euclaise/mathqa_programs huggingface dataset:
Problem: in measuring the sides of a rectangle , one side is taken 5 % in excess , and the other 4 % in deficit . find the error percent in the area calculated from these measurements .
Options: a ) 0.2 % , b ) 0.4 % , c ) 0.6 % , d ) 0.8 % , e ) 1 %
Rationale: "let x and y be the sides of the rectangle . then , correct area = xy . calculated area = ( 105 / 100 ) * x * ( 96 / 100 ) * y = ( 504 / 500 ) ( xy ) error in measurement = ( 504 / 500 ) xy - xy = ( 4 / 500 ) xy error % = [ ( 4 / 500 ) xy * ( 1 / xy ) * 100 ] % = ( 4 / 5 ) % = 0.8 % . answer d 0.8 %"
Answer: d
Python program:
a = 5 - 4
b = 5 * 4
c = b / 100
d = a - c
Problem: a box contains 100 balls , numbered from 1 to 100 . if 3 balls are selected at random and with replacement from the box . if the 3 numbers on the balls selected contain two odd and one even . what is the probability g that the first ball picked up is odd numbered ?
Options: a ) 0 , b ) 1 / 3 , c ) 1 / 2 , d ) 2 / 3 , e ) 1
Rationale: "answer - d selecting the balls either even or odd is having probability 50 / 100 = 1 / 2 we have already selected 3 balls with 2 odd numbers and 1 even number . so we have 3 combinations ooe , oeo , eoo . we have 3 outcomes and 2 are favourable as in 2 cases 1 st number is odd . so probability g is 2 / 3 . d"
Answer: d
Python program:
a = 2 / 3
Problem: a gardener wants to plant trees in his garden in such a way that the number of trees in each row should be the same . if there are 2 rows or 4 rows or 4 rows , then no tree will be left . find the least number of trees required
Options: a ) 22 , b ) 60 , c ) 4 , d ) 8 , e ) 10
Rationale: "explanation : the least number of trees that are required = lcm ( 2 , 4,4 ) = 4 . answer : c"
Answer: c
Python program:
a = 4 * 4
b = a * 2
c = b / 2
Problem: bert left the house with n dollars . he spent 1 / 4 of this at the hardware store , then $ 9 at the dry cleaners , and then half of what was left at the grocery store . when he got home , he had $ 15 left in his pocket . what was the value of n ?
Options: a ) $ 36 , b ) $ 44 , c ) $ 52 , d ) $ 60 , e ) $ 68
Rationale: started to test answer c if he had 52 , then he spent 13 at hardware store now he was left with 39 $ he spent 9 dollars on cleaning , thus he remained with 30 $ he then spent 1 / 2 of 30 , or 15 , and was left with 15 . hence , the only option that can be right is c .
Answer: c
Python program:
a = 1 / 4
b = 1 - a
c = 1/(b)
d = 9 / 2
e = d + 15 
f = c * e
g = f * 2
Problem: a company has $ 329864 in its account . what is the least amount of money ( in whole number of dollars ) that it must add to the account if the money is paid evenly among 9 of its vendors ?
Options: a ) $ 1 , b ) $ 2 , c ) $ 3 , d ) $ 4 , e ) $ 6
Rationale: to find the least amount that must be added to the account to split the money evenly among 9 of its vendors , the total divisible by 9 simply add the individual digits of the total = 3 + 2 + 9 + 8 + 6 + 4 = 32 if you add 4 , the number is divisible by 9 ( 32 + 4 ) correct option : d
Answer: d
Python program:
a = 9 - reminder
Problem: an escalator moves towards the top level at the rate of 10 ft . sec and its length is 112 feet . if a person walks on the moving escalator at the rate of 4 feet per second towards the top level , how much time does he take to cover the entire length .
Options: a ) 14 sec , b ) 10 sec , c ) 12 sec , d ) 8 sec , e ) 9 sec
Rationale: "time taken to cover the entire length = tot . dist / resultant speed = 112 / ( 10 + 4 ) = 8 sec answer : d"
Answer: d
Python program:
a = 10 + 4 
b = 112 / a
Problem: if - 2 / ( a - 6 ) = 4 / ( a + 4 ) , then a = ?
Options: a ) 2 / 3 , b ) 1 / 2 , c ) 5 / 3 , d ) 8 / 3 , e ) 7 / 3
Rationale: "multiply all terms of the given equation by ( a - 6 ) ( a + 4 ) , simplify and solve ( a - 6 ) ( a + 4 ) [ - 2 / ( a - 6 ) ] = ( a - 6 ) ( a + 4 ) [ 4 / ( a + 4 ) ] - 2 ( a + 4 ) = 4 ( a - 6 ) a = 8 / 3 correct answer d"
Answer: d
Python program:
a = 2 * 4
b = 2 / a
Problem: in a group of ducks and cows , the total number of legs are 34 more than twice the no . of heads . find the total no . of buffaloes .
Options: a ) 11 , b ) 12 , c ) 14 , d ) 17 , e ) 18
Rationale: "let the number of buffaloes be x and the number of ducks be y = > 4 x + 2 y = 2 ( x + y ) + 34 = > 2 x = 34 = > x = 17 d"
Answer: d
Python program:
a = 34 / 2
Problem: what is the units digit of ( 7 ! * 6 ! + 6 ! * 4 ! ) / 2 ?
Options: a ) 0 , b ) 1 , c ) 2 , d ) 3 , e ) 4
Rationale: "( 7 ! * 6 ! + 6 ! * 4 ! ) / 2 = 6 ! ( 7 ! + 4 ! ) / 2 = 240 ( 1680 + 24 ) / 2 = 204480 units digit of the above product will be equal to 0 answer a"
Answer: a
Python program:
a = math.factorial(7)
b = math.factorial(6)
c = a * b
d = math.factorial(7)
e = math.factorial(4)
f = d * e
g = c + f 
h = g / 7
Problem: in a division sum , the remainder is 0 . as student mistook the divisor by 12 instead of 21 and obtained 63 as quotient . what is the correct quotient ?
Options: a ) 0 , b ) 36 , c ) 13 , d ) 20 , e ) 25
Rationale: "12 * 63 = 756 756 % 21 = 36 answer : b"
Answer: b
Python program:
a = 12 * 63
b = a / 21
Problem: a cube is painted red on all faces . it is then cut into 27 equal smaller cubes . how many v cubes are painted on only 2 faces ?
Options: a ) 12 , b ) 8 , c ) 6 , d ) 10 , e ) 16
Rationale: "1 ) draw a simple cube 2 ) draw 9 squares on each face of the cube ( so that it looks like a rubik ' s cube ) - this is what the cube will look like when it ' s cut into 27 equal smaller cubes . 3 ) remember that the outside of the cube is the part that ' s painted . . . . the mini - cubes with 2 painted sides are all on the edge of the cube , in themiddleof the edge . there are 4 in front , 4 in back and 4 more on thestripthat runs around the left / top / right / bottom of the cube . v = 4 + 4 + 4 = 12 . answer a"
Answer: a
Python program:
a = 1 / 3
b = 27 ** a
c = 4 * b
Problem: a tank can supply water to a village for 30 days . if a leak at the bottom of the tank drains out 15 liters per day , the supply lasts for 20 days only . for how many days will the supply last if the leak drains out 20 liters per day ?
Options: a ) 12 , b ) 14 , c ) 15 , d ) 16 , e ) 18
Rationale: "losing 15 liters per day results in a loss of 300 liters in 20 days . so , those 300 liters were for 10 days , making daily consumption of the village 30 liters per day . thus the capacity of the tank is 30 * 30 = 900 liters . losing 20 liters plus 30 liters gives 50 liters per day . at this rate the supply will last 900 / 50 = 18 days . the answer is e ."
Answer: e
Python program:
a = 15 * 20
b = 30 - 20
c = a / b
d = c * 30
e = 15 * 20
f = 30 - 20
g = e / f
h = 20 + g 
i = d / h
Problem: the volume of a sphere with radius r is ( 4 / 3 ) * pi * r ^ 3 and the surface area is 4 * pi * r ^ 3 . if a sperical balloon has a volume of 12348 pi cubic centimeters , what is hte surface area of the balloon in square centimeters ?
Options: a ) a . 40 , b ) b . 100 , c ) c . 400 , d ) d . 1,000 , e ) e . 5,000
Rationale: "the surface area is 4 . pi . r ^ 2 ( its area remember not volume ) as 4 / 3 . pi . r ^ 3 = 12348 pi r = 21 so area = 4 . pi . r ^ 2 = 1764 . pi = 1764 x 3.14 = 5000 ( approx ) e"
Answer: e
Python program:
a = const_180 / 1000
Problem: a room of 2 m 40 cm long and 4 m 20 cm broad is to be paved with square tiles . find the least number of square tiles required to cover the floor .
Options: a ) 23 , b ) 25 , c ) 28 , d ) 60 , e ) 240
Rationale: "explanation : area of the room = 240 * 420 sq cm size of largest square tile = h . c . f of 240 cm and 420 cm = 60 cm area of 1 tile = 60 * 60 sq cm no . of tiles required = ( 240 * 420 ) / ( 60 * 60 ) = 28 answer : c ) 28"
Answer: c
Python program:
a = 2 * 100
b = a + 40 
c = 4 * 100
d = c + 20 
e = b * d
f = 2 * 100
g = f + 40 
h = 2 ** 4
i = g / h
j = i ** 2
k = e / j
Problem: how many times in a day , the hands of a clock are shows opposite directions ?
Options: a ) 12 , b ) 20 , c ) 21 , d ) 23 , e ) 22
Rationale: "sol . in 12 hours , the hands coincide or are in opposite direction 11 times . â ˆ ´ in 24 hours , the hands coincide or are in opposite direction 22 times a day . ( between 5 and 7 they point in opposite directions at 6 o ' clock only ) answer e"
Answer: e
Python program:
a = 2 * 12
b = 2 * a
c = b - 4
d = c / 2
Problem: the difference between a positive proper fraction and its reciprocal is 9 / 20 . then the fraction is :
Options: a ) 4 / 0 , b ) 4 / 1 , c ) 4 / 5 , d ) 4 / 2 , e ) 4 / 3
Rationale: "explanation : let the required fraction be x . then , ( 1 / x ) - x = 9 / 20 1 - x ^ ( 2 ) / x = 9 / 20 = > 20 - 20 * x ^ ( 2 ) = 9 * x . 20 * x ^ ( 2 ) + 9 * x - 20 = 0 . = > ( 4 * x + 5 ) ( 5 * x - 4 ) = 0 . = > x = 4 / 5 . answer : c ) 4 / 5"
Answer: c
Python program:
a = 9 - 4
b = 4 / a
Problem: a sum of money is to be distributed among a , b , c , d in the proportion of 6 : 3 : 5 : 4 . if c gets rs . 1000 more than d , what is b ' s share ?
Options: a ) 1500 , b ) 2000 , c ) 2500 , d ) 2800 , e ) 3000
Rationale: "let the shares of a , b , c and d be rs . 5 x , rs . 3 x , rs . 5 x and rs . 4 x respectively . then , 5 x - 4 x = 1000 x = 1000 . b ' s share = rs . 3 x = rs . ( 3 x 1000 ) = rs . 3000 . answer : e"
Answer: e
Python program:
a = 5 - 4
b = a * 1000
c = b * 3
Problem: a sports equipment store sold ping pong rackets for a total of $ 686 . if the average ( arithmetic mean ) price of a pair of rackets is $ 9.8 , how many pairs were sold ?
Options: a ) 50 , b ) 100 , c ) 70 , d ) 500 , e ) 980
Rationale: average price for a pair of rackets = $ 9.8 total cost = $ 9.8 * x = $ 686 x = 70 pairs were sold . answer : c
Answer: c
Python program:
a = 686 / 9
Problem: one woman and one man can build a wall together in four hours , but the woman would need the help of two girls in order to complete the same job in the same amount of time . if one man and one girl worked together , it would take them eight hours to build the wall . assuming that rates for men , women and girls remain constant , how many hours would it take one woman , one man , and one girl , working together , to build the wall ?
Options: a ) 5 / 7 , b ) 1 , c ) 10 / 7 , d ) 12 / 7 , e ) 24 / 7
Rationale: "solution : let work done by man , women and girl per hour be m , w , g respectively . then , m + w = 1 / 4 - - > ( 1 ) , w + 2 g = 1 / 4 - - > ( 2 ) and m + g = 1 / 8 - - > ( 3 ) . no . of hours it would take forone woman , one man , and one girl , working together , to build the wall , n = 1 / m + w + g from ( 1 ) and ( 2 ) , m = 2 g and from ( 3 ) g = 1 / 24 , m = 1 / 12 and w = 1 / 6 . so , n = 1 / ( 7 / 24 ) = 24 / 7 option , e"
Answer: e
Python program:
a = 4 + 1 
b = a + 4 
c = 1/(b)
d = 4 + 1 
e = 1/(d)
f = e * 2
g = c + f 
h = g / 2
i = 4 + 1 
j = 1/(i)
k = h - j
l = 3 / 2
m = k / l
n = 4 + 1 
o = 1/(n)
p = m + o 
q = 1/(p)
Problem: what is the least number to be subtracted from 1300 to make it a perfect square ?
Options: a ) 80 , b ) 25 , c ) 75 , d ) 63 , e ) 90
Rationale: "the numbers less than 1300 and are squares of certain number is 1225 . the least number that should be subtracted from 1300 to make it perfect square = 1300 - 1225 = 75 . answer : c"
Answer: c
Python program:
a = 3 * 2
b = 10 + a 
c = 100 * b
d = c - 1300
Problem: the average weight of 8 person ' s increases by 3.5 kg when a new person comes in place of one of them weighing 65 kg . what might be the weight of the new person ?
Options: a ) kg , b ) 70 kg , c ) 80 kg , d ) 90 kg , e ) 93 kg
Rationale: "total weight increased = ( 8 x 3.5 ) kg = 28 kg . weight of new person = ( 65 + 28 ) kg = 93 kg . e )"
Answer: e
Python program:
a = 8 * 3
b = a + 65
Problem: the area of a square is 6400 sq cm . find the ratio of the breadth and the length of a rectangle whose length is thrice the side of the square and breadth is 30 cm less than the side of the square ?
Options: a ) 5 : 24 , b ) 5 : 19 , c ) 5 : 13 , d ) 5 : 22 , e ) 5 : 18
Rationale: "let the length and the breadth of the rectangle be l cm and b cm respectively . let the side of the square be a cm . a 2 = 6400 a = ( 6400 ) ^ 1 / 2 = 80 l = 3 a and b = a - 30 b : l = a - 30 : 2 a = 50 : 240 = 5 : 24 answer : a"
Answer: a
Python program:
a = math.sqrt(6400)
b = a - 30
c = math.sqrt(6400)
d = c * 2
e = b / d
Problem: if xy > 0 , 1 / x + 1 / y = 15 , and 1 / xy = 5 , then ( x + y ) / 5 = ?
Options: a ) 1 / 25 , b ) 1 / 6 , c ) 3 / 5 , d ) 5 , e ) 6
Rationale: ( 1 / x + 1 / y ) = 15 canbe solved as { ( x + y ) / xy } = 5 . substituting for 1 / xy = 5 , we get x + y = 15 / 5 = = > ( x + y ) / 5 = 15 / ( 5 * 5 ) = 3 / 5 . c
Answer: c
Python program:
a = 15 / 5
b = a / 5
Problem: a man complete a journey in 10 hours . he travels first half of the journey at the rate of 21 km / hr and second half at the rate of 26 km / hr . find the total journey in km .
Options: a ) 220 km , b ) 224 km , c ) 230 km , d ) 200 km , e ) 234 km
Rationale: "0.5 x / 10 + 0.5 x / 10 = 20 - - > x / 10 + x / 10 = 40 - - > 2 x = 10 x 40 - - > x = ( 10 x 40 ) / 2 = 200 km . answer : d ."
Answer: d
Python program:
a = 21 * 26
b = a * 10
c = 21 + 26 
d = b / c
e = 2 * d
Problem: a bookseller sells his books at a 10 % markup in price . if he sells a book for $ 11.00 , how much did he pay for it ?
Options: a ) $ 14.40 , b ) $ 14.00 , c ) $ 10.00 , d ) $ 9.60 , e ) $ 5.00
Rationale: "let the cost price of book = x selling price of book = 11 $ markup % = 10 ( 110 / 100 ) x = 11 = > x = 10 answer c"
Answer: c
Python program:
a = 10 / 100
b = a * 11
c = 11 - 0
Problem: there are 60 doors marked with numbers 1 to 60 . there are 60 individuals marked 1 to 60 . an operation on a door is defined as changing the status of the door from open to closed or vice versa . all the doors are closed to start with . one at a time , one randomly chosen individual goes and operates the doors . the individual however operates only those doors which are a multiple of the number he / she is carrying . for example , the individual marked with number 5 operates the doors marked with 5 , 10 , 15 , 20 , 25 , 30 , 35 , 40 , 45 , 50 , 55 , and 60 . if every individual in the group gets one turn , then how many doors are open at the end ?
Options: a ) 0 , b ) 2 , c ) 5 , d ) 7 , e ) 9
Rationale: if a door is closed at the start , it requires an odd number of people to operate to be open at the end . only the perfect squares have an odd number of factors . the doors which are open at the end are : 1 , 4 , 9 , 16 , 25 , 36 , 49 for a total of 7 doors . the answer is d .
Answer: d
Python program:
a = 60 / 10
b = a + 1
Problem: a train 220 m long is running with a speed of 59 kmph . in what time will it pass a man who is running at 7 kmph in the direction opposite to that in which the train is going ?
Options: a ) 7 sec , b ) 8 sec , c ) 10 sec , d ) 12 sec , e ) 14 sec
Rationale: "speed of the train relative to man = ( 59 + 7 ) kmph = 66 * 5 / 18 m / sec = 55 / 3 m / sec . time taken by the train to cross the man = time taken by it to cover 220 m at ( 55 / 3 ) m / sec = ( 220 * 3 / 55 ) sec = 12 sec answer : d ."
Answer: d
Python program:
a = 220 / 1000
b = 59 - 7
c = a / b
d = c * 3600
Problem: due to construction , the speed limit along an 9 - mile section of highway is reduced from 55 miles per hour to 20 miles per hour . approximately how many minutes more will it take to travel along this section of highway at the new speed limit than it would have taken at the old speed limit ?
Options: a ) a ) 5.61 , b ) b ) 8 , c ) c ) 10 , d ) d ) 17.19 , e ) e ) 24
Rationale: "old time in minutes to cross 9 miles stretch = 9 * 60 / 55 = 9 * 12 / 11 = 9.81 new time in minutes to cross 9 miles stretch = 9 * 60 / 20 = 9 * 3 / 1 = 27 time difference = 17.19 ans : d"
Answer: d
Python program:
a = 55 + 9 
b = a - 1
c = 9 / 20
d = 9 / 55
e = c - d
f = b * e
g = max(f)
Problem: the area of a triangle will be when a = 1 m , b = 2 m , c = 7 m , a , b , c being lengths of respective sides ?
Options: a ) 3 , b ) 6 , c ) 5 , d ) 9 , e ) 1
Rationale: s = ( 1 + 2 + 7 ) / 2 = 5 answer : c
Answer: c
Python program:
a = 1 + 2 
b = a + 7 
c = b / 2
Problem: a train 125 m long takes 6 sec to cross a man walking at 5 kmph in a direction opposite to that of the train . find the speed of the train ?
Options: a ) 65 kmph , b ) 70 kmph , c ) 75 kmph , d ) 80 kmph , e ) 85 kmph
Rationale: "let the speed of the train be x kmph speed of the train relative to man = x + 5 = ( x + 5 ) * 5 / 18 m / sec 125 / [ ( x + 5 ) * 5 / 18 ] = 6 30 ( x + 5 ) = 2250 x = 70 kmph answer is b"
Answer: b
Python program:
a = 125 / 6
b = a / const_0_2778
c = b - 5
Problem: what is the units digit of the expression 14 ^ 7 − 15 ^ 4 ?
Options: a ) 0 , b ) 8 , c ) 4 , d ) 6 , e ) 3
Rationale: i think answer on this one should be b too . since we know that 14 ^ 7 > 15 ^ 4 , as will said one should always check if the number is positive .
Answer: b
Python program:
a = 4 + 3 
b = a + 2
Problem: at what rate percent on simple interest will rs . 750 amount to rs . 1050 in 5 years ?
Options: a ) 8 , b ) 3 , c ) 4 , d ) 5 , e ) 6
Rationale: "300 = ( 750 * 5 * r ) / 100 r = 8 % . answer : a"
Answer: a
Python program:
a = 1050 - 750
b = a / 750
c = b / 5
d = c * 100
Problem: the amount of time that three people worked on a special project was in the ratio of 4 to 3 to 5 . if the project took 120 hours , how many more hours did the hardest working person work than the person who worked the least ?
Options: a ) 25 hours , b ) 30 hours , c ) 20 hours , d ) 26 hours , e ) 32 hours
Rationale: "let the persons be a , b , c . hours worked : a = 4 * 120 / 12 = 40 hours b = 3 * 120 / 12 = 30 hours c = 5 * 120 / 12 = 50 hours c is the hardest worker and b worked for the least number of hours . so the difference is 50 - 30 = 20 hours . answer : c"
Answer: c
Python program:
a = 4 + 3 
b = a + 5 
c = 120 / b
d = c * 5
e = 4 + 3 
f = e + 5 
g = 120 / f
h = g * 4
i = d - h
Problem: a rectangular farm has to be fenced one long side , one short side and the diagonal . if the cost of fencing is rs . 11 per meter . the area of farm is 1200 m 2 and the short side is 30 m long . how much would the job cost ?
Options: a ) 1276 , b ) 1200 , c ) 2832 , d ) 1299 , e ) 1320
Rationale: "explanation : l * 30 = 1200 è l = 40 40 + 30 + 50 = 120 120 * 11 = 1320 answer : option e"
Answer: e
Python program:
a = 1200 / 30
b = 30 + a 
c = 30 ** 2
d = 1200 / 30
e = d ** 2
f = c + e 
g = math.sqrt(f)
h = b + g 
i = h * 11
Problem: a call center has two teams . each member of team a was able to process 3 / 5 calls as compared to each member of team b . if team a has 5 / 8 as many number of call center agents as team b , what fraction of the total calls was processed by team b ?
Options: a ) 3 / 2 , b ) 3 / 4 , c ) 8 / 11 , d ) 1 / 2 , e ) 1 / 5
Rationale: "let team b has 8 agents , so team a has 5 agents let each agent of team b picked up 5 calls , so total calls by team b = 40 so , each agent in team a picked up 3 calls , so total calls for team a = 15 fraction for team b = 40 / ( 40 + 15 ) = 8 / 11 = answer = c"
Answer: c
Python program:
a = 8 * 5
b = 8 * 5
c = 5 * 3
d = b + c 
e = a / d
Problem: jill invests $ 10000 in an account that pays an annual rate of 3.96 % , compounding semi - annually . approximately how much r does she have in her account after two years ?
Options: a ) $ 10079.44 , b ) r = $ 10815.83 , c ) $ 12652.61 , d ) $ 14232.14 , e ) $ 20598.11
Rationale: "ps . i guess one can use simple interest to solve cause the answer choices are quite spread between you can easily arrive at something near 8 % hence b the answer"
Answer: b
Python program:
a = 3 / 96
b = a / 2
c = 1 + b 
d = c ** 4
e = 10000 * d
Problem: cindy has her eye on a sundress but thinks it is too expensive . it goes on sale for 15 % less than the original price . before cindy can buy the dress , however , the store raises the new price by 25 % . if the dress cost $ 71.4 after it went on sale for 15 % off , what is the difference between the original price and the final price ?
Options: a ) $ 5.625 , b ) $ 1.00 , c ) $ 3.40 , d ) $ 5.25 , e ) $ 6.80
Rationale: "0.85 * { original price } = $ 71.4 - - > { original price } = $ 84 . { final price } = $ 71.4 * 1.25 = $ 89.25 . the difference = $ 89.25 - $ 84 = $ 5.25 answer : d ."
Answer: d
Python program:
a = 100 + 25 
b = a / 100
c = 71 * 4
d = 100 - 15
e = d / 100
f = 71 / 4
g = c - f
Problem: if ( n + 2 ) ! / n ! = 110 , n = ?
Options: a ) 2 / 131 , b ) 9 , c ) 10 , d ) 11 , e ) 12
Rationale: "( n + 2 ) ! / n ! = 110 rewrite as : [ ( n + 2 ) ( n + 1 ) ( n ) ( n - 1 ) ( n - 2 ) . . . . ( 3 ) ( 2 ) ( 1 ) ] / [ ( n ) ( n - 1 ) ( n - 2 ) . . . . ( 3 ) ( 2 ) ( 1 ) ] = 132 cancel out terms : ( n + 2 ) ( n + 1 ) = 110 from here , we might just test the answer choices . since ( 11 ) ( 10 ) = 110 , we can see that n = 9 b"
Answer: b
Python program:
a = 4 + 4 
b = a - 1
Problem: ( 1 / 5 ) ^ e * ( 1 / 4 ) ^ 18 = 1 / ( 2 ( 10 ) ^ 35 ) . what is e ?
Options: a ) 17 , b ) 18 , c ) 34 , d ) 35 , e ) 36
Rationale: we need to arrive at a common base . - - > ( 5 ) ^ ( - e ) * 2 ^ ( - 36 ) = 2 ^ ( - 36 ) * 5 ^ ( - 35 ) 5 ^ ( - e ) = 5 ^ ( - 35 ) - e = - 35 e = 35 = d
Answer: d
Python program:
a = 35 / 1
Problem: i bought two books ; for rs . 360 . i sold one at a loss of 15 % and other at a gain of 19 % and then i found each book was sold at the same price . find the cost of the book sold at a loss ?
Options: a ) 197 , b ) 210 , c ) 189 , d ) 278 , e ) 268
Rationale: "x * ( 85 / 100 ) = ( 360 - x ) 119 / 100 x = 210 answer : b"
Answer: b
Python program:
a = 100 + 19 
b = 360 * a
c = 100 - 15
d = 100 + 19 
e = c + d 
f = b / e
Problem: if n is a natural number , then ( 6 n 2 + 6 n ) is always divisible by :
Options: a ) 6 only , b ) 12 only , c ) 6 and 12 both , d ) by 18 only , e ) 15 only
Rationale: "( 6 n ^ 2 + 6 n ) = 6 n ( n + 1 ) , which is always divisible by 6 and 12 both , since n ( n + 1 ) is always even . answer c ) 6 and 12 both ."
Answer: c
Python program:
a = 6 * 100
b = 2 * 6
c = a + b
Problem: | 13 - 3 | - | 4 - 10 | = ?
Options: a ) 3 , b ) 2 , c ) 1 , d ) 0 , e ) 4
Rationale: "| 13 - 3 | - | 4 - 10 | = | 10 | - | - 6 | = 10 - 6 = 4 correct answer e"
Answer: e
Python program:
a = 13 - 3
b = 10 - 4
c = a - b
Problem: a fill pipe can fill 1 / 6 of cistern in 90 minutes in how many minutes , it can fill 5 / 6 of the cistern ?
Options: a ) 450 min , b ) 360 min , c ) 240 min , d ) 306 min , e ) 500 min
Rationale: "1 / 6 of the cistern can fill in 90 min 5 / 6 of the cistern can fill in = 90 * 6 * 5 / 6 = 450 min answer is a"
Answer: a
Python program:
a = 90 / 1
Problem: increasing the original price of an article by 6 percent and then increasing the new price by 6 percent is equivalent to increasing the original price by
Options: a ) 12.1 % , b ) 12.36 % , c ) 12.94 % , d ) 13.65 % , e ) 14.56 %
Rationale: 1.06 * 1.06 * x = 1.1236 * x the answer is b .
Answer: b
Python program:
a = 6 / 100
b = 1 + a 
c = 6 / 100
d = 1 + c 
e = b * d
f = e - 1
g = 100 * f
Problem: the monthly salaries of 6 employees in a company are $ 1000 , $ 2500 , $ 3100 , $ 3650 , $ 1500 , $ 2000 . what is the mean of the salaries of 6 employees .
Options: a ) $ 2291.7 , b ) $ 1546.8 , c ) $ 2546.5 , d ) $ 1879.3 , e ) $ 3125.3
Rationale: mean of the salaries = ( $ 1000 + $ 2500 + $ 3100 + $ 3650 + $ 1500 + $ 2000 ) / 6 = 13750 / 6 = $ 2291.7 answer is a
Answer: a
Python program:
a = 1000 + 2500 
b = a + 3100 
c = b + 3650 
d = c + 1500 
e = d + 2000 
f = e / 6
Problem: ravi and sunil are partners in a business . ravi invests rs . 18,000 for 8 months and sunil invested rs . 10000 for 10 months then after one year ratio of their profits will be
Options: a ) 1 : 3 , b ) 36 : 25 , c ) 3 : 2 , d ) 4 : 5 , e ) 20 : 45
Rationale: "= ( 18000 * 8 ) : ( 10000 * 10 ) = 144000 : 100000 = 36 : 25 answer : b"
Answer: b
Python program:
a = 8 * 3
b = 10 * 2
c = a * b
d = c * 100
e = d * 8
f = 10000 * 10
g = e / f
Problem: if | x | = 5 x - 3 , then x = ?
Options: a ) 1 , b ) 1 / 2 , c ) 2 , d ) - 1 / 2 , e ) - 1
Rationale: "answer : a approach : substituted option a i . e x = 1 . inequality satisfied . c"
Answer: c
Python program:
a = 5 - 1
b = 3 / a