euclaise/mathqa_programs huggingface dataset:
Problem: p , q , r enter into a partnership & their share are in the ratio 1 / 2 : 1 / 3 : 1 / 4 , after two months , p withdraws half of the capitals & after 10 months , a profit of rs 378 is divided among them . what is r ' s share ?
Options: a ) 108 , b ) 120 , c ) 134 , d ) 144 , e ) none of these
Rationale: explanation : the ratio of their initial investment = 1 / 2 : 1 / 3 : 1 / 4 = 6 : 4 : 3 let ' s take the initial investment of p , q and r as 6 x , 4 x and 3 x respectively a : b : c = ( 6 x * 2 + 3 x * 10 ) : 4 x * 12 : 3 x * 12 = ( 12 + 30 ) : 4 * 12 : 3 * 12 = ( 4 + 10 ) : 4 * 4 : 12 = 14 : 16 : 12 = 7 : 8 : 6 r ' s share = 378 * ( 6 / 21 ) = 108 . answer : option a
Answer: a
Python program:
a = 3 * 2
b = 378 * a
c = 4 + 3 
d = c * 3
e = b / d
Problem: light glows for every 18 seconds . how many times did it between 1 : 57 : 58 and 3 : 20 : 47 am
Options: a ) 281 , b ) 277 , c ) 283 , d ) 384 , e ) 385
Rationale: "the diff in sec between 1 : 57 : 58 and 3 : 20 : 47 is 4969 sec , 4969 / 18 = 276 . so total 277 times light ll glow answer : b"
Answer: b
Python program:
a = 2 + 47 
b = 2 + const_60 
c = 20 + b 
d = c * const_60
e = a + d 
f = e / 18
Problem: find the smallest number which leaves 2235 , 48 and 61 as remainders when divided by 26 , 39 , 52 and 65 respectively .
Options: a ) 67 , b ) 26 , c ) 99 , d ) 26 , e ) 91
Rationale: answer : d
Answer: d
Python program:
a = 48 / 2
b = a + 2
Problem: if k ^ 3 is divisible by 168 , what is the least possible value of integer k ?
Options: a ) 36 , b ) 42 , c ) 48 , d ) 54 , e ) 60
Rationale: k ^ 3 = 168 * x = 2 ^ 3 * 3 * 7 * x the factors of k must at minimum include 2 * 3 * 7 = 42 . the answer is b .
Answer: b
Python program:
a = 168 / 2
b = a / 2
Problem: a and b can do a work in 20 days , b and c in 25 days , c and a in 30 days . if a , b and c work together , they will complete the work in ?
Options: a ) 10 days , b ) 12 days , c ) 16 days , d ) 20 days , e ) 25 days
Rationale: "a + b 1 day work = 1 / 20 b + c 1 day work = 1 / 25 c + a 1 day work = 1 / 30 adding we get 2 ( a + b + c ) = 1 / 20 + 1 / 25 + 1 / 30 = 37 / 300 a + b + c 1 day work = 37 / 600 a , b , c can finish the work in 600 / 37 days = 16 days approximately answer is c"
Answer: c
Python program:
a = 1/(20)
b = 1/(25)
c = a + b 
d = 1/(30)
e = c + d 
f = e / 2
g = 1 / f
Problem: in what time will a train 100 m long cross an electric pole , it its speed be 136 km / hr ?
Options: a ) 2.6 sec , b ) 1.9 sec , c ) 8.9 sec , d ) 6.9 sec , e ) 2.9 sec
Rationale: "speed = 136 * 5 / 18 = 37.8 m / sec time taken = 100 / 37.8 = 2.6 sec . answer : a"
Answer: a
Python program:
a = 136 * const_0_2778
b = 100 / a
Problem: 5220 / ? * 15 = 2175
Options: a ) 34 , b ) 36 , c ) 33 , d ) 42 , e ) 24
Rationale: "b ( 5220 / ? ) * 15 = 2175 ? = ( 5220 * 15 ) / 2175 = > ? = 36"
Answer: b
Python program:
a = 5220 / 15
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 126 ° of the circle , what percentage of megatek employees are in manufacturing ?
Options: a ) 20 % , b ) 25 % , c ) 30 % , d ) 35 % , e ) 70 %
Rationale: answer : d 126 ° divided by 360 ° equals 0.35 , therefore the sector is equal to 35 % of the total
Answer: d
Python program:
a = 3600 / 10
b = 126 / a
c = b * 100
Problem: if n is the smallest integer such that 864 times n is the square of an integer , what is the value of n ?
Options: a ) 2 , b ) 3 , c ) 6 , d ) 12 , e ) 24
Rationale: "865 can written as = 2 * 2 * 2 * 2 * 2 * 3 * 3 * 3 - - > 2 ^ 5 * 3 ^ 3 - - - ( 1 ) so for 864 * n to be a square of an integer , the integer should have even powers to the prime numbers it composed of . here 2 already has even power - > so n has to be 3 to make the power of 3 in ( 1 ) even option b is correct"
Answer: b
Python program:
a = 864 / 2
b = a / 2
c = b / 2
d = c / 2
e = d / 3
f = e / 3
Problem: tim came second in math . when his mother asked him how much he had scored , he answered that he got the sum of the first 5 even numbers . his mother immediately worked out the answer . how much had he scored in math ?
Options: a ) 80 , b ) 30 , c ) 40 , d ) 70 , e ) 60
Rationale: "b 30 sum = ( n x n ) + n hence , 5 x 5 = 25 + 5 = 30"
Answer: b
Python program:
a = 5 + 1 
b = a * 5
Problem: what is the sum of all digits for the number 10 ^ 25 - 58 ?
Options: a ) 197 , b ) 201 , c ) 205 , d ) 209 , e ) 213
Rationale: "10 ^ 25 is a 26 - digit number : 1 followed by 25 zeros . 10 ^ 25 - 58 is a 25 - digit number : 23 9 ' s and 42 at the end . the sum of the digits is 23 * 9 + 4 + 2 = 213 . the answer is e ."
Answer: e
Python program:
a = 25 - 10
b = a - 2
c = b / 2
d = c + 10 
e = 25 - 10
f = e + 2 
g = f / 2
h = d * g
Problem: bag a contains red , white and blue marbles such that the red to white marble ratio is 1 : 3 and the white to blue marble ratio is 2 : 3 . bag b contains red and white marbles in the ratio of 1 : 4 . together , the two bags contain 24 white marbles . how many red marbles could be in bag a ?
Options: a ) 1 , b ) 3 , c ) 4 , d ) 6 , e ) 8
Rationale: "6 is the answer . bag a - r : w : b = 2 : 6 : 9 let w in bag a be 6 k bab b - r : w = 1 : 4 let w in bag b be 4 p w = 24 = 6 k + 4 p = > k = 2 , p = 3 total red ' s in bag a will be 2 k = 4 c"
Answer: c
Python program:
a = 3 * 2
b = a + 4 
c = 24 / b
Problem: a can do a piece of work in 40 days ; b can do the same in 30 days . a started alone but left the work after 10 days , then b worked at it for 10 days . c finished the remaining work in 10 days . c alone can do the whole work in ?
Options: a ) 24 days , b ) 65 days , c ) 86 days , d ) 45 days , e ) 17 days
Rationale: "10 / 40 + 10 / 30 + 10 / x = 1 x = 24 days answer : a"
Answer: a
Python program:
a = 10 + 10 
b = a / 40
c = 1 - b
d = 10 / c
Problem: what least value should be replaced by * in 2631 * 4 so the number become divisible by 3
Options: a ) 3 , b ) 4 , c ) 5 , d ) 2 , e ) 7
Rationale: "explanation : trick : number is divisible by 3 , if sum of all digits is divisible by 3 , so ( 2 + 6 + 3 + 1 + * + 4 ) = 16 + * should be divisible by 9 , 16 + 2 will be divisible by 2 , so that least number is 2 . answer : option d"
Answer: d
Python program:
a = 4 - 4
b = 4 - a
Problem: the ratio of money with ram and gopal is 7 : 17 and that with gopal and krishan is 7 : 17 . if ram has rs . 735 , krishan has ?
Options: a ) s . 4335 , b ) s . 2330 , c ) s . 1190 , d ) s . 1620 , e ) s . 2680
Rationale: ram : gopal = 7 : 17 = 49 : 119 gopal : krishan = 7 : 17 = 119 : 289 ram : gopal : krishan = 49 : 119 : 289 ram : krishan = 49 : 289 thus , 49 : 289 = 735 : n & there n = 289 x 735 / 49 = rs . 4335 answer : a
Answer: a
Python program:
a = 735 / 7
b = a * 17
c = b / 7
d = c * 17
Problem: a train 146 m long is running at a speed of 98 kmph . how long does it take to pass a man who is running at 12 kmph in the same direction as the train ?
Options: a ) 6 sec , b ) 9 sec , c ) 12 sec , d ) 18 sec , e ) 15 sec
Rationale: "answer : a . speed of the train relative to man = ( 98 - 12 ) kmph = ( 86 * 5 / 18 ) m / sec = ( 215 / 9 ) m / sec time taken by the train to cross the man = time taken by it to cover 146 m at 219 / 9 m / sec = 146 * 9 / 219 sec = 6 sec"
Answer: a
Python program:
a = 98 - 12
b = a * const_0_2778
c = 146 / b
Problem: nails and screws are manufactured at a uniform weight per nail and a uniform weight per screw . if the total weight of one screw and one nail is half that of 6 screws and one nail , then the total weight of 3 screws , and 3 nails is how many times that of 5 screws and 1 nails ?
Options: a ) a . 4 , b ) b . 5 / 2 , c ) c . 2 , d ) d . 3 / 2 , e ) e . 5 / 4
Rationale: let the weight of nail be n and that of screw be s . . so s + w = 1 / 2 * ( 6 s + 1 n ) . . . or 1 n = 4 s . . lets see the weight of 3 s and 3 n = 3 s + 3 * 4 s = 15 s . . and weight of 5 s and 1 n = 5 s + 1 * 5 s = 10 s . . ratio = 15 s / 10 s = 15 / 10 = 3 / 2 d
Answer: d
Python program:
a = 3 * 4
b = a + 3 
c = b / 10
Problem: a bottle contains a certain solution . in the bottled solution , the ratio of water to soap is 3 : 5 , and the ratio of soap to salt is four times this ratio . the solution is poured into an open container , and after some time , the ratio of water to soap in the open container is quartered by water evaporation . at that time , what is the ratio of water to salt in the solution ?
Options: a ) 9 : 100 , b ) 100 : 9 , c ) 12 : 100 , d ) 12 : 20 , e ) 13 : 100
Rationale: "water : soap = 3 : 5 soap : salt = 12 : 20 = > for 12 soap , salt = 20 = > for 5 soap , salt = ( 20 / 12 ) * 5 = 100 / 12 = 25 / 3 so , water : soap : salt = 3 : 5 : 25 / 3 = 9 : 15 : 25 after open container , water : soap : salt = 2.25 : 15 : 25 so , water : salt = 2.25 : 25 = 9 : 100 answer : a"
Answer: a
Python program:
a = 5 * 3
b = a * 3
c = 5 * 5
d = c * 5
e = b / d
Problem: the average wages of a worker during a fortnight comprising 15 consecutive working days was $ 90 per day . during the first 7 days , his average wages was $ 87 per day and the average wages during the last 7 days was $ 94 per day . what was his wage on the 8 th day ?
Options: a ) $ 83 , b ) $ 90 , c ) $ 92 , d ) $ 97 , e ) $ 104
Rationale: "average daily wage of a worker for 15 consecutive working days = 90 $ during the first 7 days , the daily average daily wage = 87 $ during the last 7 days , the daily average daily wage = 94 $ wage on 8 th day = 90 * 15 - ( 87 * 7 + 94 * 7 ) = 1350 - ( 609 + 658 ) = 1350 - 1267 = 83 answer a"
Answer: a
Python program:
a = 90 * 15
b = 87 * 7
c = 94 * 7
d = b + c 
e = a - d
Problem: at what rate percent on simple interest will rs . 750 amount to rs . 1200 in 5 years ?
Options: a ) 12 , b ) 3 , c ) 14 , d ) 5 , e ) 6
Rationale: "450 = ( 750 * 5 * r ) / 100 r = 12 % . answer : a"
Answer: a
Python program:
a = 1200 - 750
b = a / 750
c = b / 5
d = c * 100
Problem: the difference between simple and compound interest on rs . 1200 for one year at 10 % per annum reckoned half - yearly is ?
Options: a ) rs . 7 , b ) rs . 3 , c ) rs . 8 , d ) rs . 1 , e ) rs . 4
Rationale: "s . i . = ( 1200 * 10 * 1 ) / 100 = rs . 120 c . i . = [ 1200 * ( 1 + 5 / 100 ) 2 - 1200 ] = rs . 123 difference = ( 123 - 120 ) = rs . 3 . answer : b"
Answer: b
Python program:
a = 10 / 2
b = a / 100
c = b + 1 
d = c ** 2
e = 10 / 100
f = e + 1 
g = d - f
h = g * 1200
Problem: stacy and heather are 25 miles apart and walk towards each other along the same route . stacy walks at constant rate that is 1 mile per hour fast than heather ' s constant rate of 5 miles / hour . if heather starts her journey 24 minutes after stacy , how far from the original destination has heather walked when the two meet ? .
Options: a ) 9.0 mile , b ) 13.0 mile , c ) 11.0 mile , d ) 10.2 mile , e ) 12 mile
Rationale: ss - stacy ' s speed = 6 m / hr sh - heather ' s speed = 5 m / hr in 24 minutes stacy will cover = ( 24 / 60 ) * 6 = 2.4 miles now since both are walking in opposite directions , add their speeds - 6 + 5 = 11 m / hr and distance to cover is 25 - 2.4 = 22.6 time taken = distance / speed = 22.6 / 11 = 2.05 hrs heather will cover = 5 * 2.4 = 10.2 miles . answer d
Answer: d
Python program:
a = 1 + 5 
b = a / const_60
c = 24 * b
d = 25 - c
e = 1 + 5 
f = 5 + e 
g = d / f
h = g * 5
Problem: ganesh , ram and sohan together can do a work in 16 days . if ganesh and ram together can do a the same work in 24 days then , how long will take sohan to do the same work ?
Options: a ) 48 , b ) 58 , c ) 68 , d ) 78 , e ) 100
Rationale: solution : work done by three of them together in 1 day = 1 / 16 . . . . . . . . . . . . ( 1 ) work done by ganesh and ram together in 1 day = 1 / 24 . . . . . ( 2 ) so , work done by sohan in one day = ( 1 ) - ( 2 ) = ( 1 / 16 ) - ( 1 / 24 ) = 1 / 48 = > total days taken by sohan to complete the work alone = 48 days . answer a
Answer: a
Python program:
a = 1 / 16
b = 1 / 24
c = a - b
d = 1 / c
Problem: one fourth of one third of two fifth of a number is 25 . what will be 40 % of that number
Options: a ) a ) 140 , b ) b ) 150 , c ) c ) 180 , d ) d ) 200 , e ) e ) 300
Rationale: "explanation : ( 1 / 4 ) * ( 1 / 3 ) * ( 2 / 5 ) * x = 25 then x = 25 * 30 = 750 40 % of 750 = 300 answer : option e"
Answer: e
Python program:
a = 1 / 4
b = 1 / 3
c = a * b
d = 2 + 3 
e = 2 / d
f = c * e
g = 25 / f
h = g * 40
i = h / 100
Problem: the cost price of an article is 56 % of the marked price . calculate the gain percent after allowing a discount of 13 % .
Options: a ) 23.4 % , b ) 44.5 % , c ) 55.3 % , d ) 57.4 % , e ) none
Rationale: "sol . let marked price = rs . 100 . then , c . p . = rs . 56 . s . p = rs . 87 . â ˆ ´ gain % = [ 31 / 56 * 100 ] % = 55.3 % . answer c"
Answer: c
Python program:
a = 100 - 13
b = a / 56
c = b - 1
d = c * 100
Problem: two trains each 260 m in length are running on the same parallel lines in opposite directions with the speed of 80 kmph and 70 kmph respectively . in what time will they cross each other completely ?
Options: a ) 15 sec , b ) 19 sec , c ) 12.48 sec , d ) 10 sec , e ) 11 sec
Rationale: "explanation : d = 260 m + 260 m = 520 m rs = 80 + 70 = 150 * 5 / 18 = 125 / 3 t = 520 * 3 / 125 = 12.48 sec answer : option c"
Answer: c
Python program:
a = 80 * const_0_2778
b = 260 / a
Problem: 1024 people in village 720 speak tamil , 562 speak english while 346 speak both . person who don not speack english or tamil speak hindi . what is probibility that person speak hindi
Options: a ) 13 / 128 , b ) 12 / 128 , c ) 11 / 126 , d ) 11 / 127 , e ) 11 / 128
Rationale: n ( t ) = 720 n ( e ) = 562 n ( t ^ e ) = 346 n ( tue ) = 720 + 562 - 346 = 936 now , n ( h ) = 1024 - 936 = 88 p ( h ) = 88 / 1024 = 11 / 128 = 0.085 answer : e
Answer: e
Python program:
a = 562 - 346
b = 720 - 346
c = a + b 
d = c + 346 
e = 1024 - d
f = e / 1024
Problem: a train 140 m long passes a man , running at 6 kmph in the direction opposite to that of the train , in 6 seconds . the speed of the train is
Options: a ) 54 kmph , b ) 60 kmph , c ) 66 kmph , d ) 72 kmph , e ) 78 kmph
Rationale: "speed of train relative to man : 140 / 6 * 18 / 5 km / hr = 84 km / hr let speed of train = x therefore x + 6 = 84 x = 84 - 6 x = 78 km / hr answer : e"
Answer: e
Python program:
a = 6 * const_0_2778
b = a * 6
c = 140 - b
d = c / 6
e = d / const_0_2778
Problem: the speed of a train is 120 kmph . what is the distance covered by it in 8 minutes ?
Options: a ) 15 kmph , b ) 11 kmph , c ) 16 kmph , d ) 18 kmph , e ) 12 kmph
Rationale: "120 * 8 / 60 = 16 kmph answer : c"
Answer: c
Python program:
a = 8 / const_60
b = a * 120
Problem: a goods train runs at the speed of 72 kmph and crosses a 260 m long platform in 26 seconds . what is the length of the goods train ?
Options: a ) 260 m , b ) 270 m , c ) 643 m , d ) 832 m , e ) 270 m
Rationale: "speed = ( 72 x 5 / 18 ) m / sec = 20 m / sec . time = 26 sec . let the length of the train be x metres . then , x + 260 / 26 = 20 x + 260 = 520 x = 260 . answer : a"
Answer: a
Python program:
a = const_0_2778 * 72
b = 260 / a
c = 26 - b
d = const_0_2778 * 72
e = c * d
Problem: if albert ’ s monthly earnings rise by 14 % , he would earn $ 678 . if , instead , his earnings rise by only 15 % , how much ( in $ ) would he earn this month ?
Options: a ) 643 , b ) 689 , c ) 683 , d ) 690 , e ) 693
Rationale: "= 678 / 1.14 ∗ 1.15 = 683 = 683 answer is c"
Answer: c
Python program:
a = 14 / 100
b = 1 + a 
c = 678 / b
d = 15 / 100
e = 1 + d 
f = c * e
Problem: a person travels equal distances with speeds of 3 km / hr , 4 km / hr and 5 km / hr and takes a total time of 45 minutes . the total distance is ?
Options: a ) 1 km , b ) 2.87 km , c ) 3 km , d ) 4 km , e ) 5 km
Rationale: "b 3 km let the total distance be 3 x km . then , x / 3 + x / 4 + x / 5 = 45 / 60 47 x / 60 = 45 / 60 = > x = 0.95 . total distance = 3 * 0.95 = 2.87 km ."
Answer: b
Python program:
a = 45 / const_60
b = 1 / 3
c = 1 / 4
d = b + c 
e = 1 / 5
f = d + e 
g = a / f
h = g * 3
i = h * 1000
Problem: a container contains 40 litres of milk . from this container 4 litres of milk was taken out and replaced by water . this process was repeated further two times . how much milk is now contained by the container .
Options: a ) 26.34 litres , b ) 27.36 liters , c ) 28 litres , d ) 29.16 litres , e ) can not be determined
Rationale: solution amount of milk left after 3 operations [ 40 ( 1 - 4 / 40 ) 3 ] litres = ( 40 x 9 / 10 x 9 / 10 x 9 / 10 ) = 29.16 litres answer d
Answer: d
Python program:
a = 4 / 40
b = 1 - a
c = b ** 3
d = c * 40
Problem: if grapes are 90 % water and raisins are 17 % water , then how many kilograms did a quantity of raisins , which currently weighs 14 kilograms , weigh when all the raisins were grapes ? ( assume that the only difference between their raisin - weight and their grape - weight is water that evaporated during their transformation . )
Options: a ) 108.6 , b ) 110.4 , c ) 112.6 , d ) 114.8 , e ) 116.2
Rationale: "let x be the original weight of the grapes . the weight of the grape pulp was 0.1 x . since the grape pulp is 83 % of the raisins , 0.1 x = 0.83 ( 14 kg ) . then x = 8.3 * 14 = 116.2 kg . the answer is e ."
Answer: e
Python program:
a = 100 - 17
b = a / 100
c = b * 14
d = 100 - 90
e = d / 100
f = c / e
Problem: on multiplying a number f by 153 , the result obtained was 102325 . however , it is found that both the 2 ' s are wrong . find the correct result .
Options: a ) 104345 , b ) 107375 , c ) 108385 , d ) 109395 , e ) 105355
Rationale: the only thing you actually know about the correct number f is that it is divisible by 153 and has 5 as a factor . you should immediately try to find the factors of 153 and look for them in the options . 153 = 9 * 17 divisibility by 9 is easy to check . only ( d ) satisfies .
Answer: d
Python program:
a = 3 + 4 
b = a * 10
c = 3 + 4 
d = c * 100
e = d * 10
f = b + e 
g = f + 102325
Problem: at an election 2 candidates are participated a candidate got 30 % of votes and defeated by 5000 votes . 100 votes are invalid . find the total polled votes ?
Options: a ) 11520 , b ) 12600 , c ) 15000 , d ) 13560 , e ) 12560
Rationale: winners votes = 100 - 30 = 70 % invalid votes = 100 polled votes = [ ( 100 * 5000 ) / ( 2 * 70 - 100 ) ] + 100 = 12600 answer is b
Answer: b
Python program:
a = 100 - 30
b = a - 30
c = 5000 / b
d = c * 100
e = 100 + d
Problem: the marks obtained by vijay and amith are in the ratio 4 : 5 and those obtained by amith and abhishek in the ratio of 3 : 2 . the marks obtained by vijay and abhishek are in the ratio of ?
Options: a ) 6 : 8 , b ) 6 : 2 , c ) 6 : 5 , d ) 6 : 4 , e ) 6 : 2
Rationale: "4 : 5 3 : 2 - - - - - - - 12 : 15 : 10 12 : 10 6 : 5 answer : c"
Answer: c
Python program:
a = 4 * 3
b = 5 * 2
c = a / b
Problem: if a large pizza has a radius that is 10 % larger that that of a medium pizza , what is the percent increase in area between a medium and a large pizza ?
Options: a ) 15 % , b ) 21 % , c ) 25 % , d ) 30 % , e ) 36 %
Rationale: "let the radius of medium pizza be r . then the radius of large pizza is 1.1 r . the area of the medium pizza is pi * r ^ 2 the area of the large pizza is pi * ( 1.1 * r ) ^ 2 = 1.21 * pi * r ^ 2 , an increase of 21 % . the answer is b ."
Answer: b
Python program:
a = 10 / 100
b = 1 + a 
c = b ** 2
d = c - 1
e = d * 100
Problem: if a coin is flipped , the probability that the coin will land tails is 1 / 2 . if the coin is flipped 5 times , what is the probability that it will land tails up on the first 2 flips and not on the last 3 flips ?
Options: a ) 3 / 5 , b ) 1 / 32 , c ) 1 / 5 , d ) 1 / 4 , e ) 1 / 2
Rationale: ( 1 / 2 ) * ( 1 / 2 ) * ( 1 / 2 ) * ( 1 / 2 ) * ( 1 / 2 ) = 1 / 32 answer : b
Answer: b
Python program:
a = 2 ** 5
b = 1/(a)
Problem: 60 kg of an alloy a is mixed with 100 kg of alloy b . if alloy a has lead and tin in the ratio 3 : 2 and alloy b has tin and copper in the ratio 1 : 4 , then the amount of tin in the new alloy is ?
Options: a ) 24 kg , b ) 44 kg , c ) 20 kg , d ) 30 kg , e ) 52 kg
Rationale: quantity of tin in 60 kg of a = 60 * 2 / 5 = 24 kg quantity of tin in 100 kg of b = 100 * 1 / 5 = 20 kg quantity of tin in the new alloy = 24 + 20 = 44 kg answer is b
Answer: b
Python program:
a = 3 + 2 
b = 60 / a
c = b * 2
d = 1 + 4 
e = 100 / d
f = e * 1
g = c + f
Problem: what is the sum of all possible solutions to the equation √ 2 x ^ 2 − x − 9 = x + 1 ?
Options: a ) - 2 , b ) 2 , c ) 3 , d ) 5 , e ) 6
Rationale: "first of all notice that since lhs is the square root of a number , it must be non - negative ( the square root function can not give negative result ) , then the rhs must also be non - negative : x + 1 ≥ 0 - - > x ≥ − 1 square the equation : 2 x ^ 2 − x − 9 = x ^ 2 + 2 x + 1 - - > x ^ 2 − 3 x − 10 = 0 - - > x = - 2 or x = 5 . discard x = - 2 because it ' s not > = - 1 . we are left with only one root : 5 . answer : d"
Answer: d
Python program:
a = 4 + 2 
b = 9 - 4
c = a + b
Problem: pipe a can fill a tank in 10 minutes and pipe b cam empty it in 24 minutes . if both the pipes are opened together after how many minutes should pipe b be closed , so that the tank is filled in 30 minutes ?
Options: a ) 18 , b ) 27 , c ) 98 , d ) 27 , e ) 48
Rationale: "let the pipe b be closed after x minutes . 30 / 10 - x / 24 = 1 = > x / 24 = 30 / 10 - 1 = 2 = > x = 2 * 24 = 48 . answer : e"
Answer: e
Python program:
a = 30 / 10
b = a - 1
c = b * 24
Problem: if price of t . v set is reduced by 18 % , then its sale increases by 88 % , find net effect on sale value
Options: a ) 44 , b ) 54 , c ) 46 , d ) 47 , e ) 48
Rationale: "- a + b + ( ( - a ) ( b ) / 100 ) = - 18 + 88 + ( - 18 * 88 ) / 100 = - 18 + 88 - 16 = 54 answer : b"
Answer: b
Python program:
a = 100 - 18
b = a / 100
c = 100 + 88 
d = c / 100
e = b * d
f = e - 1
g = f * 100
Problem: a father said his son , ` ` i was as old as you are at present at the time of your birth . ` ` if the father age is 38 now , the son age 5 years back was :
Options: a ) 14 , b ) 19 , c ) 33 , d ) 38 , e ) 56
Rationale: "explanation : let the son ' s present age be x years . then , ( 38 - x ) = x x = 19 . son ' s age 5 years back = ( 19 - 5 ) = 14 years . answer : a"
Answer: a
Python program:
a = 38 / 2
b = a - 5
Problem: 20 machines can do a work in 5 days . how many machines are needed to complete the work in 10 days ?
Options: a ) 10 , b ) 15 , c ) 8 , d ) 12 , e ) 20
Rationale: "required number of machines = 20 * 5 / 10 = 10 answer is a"
Answer: a
Python program:
a = 20 * 5
b = a / 10
Problem: in x - y plane , there is a right triangle abc ( ∠ b = 90 o ) . if the length of ac is 225 and the slope of line segment ac is 4 / 3 , what is the length of ab ?
Options: a ) 12 , b ) 180 , c ) 24 , d ) 28 , e ) 40
Rationale: "slope = change in vertical direction / change in horizontal direction = 4 / 3 change in vertical direction = 4 x = ab change in horizontal direction = 3 x = bc ab ^ 2 + bc ^ 2 = 225 ^ 2 16 x ^ 2 + 9 x ^ 2 = 225 ^ 2 25 x ^ 2 = 225 ^ 2 x ^ 2 = 25 * 9 ^ 2 x = 45 therefore ab = 45 * 4 = 180 answer : b"
Answer: b
Python program:
a = 4 ** 2
b = 3 ** 2
c = a + b 
d = math.sqrt(c)
e = 225 / d
f = 4 * e
Problem: at company x , senior sales representatives visit the home office once every 18 days , and junior sales representatives visit the home office once every 12 days . the number of visits that a junior sales representative makes in a 2 - year period is approximately what percent greater than the number of visits that a senior representative makes in the same period ?
Options: a ) 10 % , b ) 25 % , c ) 33 % , d ) 50 % , e ) 67 %
Rationale: "each 36 - day period , senior representatives visit the home office 2 times while junior representatives visit 3 times , thus 50 % more . the answer is d ."
Answer: d
Python program:
a = 1 + 10 
b = 18 - 12
c = b - 1
d = a * c