euclaise/mathqa_programs huggingface dataset:
Problem: the average weight of 20 girls increases by 2 kg when a new girl comes in place of one of them weighing 40 kg . what might be the weight of the new girl ?
Options: a ) 85 kg , b ) 90 kg , c ) 80 kg , d ) 75 kg , e ) 70 kg
Rationale: "total weight increased = 20 x 2 kg = 40 kg . weight of new person = 40 + 40 kg = 80 kg answer : c"
Answer: c
Python program:
a = 20 * 2
b = a + 40
Problem: a ( 5 , w ^ 3 ) is the ( x , y ) coordinate of point located on the parabola y = x ^ 2 + 2 . what is the value of w ?
Options: a ) 3 . , b ) 4 . , c ) 5 . , d ) 6 . , e ) 9
Rationale: "y = x ^ 2 + 2 x = 5 y = 5 ^ 2 + 2 = 27 y is in the form w ^ 3 w ^ 3 = 27 w = 3 answer : a"
Answer: a
Python program:
a = 5 ** 2
b = a - 2
c = 2 / 5
d = b ** c
Problem: in a graduating class of 232 students , 144 took geometry and 119 took biology . what is the difference between the greatest possible number t and the smallest possible number of students that could have taken both geometry and biology ?
Options: a ) 144 , b ) 119 , c ) 113 , d ) 88 , e ) 31
Rationale: "official solution : first of all , notice that since 144 took geometry and 119 took biology , then the number of students who took both geometry and biology can not be greater than 119 . { total } = { geometry } + { biology } - { both } + { neither } ; 232 = 144 + 119 - { both } + { neither } ; { both } = 31 + { neither } . { both } is minimized when { neither } is 0 . in this case { both } = 31 . the greatest possible number t of students that could have taken both geometry and biology , is 119 . thus , the answer is 119 - 31 = 88 . answer : d ."
Answer: d
Python program:
a = 144 + 119 
b = a - 232
c = 119 - b
Problem: a certain fruit stand sold apples for $ 0.80 each and bananas for $ 0.70 each . if a customer purchased both apples and bananas from the stand for a total of $ 6.50 , what total number of apples and bananas did the customer purchase ?
Options: a ) 8 , b ) 9 , c ) 10 , d ) 11 , e ) 12
Rationale: let ' s start with 1 apple for $ 0.80 . let ' s subtract $ 0.80 from $ 6.50 until we get a multiple of $ 0.70 . $ 6.50 , $ 5.70 , $ 4.90 = 7 * $ 0.70 the customer purchased 7 bananas and 2 apples . the answer is b .
Answer: b
Python program:
a = 0 * 8
b = 6 - 5
c = b / 0
d = c + 2
Problem: what is the thousandths digit in the decimal equivalent of 62 / 5000 ?
Options: a ) 0 , b ) 1 , c ) 2 , d ) 5 , e ) 6
Rationale: "62 / 5000 = 62 / ( 5 * 10 ^ 3 ) = ( 62 / 5 ) * 10 ^ - 3 = 12.4 * 10 ^ - 3 = . 0124 thousandths digit = 2 answer c"
Answer: c
Python program:
a = 62 / 5000
b = 100 * a
c = math.floor(b)
Problem: in how many seconds will a train 180 meters long pass an oak tree , if the speed of the train is 36 km / hr ?
Options: a ) 14 , b ) 16 , c ) 18 , d ) 20 , e ) 22
Rationale: "speed = 36 * 5 / 18 = 10 m / s time = 180 / 10 = 18 seconds the answer is c ."
Answer: c
Python program:
a = const_0_2778 * 36
b = 180 / a
Problem: what number should replace the question mark ? 10 , 30 , 14 , 25 , 18 , 20 , - - - ?
Options: a ) 19 , b ) 21 , c ) 25 , d ) 22 , e ) 20
Rationale: "answer : d 10 , 30 , 14 , 25 , 18 , 20 , 22 ? there are two alternate sequences : + 4 and - 5 ."
Answer: d
Python program:
a = 2 + 0 
b = a + 10 
c = b + 10
Problem: a train of length 250 m crosses a bridge of length 180 m in 20 seconds . what is the speed of train ?
Options: a ) 33 , b ) 77.4 , c ) 25 , d ) 22 , e ) 72
Rationale: "sol : ( length of train + length of bridge ) = speed of train x time ( 250 + 180 ) = 20 x speed speed = 430 / 20 = 21.5 m / s = 77.4 km / h answer = b"
Answer: b
Python program:
a = 250 + 180 
b = a / 20
c = const_3_6 * b
Problem: a can do a work in 12 days . when he had worked for 3 days , b joinedhim . if they complete the work in 3 more days , in how manydays can balone finish the work ?
Options: a ) 2 days , b ) 4 days , c ) 5 days , d ) 6 days , e ) 9 days
Rationale: sax work done by afar 3 days : i j . . remzming war — 1 . work done by ( a + b ) for 1 day : . work done by a for 1 day 6 days d
Answer: d
Python program:
a = 3 - 1
b = 12 / a
Problem: if k is an integer and 0.0010101 x 10 ^ k is greater than 100 , what is the least possible value of k ?
Options: a ) 2 , b ) 3 , c ) 4 , d ) 5 , e ) 6
Rationale: "0.0010101 * 10 ^ k > 100 we need to move the decimal point to the right 5 places to get 101.01 this is equivalent to multiplying by 10 ^ 5 . the answer is d ."
Answer: d
Python program:
a = 100 / 0
b = math.log(a)
c = math.log(10)
d = b / c
Problem: gold is 19 times as heavy as water and copper is 9 times as heavy as water . in what ratio should these be mixed to get an alloy 18 times as heavy as water ?
Options: a ) 1 : 2 , b ) 3 : 2 , c ) 9 : 1 , d ) 5 : 2 , e ) 6 : 5
Rationale: "g = 19 w c = 9 w let 1 gm of gold mixed with x gm of copper to get 1 + x gm of the alloy 1 gm gold + x gm copper = x + 1 gm of alloy 19 w + 9 wx = x + 1 * 18 w 19 + 9 x = 18 ( x + 1 ) x = 1 / 9 ratio of gold with copper = 1 : 1 / 9 = 9 : 1 answer is c"
Answer: c
Python program:
a = 18 - 9
b = 19 - 18
c = a / b
Problem: find the ones digit of 73 ^ 350
Options: a ) 3 , b ) 5 , c ) 6 , d ) 7 , e ) 9
Rationale: "3,9 , 7,1 repeats after every four times therefore 350 / 4 = 87 + 2 remainder 9 is the ones digit so e is correct"
Answer: e
Python program:
a = 3 + 4 
b = a * 10
c = 73 - b
d = 350 / 4
e = math.floor(d)
f = e * 4
g = 350 - f
h = c ** g
i = 2 * 10
j = h - i
Problem: a man engaged a servant on the condition that he would pay him rs . 900 and a uniform after 1 year service . he served onlyfor 9 months and received uniform & rs . 650 , find the price of the uniform ?
Options: a ) rs . 90 , b ) rs . 100 , c ) rs . 150 , d ) rs . 190 , e ) rs . 200
Rationale: "9 / 12 = 3 / 4 * 900 = 675 650 - - - - - - - - - - - - - 25 1 / 4 - - - - - - - - 25 1 - - - - - - - - - ? = > rs . 100 b"
Answer: b
Python program:
a = 1 * 900
b = 3 * 4
c = b * 9
d = a - c
e = 3 * 4
f = e * 1
g = d / f
h = g * 4
Problem: a certain car dealership sells economy cars , luxury cars , and sport utility vehicles . the ratio of economy to luxury cars is 3 : 2 . the ratio of economy cars to sport utility vehicles is 5 : 3 . what is the ratio of luxury cars to sport utility vehicles ?
Options: a ) 9 : 8 , b ) 8 : 9 , c ) 3 : 2 , d ) 2 : 3 , e ) 10 : 9
Rationale: "the ratio of economy to luxury cars is 3 : 2 - - > e : l = 3 : 2 = 15 : 10 . the ratio of economy cars to sport utility vehicles is 5 : 3 - - > e : s = 5 : 3 = 15 : 9 . thus , l : s = 10 : 9 . answer : e ."
Answer: e
Python program:
a = 4 * 3
b = 3 * 3
c = a / b
d = 3 * 4
e = 2 * 4
f = d / e
g = c / f
Problem: in the coordinate plane a slope of the line k is 0.5 times the y - intercept of the line k . what is the x - intercept of the line k ?
Options: a ) - 4 , b ) 4 , c ) - 2 , d ) 1 / 2 , e ) - 2
Rationale: as y = 0.5 mx + m , from 0 = 1 / 2 mx + m we get x = - 2 . hence , the correct answer choice is e .
Answer: e
Python program:
a = 1 / 0
Problem: a motorboat can go at 21 kmph and still water . it takes 7 hours to row from a to b and back . what is the distance between a and b if the speed of the stream is 3 kmph ?
Options: a ) 65 km , b ) 85 km , c ) 55 km , d ) 72 km , e ) 40 km
Rationale: let the distance between a and b be x km . total time = x / ( 21 + 3 ) + x / ( 21 - 3 ) = 7 = > x / 24 + x / 18 = 7 = > ( 4 x + 3 x ) / 72 = 7 = > x = 72 km . answer : d
Answer: d
Python program:
a = 21 + 3 
b = 1 / a
c = 21 - 3
d = 1 / c
e = b + d 
f = 7 / e
Problem: the sum of all the digits of the integers from 18 to 21 inclusive is 24 ( 1 + 8 + 1 + 9 + 2 + 0 + 2 + 1 = 24 ) . what is the sum r of all the digits of the integers from 0 to 99 inclusive ?
Options: a ) 450 , b ) 810 , c ) 900 , d ) 1000 , e ) 1100
Rationale: "we want the sum of the digits from 0 to 99 , so i approximated : 0 - 9 - > 45 - > ( 9 + 0 ) * 10 / 2 40 - 49 - > 85 ( 13 + 4 ) * 10 / 2 90 - 99 - > 135 ( 18 + 9 ) * 10 / 2 we can see at a glance that theweightgoes up as the numbers go up ( meaning the difference between 85 and 45 is 40 , while 135 - 85 is 50 , this means that the second part of this sequence carries more weight for our result ) , so we know that the final answer has to be more than 850 ( 85 * 10 ) but close to it , and that ' s just r = 900 : the answer is c ."
Answer: c
Python program:
a = 9 + 1 
b = 9 * a
c = b / 2
d = 2 * 10
e = c * d
Problem: a total of $ 20,000 was invested in two certificates of deposit at simple annual interest rates of 4 percent and 8 percent , respectively . if the total interest on the two certificates was $ 1,440 at the end of one year , what fractional part of the $ 20.000 was invested at the higher rate ?
Options: a ) 3 / 8 , b ) 4 / 5 , c ) 1 / 2 , d ) 3 / 5 , e ) 3 / 4
Rationale: "x * 4 / 100 * 1 + ( 20000 - x ) * 8 / 100 * 1 = 1440 4 x - 8 x = 144000 - 160000 = > - 4 x = - 16000 = > x = 4000 / 4 so 16000 / 20000 = 4 / 5 answer - b"
Answer: b
Python program:
a = 1 + 4 
b = 2 * a
c = 100 * b
d = 4 * 100
e = c + d 
f = 1 + 4 
g = 2 * f
h = 4 * g
i = e + h 
j = i / 20
k = j / 8
l = k + 8 
m = l - 4
n = m / 20
Problem: in traveling from a dormitory to a certain city , a student went 1 / 5 of the way by foot , 2 / 3 of the way by bus , and the remaining 6 kilometers by car . what is the distance , in kilometers , from the dormitory to the city ?
Options: a ) 30 , b ) 58 , c ) 60 , d ) 90 , e ) 120
Rationale: "i believe there is a better way to do it . basically one of the options should satisfy the given criteria . 60 did 1 / 5 * 60 = 12 2 / 3 * 60 = 40 so total distance 52 + remaining 6 = 58 answer b"
Answer: b
Python program:
a = 1 / 5
b = 2 / 3
c = a + b 
d = 1 - c
e = 1/(d)
f = 6 * e
Problem: when positive integer x is divided by positive integer y , the remainder is 9 . if x / y = 96.12 , what is the value of y ?
Options: a ) 96 , b ) 75 , c ) 48 , d ) 25 , e ) 12
Rationale: "x = qy + 9 , where q is the quotient x / y = ( q y + 9 ) / y = q + ( 9 / y ) = 96.12 = 96 + 0.12 = > q = 96 9 / y = 0.12 = > y = 75 answer is b ."
Answer: b
Python program:
a = math.floor(96, 12)
b = 96 - 12
c = 9 / b
Problem: tom read a book containing 1000 pages by reading the same number of pages each day . if he would have finished the book 5 days earlier by reading 15 pages a day more , how many days did tom spend reading the book ?
Options: a ) 20 , b ) 18 , c ) 16 , d ) 15 , e ) 15.39
Rationale: "actually u can set up 2 equation p - - stands for the pages d - - stands for the days 1 ) p * d = 480 ( we want to find the days , sop = 480 / d ) 2 ) ( p + 15 ) ( d - 5 ) = 1000 = > pd - 5 p + 15 d - 75 = 1000 as the 1 ) stated u can put 1 ) into 2 ) = > 1000 - 5 p + 15 d - 75 = 1000 = > 15 d - 5 p = 75 put the bold one into it = > 15 d - 5 ( 480 / d ) = 75 the we get the final equation 16 d ^ 2 - 2400 = 80 d ( divide 16 ) = > d ^ 2 - 5 d - 160 = 0 so d = 15.39 days . ans : ( e )"
Answer: e
Python program:
a = 15 * 5
b = a * 4
c = 15 ** 2
d = b + c 
e = math.sqrt(d)
f = e - 15
g = f / 2
Problem: find the compound interest on $ 16,000 at 20 % per annum for 9 months , compounded quarterly
Options: a ) 2532 , b ) 2552 , c ) 2524 , d ) 2522 , e ) 2512
Rationale: "principal = $ 16000 ; time = 9 months = 3 quarters ; rate = 20 % per annum = 5 % per quarter . amount = $ [ 16000 x ( 1 + ( 5 / 100 ) ) ^ 3 ] = $ 18522 . ci . = $ ( 18522 - 16000 ) = $ 2522 . answer d ."
Answer: d
Python program:
a = 9 / 100
b = 1 + a 
c = b ** 20
d = 16 * 0
e = d - 16
Problem: the number of students in each section of a school is 24 . after admitting new students , three new sections were started . now , the total number of sections is 16 and there are 21 students in each section . the number of new students admitted is :
Options: a ) 12
b ) 42
c ) 24
d ) 28
e ) 26
Rationale: original number of sections = 16 - 3 = 13 original number of students = 24 x 13 = 312 present number of students = 21 x 16 = 336 number of new students admitted = 336 - 312 = 24 so the answer is option c ) 24 .
Answer: c
Python program:
a = 16 * 21
b = 16 - 3
c = 24 * b
d = a - c
Problem: a man crosses a 600 m long street in 5 minutes . what is his speed in km per hour ?
Options: a ) 7 km / hr , b ) 7.2 km / hr , c ) 5.2 km / hr , d ) 10 km / hr , e ) 5 km / hr
Rationale: speed = 600 / 5 * 60 = 2 m / sec converting m / sec to km / hr . = 2 * 18 / 5 = 7.2 km / hr answer is b
Answer: b
Python program:
a = 600 / 1000
b = 5 / const_60
c = a / b
Problem: if the sum of the 4 th term and the 12 th term of an arithmetic progression is 24 , what is the sum of the first 15 terms of the progression ?
Options: a ) 300 , b ) 240 , c ) 220 , d ) 200 , e ) 180
Rationale: "4 th term + 12 th term = 24 i . e . , ( a + 3 d ) + ( a + 11 d ) = 24 now , sum of first 15 terms = ( 15 / 2 ) * [ 2 a + ( 15 - 1 ) d ] = ( 15 / 2 ) * [ 2 a + 14 d ] = ( 15 / 2 ) * 24 - - - - - - - - - - - - - - - from ( 1 ) = 180 answer : e"
Answer: e
Python program:
a = 15 / 2
b = a * 24
Problem: how many 4 - digit positive integers are there , where each digit is positive , and no 3 adjacent digits are same ?
Options: a ) 1236 , b ) 3528 , c ) 4096 , d ) 4608 , e ) 6561
Rationale: first digit . . 9 posibilities second digit , 8 possibilities third digit , 7 possibilities fourth digit , 7 possibilities . 9 * 8 * 7 * 7 = 3528 . b
Answer: b
Python program:
a = 4 + 3 
b = 4 + 3 
c = a * b
d = 4 + 4 
e = 3 * 3
f = d * e
g = c * f
Problem: 15 lts are taken of from a container full of liquid a and replaced with liquid b . again 15 more lts of the mixture is taken and replaced with liquid b . after this process , if the container contains liquid a and b in the ratio 9 : 16 , what is the capacity of the container w ?
Options: a ) a : 45 , b ) b : 25 , c ) c : 37.5 , d ) d : 36 , e ) e : 42
Rationale: "if you have a 37.5 liter capacity , you start with 37.5 l of a and 0 l of b . 1 st replacement after the first replacement you have 37.5 - 15 = 22.5 l of a and 15 l of b . the key is figuring out how many liters of a and b , respectively , are contained in the next 15 liters of mixture to be removed . the current ratio of a to total mixture is 22.5 / 37.5 ; expressed as a fraction this becomes ( 45 / 2 ) / ( 75 / 2 ) , or 45 / 2 * 2 / 75 . canceling the 2 s and factoring out a 5 leaves the ratio as 9 / 15 . note , no need to reduce further as we ' re trying to figure out the amount of a and b in 15 l of solution . 9 / 15 of a means there must be 6 / 15 of b . multiply each respective ratio by 15 to get 9 l of a and 6 l of b in the next 15 l removal . final replacement the next 15 l removal means 9 liters of a and 6 liters of b are removed and replaced with 15 liters of b . 22.5 - 9 = 13.5 liters of a . 15 liters of b - 6 liters + 15 more liters = 24 liters of b . test to the see if the final ratio = 9 / 16 ; 13.5 / 24 = ( 27 / 2 ) * ( 1 / 24 ) = 9 / 16 . choice c is correct ."
Answer: c
Python program:
a = 9 + 16 
b = 9 / a
c = math.sqrt(b)
d = 1 - c
e = 15 / d
Problem: a number when divided by 45 , gives 30 as quotient and 0 as remainder . what will be the remainder when dividing the same number by 15
Options: a ) a ) 0 , b ) b ) 3 , c ) c ) 4 , d ) d ) 6 , e ) e ) 7
Rationale: explanation : p ÷ 45 = 30 = > p = 30 * 45 = 1350 p / 15 = 1350 / 15 = 90 , remainder = 0 answer : option a
Answer: a
Python program:
a = 45 * 30
b = a / 15
Problem: a vendor buys 10 t - shirts at an average price of $ 14 per t - shirt . he then buys 15 more t - shirts at an average price of $ 11 per t - shirt . what is the average price s per t - shirt that the vendor paid for these purchases ?
Options: a ) $ 12.20 , b ) $ 12.50 , c ) $ 12.55 , d ) $ 12.70 , e ) $ 13.00
Rationale: "correct answer : a explanation : the relevant formula for this problem is average s = ( sum ) / ( number of terms ) . another way to look at the formula is sum = average x number of terms . for the first purchase , the vendor ' s sum ( total cost ) was $ 140 , since 14 x 10 = 140 . for the second purchase , the vendor ' s cost was $ 165 , since 11 x 15 = 165 . the grand sum is then $ 140 + $ 165 , which equals $ 305 . the total number of shirts purchased was 25 , so to get the average price per shirt , we divide 305 by 25 , which equals $ 12.20 . as a result , the correct answer is a . note : a relative understanding of weighted average offers a shortcut to this problem . because the true average of 11 and 14 is 12.5 , but the vendor sells more shirts at the lower price than at the higher price , the weighted average must be less than $ 12.50 ; only answer choice a is a possibility ."
Answer: a
Python program:
a = 10 + 14 
b = a / 2
c = const_0_25 + const_0_25 
d = b + c
Problem: of the families in city x in 1904 , 50 percent owned a personal computer . the number of families in city x owning a computer in 1908 was 30 percent greater than it was in 1904 , and the total number of families in city x was 5 percent greater in 1908 than it was in 1904 . what percent of the families in city x owned a personal computer in 1908 ?
Options: a ) 61.90 % , b ) 52.20 % , c ) 56.20 % , d ) 70.45 % , e ) 74.41 %
Rationale: "say a 100 families existed in 1904 then the number of families owning a computer in 1904 - 50 number of families owning computer in 1908 = 50 * 130 / 100 = 65 number of families in 1908 = 105 the percentage = 65 / 105 * 100 = 61.90 % . option : a"
Answer: a
Python program:
a = 30 + 100 
b = a * 50
c = b / 100
d = 100 + 5 
e = c / d
f = 100 * e
Problem: a merchant marks his goods up by 40 % and then offers a discount of 20 % on the marked price . what % profit does the merchant make after the discount ?
Options: a ) 21 % , b ) 25 % , c ) 69 % , d ) 31 % , e ) 12 %
Rationale: "let the price be 100 . the price becomes 140 after a 40 % markup . now a discount of 20 % on 140 . profit = 112 - 100 12 % answer e"
Answer: e
Python program:
a = 40 + 100 
b = 40 + 100 
c = b * 20
d = c / 100
e = a - d
f = e - 100
Problem: during a certain two - week period , 70 percent of the movies rented from a video store were comedies , and of the remaining movies rented , there were 4 times as many dramas as action movies . if no other movies were rented during that two - week period and there were a action movies rented , then how many comedies , in terms of a , were rented during that two - week period ?
Options: a ) 16 a , b ) 13 a , c ) 14 a , d ) 11 2 / 3 a , e ) 12 a
Rationale: "total movies = 100 . comedies = 70 . action + drama = 30 . since there were 5 times as many dramas as action movies , then action + 4 * action = 30 - - > action = a = 6 . comedies = 70 = 14 a . answer : d ."
Answer: d
Python program:
a = 4 + 1 
b = 70 / a
c = math.floor(b)
Problem: there were two candidates in an election . winner candidate received 58 % of votes and won the election by 288 votes . find the number of votes casted to the winning candidate ?
Options: a ) 776 , b ) 1044 , c ) 299 , d ) 257 , e ) 125
Rationale: "w = 58 % l = 42 % 58 % - 42 % = 16 % 16 % - - - - - - - - 288 58 % - - - - - - - - ? = > 1044 answer : b"
Answer: b
Python program:
a = 100 - 58
b = 58 - a
c = b / 100
d = 288 / c
e = d * 58
f = e / 100
Problem: 4 / 15 of 5 / 7 of a number is greater than 4 / 9 of 2 / 5 of the same number by 8 . what is half of that number ?
Options: a ) 305 , b ) 315 , c ) 345 , d ) 325 , e ) 335
Rationale: let the number be x . then 4 / 15 of 5 / 7 of x - 4 / 9 of 2 / 5 of x = 8  4 / 21 x - 8 / 45 x = 8 ( 4 / 21 - 8 / 45 ) x = 8  ( 60 - 56 ) / 315 x = 8  4 / 315 x = 8 x = ( 8 * 315 ) / 4 = 630  1 / 2 x = 315 hence required number = 315 answer is b .
Answer: b
Python program:
a = 4 / 15
b = 5 / 7
c = a * b
d = 2 / 5
e = 4 / 9
f = d * e
g = c - f
h = 8 / g
i = h / 2
Problem: a producer of tea blends two varieties of tea from two tea gardens one costing rs 18 per kg and another rs 20 per kg in the ratio 5 : 3 . if he sells the blended variety at rs 20 per kg , then his gain percent is
Options: a ) 7 % , b ) 13 % , c ) 14 % , d ) 15 % , e ) 16 %
Rationale: "explanation : suppose he bought 5 kg and 3 kg of tea . cost price = rs . ( 5 x 18 + 3 x 20 ) = rs . 150 . selling price = rs . ( 8 x 20 ) = rs . 160 . profit = 160 - 150 = 10 so , profit % = ( 10 / 150 ) * 100 = 7 % option a"
Answer: a
Python program:
a = 5 + 3 
b = 20 * a
c = 5 * 18
d = 3 * 20
e = c + d 
f = b - e
g = f * 100
h = 5 * 18
i = 3 * 20
j = h + i 
k = g / j
Problem: what is the total number of y integers between 100 and 200 that are divisible by 3 ?
Options: a ) 33 , b ) 32 , c ) 31 , d ) 30 , e ) 29
Rationale: yes there is a different way of arriving at that answer . . . . u can also use airthmetic progression to get the answer since the first term to be divisble by 3 is 102 . . take that as a . . the starting no and since 198 is the last digit to be divisible by 3 take that as n . . . since the difference is 3 take that as d no u have to find what term is 198 take that as nth term the formula for that is n = a + ( n - 1 ) * d 198 = 102 + ( n - 1 ) * 3 from this u get n = 33
Answer: a
Python program:
a = 200 - 2
b = 100 + 2 
c = a - b
d = c / 3
e = d + 1
Problem: if each participant of a chess tournament plays exactly one game with each of the remaining participants , then 136 games will be played during the tournament . find the number of participants .
Options: a ) 15 , b ) 16 , c ) 17 , d ) 18 , e ) 19
Rationale: let p be the number of participants . pc 2 = 136 ( p ) ( p - 1 ) = 272 = 17 * 16 p = 17 the answer is c .
Answer: c
Python program:
a = 136 * 2
b = a * 4
c = b + 1 
d = math.sqrt(c)
e = d + 1 
f = e / 2
Problem: a , b and c can do a piece of work in 4 days , 8 days and 20 days respectively . how long will they taken , if all the three work together ?
Options: a ) 2 , b ) 4 , c ) 5 , d ) 67 , e ) 2 6 / 17
Rationale: "1 / 4 + 1 / 8 + 1 / 20 = 17 / 40 = > 40 / 17 = > 2 6 / 17 days answer : e"
Answer: e
Python program:
a = 1/(20)
b = 1/(4)
c = 1/(8)
d = b + c 
e = a + d 
f = 1/(e)
Problem: for the past n days , the average ( arithmetic mean ) daily production at a company was 40 units . if today ' s production of 90 units raises the average to 45 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 ) - - > 40 n = ( total production for n days ) ; ( total production for n days ) + 90 = ( average production for n + 1 days ) * ( n + 1 ) - - > 40 n + 90 = 45 * ( n + 1 ) - - > n = 9 answer : d ."
Answer: d
Python program:
a = 90 - 40
b = 45 - 40
c = a / b
d = c - 1
Problem: in the johnsons ' monthly budget , the dollar amounts allocated to household expenses , food , and miscellaneous items are in the ratio 5 : 4 : 1 , respectively . if the total amount allocated to these 3 categories is $ 1800 , what is the amount allocated to food ?
Options: a ) $ 900 , b ) $ 720 , c ) $ 675 , d ) $ 450 , e ) $ 225
Rationale: to solve this question , it will be best to first express the given ratio using variable multipliers . thus , we have : household expenses : food : miscellaneous = 5 x : 4 x : x since we are told that the total amount allocated to these categories is $ 1,800 we can set up the equation : 5 x + 4 x + x = 1,800 10 x = 1,800 x = 180 thus , the total amount allocated to food is 4 x 180 = $ 720 . answer b .
Answer: b
Python program:
a = 5 + 4 
b = a + 1 
c = 1800 / b
d = c * 4
Problem: one ton has 2600 pounds , and one pound has 16 ounces . how many packets containing wheat weighing 16 pounds and 4 ounces each would totally fill a gunny bag of capacity 13 tons ?
Options: a ) 2080 , b ) 1700 , c ) 2350 , d ) 2500 , e ) 8000
Rationale: "16 pounds and 4 ounces = 16 * 16 + 4 = 260 ounces . 13 tons = 13 * 2600 pound = 13 * 2600 * 16 ounces . hence the answer is ( 13 * 2600 * 16 ) / 260 = 2080 . answer : a ."
Answer: a
Python program:
a = 13 * 2600
b = a * 16
c = 16 * 16
d = c + 4 
e = b / d
Problem: what is the remainder when 8 ^ 381 is divided by 5 ?
Options: a ) 0 , b ) 1 , c ) 2 , d ) 3 , e ) 4
Rationale: i also agree that the remainder is ' 3 ' ( using the last digit of the powers of 7 ) . could we have the official answer please ? d
Answer: d
Python program:
a = 5 / 2
b = 8 * 8
c = a - b