same time , the tank is losing water from two drains at a rate of 1 kiloliter every 4 minutes and every 6 minutes . how many minutes does it take to fill the tank completely ?
Options: a ) 8 , b ) 12 , c ) 18 , d ) 24 , e ) 36
Rationale: "in : we have : 1,000 / 2 min = 500 litres per minute out : we have : 1,000 / 4 + 1,000 / 6 then do : in - out to figure out the net inflow per minute ( you get 83.3 ) . then divide the total number of litres you need ( 3,000 by that net inflow to get the minutes ) - 36 min . answer e ."
Answer: e
Python program:
a = 6 + 4 
b = a + 2 
c = 6000 / 2
d = b * c
e = d / 1000
Problem: rs . 1040 is divided amongst a , b , c so that 2 times a ' s share , 3 times b ' s share and 4 times c ' s share are all equal . find a ' s share ?
Options: a ) 177 , b ) 150 , c ) 817 , d ) 480 , e ) 616
Rationale: a + b + c = 1040 2 a = 3 b = 4 c = x a : b : c = 1 / 2 : 1 / 3 : 1 / 4 = 6 : 4 : 3 6 / 13 * 1040 = rs . 480 answer : d
Answer: d
Python program:
a = 4 / 2
b = 4 / 3
c = a + b 
d = c + 1 
e = 1040 / d
Problem: salesperson a ' s compensation for any week is $ 300 plus 6 percent of the portion of a ' s total sales above $ 1,000 for that week . salesperson b ' s compensation for any week is 8 percent of b ' s total sales for that week . for what amount of total weekly sales would both salespeople earn the same compensation ?
Options: a ) $ 21,000 , b ) $ 18,000 , c ) $ 12,000 , d ) $ 8000 , e ) $ 4000
Rationale: "300 + 0.06 ( x - 1000 ) = 0.08 x 0.02 x = 240 x = $ 12,000 the answer is c ."
Answer: c
Python program:
a = 6 / 100
b = a * 1
c = 300 - b
d = 8 / 100
e = 6 / 100
f = d - e
g = c / f
h = 6 / 100
i = h * 1
j = 300 - i
k = 8 / 100
l = 6 / 100
m = k - l
n = j / m
o = g + n 
p = o / 1
Problem: if the number is decreased by 5 and divided by 7 the result is 7 . what would be the result if 6 is subtracted and divided by 8 ?
Options: a ) 4 , b ) 6 , c ) 8 , d ) 5 , e ) 3
Rationale: explanation : let the number be x . then , ( x - 5 ) / 7 = 7 = > x - 5 = 49 x = 54 . : ( x - 6 ) / 8 = ( 54 - 6 ) / 8 = 6 answer : option b
Answer: b
Python program:
a = 7 * 7
b = a + 5 
c = b - 6
d = c / 8
Problem: ( x + 5 ) is a factor in x ^ 2 - mx - 40 . what is the value of m ?
Options: a ) 1 , b ) 2 , c ) 4 , d ) 3 , e ) 5
Rationale: "i solved the second degree equation and found it like this : x ^ 2 - mx - 40 = 0 ( x - 8 ) ( x + 5 ) = 0 x = 8 or x = - 5 substituting both values for x in the equation we find : x ^ 2 - mx - 40 = > ( - 5 ) ^ 2 - m ( - 5 ) = 40 = > 25 + 5 m = 40 = > 5 m = 40 - 25 = 15 = > m = 3 and with 8 , using a similar process we end up with : ( 8 ) ^ 2 - m ( 8 ) = 40 - 8 m = 40 - 64 = - 24 m = 3 ao , ans d"
Answer: d
Python program:
a = 40 / 5
b = a - 5
Problem: in a rectangular coordinate system , what is the area of a quadrilateral whose vertices have the coordinates ( 4 , - 3 ) , ( 4 , 7 ) , ( 10 , 4 ) , ( 10 , - 7 ) ?
Options: a ) 51 , b ) 54 , c ) 57 , d ) 60 , e ) 63
Rationale: "by graphing the points , we can see that this figure is a trapezoid . a trapezoid is any quadrilateral that has one set of parallel sides , and the formula for the area of a trapezoid is : area = ( 1 / 2 ) × ( base 1 + base 2 ) × ( height ) , where the bases are the parallel sides . we can now determine the area of the quadrilateral : area = 1 / 2 × ( 10 + 11 ) × 6 = 63 . the answer is e ."
Answer: e
Python program:
a = 3 + 7 
b = 4 + 7 
c = a + b 
d = 10 - 4
e = c * d
f = e / 4
Problem: a sum is divided among b , c and d in such a way that for each rupee b gets , c gets 150 paisa and d gets 50 paisa . if the share of c is rs . 40 , what is the total amount ?
Options: a ) 70 , b ) 75 , c ) 80 , d ) 85 , e ) 90
Rationale: b : c : d = 100 : 150 : 100 20 : 30 : 10 30 - - - 40 60 - - - ? = > 80 answer : c
Answer: c
Python program:
a = 50 / 50
b = 100 / 50
c = 150 / 50
d = b + c 
e = a + d 
f = 150 / 50
g = e / f
h = g * 40
Problem: find the average marks of all the students in 2 separate classes , if the average marks of students in the first class of 58 students is 67 and that of another class of 52 students is 82 .
Options: a ) 74.1 , b ) 56.3 , c ) 67.8 , d ) 79.7 , e ) 19.4
Rationale: "sum of the marks for the class of 58 students = 58 * 67 = 3886 sum of the marks for the class of 52 students = 52 * 82 = 4264 sum of the marks for the class of 110 students = 3886 + 4262 = 8150 average marks of all the students = 4200 / 80 = 74.1 answer : a"
Answer: a
Python program:
a = 58 * 67
b = 52 * 82
c = a + b 
d = 58 + 52 
e = c / d
Problem: four horses are tethered at four corners of a square plot of side 63 metres so that they just can not reach one another . the area left ungrazed is :
Options: a ) 675.5 m 2
b ) 780.6 m 2
c ) 785.8 m 2
d ) 850.5 m 2
e ) 950.5 m 2
Rationale: required area = ( 63 * 63 – 4 * 1 / 4 * 22 / 7 * 63 / 2 * 63 / 2 ) = 850.5 m 2 answer : d
Answer: d
Python program:
a = 63 * 63
b = 4 * const_0_25
c = b * math.pi
d = 63 / 2
e = c * d
f = 63 / 2
g = e * f
h = a - g
Problem: mixture contains alcohol and water in the ratio 4 : 3 . if 7 liters of water is added to the mixture , the ratio becomes 4 : 5 . find the quantity of alcohol in the given mixture .
Options: a ) 10 , b ) 99 , c ) 5 , d ) 22 , e ) 29
Rationale: "let the quantity of alcohol and water be 4 x litres and 3 x litres respectively 28 x = 4 ( 3 x + 5 ) 16 x = 20 x = 1.25 quantity of alcohol = ( 4 x 1.25 ) litres = 5 litres . answer : c"
Answer: c
Python program:
a = 4 * 5
b = 7 * 4
c = 3 * 4
d = b - c
e = a / d
f = e * 4
Problem: find the value of 1 / ( 3 + 1 / ( 3 + 1 / ( 3 - 1 / 3 ) ) ) ?
Options: a ) 13 / 89 , b ) 15 / 87 , c ) 27 / 89 , d ) 27 / 87 , e ) 89 / 27
Rationale: "1 / [ 3 + ( 1 / ( 3 + 1 / ( 3 - 1 / 3 ) ) ) ] = > 1 / [ 3 + 1 / ( 3 + 1 / ( 8 / 3 ) ) ] = > 1 / [ 3 + 1 / ( 3 + 3 / 8 ) ] = > 1 / [ 3 + 8 / 27 ] = > 1 / ( 89 / 27 ) = > 27 / 89 c )"
Answer: c
Python program:
a = 1 / 3
b = 3 - a
c = 1 / b
d = 3 + c 
e = 1 / d
f = 3 + e 
g = 1 / f
Problem: 18 men can complete a piece of work in 20 days . in how many days can 15 men complete that piece of work ?
Options: a ) 23 , b ) 27 , c ) 20 , d ) 24 , e ) 11
Rationale: "18 * 20 = 15 * x = > x = 24 days answer : d"
Answer: d
Python program:
a = 20 * 18
b = a / 15
Problem: the market value of a 10.5 % stock , in which an income of rs . 756 is derived by investing rs . 9000 , brokerage being 1 / 4 % , is :
Options: a ) 113.2 , b ) 114 , c ) 114.75 , d ) 124 , e ) 124.75
Rationale: "face value = rs . 9000 . dividend = 10.5 % . annual income = rs . 756 . brokerage per rs . 100 = rs . 0.25 . dividend is always paid on the face value of a share . face value * dividend / ( market value + brokerage per rs . 100 ) = annual income . = 9000 * 10.5 / 756 = market value of rs . 100 stock + brokerage per rs . 100 . = market value of rs . 100 stock + brokerage per rs . 100 = rs . 125 . = market value of rs . 100 stock = rs . 125 - re . 0.25 . = market value of rs . 100 stock = rs . 124.75 . answer : e"
Answer: e
Python program:
a = 9000 / 756
b = a * 10
c = 1 / 4
d = b - c
Problem: a dog takes 2 leaps for every 3 leaps of a hare . if one leap of the dog is equal to 5 leaps of the hare , the ratio of the speed of the dog to that of the hare is :
Options: a ) 9 : 3 , b ) 3 : 10 , c ) 2 : 3 , d ) 6 : 3 , e ) 10 : 3
Rationale: "explanation : dog : hare = ( 2 * 5 ) leaps of hare : 3 leaps of hare = 10 : 3 answer : e"
Answer: e
Python program:
a = 2 * 5
b = a / 3