euclaise/mathqa_programs huggingface dataset:
Problem: share rs . 4800 among john , jose & binoy in the ration 2 : 4 : 6 . find the amount received by john ?
Options: a ) 900 , b ) 980 , c ) 1600 , d ) 1240 , e ) 1400
Rationale: amount received by sanjay . 4 / 12 x 4800 = 1600 = ( related ratio / sum of ratio ) x total amount so , the amount received by sanjay is 1600 . c
Answer: c
Python program:
a = 4800 / 2
b = 4800 / 6
c = a - b
Problem: the total circumference of two circles is 25 . if the first circle has a circumference that is exactly twice the circumference of the second circle , then what is the approximate sum of their two radii ?
Options: a ) 5.7 , b ) 6.0 , c ) 4.0 , d ) 9.7 , e ) 18.0
Rationale: "let r = radius of smaller circle . let r = radius of larger circle therefore : 2 π r + 2 π r = 25 where 2 r = r thus : 2 π r + 4 π r = 25 6 π r = 25 r = approx 1.33 π r + 2 r π = 25 3 π r = 25 r = approx 2.65 r + r = approx 3.98 = 4.0 answer : c"
Answer: c
Python program:
a = 25 / 3
b = a / 3
c = 25 / 3
d = c * 2
e = d / 3
f = b + e 
g = f / 2
Problem: the length of a train and that of a platform are equal . if with a speed of 144 k / hr , the train crosses the platform in one minute , then the length of the train ( in meters ) is ?
Options: a ) 757 , b ) 758 , c ) 718 , d ) 1200 , e ) 738
Rationale: "speed = [ 144 * 5 / 18 ] m / sec = 40 m / sec ; time = 1 min . = 60 sec . let the length of the train and that of the platform be x meters . then , 2 x / 60 = 40 è x = 40 * 60 / 2 = 1200 answer : d"
Answer: d
Python program:
a = 144 * 1000
b = const_60 / 1
c = a / b
d = c / 2
Problem: the cost of 10 kg of mangos is equal to the cost of 24 kg of rice . the cost of 6 kg of flour equals the cost of 2 kg of rice . the cost of each kg of flour is $ 20.50 . find the total cost of 4 kg of mangos , 3 kg of rice and 5 kg of flour ?
Options: a ) 347.4 , b ) 987.4 , c ) 877.4 , d ) 637.4 , e ) 667.4
Rationale: "c $ 877.40 let the costs of each kg of mangos and each kg of rice be $ a and $ r respectively . 10 a = 24 r and 6 * 20.50 = 2 r a = 12 / 5 r and r = 61.5 a = 147.6 required total cost = 4 * 147.6 + 3 * 61.5 + 5 * 20.5 = 590.4 + 184.5 + 102.5 = $ 877.40"
Answer: c
Python program:
a = 24 / 10
b = 20 * 50
c = b / 2
d = a * c
e = 4 * d
f = 20 * 50
g = f / 2
h = 3 * g
i = e + h 
j = 5 * 20
k = i + j
Problem: a is 1.5 times as fast as b . a alone can do the work in 30 days . if a and b working together in how many days will the work be completed ?
Options: a ) 23 , b ) 18 , c ) 21 , d ) 24 , e ) 25
Rationale: "a can finish 1 work in 30 days b can finish 1 / 1.5 work in 30 days - since a is 1.5 faster than b this means b can finish 1 work in 30 * 1.5 days = 45 days now using the awesome gmat formula when two machines work together they can finish the job in = ab / ( a + b ) = 45 * 30 / ( 45 + 30 ) = 20 * 30 / 50 = 18 days so answer is b"
Answer: b
Python program:
a = 1 / 30
b = 1 / 30
c = b / 1
d = a + c 
e = 1 / d
Problem: if the numbers 1 to 95 are written on 95 pieces of paper , ( one on each ) and one piece is picked at random , then what is the probability that the number drawn is neither prime nor composite ?
Options: a ) 1 / 50 , b ) 1 / 25 , c ) 1 / 95 , d ) 1 , e ) 2
Rationale: "there are 25 primes , 69 composite numbers from 1 to 95 . the number which is neither prime nor composite is 1 . therefore , required probability = 1 / 95 . answer : c"
Answer: c
Python program:
a = 1 / 95
Problem: a train running at 1 / 6 of its own speed reached a place in 24 hours . how much time could be saved if the train would have run at its own speed ?
Options: a ) 8 hrs , b ) 20 hrs , c ) 12 hrs , d ) 15 hrs , e ) 6 hrs
Rationale: "time taken if run its own speed = 1 / 6 * 24 = 4 hrs time saved = 24 - 4 = 20 hrs answer : b"
Answer: b
Python program:
a = 1 / 6
b = a * 24
Problem: a watch was sold at a loss of 10 % . if it was sold for rs . 168 more , there would have been a gain of 4 % . what is the cost price ?
Options: a ) s : 1000 , b ) s : 1067 , c ) s : 1200 , d ) s : 1028 , e ) s : 1027
Rationale: "90 % 104 % - - - - - - - - 14 % - - - - 168 100 % - - - - ? = > rs : 1200 answer : c"
Answer: c
Python program:
a = 168 * 100
b = 100 + 4 
c = 100 - 10
d = b - c
e = a / d
Problem: a pump can fill a tank with a water in 2 hours . because of a leak , it took 3 hours to fill the tank . the leak can drain all the water of the full tank in how many hours ?
Options: a ) 2 , b ) 3 , c ) 4 , d ) 5 , e ) 6
Rationale: the rate of the pump + leak = 1 / 3 1 / 2 - leak ' s rate = 1 / 3 leak ' s rate = 1 / 2 - 1 / 3 = 1 / 6 the leak will empty the tank in 6 hours . the answer is e .
Answer: e
Python program:
a = 1 / 2
b = 1 / 3
c = a - b
d = 1 / c
Problem: if each edge of a cube is doubled , then its volume :
Options: a ) becomes 8 times
b ) becomes 9 times
c ) is double
d ) becomes 6 times
e ) none
Rationale: sol . let original edge = a . then , volume = a ³ new edge = 2 a . so , new volume = ( 2 a ) ³ = 8 a ³ ∴ volume becomes 8 times answer a
Answer: a
Python program:
a = 2 ** 3
Problem: a started a business with an investment of rs . 70000 and after 6 months b joined him investing rs . 120000 . if the profit at the end of a year is rs . 52000 , then the share of a is ?
Options: a ) s . 28028 , b ) s . 28000 , c ) s . 28003 , d ) s . 28029 , e ) s . 24029
Rationale: "ratio of investments of a and b is ( 70000 * 12 ) : ( 120000 * 6 ) = 7 : 6 total profit = rs . 52000 share of b = 7 / 13 ( 52000 ) = rs . 28000 answer : b"
Answer: b
Python program:
a = const_60 * 100
b = 52000 - a
Problem: on a trip , a cyclist averaged 9 miles per hour for the first 18 miles and 10 miles per hour for the remaining 12 miles . if the cyclist returned immediately via the same route and took a total of 7.2 hours for the round trip , what was the average speed ( in miles per hour ) for the return trip ?
Options: a ) 6.9 , b ) 7.2 , c ) 7.5 , d ) 7.8 , e ) 8.1
Rationale: "the time to go 30 miles was 18 / 9 + 12 / 10 = 2 + 1.2 = 3.2 hours . the average speed for the return trip was 30 miles / 4 hours = 7.5 mph . the answer is c ."
Answer: c
Python program:
a = 18 + 12 
b = 18 / 9
c = 12 / 10
d = b + c 
e = 7 - 2
f = a / e
Problem: in town p , 60 percent of the population are employed , and 42 percent of the population are employed males . what percent of the employed people in town p are females ?
Options: a ) 20 % , b ) 25 % , c ) 30 % , d ) 35 % , e ) 40 %
Rationale: "the percent of the population who are employed females is 60 - 42 = 18 % the percent of employed people who are female is 18 % / 60 % = 30 % . the answer is c ."
Answer: c
Python program:
a = 60 - 42
b = a / 60
c = b * 100
Problem: an integer n between 1 and 100 , inclusive , is to be chosen at random . what is the probability that n ( n + 1 ) will be divisible by 5 ?
Options: a ) 1 / 9 , b ) 1 / 3 , c ) 1 / 2 , d ) 2 / 3 , e ) 2 / 5
Rationale: "n ( n + 1 ) to be divisible by 3 either n or n + 1 must be a multiples of 3 . in each following group of numbers : { 1 , 2 , 3 , 4 , 5 } , { 6 , 7 , 8 , 9 , 10 } , . . . , { 96 , 97 , 98 , 99,100 } there is exactly 1 numbers out of 5 satisfying the above condition . for example in { 1 , 2 , 3 , 4 , 5 } n can be : 4 or 5 . thus , the overall probability is 2 / 5 . answer : d ."
Answer: e
Python program:
a = 100 / 5
b = a / 100
c = b * 2
Problem: when positive integer n is divided by 5 , the remainder is 1 . when n is divided by 7 , the remainder is 3 . what is the smallest positive integer k such that k + n is a multiple of 38 ?
Options: a ) 3 , b ) 4 , c ) 7 , d ) 32 , e ) 35
Rationale: "n = 5 p + 1 = 6,11 , 16,21 , 26,31 n = 7 q + 3 = 3 , 10,17 , 24,31 = > n = 38 m + 31 to get this , we need to take lcm of co - efficients of p and q and first common number in series . so we need to add 7 more to make it 38 m + 38 answer - c"
Answer: c
Python program:
a = 38 - reminder
Problem: jane started baby - sitting when she was 18 years old . whenever she baby - sat for a child , that child was no more than half her age at the time . jane is currently 34 years old , and she stopped baby - sitting 12 years ago . what is the current age of the oldest person for whom jane could have baby - sat ?
Options: a ) 20 , b ) 21 , c ) 22 , d ) 23 , e ) 25
Rationale: "check two extreme cases : jane = 18 , child = 9 , years ago = 34 - 18 = 16 - - > child ' s age now = 9 + 16 = 25 ; jane = 22 , child = 11 , years ago = 34 - 22 = 12 - - > child ' s age now = 11 + 12 = 23 . answer : e ."
Answer: e
Python program:
a = 18 / 2
b = 34 - 18
c = a + b
Problem: each of the integers from 0 to 9 , inclusive , is written on a separate slip of blank paper and the ten slips are dropped into a hat . if 5 of the slips are the drawn , without replacement , what is the probability that all 5 have a odd number written on it ?
Options: a ) 1 / 12 , b ) 1 / 10 , c ) 1 / 8 , d ) 1 / 24 , e ) 5 / 9
Rationale: "key is that there is no replacement , so each successive choice will become more skewed towards picking a neg ( i . e . the pool of positives decreases , while the pool of negatives stay the same ) p ( + on 1 st pick ) = 5 / 10 p ( + on 2 nd pick ) = 4 / 9 p ( + on 3 rd pick ) = 3 / 8 p ( + on 4 rd pick ) = 2 / 7 p ( + on 5 rd pick ) = 1 / 6 5 / 10 * 4 / 9 * 3 / 8 * 2 / 7 * 1 / 6 = 1 / 252 a"
Answer: a
Python program:
a = 5 + 1 
b = 9 + 1 
c = a / b
d = 5 + 1 
e = d - 1
f = 9 + 1 
g = f - 1
h = e / g
i = c * h
j = 5 + 1 
k = j - 1
l = k - 1
m = 9 + 1 
n = m - 1
o = n - 1
p = l / o
q = i * p
r = 5 + 1 
s = r - 1
t = s - 1
u = t - 1
v = 9 + 1 
w = v - 1
x = w - 1
y = x - 1
z = u / y
A = q * z
Problem: of the total amount that jill spent on a shopping trip , excluding taxes , she spent 50 percent on clothing , 20 percent on food , and 30 percent on other items . if jill paid a 4 percent tax on the clothing , no tax on the food , and an 10 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 ) 2.8 % , b ) 3.6 % , c ) 4.4 % , d ) 5 % , e ) 6.0 %
Rationale: let amount spent by jill = 100 clothing = 50 , food = 20 , others = 30 tax on clothing = 2 tax on others = 3 percentage = 5 / 100 = 5 % answer : d
Answer: d
Python program:
a = 4 / 100
b = 50 * a
c = 10 / 100
d = 30 * c
e = b + d 
f = e / 100
g = f * 100
Problem: jeff has 252 ounces of peanut butter in 16 , 28 . and 40 ounce jars . he has an equal number of each sized jar . how many jars of peanut butter does jeff have ?
Options: a ) 9 , b ) 8 , c ) 7 , d ) 10 , e ) 11
Rationale: let p equal the number of each sized jar then 16 p + 28 p + 40 p = 252 84 p = 252 p = 3 therefore , the total number of jars of peanut butter jeff has = 3 p = 9 answer : a
Answer: a
Python program:
a = 16 + 28 
b = a + 40 
c = 252 / b
d = c * 3
Problem: if 20 men can build a wall 66 metres long in 12 days , what length of a similar can be built by 86 men in 8 days ?
Options: a ) 189.2 mtrs , b ) 378.4 mtrs , c ) 478.4 mtrs , d ) 488.4 mtrs , e ) 578.4 mtrs
Rationale: "if 20 men can build a wall 66 metres long in 12 days , length of a similar wall that can be built by 86 men in 8 days = ( 66 * 86 * 8 ) / ( 12 * 20 ) = 189.2 mtrs answer : a"
Answer: a
Python program:
a = 86 * 8
b = 20 * 12
c = a / b
d = 66 * c
Problem: carmen made a sculpture from small pieces of wood . the sculpture is 2 feet 10 inches tall . carmen places her sculpture on a base that is 4 inches tall . how tall are the sculpture andbase together ?
Options: a ) 3.17 feet
b ) 3.2 feet
c ) 3.3 feet
d ) 3.4 feet
e ) 3.5 feet
Rationale: we know 1 feet = 12 inch then 2 feet = 24 inch 24 + 10 = 34 then 34 + 4 = 38 38 / 12 = 3.17 feet answer : a
Answer: a
Python program:
a = 2 + 10 
b = a * 2
c = b + 10 
d = c + 4 
e = 2 + 10 
f = d / e
Problem: the average of 6 no . ' s is 2.5 . the average of 2 of them is 1.1 , while the average of the other 2 is 1.4 . what is the average of the remaining 2 no ' s ?
Options: a ) 2.3 , b ) 2.6 , c ) 3.6 , d ) 4.5 , e ) 5
Rationale: "sum of the remaining two numbers = ( 2.5 * 6 ) - [ ( 1.1 * 2 ) + ( 1.4 * 2 ) ] = 15 - ( 2.2 + 2.8 ) = 15 - 5 = 10 required average = ( 10 / 2 ) = 5 answer : e"
Answer: e
Python program:
a = 6 * 2
b = 2 * 1
c = 2 * 1
d = b + c 
e = a - d
f = e / 2
Problem: the sum of the first 92 positive even integers is 2,550 . what is the sum of the odd integers from 101 to 200 , inclusive ?
Options: a ) 5,050 , b ) 7,500 , c ) 10,500 , d ) 11,700 , e ) 19,600
Rationale: "101 + 103 + . . . . . . . 199 if we remove 100 from each of these it will be sum of 1 st 100 odd numbers . so 101 + 103 + . . . . . . . 199 = 92 * 100 + ( 1 + 3 + 5 + 7 + . . . . . . ) sum of 1 st 100 natural numbers = ( 100 * 101 ) / 2 = 5050 sum of 1 st 92 positive even integers = 2550 sum of 1 st 100 odd numbers = 5050 - 2550 = 2500 so 101 + 103 + . . . . . . . 199 = 92 * 100 + ( 1 + 3 + 5 + 7 + . . . . . . ) = 9200 + 2500 = 11700 d is the answer ."
Answer: d
Python program:
a = 200 + 101 
b = a / 2
c = 200 - 101
d = c / 2
e = d + 1 
f = b * e
Problem: a is an integer greater than 9 but less than 21 , b is an integer greater than 19 but less than 31 , what is the range of a / b ?
Options: a ) 1 / 4 , b ) 1 / 2 , c ) 2 / 3 , d ) 1 , e ) 5 / 4
Rationale: min value of a / b will be when b is highest and a is lowest - - - > a = 10 and b = 30 so , a / b = 1 / 3 max value of a / b will be when b is lowest and a is highest - - - > a = 20 and b = 20 so , a / b = 1 range is 1 - ( 1 / 3 ) = 2 / 3 . answer should be c
Answer: c
Python program:
a = 21 - 1
b = 19 + 1 
c = a / b
d = 9 + 1 
e = 31 - 1
f = d / e
g = c - f
Problem: if 18 percent of the students at a certain school went to a camping trip and took more than $ 100 , and 75 percent of the students who went to the camping trip did not take more than $ 100 , what percentage of the students at the school went to the camping trip ?
Options: a ) 95 , b ) 90 , c ) 85 , d ) 78 , e ) 72
Rationale: "let x be the number of students in the school . 0.18 x students went to the trip and took more than 100 $ . they compose ( 100 - 75 ) = 25 % of all students who went to the trip . therefore the toal of 0.18 x / 0.25 = 0.72 x students went to the camping which is 72 % . the answer is e"
Answer: e
Python program:
a = 100 - 75
b = a / 100
c = 18 / b
Problem: a couple decides to have 2 children . if they succeed in having 2 children and each child is equally likely to be a boy or a girl , what is the probability that they will have exactly 1 girl and 1 boy ?
Options: a ) 1 / 2 , b ) 3 / 4 , c ) 1 , d ) 2 , e ) 3
Rationale: "sample space = 2 ^ 2 = 4 . favourable events = { bg } , { gb } , probability = 2 / 4 = 1 / 2 . ans ( a ) ."
Answer: a
Python program:
a = math.factorial(2)
b = math.factorial(1)
c = a / b
d = 1 / 1
e = d ** 2
f = c * e
g = 1 - f
Problem: a computer manufacturer produces a certain electronic component at a cost of $ 80 per component . shipping costs for delivering the components are $ 5 per unit . further , the manufacturer has costs of $ 16,500 a month related to the electronic component regardless of how many it produces . if the manufacturer produces and sells 150 components a month , what is the lowest price it can sell them for such that the costs do n ' t exceed the revenues ?
Options: a ) $ 28 , b ) $ 82 , c ) $ 110 , d ) $ 138 , e ) $ 195
Rationale: by the question , the equation would be 150 p - 85 * 150 - 16500 = 0 p being the price we want to find and equation resulting zero means revenue and costs are equal so we can get the minimum price of the component . solving the equation , we get p = $ 195 . answer e for me .
Answer: e
Python program:
a = 4 * 4
b = a * 1000
c = 5 * 100
d = b + c 
e = 80 + 5 
f = e * 150
g = d + f 
h = g / 150
Problem: a particular library has 75 books in a special collection , all of which were in the library at the beginning of the month . these book are occasionally loaned out through an inter - library program . if , by the end of the month , 70 percent of books that were loaned out are returned and there are 60 books in the special collection at that time , how many books of the special collection were loaned out during that month ?
Options: a ) 20 , b ) 30 , c ) 35 , d ) 40 , e ) 50
Rationale: "i did n ' t understand how did we get 100 ? total = 75 books . 65 % of books that were loaned out are returned - - > 100 % - 70 % = 30 % of books that were loaned out are not returned . now , there are 60 books , thus 76 - 60 = 16 books are not returned . { loaned out } * 0.30 = 7 - - > { loaned out } = 50 . answer : e ."
Answer: e
Python program:
a = 75 - 60
b = 70 / 100
c = 1 - b
d = a / c
Problem: a , b and c play a cricket match . the ratio of the runs scored by them in the match is a : b = 2 : 3 and b : c = 2 : 5 . if the total runs scored by all of them are 100 , the runs scored by c are ?
Options: a ) 59 , b ) 58 , c ) 60 , d ) 61 , e ) 12
Rationale: "a : b = 2 : 3 b : c = 2 : 5 a : b : c = 4 : 6 : 15 15 / 25 * 100 = 60 answer : c"
Answer: c
Python program:
a = 2 / 3
b = 5 / 2
c = a + b 
d = c + 2 
e = 100 / d
f = e * 5
Problem: the average age of an adult class is 50 years . 12 new students with an avg age of 32 years join the class . therefore decreasing the average by 4 years . find what was the original average age of the class ?
Options: a ) 10 , b ) 12 , c ) 42 , d ) 20 , e ) 22
Rationale: "let original strength = y then , 50 y + 12 x 32 = ( y + 12 ) x 46 â ‡ ’ 50 y + 384 = 46 y + 552 â ‡ ’ 4 y = 168 â ˆ ´ y = 42 c"
Answer: c
Python program:
a = 50 - 4
b = 12 * a
c = 12 * 32
d = b - c
e = d / 4
Problem: anne and katherine are both saving money from their summer jobs to buy bicycles . if anne had $ 150 less , she would have exactly 1 / 3 as much as katherine . and if katherine had twice as much , she would have exactly 3 times as much as anne . how much money have they saved together ? (
Options: a ) $ 300 , b ) $ 400 , c ) $ 450 , d ) $ 625 , e ) $ 750
Rationale: if anne had $ 150 less , katherine would have three times more than anne . make this statement into an equation and simplify : 3 ( a – 150 ) = k 3 a – 450 = k and if katherine had twice as much , she would have three times more than anne : 2 k = 3 a substitute 3 a – 450 for k into the last equation and solve for a 2 ( 3 a – 450 ) = 3 a 6 a – 900 = 3 a – 900 = – 3 a 300 = a now substitute 300 for a into the same equation and solve for k : 2 k = 3 ( 300 ) 2 k = 900 k = 450 thus , together anne and katherine have 300 + 450 = 750 correct answer e ) $ 750
Answer: e
Python program:
a = 3 * 150
b = 2 / 3
c = 3 * 150
d = b * c
e = a + d
Problem: a train crosses a platform of 120 m in 15 sec , same train crosses another platform of length 180 m in 18 sec . then find the length of the train ?
Options: a ) 145 , b ) 180 , c ) 181 , d ) 184 , e ) 150
Rationale: "length of the train be ‘ x ’ x + 120 / 15 = x + 180 / 18 6 x + 720 = 5 x + 900 x = 180 m answer : option b"
Answer: b
Python program:
a = 15 / 3
b = 15 / a
c = 180 * b
d = 15 / 3
e = 18 / d
f = 120 * e
g = c - f
Problem: a ’ s speed is 32 / 27 times that of b . if a and b run a race , what part of the length of the race should a give b as a head start , so that the race ends in a dead heat ?
Options: a ) 5 / 32 , b ) 5 / 27 , c ) 1 / 27 , d ) 1 / 32 , e ) 27 / 32
Rationale: "we have the ratio of a ’ s speed and b ’ s speed . this means , we know how much distance a covers compared with b in the same time . this is what the beginning of the race will look like : ( start ) a _________ b ______________________________ if a covers 32 meters , b covers 27 meters in that time . so if the race is 32 meters long , when a reaches the finish line , b would be 5 meters behind him . if we want the race to end in a dead heat , we want b to be at the finish line too at the same time . this means b should get a head start of 5 meters so that he doesn ’ t need to cover that . in that case , the time required by a ( to cover 32 meters ) would be the same as the time required by b ( to cover 27 meters ) to reach the finish line . so b should get a head start of 5 / 32 th of the race . answer ( a )"
Answer: a
Python program:
a = 32 - 27
b = a / 32
Problem: how many cubes of 4 cm edge can be put in a cubical box of 1 m edge .
Options: a ) 17725 cm , b ) 15625 cm , c ) 12786 cm , d ) 12617 cm , e ) 12187 cm
Rationale: "number of cubes = 100 â ˆ — 100 â ˆ — 100 / 4 * 4 * 4 = 15625 note : 1 m = 100 cm answer : b"
Answer: b
Python program:
a = volume_cube / (
Problem: how many integers between 324,700 and 375,600 have tens digit 1 and units digit 3 ?
Options: a ) 509 , b ) 624 , c ) 756 , d ) 832 , e ) 947
Rationale: "the integers are : 324,713 324,813 etc . . . 375,513 the number of integers is 3756 - 3247 = 509 the answer is a ."
Answer: a
Python program:
a = 2 * 100
b = 3 + 4 
c = b * 10
d = a + c 
e = d + 2 
f = 375 - 600
Problem: if the space diagonal of cube c is 5 inches long , what is the length , in inches , of the diagonal of the base of cube c ?
Options: a ) 5 / ( √ 6 )
b ) 5 · √ ( 2 / 3 )
c ) 5 · √ ( 3 / 2 )
d ) 5 · √ 3
e ) 5 · √ 6
Rationale: n cube c , let ' s say that each side has side length x so , the diagonal = √ ( x ² + x ² + x ² ) = √ ( 3 x ² ) here , we ' re told that the diagonal has length 5 , so we can write : 5 = √ ( 3 x ² ) square both sides to get : 25 = 3 x ² divide both sides by 3 to get : 25 / 3 = x ² square root both sides : √ ( 25 / 3 ) = x or . . . . ( √ 25 ) / ( √ 3 ) = x simplify : 5 / ( √ 3 ) = x answer : b
Answer: b
Python program:
a = 5 * 1
Problem: a train running at the speed of 58 km / hr crosses a pole in 9 sec . what is the length of the train ?
Options: a ) 145 m , b ) 786 m , c ) 566 m , d ) 546 m , e ) 445 m
Rationale: "speed = 58 * 5 / 18 = 145 / 9 m / sec length of the train = speed * time = 145 / 9 * 9 = 145 m answer : a"
Answer: a
Python program:
a = 58 * 1000
b = a / 3600
c = b * 9
Problem: if x and y are both odd prime numbers and x < y , how many distinct positive integer w factors does 2 xy have ?
Options: a ) 3 , b ) 4 , c ) 6 , d ) 8 , e ) 12
Rationale: since 2 xy prime w factors are x ^ 1 * y ^ 1 * 2 ^ 1 , its total number or factors must be ( 1 + 1 ) ( 1 + 1 ) ( 1 + 1 ) = 2 ^ 3 = 8 . thus , i think d would be the correct answer .
Answer: d
Python program:
a = 1 + 1 
b = 2 * a
c = 1 + 1 
d = b * c
Problem: if it takes 4 identical printing presses exactly 6 hours to print 8000 newspapers , how long would it take 2 of these presses to print 6000 newspapers ?
Options: a ) 5 hrs , b ) 7 hrs , c ) 8 hrs , d ) 9 hrs 50 mins , e ) 9 hrs
Rationale: 4 presses - 8,000 newspapers - 6 hours ; 2 presses - 4,000 newspapers - 6 hours ; ( 360 mins ) 2 presses - 6,000 newspapers - 360 / 4000 * 6000 = 540 mins = 9 hrs answer : e
Answer: e
Python program:
a = 4 / 2
b = 6000 / 8000
c = a * b
d = 6 * c
Problem: if ( t - 8 ) is a factor of t ^ 2 - kt - 43 , then k =
Options: a ) 16 , b ) 12 , c ) 2 , d ) 3 , e ) 14
Rationale: "t ^ 2 - kt - 48 = ( t - 8 ) ( t + m ) where m is any positive integer . if 48 / 8 = 6 , then we know as a matter of fact that : m = + 6 and thus k = 8 - 6 = 3 t ^ 2 - kt - m = ( t - a ) ( t + m ) where a > m t ^ 2 + kt - m = ( t - a ) ( t + m ) where a < m t ^ 2 - kt + m = ( t - a ) ( t - m ) t ^ 2 + kt + m = ( t + a ) ( t + m ) d"
Answer: d
Python program:
a = 10 + 2
Problem: a batsman in his 12 th innings makes a score of 55 and thereby increases his average by 1 runs . what is his average after the 12 th innings if he had never been ‘ not out ’ ?
Options: a ) 42 , b ) 43 , c ) 44 , d ) 45 , e ) 46
Rationale: "let ‘ x ’ be the average score after 12 th innings ⇒ 12 x = 11 × ( x – 1 ) + 55 ∴ x = 44 answer c"
Answer: c
Python program:
a = 12 * 1
b = 55 - a
c = b + 1
Problem: find large number from below question the difference of two numbers is 2415 . on dividing the larger number by the smaller , we get 21 as quotient and the 15 as remainder
Options: a ) 1209 , b ) 1324 , c ) 1245 , d ) 1300 , e ) 2535
Rationale: "let the smaller number be x . then larger number = ( x + 2415 ) . x + 2415 = 21 x + 15 20 x = 2400 x = 120 large number = 120 + 2415 = 2535 answer : e"
Answer: e
Python program:
a = 2415 - 15
b = 21 - 1
c = a / b
d = c * 21