euclaise/mathqa_programs huggingface dataset:
Problem: subash can copy 50 pages in 10 hrs . subash and prakash together can copy 300 pages in 40 hours . in how much time prakash can copy 25 pages .
Options: a ) 8 , b ) 10 , c ) 12 , d ) 14 , e ) 16
Rationale: "subhas ' s 1 hr copy page = 50 / 10 = 5 page ( subhas + prakash ) ' s 1 hr copy page = 300 / 40 = 7.5 page from above prakash ' s 1 hr copy page = 2.5 page so time taken in 30 page ' s copy = ( 25 / 2.5 ) = 10 hrs answer : b"
Answer: b
Python program:
a = 300 / 40
b = 50 / 10
c = a - b
d = math.floor(c)
Problem: if p and q are positive integers each greater than 1 , and 17 ( p + 1 ) = 25 ( q + 1 ) , what is the least possible value of p + q ?
Options: a ) 36 , b ) 42 , c ) 40 , d ) 46 , e ) none
Rationale: "17 ( p + 1 ) = 29 ( q + 1 ) - - > ( p + 1 ) / ( q + 1 ) = 29 / 17 - - > the least positive value of p + 1 is 25 , so the least value of p is 24 and the least positive value of q + 1 is 17 , so the least value of q is 16 - - > the least value of p + q is 24 + 16 = 40 . answer : c ."
Answer: c
Python program:
a = 25 + 17 
b = a - 2
Problem: what will be the cost of building a fence around a square plot with area equal to 289 sq ft , if the price per foot of building the fence is rs . 54 ?
Options: a ) 3672 , b ) 920 , c ) 7290 , d ) 6928 , e ) 3729
Rationale: "explanation : let the side of the square plot be a ft . a 2 = 289 = > a = 17 length of the fence = perimeter of the plot = 4 a = 68 ft . cost of building the fence = 68 * 54 = rs . 3672 . answer : option a"
Answer: a
Python program:
a = math.sqrt(289)
b = square_perimeter * (
Problem: excluding stoppages , the speed of a train is 45 kmph and including stoppages it is 33 kmph . of how many minutes does the train stop per hour ?
Options: a ) 73 , b ) 83 , c ) 16 , d ) 83 , e ) 28
Rationale: "explanation : t = 12 / 45 * 60 = 16 answer : option c"
Answer: c
Python program:
a = 33 / 45
b = const_60 * a
c = const_60 - b
Problem: worker a takes 8 hours to do a job . worker b takes 10 hours to do the same job . how long should it take both a and b , working together but independently , to do the same job ?
Options: a ) 70 hours , b ) 40 / 9 hours , c ) 9 hours , d ) 16 hours , e ) 20 hours
Rationale: "a ’ s 1 hour ' s work = 1 / 8 b ' s 1 hour ' s work = 1 / 10 ( a + b ) ' s 1 hour ' s work = ( 1 / 8 ) + ( 1 / 10 ) = 9 / 40 both a and b will finish the work in 40 / 9 days . answer b 40 / 9 hours"
Answer: b
Python program:
a = 1 / 8
b = 1 / 10
c = a + b 
d = 1 / c
Problem: rectangle dimensions were given , 2 doors dimensions given , 2 windows dimensions given . 70 cm wide wallpaper to be covered on the walls of this room . cost of wallpaper is 60 per meter . . calculate total cost
Options: a ) 20 , b ) 25 , c ) 30 , d ) 60 , e ) 70
Rationale: area of room = ( l * b ) m ^ 2 area of door + window = ( d + w ) m ^ 2 remaining area = ( ( l * b ) - ( d + w ) ) m ^ 2 so length = remaining area / 0.70 m total cost = length * 60 - - - ans and total cost = 60 answer : d
Answer: d
Python program:
a = 60 * 1
Problem: set s consists of integers { 12 , 34 } . if two numbers are chosen from set s at random , what is the probability that the sum of 2 numbers is more than 6 ?
Options: a ) 1 / 3 , b ) 1 / 6 , c ) 2 / 3 , d ) 2 / 5 , e ) 3 / 7
Rationale: number of ways you can choose 2 from 4 = 4 c 2 = 6 e = event of getting the 2 numbers is more than 6 = ( 3,4 ) = 1 probability = 1 / 6 answer is b
Answer: b
Python program:
a = 1/(6)
Problem: in a sample of 800 high school students in which all students are either freshmen , sophomores , juniors , or seniors , 23 percent are juniors and 75 percent are not sophomores . if there are 160 seniors , how many more freshmen than sophomores are there among the sample of students ?
Options: a ) 42 , b ) 48 , c ) 56 , d ) 64 , e ) 72
Rationale: 200 are sophomores . the number of freshmen is 600 - 160 - 0.23 ( 800 ) = 256 the answer is c .
Answer: c
Python program:
a = 160 / 800
b = a * 100
c = 100 - b
d = c - 23
e = 100 - 75
f = d - e
g = f * 800
h = g / 100
i = 100 - 75
j = i * 800
k = j / 100
l = h - k
Problem: the manager of a produce market purchased a quantity of tomatoes for $ 0.80 per pound . due to improper handling , 10 percent of the tomatoes , by weight , were ruined and discarded . at what price per pound should the manager sell the remaining tomatoes if she wishes to make a profit on the sale of the tomatoes equal to 9 percent of the cost of the tomatoes .
Options: a ) $ 0.94 , b ) $ 0.97 , c ) $ 0.98 , d ) $ 1.00 , e ) $ 1.20
Rationale: "assume the manager bought 100 tomatoes . cost price = 80 given : 10 % are damaged - - > available tomatoes to sell = 90 90 * x - 80 = 0.09 * 80 90 x - 80 = 7.2 90 x = 87.2 x = 87.2 / 90 = 0.968 x is slightly under 0.9688 = 0.97 answer : b"
Answer: b
Python program:
a = 9 / 100
b = 1 + a 
c = 100 - 10
d = c / 100
e = 0 / 80
f = b * e
Problem: if a coin has an equal probability of landing heads up or tails up each time it is flipped , what is the probability that the coin will land heads up exactly once in 3 consecutive flips ?
Options: a ) 0.125 , b ) 0.25 , c ) 0.75 , d ) 0.375 , e ) 0.666
Rationale: "total number of ways in which h or t can appear in 3 tosses of coin is = 2 * 2 * 2 = 8 ways for 2 t and 1 h thus probability is = p ( htt ) + p ( tth ) + p ( tht ) = 1 / 8 + 1 / 8 + 1 / 8 = 3 / 8 = . 375 answer : d"
Answer: d
Python program:
a = 1 / 2
b = a ** 3
c = b * 3
Problem: the average weight of 10 person ' s increases by 2.5 kg when a new person comes in place of one of them weighing 50 kg . what might be the weight of the new person ?
Options: a ) 76 kg , b ) 76.5 kg , c ) 75 kg , d ) data inadequate , e ) none of these
Rationale: "explanation : total weight increased = ( 10 x 2.5 ) kg = 25 kg . weight of new person = ( 50 + 25 ) kg = 75 kg . answer : c"
Answer: c
Python program:
a = 10 * 2
b = a + 50
Problem: the speed of a boat in still water is 15 km / hr and the rate of current is 3 km / hourr . the distance travelled downstream in 24 mins is ?
Options: a ) 6 km , b ) 7 km , c ) 7.2 km , d ) 8 km , e ) 8.4 km
Rationale: "speed of a boat in still water = 15 km / hr speed of the current = 3 km / hr speed downstream = ( 15 + 3 ) = 18 km / hr distance travelled downstream in 24 minutes = 2460 × 18 = 2 × 185 = 7.2 km c"
Answer: c
Python program:
a = 24 / const_60
b = 15 + 3 
c = a * b
Problem: if 1 tic equals 4 tacs and 5 tacs equal 8 tocs , what is the ratio of one tic to one toc ?
Options: a ) 15 / 2 , b ) 6 / 5 , c ) 5 / 6 , d ) 32 / 5 , e ) 1 / 15
Rationale: "tic = 4 * tac and 5 * tac = 8 * toc ; 5 * tic = 20 * tac and 20 * tac = 32 * toc - - > 5 * tic = 32 * toc - - > tic / toc = 32 / 5 . answer : d ."
Answer: d
Python program:
a = 8 / 1
b = 4 / 1
c = a + b
Problem: a man can row upstream at 22 kmph and downstream at 42 kmph , and then find the speed of the man in still water ?
Options: a ) 29 , b ) 92 , c ) 30 , d ) 32 , e ) 23
Rationale: "us = 22 ds = 42 m = ( 42 + 22 ) / 2 = 32 answer : d"
Answer: d
Python program:
a = 22 + 42 
b = a / 2
Problem: if the side length of square b is five times that of square a , the area of square b is how many times the area of square a ?
Options: a ) 5 , b ) 15 , c ) 25 , d ) 35 , e ) 45
Rationale: "let x be the side length of square a . then the area of square a is x ^ 2 . the area of square b is ( 5 x ) ^ 2 = 25 x ^ 2 . the answer is c ."
Answer: c
Python program:
a = 4 * 4
Problem: the average weight of 20 oarsmen in a boat is increased by 2 kg when one of the crew , who weight 40 kg is replaced by a new man . find the weight of the new man .
Options: a ) 60 kg , b ) 50 kg , c ) 92 kg , d ) 80 kg , e ) 70 kg
Rationale: total weight increased = 2 * 20 = 40 kg weight of the new man = 40 + 40 = 80 kg answer is d
Answer: d
Python program:
a = 2 * 20
b = a + 40
Problem: in a club with 310 peopl , 138 play tennis , 255 play baseball , and 94 people play both sports . how many people do not pla a sport ?
Options: a ) 9
b ) 8
c ) 4
d ) 10
e ) 11
Rationale: take 94 off the baseball players - - > 161 then 161 + 138 = 299 play either baseball or tennis 310 - 299 = 11 answer is e
Answer: e
Python program:
a = 310 - 138
b = 255 - 94
c = a - b
Problem: a 14 % stock yielding 8 % is quoted at ?
Options: a ) 165 , b ) 170 , c ) 175 , d ) 180 , e ) 185
Rationale: "assume that face value = rs . 100 as it is not given to earn rs . 8 , money invested = rs . 100 to earn rs . 14 , money invested = 100 × 14 / 8 = rs . 175 ie , market value of the stock = rs . 175 answer is c ."
Answer: c
Python program:
a = 100 / 8
b = a * 14
Problem: at present the ratio between the ages of arun and deepak is 4 : 3 . after 6 years , arun ' s age will be 26 years . what is the age of deepak at present ?
Options: a ) 15 , b ) 21 , c ) 23 , d ) 12 , e ) 25
Rationale: let the present ages of arun and deepak be 4 x years and 3 x years respectively 4 x + 6 = 26 4 x = 20 x = 5 deepak ' s age = 3 x = 15 years answer is a
Answer: a
Python program:
a = 26 - 6
b = a * 3
c = b / 4
Problem: working together , jose and jane can complete an assigned task in 5 days . however , if jose worked alone and complete half the work and then jane takes over the task and completes the second half of the task , the task will be completed in 15 days . how long will jose take to complete the task if he worked alone ? assume that jane is more efficient than jose
Options: a ) 26 days , b ) 15 days , c ) 60 days , d ) 65 days , e ) 36 days
Rationale: "assume : jose does 1 job in x days , so jose does 1 / x job in a day jane does 1 job in y days , so jane does 1 / y job in a day together , they does ( x + y ) / xy job in a day . this is equals to 1 / 20 . so ( x + y ) / xy = 1 / 5 5 ( x + y ) = xy next , we ' re told 1 job takes 15 days to complete if jose and jane each does half the work . so since jose does 1 job in x days , he wil need x / 2 days to do half the job . jane similarly will need y / 2 days to do the other half . x / 2 + y / 2 = 15 x + y = 30 so xy = 150 the answer choices are : 26 days 15 days 60 days 65 days 36 days from the answer choices , so i ' ll go for 15 days for jose and 10 days for jane . answer : b"
Answer: b
Python program:
a = 3 * 5
Problem: two years ago , ram put $ 1,000 into a savings account . at the end of the first year , his account had accrued $ 100 in interest bringing his total balance to $ 1,100 . the next year , his account balance increased by 20 % . at the end of the two years , by what percent has sam ' s account balance increased from his initial deposit of $ 1,000 ?
Options: a ) 40 % , b ) 25 % , c ) 35 % , d ) 30 % , e ) 32 %
Rationale: "investment 1000 dollars 1 st year total gained = 100 total amount end of first year = 1100 second year account increased by 20 % = 1100 * 0.2 = 220 therefore total amount by second year end = 1320 so total percentage increase in money = ( 1320 - 1000 ) * 100 / 1000 = 32 % correct answer e = 32 %"
Answer: e
Python program:
a = 20 / 100
b = a * 1
c = b + 100 
d = c / 1
e = d * 100
Problem: a gets 3 times as much money as b gets , b gets only rs . 25 more then what c gets . the 3 gets rs . 645 in all . find the share of b ?
Options: a ) 134 , b ) 120 , c ) 218 , d ) 140 , e ) 145
Rationale: a + b + c = 645 a = 3 b 3 b + b + b - 25 = 645 5 b = 670 b = 134 answer : a
Answer: a
Python program:
a = 645 + 25 
b = 3 + 1 
c = b + 1 
d = a / c
Problem: if ( a - b - c + d = 13 ) and ( a + b - c - d = 3 ) , what is the value of ( b - d ) ^ 2 ?
Options: a ) 4 . , b ) 8 . , c ) 12 . , d ) 25 . , e ) 64 .
Rationale: "eq 1 : a - b - c + d = 13 eq 2 : a + b - c - d = 3 ( 1 ) subtract eq 1 from eq 2 a - b - c + d = 13 - a + b - c - d = 3 - - - - - - - - - - - - - - - - - - - - - - - - - 2 b + 2 d = 10 ( 2 ) simplify - b + d = 5 b - d = - 5 ( b - d ) ^ 2 = ( - 5 ) ^ 2 = 25 my answer : d"
Answer: d
Python program:
a = 13 + 3 
b = a / 2
c = 3 - b
d = c ** 2
Problem: dhoni spent 20 percent of his earning last month on rent and 5 percent less than what he spent on rent to purchase a new dishwasher . what percent of last month ' s earning did dhoni have left over ?
Options: a ) 61 % , b ) 62 % , c ) 65 % , d ) 64 % , e ) 50 %
Rationale: say dhoni ' s earning last month was $ 100 . dhoni spent 20 percent of his earning last month on rent - - > $ 20 on rent ; 5 percent less than what he spent on rent to purchase a new dishwasher - - > $ 20 * 0.95 = $ 19 on the dishwasher . left over amount 100 - ( 20 + 19 ) = $ 61 answer : a
Answer: a
Python program:
a = 5 / 100
b = 1 - a
c = 20 * b
d = 20 + c 
e = 100 - d
Problem: if a ' s height is 20 % less than that of b , how much percent b ' s height is more than that of a ?
Options: a ) 66.66 % , b ) 66.68 % , c ) 66.766 % , d ) 86.66 % , e ) 25 %
Rationale: "excess of b ' s height over a ' s = [ ( 20 / ( 100 - 20 ) ] x 100 % = 25 % answer : e )"
Answer: e
Python program:
a = 100 - 20
b = 20 / a
c = b * 100
Problem: a set of football matches is to be organized in a ` ` round - robin ' ' fashion , i . e . , every participating team plays a match against every other team once and only once . if 15 matches are totally played , how many teams participated ?
Options: a ) 4 , b ) 5 , c ) 6 , d ) 7 , e ) 8
Rationale: 2 ways to solve this problem . . summation ( x ) = n ( n - 1 ) / 2 n ( n - 1 ) / 2 = 15 ; n ^ 2 - n - 30 = 0 ans : 6 answer : c
Answer: c
Python program:
a = 15 - 10
b = a + 1
Problem: the average weight of 8 sailors in a boat is increased by 1 kg if one of them weighing 56 kg is replaced by a new sailor . the weight of the new sailor is ?
Options: a ) 57 kg , b ) 60 kg , c ) 64 kg , d ) 62 kg , e ) 66 kg
Rationale: the sailor weighing 56 kg is replaced and the average is increased by 1 kg . hence , the weight of the new sailor is ( 56 + increase in total weight ) = 56 + 1 x 8 = 56 + 8 = 64 kg . answer : c
Answer: c
Python program:
a = 56 + 8
Problem: there are some sweets in party , 1 / 3 rd eaten by kids . then 2 / 5 th of the remaining by men , then 2 / 3 rd of the remaining by women . at last 2 were remaining . how many sweets were in total ?
Options: a ) 45 , b ) 27 , c ) 15 , d ) 26 , e ) 91
Rationale: sol : if x sweets were there in total , then x × ( 1 – 1 / 3 ) × ( 1 – 2 / 5 ) × ( 1 – 2 / 3 ) = 2 x × 2 / 3 × 3 / 5 × 1 / 3 = 2 x = 15 answer : c
Answer: c
Python program:
a = 1 / 3
b = 1 - a
c = 2 / 5
d = 1 / 3
e = 1 - d
f = c * e
g = b - f
h = 2 / 3
i = 1 / 3
j = 1 - i
k = 2 / 5
l = 1 / 3
m = 1 - l
n = k * m
o = j - n
p = h * o
q = g - p
r = 2 / q
Problem: the cost of 100 articles is equal to selling price of 90 . find the gain or loss percent ?
Options: a ) 11 % , b ) 20 % , c ) 27 % , d ) 32 % , e ) 49 %
Rationale: "c . p . of each article be $ 1 c . p . of 90 articles = 100 gain % = 10 / 90 * 100 = 11 % approximately answer is a"
Answer: a
Python program:
a = 90 / 90
b = a * 100
Problem: a bag contains 5 green balls and 9 white balls . if two balls are drawn simultaneously , what is the probability that both balls are the same colour ?
Options: a ) 11 / 21 , b ) 17 / 42 , c ) 23 / 42 , d ) 46 / 91 , e ) 51 / 91
Rationale: "the total number of ways to draw two balls is 14 c 2 = 91 the number of ways to draw two green balls is 5 c 2 = 10 the number of ways to draw two white balls is 9 c 2 = 36 p ( two balls of the same colour ) = 46 / 91 the answer is d ."
Answer: d
Python program:
a = 5 + 9 
b = 9 / a
c = 9 - 1
d = 5 + 9 
e = d - 1
f = c / e
g = b * f
h = 5 - 1
i = 5 + 9 
j = i - 1
k = h / j
l = 5 + 9 
m = 5 / l
n = k * m
o = g + n
Problem: a no . when divided by 223 gives a remainder 43 , what remainder will beobtained by dividingthe same no . 17 ?
Options: a ) 2 , b ) 7 , c ) 9 , d ) 11 , e ) 15
Rationale: "223 + 43 = 266 / 17 = 11 ( remainder ) d"
Answer: d
Python program:
a = 223 + 43 
b = a / 17
Problem: find the 25 % of rs . 400 .
Options: a ) s . 50 , b ) s . 70 , c ) s . 100 , d ) s . 80 , e ) s . 60
Rationale: "explanation : 25 % of 400 = > 25 / 100 * 400 = rs . 100 answer : c"
Answer: c
Python program:
a = 25 / 100
b = 400 * a
Problem: a shop owner sells 40 mtr of cloth and gains sp of 10 mtrs . find the gain % ?
Options: a ) 33.33 % , b ) 40 % , c ) 50 % , d ) 66.67 % , e ) 70 %
Rationale: "here , selling price of 10 m cloth is obtained as profit . profit of 10 m cloth = ( s . p . of 40 m cloth ) – ( c . p . of 40 m cloth ) selling price of 30 m cloth = selling price of 40 m of cloth let cost of each metre be rs . 100 . therefore , cost price of 30 m cloth = rs . 3000 and s . p . of 30 m cloth = rs . rs . 4000 profit % = 10 / 30 × 100 = 33.33 % profit of 33.33 % was made by the merchant . a"
Answer: a
Python program:
a = 40 - 10
b = 10 / a
c = b * 100
Problem: ajay spends 50 % of his monthly income on household items , 25 % of his monthly income on buying cloths , 15 % of his monthly income on medicines and saves the remaining amount which is rs . 9000 . find his monthly income .
Options: a ) rs . 90000 , b ) rs . 36000 , c ) rs . 50000 , d ) rs . 45000 , e ) none of these
Rationale: savings 10 % - 9000 expenditure 90 % - 81000 total - 90000 answer : a
Answer: a
Python program:
a = 50 + 25 
b = a + 15 
c = 100 - b
d = c / 100
e = 9000 / d
Problem: the measurement of a rectangular box with lid is 50 cmx 30 cmx 38 cm . find the volume of the largest sphere that can be inscribed in the box ( in terms of π cm 3 ) . ( hint : the lowest measure of rectangular box represents the diameter of the largest sphere )
Options: a ) 288 , b ) 4500 , c ) 7200 , d ) 864 , e ) 9640
Rationale: "d = 30 , r = 15 ; volume of the largest sphere = 4 / 3 π r 3 = 4 / 3 * π * 15 * 15 * 15 = 4500 π cm 3 answer : b"
Answer: b
Python program:
a = 4 / 3
b = 3 ** 3
c = a * b
Problem: if an article is sold at 12 % profit instead of 16 % profit , then the profit would be rs . 105 less . what is the cost price ?
Options: a ) rs . 3000 , b ) rs . 4000 , c ) rs . 3500 , d ) rs . 4500 , e ) rs . 6000
Rationale: "explanation : let the cost price of an article be rs . x . ( 16 % of x ) - ( 12 % of x ) = 105 16 x / 100 - 12 x / 100 = 105 = > 4 x = 160 * 100 = > x = 1500 cost price = rs . 4000 answer : b"
Answer: b
Python program:
a = 105 / 16
b = a * 100
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 16 times as heavy as water ?
Options: a ) 1 : 2 , b ) 7 : 3 , c ) 4 : 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 * 16 w 19 + 9 x = 16 ( x + 1 ) x = 3 / 7 ratio of gold with copper = 1 : 3 / 7 = 7 : 3 answer is b"
Answer: b
Python program:
a = 16 - 9
b = 19 - 16
c = a / b
Problem: a question paper has 2 parts , a & b , each containing 7 questions . if a student has to choose 5 from part a & 4 from part b , in how many ways can he choose the questions ?
Options: a ) 1100 , b ) 1200 , c ) 1235 , d ) 1354 , e ) 735
Rationale: "there 7 questions in part a out of which 5 question can be chosen as = 7 c 5 . similarly , 4 questions can be chosen from 7 questions of part b as = 7 c 4 . hence , total number of ways , = 7 c 5 * 7 c 4 = [ 7 ! / ( 2 ! 5 ! ) ] * [ 7 ! / ( 3 ! * 4 ! ) ] = { 21 } * { 7 * 6 * 5 * 4 / ( 4 * 3 * 2 * 1 ) } = 735 . e"
Answer: e
Python program:
a = math.comb(7, 5)
b = math.comb(7, 4)
c = a * b
d = c / 7
Problem: a man has some hens and cows . if the number of heads be 60 and the number of feet equals 200 , then the number of hens will be :
Options: a ) 22 , b ) 25 , c ) 24 , d ) 20 , e ) 28
Rationale: "explanation : let the number of hens be x and the number of cows be y . then , x + y = 60 . . . . ( i ) and 2 x + 4 y = 200 x + 2 y = 100 . . . . ( ii ) solving ( i ) and ( ii ) we get : x = 20 , y = 40 . the required answer = 20 . answer : d"
Answer: d
Python program:
a = 60 * 4
b = a - 200
c = b / 2
Problem: what is the difference between 62 % of 150 nd 20 % of 250 .
Options: a ) 16 , b ) 17 , c ) 43 , d ) 19 , e ) 20
Rationale: ( 62 / 100 ) * 150 â € “ ( 20 / 100 ) * 250 93 - 50 = 43 answer : c
Answer: c
Python program:
a = 62 * 150
b = a / 100
c = 20 * 250
d = c / 100
e = b - d
Problem: of the total amount that jill spent on a shopping trip , excluding taxes , she spent 50 percent on clothing , 25 percent on food , and 25 percent on other items . if jill paid a 10 percent tax on the clothing , no tax on the food , and an 20 percent tax on all other items , then the total tax that she paid was what percent of the total amount that she spent , excluding taxes ?
Options: a ) 5 , b ) 10 , c ) 15 , d ) 20 , e ) 25
Rationale: "assume she has $ 200 to spend . tax clothing = 50 % = $ 100 = $ 10.00 food = 25 % = $ 50 = $ 0.00 items = 25 % = $ 50 = $ 10.00 total tax = $ 20.00 % of total amount = 20 / 200 * 100 = 10 % answer b"
Answer: b
Python program:
a = 10 / 100
b = 50 * a
c = 20 / 100
d = 25 * c
e = b + d 
f = e / 100
g = f * 100
Problem: if a 2 - b 2 = 11 and a * b = 5 , find a 4 + b 4 .
Options: a ) 62 , b ) 181 , c ) 170 , d ) 171 , e ) 50
Rationale: "a 2 - b 2 = 11 : given a 4 + b 4 - 2 a 2 b 2 = 112 : square both sides and expand . a * b = 2 : given a 2 b 2 = 52 : square both sides . a 4 + b 4 - 2 ( 25 ) = 121 : substitute a 4 + b 4 = 171 correct answer d"
Answer: d
Python program:
a = 11 ** 2
b = 5 ** 2
c = b * 2
d = a + c
Problem: on july 1 of last year , total employees at company e was decreased by 10 percent . without any change in the salaries of the remaining employees , the average ( arithmetic mean ) employee salary was 10 percent more after the decrease in the number of employees than before the decrease . the total of the combined salaries of all the employees at company e after july 1 last year was what percent of that before july 1 last year ?
Options: a ) 90 % , b ) 99 % , c ) 100 % , d ) 101 % , e ) 110 %
Rationale: "let the number of employees before jul 1 be 100 then av sal 1 = total 1 / 100 after jul 1 employees = 90 av sal 2 = total 2 / 90 now from the question av 2 = av 1 + 10 % total 2 / 90 = total 1 / 100 + 1 / 10 * total 1 / 100 total 2 / 90 = 11 total 1 / 1000 total 2 = 99 total 1 / 100 now percent = total 2 / total 1 * 100 = 99 total 1 / total 1 = 99 answer : b"
Answer: b
Python program:
a = 10 * 10
Problem: if q and d are both integers , q > d , and - 3 q > 19 , then the largest value of d would be ?
Options: a ) - 5 , b ) - 6 , c ) - 7 , d ) - 8 , e ) - 10
Rationale: no , your thinking is incorrect . when we know that q > d and q < - 6.33 , the largest value of q can be - 7 while if q = - 7 , then largest value of d < - 7 will be - 8 . for negative numbers , - 7 > - 8 and - 8 > - 10 . you are right in saying that d can take any value less than - 7 - - - > d could be - 8 , - 9 , - 10 . . . . and out of all these values , - 8 is the greatest . look at the numbers on the number line . for any 2 numbers , the ones on the right are greater than the ones on the left : . . . . . . . - 11 - 10 - 9 - 8 - 7 - 6 - 5 . . . . . 0 1 2 3 4 5 6 . . . ( - 11 < - 10 , - 10 < - 8 , 4 < 5 etc ) . so , as per the question if d < q and q = - 7 , then d ' s largest ' possible ' value has to be - 8 . - 10 is smaller than - 8 = d
Answer: d
Python program:
a = 19 / negate
b = math.floor(a)
Problem: a small company reduced its faculty by approximately 15 percent to 195 employees . what was the original number of employees ?
Options: a ) a ) 182 , b ) b ) 208 , c ) c ) 220 , d ) d ) 229 , e ) e ) 302
Rationale: "if x is the original number of employees , then after 15 % reduction in employees number is . 85 x but we are given . 85 x = 195 x = 229 so the original number of employees is 229 correct answer - d"
Answer: d
Python program:
a = 100 - 15
b = a / 100
c = 195 / b
Problem: a man is 30 years older than his son . in three years , his age will be twice the age of his son . the present age of his son is :
Options: a ) 20 , b ) 21 , c ) 27 , d ) 23 , e ) 24
Rationale: "let the son ' s present age be x years . then , man ' s present age = ( x + 30 ) years . ( x + 30 ) + 3 = 2 ( x + 3 ) x + 33 = 2 x + 6 x = 27 . answer : c"
Answer: c
Python program:
a = 2 * 2
b = a - 2
c = 30 - b
d = 2 - 1
e = c / d
Problem: henry earns $ 120 a week from his job . his income increased and now makes $ 180 a week . what is the percent increase ?
Options: a ) 70 % , b ) 60 % , c ) 50 % , d ) 40 % , e ) 30 %
Rationale: increase = ( 60 / 120 ) * 100 = ( 1 / 2 ) * 100 = 50 % . c
Answer: c
Python program:
a = 180 - 120
b = a / 120
c = b * 100