euclaise/mathqa_programs huggingface dataset:
Problem: at 1 : 00 pm , a truck left city p and headed toward city q at a constant speed of 50 km / h . one hour later , a car left city q and headed toward city p along the same road at a constant speed of 40 km / h . if the distance between city p and city q is 230 km , at what time will the truck and the car meet each other ?
Options: a ) 4 : 00 , b ) 4 : 30 , c ) 5 : 00 , d ) 5 : 30 , e ) 6 : 00
Rationale: "at 2 : 00 pm , the truck and the car are 180 km apart . the truck and the car complete a distance of 90 km each hour . the time it takes to meet is 180 / 90 = 2 hours . they will meet at 4 : 00 pm . the answer is a ."
Answer: a
Python program:
a = 230 / 50
b = a - 1
c = 40 / 50
d = 1 + c 
e = b / d
Problem: a certain telescope increases the visual range at a particular location from 50 kilometers to 150 kilometers . by what percent is the visual range increased by using the telescope ?
Options: a ) 30 % , b ) 33 1 / 2 % , c ) 40 % , d ) 60 % , e ) 200 %
Rationale: original visual range = 50 km new visual range = 150 km percent increase in the visual range by using the telescope = ( 150 - 50 ) / 50 * 100 % = 2 * 100 % = 200 % answer e
Answer: e
Python program:
a = 150 - 50
b = a / 50
c = b * 100
Problem: a contractor undertakes to built a walls in 50 days . he employs 60 peoples for the same . however after 25 days he finds that only 40 % of the work is complete . how many more man need to be employed to complete the work in time ?
Options: a ) 25 , b ) 90 , c ) 35 , d ) 20 , e ) none of these
Rationale: "60 men complete 0.4 work in 25 days . applying the work rule , m 1 × d 1 × w 2 = m 2 × d 2 × w 1 we have , 60 × 25 × 0.6 = m 2 × 25 × 0.4 or m 2 = 60 × 25 × 0.6 / 25 × 0.4 = 90 men answerb"
Answer: b
Python program:
a = 100 - 40
b = a / 100
c = 60 * b
d = 4 / 10
e = c / d
Problem: excluding stoppages , the average speed of a bus is 50 km / hr and including stoppages , the average speed of the bus is 40 km / hr . for how many minutes does the bus stop per hour ?
Options: a ) 12 min , b ) 18 min , c ) 16 min , d ) 20 min , e ) 26 min
Rationale: "in 1 hr , the bus covers 50 km without stoppages and 40 km with stoppages . stoppage time = time take to travel ( 50 - 40 ) km i . e 10 km at 50 km / hr . stoppage time = 10 / 50 hrs = 12 min answer : a"
Answer: a
Python program:
a = 1 * const_60
b = 40 / 50
c = b * const_60
d = a - c
Problem: the total marks obtained by a student in mathematics and physics is 20 and his score in chemistry is 20 marks more than that in physics . find the average marks scored in mathamatics and chemistry together .
Options: a ) 40 , b ) 26 , c ) 20 , d ) 28 , e ) 22
Rationale: "let the marks obtained by the student in mathematics , physics and chemistry be m , p and c respectively . given , m + c = 20 and c - p = 20 m + c / 2 = [ ( m + p ) + ( c - p ) ] / 2 = ( 20 + 20 ) / 2 = 20 . answer : c"
Answer: c
Python program:
a = 20 + 20 
b = a / 2
Problem: how many numbers from 10 to 10000 are exactly divisible by 9 ?
Options: a ) 900 , b ) 1000 , c ) 1110 , d ) 1200 , e ) 1400
Rationale: "10 / 9 = 1 and 10000 / 9 = 1111 = = > 1111 - 1 = 1110 . therefore 1110 answer : c"
Answer: c
Python program:
a = 10000 / 9
b = math.floor(a)
c = b * 9
d = 10 / 9
e = math.floor(d)
f = e + 1 
g = f * 9
h = c - g
i = h / 9
j = i + 1
Problem: the average age of 36 students in a group is 14 years . when teacher ' s age is included to it , the average increases by one . what is the teacher ' s age in years ?
Options: a ) 21 years , b ) 71 years , c ) 51 years , d ) 91 years , e ) 11 years
Rationale: "explanation : age of the teacher = ( 37 * 15 - 36 * 14 ) years = 51 years . answer : c"
Answer: c
Python program:
a = 36 + 1
Problem: find the principle on a certain sum of money at 5 % per annum for 4 years if the amount being rs . 1120 ?
Options: a ) 933 , b ) 1067 , c ) 1977 , d ) 1056 , e ) 1097
Rationale: "1120 = p [ 1 + ( 5 * 4 ) / 100 ] p = 933 answer : a"
Answer: a
Python program:
a = 5 * 4
b = a / 100
c = 1 + b 
d = 1120 / c
Problem: out of 10 students in a class , 4 are from maharashtra , 3 are from karnataka , and 3 are from goa . four students are to be selected at random . what are the chances that at least one is from karnataka ?
Options: a ) 1 / 3 , b ) 4 / 9 , c ) 5 / 6 , d ) 3 / 7 , e ) 1 / 4
Rationale: "total possible ways of selecting 4 students out of 10 = 10 c 4 = ( 10 * 9 * 8 * 7 ) / ( 4 * 3 * 2 * 1 ) = 210 the number of ways of selecting a 4 students in which no student belongs to karnataka = 7 c 4 number of ways of selecting atleast one student from karnataka = 15 c 4 - 7 c 4 = 175 probability = 175 / 210 = 5 / 6 answer is c"
Answer: c
Python program:
a = math.factorial(10)
b = 10 - 4
c = math.factorial(b)
d = a / c
e = math.factorial(4)
f = d / e
g = 10 - 3
h = math.factorial(g)
i = 10 - 3
j = i - 4
k = math.factorial(j)
l = h / k
m = math.factorial(4)
n = l / m
o = f - n
p = math.factorial(10)
q = 10 - 4
r = math.factorial(q)
s = p / r
t = math.factorial(4)
u = s / t
v = o / u
Problem: a sum was put at simple interest at a certain rate for 3 years had it been put at 3 % higher rate , it would have fetched 81 more . find the sum .
Options: a ) 500 , b ) 600 , c ) 700 , d ) 800 , e ) 900
Rationale: "difference in s . i . = p × t / 100 ( r 1 − r 2 ) ⇒ 81 = p × 3 x 3 / 100 ( ∵ r 1 - r 2 = 2 ) ⇒ p = 81 × 100 / 3 x 3 = 900 answer e"
Answer: e
Python program:
a = 3 / 100
b = a * 3
c = 81 / b
Problem: the least whole number which when subtracted from both the terms of the ratio 6 : 7 to give a ratio less than 16 : 21 , is
Options: a ) 3 , b ) 4 , c ) 5 , d ) 6 , e ) 7
Rationale: "explanation : let x is subtracted . then , ( 6 − x ) / ( 7 − x ) < 16 / 21 21 ( 6 — x ) < 16 ( 7 — x ) = > 5 x > 14 = x > 2.8 least such number is 3 option a"
Answer: a
Python program:
a = 21 * 6
b = 7 * 16
c = a - b
d = 21 - 16
e = c / d
f = 2 / 10
g = e + f
Problem: the total cost of 100 paper plates and 200 paper cups is $ 6.00 at the same rates what is the total cost of 20 of the plates and 40 of the cups ?
Options: a ) $ . 90 , b ) $ 1.00 , c ) $ 1.20 , d ) $ 1.50 , e ) $ 1.60
Rationale: u dont need to go through all this what u have with u is 100 p + 200 c = $ 6.00 just divide the equation by 5 and you will get what u are looking for 20 p + 40 c = $ 1.20 therefore oa is c
Answer: c
Python program:
a = 20 / 100
b = a * 6
Problem: if the price of sugar rises from rs . 3 per kg to rs . 5 per kg , a person , to have no increase in the expenditure on sugar , will have to reduce his consumption of sugar by
Options: a ) 15 % , b ) 20 % , c ) 25 % , d ) 30 % , e ) 40 %
Rationale: sol . let the original consumption = 100 kg and new consumption = x kg . so , 100 x 3 = x × 5 = x = 60 kg . ∴ reduction in consumption = 40 % . answer e
Answer: e
Python program:
a = 1 * 3
b = a / 5
c = 1 - b
d = c * 100
Problem: a 1200 m long train crosses a tree in 120 sec , how much time will i take to pass a platform 300 m long ?
Options: a ) 176 sec , b ) 190 sec , c ) 178 sec , d ) 150 sec , e ) 276 sec
Rationale: "l = s * t s = 1200 / 120 s = 10 m / sec . total length ( d ) = 1500 m t = d / s t = 1500 / 10 t = 150 sec answer : d"
Answer: d
Python program:
a = 1200 + 300 
b = 1200 / 120
c = a / b
Problem: find the average of all prime numbers between 30 and 50 .
Options: a ) 30 , b ) 33.6 , c ) 39.8 , d ) 44.9 , e ) none
Rationale: "sol . there are five prime numbers between 30 and 50 . they are 31 , 37 , 41 , 43 and 47 ∴ required average = [ 31 + 37 + 41 + 43 + 47 / 5 ] = 199 / 5 = 39.8 answer c"
Answer: c
Python program:
a = 30 + 1 
b = 4 + 0 
c = b + 2 
d = a + c 
e = 50 - 4
f = 50 - 2
g = e + f 
h = d + g 
i = h / 30
Problem: there are 2 available positions and 50 candidates , one half of whom are democrats and another half are republicans . if it was decided that the positions would be filled at random , then what is the probability w that the both positions will be taken by members of just one party ?
Options: a ) 1 / 25 , b ) 12 / 49 , c ) 1 / 4 , d ) 24 / 49 , e ) 1 / 2
Rationale: "w probability of one party having both spots : ( 1 / 2 ) * ( 24 / 49 ) = 12 / 49 ( 1 / 2 ) or ( 25 / 50 ) because it does not matter which party or which person gets the first spot . ( 24 / 49 ) because after one person from a particular party is chosen , there are 24 members of the same party left out of 49 total candidates . since this result can happen for both parties , ( 12 / 49 ) + ( 12 / 49 ) = ( 24 / 49 ) answer : d"
Answer: d
Python program:
a = 50 / 2
b = a - 1
c = 50 - 1
d = b / c
e = 50 / 2
f = e / 50
g = d * f
h = g * 2
Problem: a gambler bought $ 3,000 worth of chips at a casino in denominations of $ 30 and $ 100 . that evening , the gambler lost 16 chips , and then cashed in the remainder . if the number of $ 30 chips lost was 2 more or 2 less than the number of $ 100 chips lost , what is the largest amount of money that the gambler could have received back ?
Options: a ) $ 2,040 , b ) $ 2,120 , c ) $ 1,960 , d ) $ 1,920 , e ) $ 2,030
Rationale: "in order to maximize the amount of money that the gambler kept , we should maximize # of $ 30 chips lost and minimize # of $ 100 chips lost , which means that # of $ 30 chips lost must be 2 more than # of $ 100 chips lost . so , if # of $ 30 chips lost is x then # of $ 100 chips lost should be x - 2 . now , given that total # of chips lost is 16 : x + x - 2 = 16 - - > x = 9 : 9 $ 30 chips were lost and 9 - 2 = 7 $ 100 chips were lost . total worth of chips lost is 9 * 30 + 7 * 100 = $ 970 , so the gambler kept $ 3,000 - $ 970 = $ 2,030 . answer : e"
Answer: e
Python program:
a = 3 * 1000
b = 16 + 2 
c = b / 2
d = c * 30
e = 16 + 2 
f = e / 2
g = f - 2
h = g * 100
i = d + h 
j = a - i
Problem: an association of mathematics teachers has 1,260 members . only 445 of these members cast votes in the election for president of the association . what percent of the total membership voted for the winning candidate if the winning candidate received 60 percent of the votes cast ?
Options: a ) 75 % , b ) 58 % , c ) 42 % , d ) 34 % , e ) 22 %
Rationale: "total umber of members = 1260 number of members that cast votes = 445 since , winning candidate received 60 percent of the votes cast number of votes for winning candidate = ( 60 / 100 ) * 445 = 267 percent of total membership that voted for winning candidate = ( 267 / 1260 ) * 100 = 21.19 % answer e"
Answer: e
Python program:
a = 60 / 100
b = a * 445
c = 4 ** 2
d = 100 * c
e = b / d
f = e * 100
Problem: what is the smallest positive integer x , such that 5000 x is a perfect cube ?
Options: a ) 4 , b ) 6 , c ) 8 , d ) 25 , e ) 18
Rationale: "take out the factors of 5000 that will come 10 ^ 3 * 5 . for perfect cube you need every no . raise to the power 3 . for 5000 x to be a perfect cube , you need two 5 that means 25 . d is the answer ."
Answer: d
Python program:
a = 3 + 4
Problem: a leak in the bottom of a tank can empty the full tank in 6 hours . an inlet pipe fills water at the rate of 6 litres a minute . when the tank is full , the inlet is opened and due to the leak , the tank is empty in 12 hours . how many litres does the cistern hold ?
Options: a ) 7580 , b ) 7960 , c ) 8290 , d ) 4320 , e ) none
Rationale: "solution work done by the inlet in 1 hour = ( 1 / 6 - 1 / 12 ) = 1 / 12 . work done by the inlet in 1 min . = ( 1 / 12 × 1 / 60 ) = 0.001389 volume of 0.001389 part = 6 litres . therefore , volume of whole = 1 / 0.001389 x 6 ‹ = › 4320 litres . answer d"
Answer: d
Python program:
a = 12 * const_60
b = 6 * a
c = 12 * const_60
d = 6 * const_60
e = c / d
f = e - 1
g = b / f
Problem: maxwell leaves his home and walks toward brad ' s house . one hour later , brad leaves his home and runs toward maxwell ' s house . if the distance between their homes is 24 kilometers , maxwell ' s walking speed is 4 km / h , and brad ' s running speed is 6 km / h . what is the total time it takes maxwell before he meets up with brad ?
Options: a ) 3 , b ) 4 , c ) 5 , d ) 6 , e ) 8
Rationale: "total distance = 24 kms maxwell speed = 4 kms / hr maxwell travelled for 1 hour before brad started , therefore maxwell traveled for 4 kms in 1 hour . time taken = total distance / relative speed total distance after brad started = 20 kms relative speed ( opposite side ) ( as they are moving towards each other speed would be added ) = 6 + 4 = 10 kms / hr time taken to meet brad after brad started = 20 / 10 = 2 hrs distance traveled by maxwell = maxwell ' s speed * time taken = 4 * 2 = 8 + 4 = 12 kms . . . therefore total time taken by maxwell to meet brad = distance travelled by maxwell / maxwell ' s speed = 12 / 4 = 3 hrs . . . answer a"
Answer: a
Python program:
a = 24 + 6 
b = 4 + 6 
c = a / b
Problem: one robot builds a robot in 1 hour , another one builds a robot in 2 hours . the 2 robots work together and when a new robot is complete , it joins the others , working at a constant rate of one robot in 2 hours . how much time will it take until there are 3 robots altogether , if the robots build only one robot at a time ?
Options: a ) 40 min , b ) 94 min , c ) 110 min , d ) 112 min , e ) 120 min
Rationale: "first the 2 robots work at the rate of 1 + 1 / 2 = 3 / 2 so they complete one robot in 2 / 3 rd of an hour = 40 minutes - ( 1 ) and now we have 3 robots in 40 minutes answer - a"
Answer: a
Python program:
a = 1/(1)
b = 1/(2)
c = a + b 
d = 1/(2)
e = c + d 
f = 1/(e)
g = 1/(1)
h = 1/(2)
i = g + h 
j = 1/(i)
k = f + j
Problem: if 20 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 ) 80 , e ) 75
Rationale: "let x be the number of students in the school . 0.2 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 0.2 x / 0.25 = 0.8 x students went to the camping which is 80 % . the answer is d"
Answer: d
Python program:
a = 100 - 75
b = a / 100
c = 20 / b
Problem: in a group of 400 readers who read science fiction or literacy works or both , 250 read science fiction and 230 read literacy works . how many read both science fiction and literacy works ?
Options: a ) 70 , b ) 80 , c ) 90 , d ) 100 , e ) 110
Rationale: "consider total number of reader n ( s u l ) = 400 people who read science fiction n ( s ) = 250 people who read literacy works n ( l ) = 230 both science fiction and literacy n ( s ∩ l ) = ? n ( s u l ) = n ( s ) + n ( l ) - n ( s ∩ l ) 400 = 250 + 230 - n ( s ∩ l ) n ( s ∩ l ) = 480 - 400 n ( s ∩ l ) = 80 so people read both science fiction and literacy works are 80 answer : b"
Answer: b
Python program:
a = 250 + 230 
b = a - 400
Problem: if 12 men and 16 boys can do a piece of work in 5 days and 13 men together will 24 boys can do it in 4 days . compare the daily work done by a man with that of a boy ?
Options: a ) 2 : 5 , b ) 2 : 9 , c ) 2 : 4 , d ) 2 : 1 , e ) 2 : 2
Rationale: 12 m + 16 b - - - - - 5 days 13 m + 24 b - - - - - - - 4 days 60 m + 80 b = 52 m + 96 b 8 m = 16 b = > 1 m = 2 b m : b = 2 : 1 answer : d
Answer: d
Python program:
a = 4 * 24
b = 5 * 16
c = a - b
d = 5 * 12
e = 4 * 13
f = d - e
g = c / f
Problem: the pilot of a small aircraft with a 40 - gallon fuel tank wants to fly to cleveland , which is 480 miles away . the pilot recognizes that the current engine , which can fly only 10 miles per gallon , will not get him there . by how many miles per gallon must the aircraft ’ s fuel efficiency be improved to make the flight to cleveland possible ?
Options: a ) 2 , b ) 4 , c ) 12 , d ) 40 , e ) 160
Rationale: "actual miles / gallon is = 480 / 40 = 12 miles / gallon . current engine miles / gallon is 10 miles / gallon . additional 2 miles / gallon is required to match the actual mileage . imo option a ."
Answer: a
Python program:
a = 480 / 40
b = a - 10
Problem: a certain bus driver is paid a regular rate of $ 12 per hour for any number of hours that does not exceed 40 hours per week . for any overtime hours worked in excess of 40 hours per week , the bus driver is paid a rate that is 75 % higher than his regular rate . if last week the bus driver earned $ 976 in total compensation , how many total hours did he work that week ?
Options: a ) 60 , b ) 68 , c ) 65 , d ) 64 , e ) 61
Rationale: "for 40 hrs = 40 * 12 = 480 excess = 976 - 480 = 496 for extra hours = . 75 ( 12 ) = 9 + 12 = 21 number of extra hrs = 496 / 21 = 23.62 total hrs = 40 + 23.62 = 63.62 = 64 approx . answer d 64"
Answer: d
Python program:
a = 12 * 40
b = 976 - a
c = 100 + 75 
d = 12 * c
e = d / 100
f = b / e
g = 40 + f
Problem: three numbers are in the ratio 3 : 4 : 5 and their average is 36 . the largest number is :
Options: a ) 30 , b ) 98 , c ) 27 , d ) 21 , e ) 45
Rationale: "explanation : let the numbers be 3 x , 4 x and 5 x , then , ( 3 x + 4 x + 5 x ) / 3 = 36 = > 12 x = 36 * 3 = > x = 9 largest number 5 x = 5 * 9 = 45 answer : e"
Answer: e
Python program:
a = 3 * 5
b = a * 100
c = 4 * 5
d = b + c
Problem: 5 cats can catch 5 mice in 5 minutes . how many cats does it take to catch 100 mice in 100 minutes ?
Options: a ) 1 , b ) 2 , c ) 3 , d ) 4 , e ) 5
Rationale: let x be no . of cat 5 cat catch 5 mice in 5 min 5 cat catch 1 mice in ( 5 / 5 = 1 min ) 1 cat catch 1 mice in 1 * 5 = 5 min 1 cat catch 100 mice in 5 * 100 min x cat catch 100 mice in ( 5 * 100 ) / x min a / q ( 5 * 100 ) / x = 100 = > 5 * 100 = x * 100 = > x = 5 answer : e
Answer: e
Python program:
a = 5 * 4
b = 100 / a
Problem: the tax on a commodity is diminished by 19 % and its consumption increased by 15 % . the effect on revenue is ?
Options: a ) 2 % , b ) 8.85 % , c ) 5.85 % , d ) 6.85 % , e ) 1 %
Rationale: "100 * 100 = 10000 81 * 115 = 9315 - - - - - - - - - - - 10000 - - - - - - - - - - - 685 100 - - - - - - - - - - - ? = > 6.85 % decrease answer : d"
Answer: d
Python program:
a = 15 / 100
b = 1 + a 
c = 19 / 100
d = 1 - c
e = b * d
f = e * 100
g = 100 - f
Problem: when a train travels at a speed of 60 kmph , it reaches the destination on time . when the same train travels at a speed of 50 kmph , it reaches its destination 15 min late . what is the length of journey ?
Options: a ) 75 km , b ) 50 km , c ) 60 km , d ) 85 km , e ) 95 km
Rationale: "let x be the time reached with the speed 60 km / h 50 km / h - - - - > x + 15 distance is equal so 60 ( km / h ) × xhr = 50 ( km / h ) × ( x + 15 ) hr so 60 x = 50 x + 750 so the would be in km and x = 75 so 75 km answer : a"
Answer: a
Python program:
a = 15 / const_60
b = a * 50
c = b / 50
d = const_60 * c
Problem: if x is less than y by 40 % then y exceed x by :
Options: a ) 33.33 % , b ) 25 % , c ) 75 % , d ) 66.66 % , e ) none of these
Rationale: "using formula ( x / ( 100 - x ) * 100 ) where x is percentage decrease ( here it is 40 % ) = > 40 / ( 100 - 40 ) * 100 = 66.66 % answer : d"
Answer: d
Python program:
a = 100 - 40
b = 100 / a
c = b - 1
d = c * 100
Problem: p is 20 % more efficient than q . p can complete a work in 22 days . if p and q work together , how many days will it take to complete the same work ?
Options: a ) 8 , b ) 11 , c ) 12 , d ) 15 , e ) 16
Rationale: "the work done by p in 1 day = 1 / 22 let work done by q in 1 day = q q × ( 120 / 100 ) = 1 / 22 q = 100 / ( 22 × 120 ) = 10 / ( 22 × 12 ) the work done by p and q in 1 day = 1 / 22 + 10 / ( 22 × 12 ) = 22 / ( 22 × 12 ) = 1 / 12 p and q together can do the work in 12 days . the answer is c ."
Answer: c
Python program:
a = 20 / 100
b = a + 1 
c = b * 22
d = 20 / 100
e = d + 1 
f = e + 1 
g = c / f
Problem: a school has 4 section of chemistry in class x having 55 , 35 , 45 and 42 students . the mean marks obtained in chemistry test are 50 , 60 , 55 and 45 respectively for the 4 sections . determine the overall average of marks per student .
Options: a ) 50.15 , b ) 52.06 , c ) 51.25 , d ) 53.06 , e ) none of the above
Rationale: "required average marks = 55 ã — 50 + 35 ã — 60 + 45 ã — 55 + 42 ã — 45 / 55 + 35 + 45 + 42 = 2750 + 2100 + 2475 + 1890 / 162 = 9215 â  „ 177 = 52.06 answer b"
Answer: b
Python program:
a = 55 * 50
b = 35 * 60
c = a + b 
d = 45 * 55
e = c + d 
f = 42 * 45
g = e + f 
h = 55 + 35 
i = h + 45 
j = i + 42 
k = g / j
Problem: rs . 2600 is divided so that 4 times the first share , thrice the 2 nd share and twice the third share amount to the same . what is the value of the third share ?
Options: a ) s . 1200 , b ) s . 1542 , c ) s . 1528 , d ) s . 1540 , e ) s . 1549
Rationale: "a + b + c = 2600 4 a = 3 b = 2 c = x a : b : c = 1 / 4 : 1 / 3 : 1 / 2 = 3 : 4 : 6 6 / 13 * 2600 = rs . 1200 answer : a"
Answer: a
Python program:
a = 4 + 2 
b = a + 3 
c = 2600 / b
d = 4 * c
Problem: the difference of two numbers is 1355 . on dividing the larger number by the smaller , we get 6 as quotient and the 15 as remainder . what is the smaller number ?
Options: a ) 240 , b ) 270 , c ) 295 , d ) 268 , e ) 252
Rationale: "let the smaller number be x . then larger number = ( x + 1355 ) . x + 1355 = 6 x + 15 5 x = 1340 x = 268 smaller number = 270 . answer d"
Answer: d
Python program:
a = 1355 + 15 
b = 6 - 1
c = a / b
Problem: if a radio is purchased for rs 490 and sold for rs 465.50 find the loss % ?
Options: a ) 5 % , b ) 4 % , c ) 6 % , d ) 8 % , e ) 7 %
Rationale: c . p = rs 490 s . p = rs 465.50 loss = c . p - s . p = 490 - 465.50 = rs 24.50 loss % = ( loss * 100 ) / c . p % = ( 24.50 * 100 ) / 490 % = 5 % answer a 5 %
Answer: a
Python program:
a = 490 - 465
b = a * 100
c = b / 490
Problem: if a person cover 3 / 5 part of his journey by train , 7 / 20 part of his journey by bus and rest 6.5 km . by walk . what is total distance of his journey ?
Options: a ) 65 km , b ) 100 km , c ) 120 km , d ) 130 km , e ) 75 km
Rationale: let total distance be = x km . then , 3 x / 5 + 7 x / 20 + 6.5 = x ; 12 x + 7 x + 130 = 20 x ; x = 130 hence total distance = 130 km . answer d
Answer: d
Python program:
a = 3 / 5
b = 7 / 20
c = a + b 
d = 1 - c
e = 6 / 5
Problem: water consists of hydrogen and oxygen , and the approximate ratio , by mass , of hydrogen to oxygen is 2 : 16 . approximately how many grams of oxygen are there in 144 grams of water ?
Options: a ) 16 , b ) 72 , c ) 112 , d ) 128 , e ) 142
Rationale: "see h / o = 2 / 16 add 1 to both sides : h / o + 1 = 2 / 16 + 1 take lcm ( h + o ) / o = ( 2 + 16 ) / 16 water / o = 18 / 16 now that we have the water to oxygen ratio , put in the amount of water i . e . 144 gm = > o = 144 * 16 / 18 = 128 answer : d"
Answer: d
Python program:
a = 2 + 16 
b = 144 / a
c = 2 * b
Problem: the h . c . f . of two numbers is 16 and the other two factors of their l . c . m . are 13 and 14 . the larger of the two numbers is :
Options: a ) 276 , b ) 299 , c ) 224 , d ) 345 , e ) 365
Rationale: "clearly , the numbers are ( 16 x 13 ) and ( 16 x 14 ) . larger number = ( 23 x 14 ) = 224 . answer : option c"
Answer: c
Python program:
a = 16 * 14
Problem: at a certain resort , each of the 39 food service employees is trained to work in a minimum of 1 restaurant and a maximum of 3 restaurants . the 3 restaurants are the family buffet , the dining room , and the snack bar . exactly 21 employees are trained to work in the family buffet , 18 are trained to work in the dining room , and 12 are trained to work in the snack bar . if 4 employees are trained to work in exactly 2 restaurants , how many employees are trained to work in all 3 restaurants ?
Options: a ) 2 , b ) 3 , c ) 4 , d ) 5 , e ) 6
Rationale: "39 = 21 + 18 + 12 - 4 - 2 x 2 x = 21 + 18 + 12 - 4 - 39 = 47 - 39 = 8 x = 4 c"
Answer: c
Python program:
a = 21 + 18 
b = a + 12 
c = b - 4
d = c - 39
e = d / 2
Problem: how many 4 digit number contain number 2 ?
Options: a ) 3168 , b ) 3268 , c ) 3368 , d ) 3468 , e ) 3568
Rationale: "total 4 digit no . = 9 * 10 * 10 * 10 = 9000 not containing 2 = 8 * 9 * 9 * 9 = 5832 total 4 digit number contain 2 = 9000 - 5832 = 3168 answer : a"
Answer: a
Python program:
a = 1000 - 10
b = 4 * 4
c = 10 * b
d = 4 * 2
e = c * d
f = a - e
g = f + 10