euclaise/mathqa_programs huggingface dataset:
Problem: if the selling price of 8 articles is same as the cost price of 12 articles . find the gain or loss percentage ?
Options: a ) 30 % gain , b ) 30 % loss , c ) 50 % gain , d ) 50 % loss , e ) 60 % loss
Rationale: "explanation : let the c . p of each article be re 1 . then , s . p of 8 articles = c . p of 12 articles = rs . 12 / - now , c . p of 8 articles = rs . 8 / - , s . p of 8 articles = rs 12 / - gain = rs ( 12 - 10 ) = rs 4 / - . gain % = ( 4 / 8 * 100 ) % = 50 % gain answer : option c"
Answer: c
Python program:
a = 8 - 12
Problem: janet invited her boy and girl friends to her party at the ratio of 3 : 7 . if 30 % of the boys and 70 % of the girls will be coming for the party from texas , how many janet invited friends will be coming from texas .
Options: a ) 62 % , b ) 52 % , c ) 57 % , d ) 56 % , e ) 58 %
Rationale: let total no of janet invited friends be 100 , boys 30 and girls 70 , so total number of janet ' s invited guests coming from texas for both boys and girls respectively 30 * 30 / 100 = 9 and 70 * 70 / 100 = 49 so total 58 of janet ' s invited guest out of the 100 invited guests will be coming from texas . . so required % is 58 % answer : e
Answer: e
Python program:
a = 70 / 100
b = a * 7
c = 30 / 100
d = c * 3
e = b + d 
f = e * 10
Problem: david works at a science lab that conducts experiments on bacteria . the population of the bacteria multiplies at a constant rate , and his job is to notate the population of a certain group of bacteria each hour . at 1 p . m . on a certain day , he noted that the population was 500 and then he left the lab . he returned in time to take a reading at 4 p . m . , by which point the population had grown to 13,500 . now he has to fill in the missing data for 2 p . m . and 3 p . m . what was the population at 3 p . m . ?
Options: a ) 6500 , b ) 3500 , c ) 2500 , d ) 4500 , e ) 2000
Rationale: "let the rate be x , then population of the bacteria after each hour can be given as 500,500 x , 500 ( x ^ 2 ) , 500 ( x ^ 3 ) now population at 4 pm = 13,500 thus we have 500 ( x ^ 3 ) = 13,500 = 27 thus x = 3 therefore population at 3 pm = 500 ( 9 ) = 4,500 answer : d"
Answer: d
Python program:
a = 2 * 4
b = a * 500
c = b / 500
d = c ** const_0_33
e = d * 500
f = 2 * 4
g = f * 500
h = g / 500
i = h ** const_0_33
j = e * i
Problem: a can do a piece of work in 4 hours ; b and c together can do it in 3 hours , while a and c together can do it in 3 hours . how long will b alone take to do it ?
Options: a ) 12 , b ) 9 , c ) 8 , d ) 6 , e ) 4
Rationale: "a ' s 1 hour ' s work = 1 / 4 ; ( b + c ) ' s 1 hour ' s work = 1 / 3 ; ( a + c ) ' s 1 hour ' s work = 1 / 3 . ( a + b + c ) ' s 1 hour ' s work = ( 1 / 4 + 1 / 3 ) = 7 / 12 . b ' s 1 hour ' s work = ( 7 / 12 - 1 / 3 ) = 1 / 4 . therefore a alone will take 4 hours to do the work . e"
Answer: e
Python program:
a = 1 / 3
b = 1 / 3
c = 1 / 4
d = b - c
e = a - d
f = 1 / e
Problem: 2 , 5 , 10 , 17 , . .
Options: a ) 5 , b ) 8 , c ) 26 , d ) 7 , e ) 12
Rationale: "explanation : numbers are ( 1 * 1 ) + 1 = 2 ( 2 * 2 ) + 1 = 5 ( 3 * 3 ) + 1 = 10 ( 4 * 4 ) + 1 = 17 ( 5 * 5 ) + 1 = 26 answer : c"
Answer: c
Python program:
a = negate - (
Problem: cost is expressed by the formula tb ^ 4 . if b is doubled , the new cost is what percent of the original cost ?
Options: a ) 200 , b ) 600 , c ) 800 , d ) 1600 , e ) 50
Rationale: "original cost c 1 = t 1 * b 1 ^ 4 new cost c 2 = t 2 * b 2 ^ 4 . . . . only b is doubled so t 2 = t 1 and b 2 = 2 b 1 c 2 = t 2 * ( 2 b 1 ) ^ 4 = 16 ( t 1 * b 1 ^ 4 ) = 16 c 1 16 times c 1 = > 1600 % of c 1 ans d = 1600"
Answer: d
Python program:
a = 2 ** 4
b = a * 100
Problem: 3 people each took 5 tests . if the ranges of their scores in the 5 practice tests were 17 , 28 and 35 , 45 what is the minimum possible range in scores of the 3 test - takers ?
Options: a ) a 17 , b ) b ) 28 , c ) c ) 35 , d ) d ) 45 , e ) e ) 80
Rationale: it is finding the minimum range between all their scores , if all test taker scores are between 0 and maximum range we will have : a - 0 and 17 b - 0 and 28 c - 0 and 35 d - 0 and 45 therefore the minimum range is 45 , it cant be any lower however you play with the numbers . d
Answer: d
Python program:
a = 35 + 5 
b = a + 5
Problem: a sum of money is distributed among a , b , c , d in the proportion of 5 : 3 : 2 : 3 . if a gets $ 1000 more than b , what is the c ' s share ?
Options: a ) $ 2000 , b ) $ 5000 , c ) $ 8000 , d ) $ 1500 , e ) $ 1000
Rationale: "let the shares of a , b , c , d are 5 x , 3 x , 2 x , 3 x 5 x - 3 x = 1000 x = 500 c ' s share = 2 x = $ 1000 answer is e"
Answer: e
Python program:
a = 1000 + 1000 
b = a * 2
c = b / 4
d = c * 3
e = d / 3
Problem: a train 125 m long passes a man , running at 5 km / hr in the same direction in which the train is going , in 15 seconds . the speed of the train is :
Options: a ) 22 , b ) 50 , c ) 99 , d ) 35 , e ) 12
Rationale: speed of the train relative to man = ( 125 / 15 ) m / sec = ( 25 / 3 ) m / sec . [ ( 25 / 3 ) * ( 18 / 5 ) ] km / hr = 30 km / hr . let the speed of the train be x km / hr . then , relative speed = ( x - 5 ) km / hr . x - 5 = 30 = = > x = 35 km / hr . answer : d
Answer: d
Python program:
a = 5 * const_0_2778
b = a * 5
c = 125 - b
d = c / 5
e = d / const_0_2778
Problem: two boys starts from the same place walking at the rate of 5.5 kmph and 7.5 kmph respectively in the same direction . what time will they take to be 32 km apart ?
Options: a ) 18 , b ) 16 , c ) 19 , d ) 15 , e ) 34
Rationale: "explanation : relative speed = 7.5 - 5.5 = 2 kmph ( because they walk in the same direction ) distance = 32 km time = distance / speed = 32 / 2 = 16 hr answer : b"
Answer: b
Python program:
a = 7 - 5
b = 32 / a
Problem: two thirds of the roads from a to b are at least 5 miles long , and 1 / 2 of the roads from b to c are at least 5 miles long . if you randomly pick a road from a to b and then randomly pick a road from b to c , what is the probability that at least one of the roads you pick is at least 5 miles long ?
Options: a ) 5 / 6 , b ) 1 / 4 , c ) 2 / 3 , d ) 3 / 4 , e ) 11 / 12
Rationale: "so please : find the probability of the event thatnoneof the roads you pick will be at least 5 miles long and subtract from 1 to get the probability thatat least oneof the roads you pick will be at least 5 miles long : p = 1 - 1 / 3 * 1 / 2 = 5 / 6 . answer : a ."
Answer: a
Python program:
a = 2 / 3
b = 1 - a
c = 1 / 2
d = 1 - c
e = b * d
f = 1 - e
Problem: the difference between a number and its two - fifth is 510 . what is 15 % of that number ?
Options: a ) 152.01 , b ) 85 , c ) 76 , d ) 168.2 , e ) 127.5
Rationale: "let the number be x . then , x - 2 / 5 x = 510 x = ( 510 * 5 ) / 3 = 850 15 % of 850 = 127.5 . answer : e"
Answer: e
Python program:
a = 4 + 1 
b = 510 * a
c = 1 + 2 
d = b / c
Problem: the average salary of all the workers in a workshop is rs . 8000 . the average salary of 7 technicians is rs . 18000 and the average salary of the rest is rs . 6000 . the total number of workers in the workshop is
Options: a ) 20 , b ) 21 , c ) 42 , d ) 23 , e ) 24
Rationale: "solution let the toatl number of workers be x . then 8000 x = ( 18000 x 7 ) + 6000 ( x - 7 ) x = 42 answer c"
Answer: c
Python program:
a = 18000 - 8000
b = 7 * a
c = 8000 - 6000
d = b / c
e = 7 + d
Problem: a sum of rs . 427 is to be divided among a , b and c in such a way that 3 times a ’ s share , 4 times b ’ s share and 7 times c ’ s share are all equal . the share of c is ?
Options: a ) 23 , b ) 87 , c ) 84 , d ) 26 , e ) 19
Rationale: given total sum = rs . 427 and given that 3 times a ’ s share , 4 times b ’ s share and 7 times c ’ s share are all equal . = > 3 a = 4 b = 7 c but given = > a + b + c = 427 now express a and b in terms of c i . e = > ( 7 c / 3 ) + ( 7 c / 4 ) + c = 427 = > c = 84 answer : c
Answer: c
Python program:
a = 7 / 7
b = 7 / 3
c = 7 / 4
d = b + c 
e = a + d 
f = 427 / e
Problem: if x and t are integers and 2 x – t = 11 , then 4 x + t can not be
Options: a ) – 5 , b ) 1 , c ) 13 , d ) 17 , e ) 551
Rationale: 2 x - t = 11 . . . . t = 2 x - 11 4 x + t = 4 x + 2 x - 11 = 6 x - 11 6 x - 11 = - 5 . . . x = 1 6 x - 11 = 1 . . . x = 2 6 x - 11 = 13 . . . x = 4 6 x - 11 = 17 . . x is not integer 6 x - 11 = 551 . . x is not integer i think the choice e is 55 not 551 . otherwise both de can not be solution = d
Answer: d
Python program:
a = 4 + 11 
b = a + 2
Problem: excluding stoppages , the speed of a bus is 40 kmph and including stoppages , it is 30 kmph . for how many minutes does the bus stop per hour ?
Options: a ) 10 min , b ) 12 min , c ) 18 min , d ) 15 min , e ) 20 min
Rationale: "due to stoppages , it covers 10 km less . time taken to cover 10 km = ( 10 / 40 x 60 ) min = 15 min answer : d"
Answer: d
Python program:
a = 40 - 30
b = a / 40
c = const_60 * b
Problem: the megatek corporation is displaying its distribution of employees by department in a circle graph . the size of each sector of the graph representing a department is proportional to the percentage of total employees in that department . if the section of the circle graph representing the manufacturing department takes up 54 ° of the circle , what percentage of megatek employees are in manufacturing ?
Options: a ) 15 % , b ) 25 % , c ) 30 % , d ) 35 % , e ) 72 %
Rationale: answer : a 54 ° divided by 360 ° equals 0.15 , therefore the sector is equal to 15 % of the total
Answer: a
Python program:
a = 3600 / 10
b = 54 / a
c = b * 100
Problem: nicky and cristina are running a 100 meter race . since cristina is faster than nicky , she gives him a 12 second head start . if cristina runs at a pace of 5 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 ) 30 , b ) 35 , c ) 40 , d ) 25 , e ) 60
Rationale: "the distance traveled by both of them is the same at the time of overtaking . 3 ( t + 12 ) = 5 t t = 18 . cristina will catch up nicky in 18 seconds . so in 18 seconds cristina would cover = 18 * 5 = 90 meter . now time taken my nicky to cover 90 meter = 90 / 3 = 30 seconds . a"
Answer: a
Python program:
a = 3 * 12
b = a / 3
c = 3 * 12
d = 5 - 3
e = c / d
f = b + e
Problem: an engineer designed a ball so that when it was dropped , it rose with each bounce exactly one - half as high as it had fallen . the engineer dropped the ball from a 20 - meter platform and caught it after it had traveled 55 meters . how many times did the ball bounce ?
Options: a ) 5 , b ) 6 , c ) 3 , d ) 8 , e ) 9
Rationale: "going down = 20 m going up = 10 - - > total = 30 going down = 10 - - > total = 40 going up = 5 - - > total = 45 going down = 5 - - > total = 50 going up = 2.5 - - > total = 52.5 going down = 2.5 - - > total = 55 ( caught ) no of bouncing = 3 answer : c"
Answer: c
Python program:
a = 20 / 2
b = a / 2
Problem: find the value of 582964 x 99999 = m ?
Options: a ) 58210607666 , b ) 58310607896 , c ) 58295817036 , d ) 58591650836 , e ) 58310692816
Rationale: "582964 x 99999 = 582964 x ( 10000 - 1 ) = 582964 x 100000 - 582964 x 1 = 58296400000 - 582964 = 58295817036 c"
Answer: c
Python program:
a = 99999 - 4
b = a * 582964
Problem: a big container is 30 % full with water . if 18 liters of water is added , the container becomes 3 / 4 full . what is the capacity of the big container ?
Options: a ) 36 liters , b ) 40 liters , c ) 45 liters , d ) 54 liters , e ) 60 liters
Rationale: "a big container is 30 % full with water and after 18 liters of water is added , the container becomes 75 % full . hence these 18 liters account for 45 % of the container , which means that the capacity of it is 18 / 0.45 = 40 liters . or : if the capacity of the container is x liters then : 0.3 x + 18 = 0.75 x - - > x = 40 liters . answer : b ."
Answer: b
Python program:
a = 3 / 4
b = 30 / 100
c = a - b
d = 18 / c
Problem: ( 18.6 x 17.2 ÷ 0.6 ) x 27.5 = ?
Options: a ) 12132 , b ) 14678 , c ) 12708 , d ) 14663 , e ) 15688
Rationale: "explanation : ( 319.92 ÷ 0.6 ) x 27.5 = 533.2 x 27.5 = 14663 answer : option d"
Answer: d
Python program:
a = 4 + 1 
b = a ** 4
c = 18 * 6
Problem: a 300 m long train crosses a platform in 51 sec while it crosses a signal pole in 18 sec . what is the length of the platform ?
Options: a ) 287 , b ) 350 , c ) 828 , d ) 277 , e ) 550
Rationale: "speed = 300 / 18 = 50 / 3 m / sec . let the length of the platform be x meters . then , ( x + 300 ) / 5 a = 50 / 3 3 x + 900 = 2550 = > x = 550 m . answer : e"
Answer: e
Python program:
a = speed * (
b = a - 51
Problem: 16.02 ã — 0.0001 = ?
Options: a ) 0.1602 , b ) 0.001602 , c ) 1.6021 , d ) 0.01602 , e ) none of these
Rationale: "16.02 ã — 0.0001 = 0.001602 the answer is b ."
Answer: b
Python program:
a = 16 / 2
b = a * 100
Problem: at an election 2 candidates are participated and a candidate got 30 % of votes and defeated by 1000 . and 100 votes are invalid . find the total polled votes ?
Options: a ) 2150 , b ) 2600 , c ) 3120 , d ) 1500 , e ) 1895
Rationale: "winner votes = 100 - 30 = 70 polled votes = [ ( 100 * 1000 ) / 2 * 70 - 100 ] + 100 = 2600 answer is b"
Answer: b
Python program:
a = 1000 + 100 
b = 30 * 2
c = b / 100
d = 1 - c
e = a / d
Problem: find avrg speed if a man travels at speed of 32 km / hr up and 48 km / hr dawn at an altitude of 230 m .
Options: a ) 25.8 , b ) 26.8 , c ) 38.4 , d ) 34.4 , e ) 29.8
Rationale: "avg speed = 2 * x * y / ( x + y ) = 2 * 32 * 48 ( 32 + 48 ) = 38.4 answer : c"
Answer: c
Python program:
a = 2 * 32
b = a * 48
c = 32 + 48 
d = b / c
Problem: what is the least integer greater than – 1 + 0.5 ?
Options: a ) – 2 , b ) – 1 , c ) 0 , d ) 1 , e ) 2
Rationale: "this question is just about doing careful arithmetic and remembering what makes a numberbiggerorsmallercompared to another number . first , let ' s take care of the arithmetic : ( - 1 ) + ( 0.5 ) = - 0.5 on a number line , since we ' re adding + . 5 to a number , the total moves to the right ( so we ' re moving from - 1 to - 0.5 ) . next , the question asks for the least integer that is greater than - 0.5 again , we can use a number line . numbers become greater as you move to the right . the first integer to the right of - 0.5 is 0 . final answer : c"
Answer: c
Python program:
a = 0 + 5
Problem: the average age of 15 students of a class is 15 years . out of these , the average age of 7 students is 14 years and that of the other 7 students is 16 years , the age of the 15 th student is
Options: a ) 11 , b ) 12 , c ) 13 , d ) 14 , e ) 15
Rationale: "explanation : age of the 15 th student = [ 15 * 15 - ( 14 * 7 + 16 * 7 ) ] = 15 years . answer : e"
Answer: e
Python program:
a = 15 * 15
b = 7 * 14
c = 7 * 16
d = b + c 
e = a - d
Problem: joe invested a certain sum of money in a simple interest bond whose value grew to $ 400 at the end of 3 years and to $ 500 at the end of another 5 years . what was the rate of interest in which he invested his sum ?
Options: a ) 4.76 % , b ) 5.88 % , c ) 6.33 % , d ) 7.75 % , e ) 8.33 %
Rationale: in 5 years , the value grew $ 100 , so the simple interest was $ 20 per year . in 3 years , the total interest was 3 * $ 20 = $ 60 the principal is $ 400 - $ 60 = 340 . the interest rate is $ 20 / $ 340 = 1 / 17 which is about 5.88 % the answer is b .
Answer: b
Python program:
a = 500 - 400
b = a / 5
c = 500 - 400
d = c / 5
e = d * 3
f = 400 - e
g = b / f
h = g * 100
Problem: a doctor prescribed 24 cubic centimeters of a certain drug to a patient whose body weight was 120 pounds . if the typical dosage is 2 cubic centimeters per 15 pounds of the body weight , by what percent was the prescribed dosage greater than the typical dosage ?
Options: a ) 8 % , b ) 9 % , c ) 50 % , d ) 12.5 % , e ) 14.8 %
Rationale: "typical dosage per 15 pound of the body weight = 2 c . c typical dosage per 120 pound of the body weight = 2 * ( 120 / 15 ) = 2 * 8 = 16 c . c dosage prescribed by doctor for 120 pound patient = 24 c . c % prescribed dosage greater than the typical dosage = ( 24 - 16 / 16 ) * 100 % = ( 8 / 16 ) * 100 % = 50 % answer d"
Answer: d
Python program:
a = 2 / 15
b = a * 120
c = b - 24
d = 2 / 15
e = d * 120
f = c / e
g = f * 100
Problem: in february wilson ’ s earnings were 40 percent of his family ’ s total income . in march wilson earned 25 percent less than in february . if the rest of his family ’ s income was the same in both months , then , in march , wilson ’ s earnings were approximately what percent z of his family ’ s total income ?
Options: a ) 15 % , b ) 17 % , c ) 24 % , d ) 30 % , e ) 33 %
Rationale: "lets suppose the total family income in feb = 100 x wilson ' s earning in feb = 40 % of 100 x = 40 x earnings of remaining family in feb = 100 x - 40 x = 60 x wilson ' s earning in march = 75 % of wilson ' s feb earnings = 75 % of 40 x = 30 x earnings of remaining family in march = earnings of remaining family in feb = 60 x thus wilson ' s earning as % of total family income in march z = 30 x / ( 30 + 60 ) x = 30 x / 90 x = 33.33 % thus answer is e"
Answer: e
Python program:
a = 40 / 100
b = 25 / 100
c = 40 / 100
d = b * c
e = a - d
f = 25 / 100
g = 40 / 100
h = f * g
i = 1 - h
j = e / i
k = j * 100
Problem: how many different positive integers are factors of 324 ?
Options: a ) 9 , b ) 16 , c ) 25 , d ) 36 , e ) 49
Rationale: "18 × 18 = 6 ^ 2 × 3 ^ 2 so total factors = ( 5 + 1 ) ( 5 + 1 ) = 36 answer : d"
Answer: d
Python program:
a = 2 ** 2
b = a + 2
Problem: a reduction in the price of petrol by 10 % enables a motorist to buy 5 gallons more for $ 250 . find the original price of petrol ?
Options: a ) $ 11 , b ) $ 5 , c ) $ 45 , d ) $ 400 , e ) $ 5.5
Rationale: "price decreased by 10 % , so 9 / 10 times , which means that original gallons bought increased 10 / 9 times . since this increase equals to 5 gallons then 45 gallons were bought originally ( 45 * 10 / 9 = 50 - - > increase 5 gallons ) . hence original price was 250 / 45 = $ 5.5 answer : e ."
Answer: e
Python program:
a = 10 / 100
b = 1 - a
c = b * 250
d = 250 - c
e = 1 / 2
f = 5 - e
g = d / f
Problem: ( 258 % of 1265 ) ÷ 6 = ?
Options: a ) a ) 125 , b ) b ) 175 , c ) c ) 225 , d ) d ) 375 , e ) e ) 544
Rationale: "explanation : ? = ( 258 x 1265 / 100 ) ÷ 6 = 326370 / 600 = 544 answer : option e"
Answer: e
Python program:
a = 258 / 100
b = a * 1265
c = b / 6
Problem: if ( 1 / 5 ) ^ n * ( 1 / 4 ) ^ 18 = 1 / ( 2 * ( 10 ) ^ 35 ) , then n =
Options: a ) 40 , b ) 45 , c ) 35 , d ) 30 , e ) 25
Rationale: ( 1 / 5 ) ^ m ( 1 / 4 ) ^ 18 = 1 / { 2 ( 10 ) ^ 35 } 2 ( 10 ) ^ 35 / 4 ^ 18 = 5 ^ m [ 2 ( 2 ^ 35 ) ( 5 ^ 35 ) ] / [ 2 ^ 36 ] = 5 ^ m 5 ^ 35 = 5 ^ m n = 35 c
Answer: c
Python program:
a = 35 - 10
b = a + 10
Problem: let exp ( m , n ) = m to the power n . if exp ( 10 , m ) = n exp ( 22 ) where m and n are integers then n = ___ ?
Options: a ) 24 , b ) 25 , c ) 26 , d ) 27 , e ) 28
Rationale: 10 ^ m = n * ( 2 ^ 2 ) ( 2 * 5 ) ^ m = n * ( 2 ^ 2 ) ( 2 ^ m ) * ( 5 ^ m ) = n * ( 2 ^ 2 ) now equate both side we get m = 2 and ( 5 ^ m ) = n ( 5 ^ 2 ) = n = > n = 25 answer : b
Answer: b
Python program:
a = 10 ** 2
b = 2 ** 2
c = a / b
Problem: if [ x ] is the greatest integer less than or equal to x , what is the value of [ - 5.6 ] + [ 3.4 ] + [ 12.7 ] ?
Options: a ) 3 , b ) 5 , c ) 7 , d ) 9 , e ) 10
Rationale: "you are asked what the closest lesser integer value to [ x ] is . [ - 5.6 ] = - 6.0 [ 3.4 ] = 3.0 [ 12.7 ] = 12.0 therefore , answer is : - 6.0 + 3.0 + 12.0 = 9.0 option d ."
Answer: a
Python program:
a = 3 + 4 
b = a - 5
Problem: in a forest 150 deer were caught , tagged with electronic markers , then released . a week later , 50 deer were captured in the same forest . of these 50 deer , it was found that 5 had been tagged with the electronic markers . if the percentage of tagged deer in the second sample approximates the percentage of tagged deer in the forest , and if no deer had either left or entered the forest over the preceding week , what is the approximate number of deer in the forest ?
Options: a ) 150 , b ) 750 , c ) 1,250 , d ) 1,500 , e ) 2,500
Rationale: "given 150 deers were caught and they are tagged in the first slot . in the second slot , 50 were caught and 5 we tagged then 10 % of them are tagged . given this 10 % approximates the percentage of tagged deer in the forest . . here number is 150 . . then 100 % is 1500 . . is the number of deers population in the forest . . answer : d is correct answer . ."
Answer: d
Python program:
a = 50 * 5
Problem: the sum of four consecutive even numbers is 84 . what would be the smallest number ?
Options: a ) 33 , b ) 88 , c ) 70 , d ) 123 , e ) 18
Rationale: "let the four consecutive even numbers be 2 ( x - 2 ) , 2 ( x - 1 ) , 2 x , 2 ( x + 1 ) their sum = 8 x - 4 = 84 = > x = 11 smallest number is : 2 ( x - 2 ) = 18 . answer : e"
Answer: e
Python program:
a = 84 - 10
b = a - 2
c = b / 4
d = c + 2 
e = d + 2 
f = e ** 2
g = 84 - 10
h = g - 2
i = h / 4
j = i + 2 
k = j + 2 
l = k + 2 
m = l ** 2
n = f + m 
o = 84 - 10
p = o - 2
q = p / 4
r = q ** 2
s = 84 - 10
t = s - 2
u = t / 4
v = u + 2 
w = v ** 2
x = r + w 
y = n + x
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 52 units per day , what is the value of n ?
Options: a ) 30 , b ) 19 , 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 = 52 * ( n + 1 ) - - > n = 19 . or as 40 extra units increased the average for n + 1 days by 2 units per day then 40 / ( n + 1 ) = 2 - - > n = 19 . answer : b ."
Answer: b
Python program:
a = 90 - 50
b = 52 - 50
c = a / b
d = c - 1
Problem: an escalator moves towards the top level at the rate of 8 ft . sec and its length is 160 feet . if a person walks on the moving escalator at the rate of 2 feet per second towards the top level , how much time does he take to cover the entire length .
Options: a ) 14 sec , b ) 10 sec , c ) 16 sec , d ) 8 sec , e ) 9 sec
Rationale: "time taken to cover the entire length = tot . dist / resultant speed = 160 / ( 8 + 2 ) = 16 sec answer : c"
Answer: c
Python program:
a = 8 + 2 
b = 160 / a
Problem: ( 1000 ) 7 ÷ ( 10 ) 15 = ?
Options: a ) 10 , b ) 100 , c ) 1000000 , d ) 10000 , e ) none of these
Rationale: "explanation : = ( 103 ) 7 / ( 10 ) 15 = ( 10 ) 21 / ( 10 ) 15 = 10 ( 6 ) = 1000000 option c"
Answer: c
Python program:
a = 1000 * 10
Problem: a person spends 40 % of his salary on food , 25 % on house rent , 15 % on entertainment and 5 % on conveyance . if his savings at the end of the month is rs . 3000 , then his salary per month in rupees is :
Options: a ) 20000 , b ) 6000 , c ) 8000 , d ) 10000 , e ) none of these
Rationale: "total expenditure = 40 + 25 + 15 + 5 = 85 % saving = ( 100 - 85 ) = 15 % 15 / 100 × salary = 3000 , salary = 20000 rs . answer : a"
Answer: a
Python program:
a = 3000 * 100
b = a / 5
Problem: the l . c . m of two numbers is 48 . the numbers are in the ratio 8 : 3 . the sum of numbers is :
Options: a ) 22 , b ) 30 , c ) 40 , d ) 50 , e ) 60
Rationale: "let the numbers be 8 x and 3 x . then , their l . c . m = 24 x . so , 24 x = 48 or x = 2 . the numbers are 16 and 6 . hence , required sum = ( 16 + 6 ) = 22 . answer : a"
Answer: a
Python program:
a = 8 * 48
b = a / 3
Problem: when positive integer e is divided by 13 , the remainder is 2 . when n is divided by 8 , the remainder is 5 . how many such values are less than 180 ?
Options: a ) 0 , b ) 1 , c ) 2 , d ) 3 , e ) 4
Rationale: the equation that can be formed e is 13 x + 2 = 8 y + 5 . . 13 x - 3 = 8 y . . . as we can see x can take only odd values as the rhs will always be even . . also x can take values till 13 as 13 * 14 > 180 . . now we have to substitue x as 1 , 35 , 79 , 1113 . . . once we find 7 fitting in , any other value need not be checked as every 4 th value will give us answer so next value will be 15 . . ans 1 . . b
Answer: b
Python program:
a = 13 - 5
b = 5 + 2 
c = a - b