euclaise/mathqa_programs huggingface dataset:
Problem: 3 types of tea the a , b , c costs rs . 95 / kg , 100 / kg and 70 / kg respectively . how many kgs of each should be blended to produce 100 kg of mixture worth rs . 90 / kg , given that the quantities of band c are equal
Options: a ) 70 , 1515 , b ) 50 , 2525 , c ) 60 , 2020 , d ) 40 , 3030 , e ) 20 , 3030
Rationale: given quantities of b and c are equal . therefore instead of considering them as a different quantities take average of both and consider it as a single entity . so the cost of the mixture ` ` d ' ' ( equal quantities of ` ` b ' ' and ` ` c ' ' ) is 170 / 2 = 85 rs / kg now the tea contains only ` ` a ' ' of 95 rs / per and ` ` d ' ' of 85 rs / kg . it is clearly seen that ` ` a ' ' is 5 more and ` ` d ' ' is 5 less than the required cost per kg . therefore 50 / 50 will go well . a = 50 kg and d = 50 kg . ( d = b & c in equal ratio ) . therefore b & c = 25 kg each . ( a : b : c ) = ( 50 , 2525 ) answer : b
Answer: b
Python program:
a = 100 - 70
b = 100 - 95
c = a * b
d = c * 10
Problem: # p is defined as 2 p - 20 for any number p . what is p , if # ( # ( # p ) ) = 6 ?
Options: a ) – 108 , b ) – 44 , c ) 10 , d ) 16 , e ) 18.25
Rationale: # p = 2 p - 20 - - - > # ( # p ) = 2 ( 2 p - 20 ) - 20 = 4 p - 60 and thus # ( 4 p - 60 ) = 2 ( 4 p - 60 ) - 20 = 8 p - 140 = 6 - - - > 8 p = 146 - - - > p = 18.25 , e is the correct answer .
Answer: e
Python program:
a = 20 * 6
b = 20 + a 
c = b + 6 
d = 2 * 4
e = c / d
Problem: a watch was sold at a loss of 9 % . if it was sold for rs . 220 more , there would have been a gain of 4 % . what is the cost price ?
Options: a ) 1000 , b ) 2876 , c ) 1977 , d ) 2778 , e ) 1692
Rationale: "91 % 104 % - - - - - - - - 13 % - - - - 220 100 % - - - - ? = > rs . 1692 answer : e"
Answer: e
Python program:
a = 220 * 100
b = 100 + 4 
c = 100 - 9
d = b - c
e = a / d
Problem: two persons a and b can complete a piece of work in 30 days and 60 days respectively . if they work together , what part of the work will be completed in 10 days ?
Options: a ) 1 / 8 , b ) 1 / 3 , c ) 1 / 6 , d ) 1 / 2 , e ) 5 / 3
Rationale: a ' s one day ' s work = 1 / 30 b ' s one day ' s work = 1 / 60 ( a + b ) ' s one day ' s work = 1 / 30 + 1 / 60 = 1 / 20 the part of the work completed in 10 days = 10 ( 1 / 20 ) = 1 / 2 . answer : d
Answer: d
Python program:
a = 1 / 30
b = 1 / 60
c = a + b 
d = 10 * c
Problem: by travelling at 30 kmph , a person reaches his destination on time . he covered two - third the total distance in one - third of the total time . what speed should he maintain for the remaining distance to reach his destination on time ?
Options: a ) 19 kmph , b ) 15 kmph , c ) 12 kmph , d ) 20 kmph , e ) 23 kmph
Rationale: "let the time taken to reach the destination be 3 x hours . total distance = 30 * 3 x = 90 x km he covered 2 / 3 * 90 x = 60 x km in 1 / 3 * 3 x = x hours so , the remaining 30 x km , he has to cover in 2 x hours . required speed = 30 x / 2 x = 15 kmph . answer : b"
Answer: b
Python program:
a = 30 * 3
b = 30 * 3
c = b * 2
d = c / 3
e = a - d
f = 3 - 1
g = e / f
Problem: 33 1 / 3 % of 270 ?
Options: a ) 80 , b ) 90 , c ) 110 , d ) 120 , e ) 130
Rationale: "33 1 / 3 % = 1 / 3 1 / 3 × 270 = 90 b )"
Answer: b
Python program:
a = 1 / 3
b = 33 + a 
c = b * 270
d = c / 100
Problem: mr . hernandez , who was a resident of state x for only 8 months last year , had a taxable income of $ 22,500 for the year . if the state tax rate were 6 percent of the year ’ s taxable income prorated for the proportion of the year during which the taxpayer was a resident , what would be the amount of mr . hernandez ’ s state x tax for last year ?
Options: a ) $ 900 , b ) $ 720 , c ) $ 600 , d ) $ 300 , e ) $ 60
Rationale: "total tax for the year = 22,500 x 6 % = 1350 as stated annual tax is prorated as per the duration of stay . prorated tax = 1350 ( 8 / 12 ) = 900 answer a"
Answer: a
Python program:
a = 6 * 100
b = a * 100
c = 100 * const_0_25
d = c * 100
e = b + d 
f = e / 100
g = f * 6
h = g * 8
i = 3 * 6
j = h / i
Problem: in an office in singapore there are 60 % female employees . 50 % of all the male employees are computer literate . if there are total 62 % employees computer literate out of total 1300 employees , then the no . of female employees who are computer literate ?
Options: a ) 546 , b ) 674 , c ) 672 , d ) 960 , e ) none
Rationale: "solution : total employees , = 1300 female employees , 60 % of 1300 . = ( 60 * 1300 ) / 100 = 780 . then male employees , = 520 50 % of male are computer literate , = 260 male computer literate . 62 % of total employees are computer literate , = ( 62 * 1300 ) / 100 = 806 computer literate . thus , female computer literate = 806 - 260 = 546 . answer : option a"
Answer: a
Python program:
a = 62 / 100
b = 60 / 100
c = 1 - b
d = 50 / 100
e = c * d
f = a - e
g = f * 1300
Problem: each digit 1 through 5 is used exactly once to create a 5 - digit integer . if the 5 and the 4 can not be adjacent digits in the integer , how many 5 - digit integers are possible ?
Options: a ) 48 , b ) 66 , c ) 76 , d ) 78 , e ) 72
Rationale: "number of arrangements using 5 distinct digits = 5 ! number of arrangements in which 4 and 5 are adjacent - consider 4 and 5 together as one group . now you have 4 numbers / groups to arrange which can be done in 4 ! ways . in each of these arrangements , 4 and 5 can be arranged as 45 or 54 . number of arrangements in which 3 and 4 are not adjacent = 5 ! - 2 * 4 ! = 72 answer : e"
Answer: e
Python program:
a = 5 * 4
b = a * 5
c = b * 2
d = 4 * 5
e = d * 2
f = e * 2
g = c - f
Problem: susan drove an average speed of 15 miles per hour for the first 40 miles of a tripthen at a average speed of 60 miles / hr for the remaining 20 miles of the trip if she made no stops during the trip what was susan ' s avg speed in miles / hr for the entire trip
Options: a ) 35 , b ) 20 , c ) 45 , d ) 50 , e ) 55
Rationale: avg . speed = total distance / total time total distance = 60 miles total time = 40 / 15 + 20 / 60 = 3 avg . speed = 20 . answer - b
Answer: b
Python program:
a = 40 + 20 
b = 40 / 15
c = 20 / 60
d = b + c 
e = a / d
Problem: the sides of a triangle are in the ratio 5 : 12 : 13 and its perimeter is 480 m , its area is ?
Options: a ) 150 , b ) 240 , c ) 277 , d ) 261 , e ) 281
Rationale: "5 x + 12 x + 13 x = 480 = > x = 16 a = 80 , b = 192 , c = 208 s = ( 80 + 192 + 208 ) / 2 = 240 answer : b"
Answer: b
Python program:
a = 5 + 12 
b = a + 13 
c = 480 / b
d = 480 * c
Problem: the perimeter of a semi circle is 113 cm then the radius is ?
Options: a ) 17 , b ) 28 , c ) 19 , d ) 11 , e ) 22
Rationale: "36 / 7 r = 113 = > r = 22 answer : e"
Answer: e
Python program:
a = 2 + math.pi 
b = 113 / a
Problem: a boat having a length 4 m and breadth 3 m is floating on a lake . the boat sinks by 1 cm when a man gets on it . the mass of the man is :
Options: a ) 12 kg , b ) 120 kg , c ) 72 kg , d ) 96 kg , e ) none of these
Rationale: "explanation : volume of water displaced = ( 4 x 3 x 0.01 ) m 3 = 0.12 m 3 . ∴ mass of man = volume of water displaced x density of water = ( 0.12 x 1000 ) kg = 120 kg . answer : b"
Answer: b
Python program:
a = 4 * 3
b = 1 / 100
c = a * b
d = c * 1000
Problem: a train 450 m long running at 108 kmph crosses a platform in 25 sec . what is the length of the platform ?
Options: a ) 271 , b ) 266 , c ) 350 , d ) 277 , e ) 300
Rationale: "length of the platform = 108 * 5 / 18 * 25 = 750 – 450 = 300 answer : e"
Answer: e
Python program:
a = 108 * const_0_2778
b = 25 * a
c = b - 450
Problem: when the price of sugar was increased by 32 % , a family reduced its consumption in such a way that the expenditure on sugar was only 10 % more than before . if 30 kg were consumed per month before , find the new monthly consumption .
Options: a ) 20 kg , b ) 25 kg , c ) 30 kg , d ) 35 kg , e ) none of these
Rationale: since , expenditure = price × consumption ∴ 110 % of 30 = 132 ⁄ 100 × new consumption ⇒ 110 ⁄ 100 × 30 = 132 ⁄ 100 × new consumption ⇒ new consumption = 25 kg answer b
Answer: b
Python program:
a = 100 + 10 
b = 100 + 32 
c = a / b
d = c * 30
Problem: find the 25 th term of an arithmetic progression whose first term is 5 and the common difference is 7 .
Options: a ) 145 , b ) 38 , c ) 173 , d ) 156 , e ) 189
Rationale: n th term of a . p = a + ( n - 1 ) * d = 5 + ( 25 - 1 ) * 7 , = 5 + 168 = 173 . answer : c
Answer: c
Python program:
a = 25 - 1
b = a * 7
c = b + 5
Problem: in a graduating class , 40 percent of the students are male . in this class , 50 percent of the male students and 30 percent of the female students are 25 years old or older . if one student in the class is randomly selected , approximately what is the probability that he or she will be less than 25 years old ?
Options: a ) 0.56 , b ) 0.62 , c ) 0.68 , d ) 0.74 , e ) 0.8
Rationale: let x be the total number of students . the number students who are younger than 25 is 0.5 * 0.4 x + 0.7 * 0.6 x = 0.62 x the answer is b .
Answer: b
Python program:
a = 40 / 100
b = 50 / 100
c = a * b
d = 30 / 100
e = 40 / 100
f = 1 - e
g = d * f
h = c + g 
i = 1 - h
Problem: the function g ( a ) is defined for integers a such that if a is even , g ( a ) = a / 2 and if a is odd , g ( a ) = a + 5 . given that g ( g ( g ( g ( g ( a ) ) ) ) ) = 19 , how many possible values for a would satisfy this equation ?
Options: a ) 1 , b ) 5 , c ) 7 , d ) 8 , e ) 11
Rationale: let me define terms : in g ( a ) = r a is argument , r is result , g ( ) is function , in g ( g ( g ( g ( g ( a ) ) ) ) ) , g 1 is inner most , g 5 is outermost for identification . from definition of function g , we can deduce that : if result is even then two possibilities for argument = 1 even 1 odd if result is odd then one possibility for argument = 1 even since final result = 19 = odd possibilities : g 1 : 1 even g 2 : 1 * ( even , odd ) = 1 even 1 odd g 3 : 1 * ( even , odd ) + 1 even = 2 even 1 odd g 4 : 2 * ( even , odd ) + 1 even = 3 even 2 odd g 5 : 3 * ( even , odd ) + 2 even = 5 even 3 odd = total 8 ans d it is !
Answer: d
Python program:
a = 5 + 2 
b = a + 1
Problem: there are 16 bees in the hive , then 9 more fly . how many bees are there in all ?
Options: a ) 7 , b ) 33 , c ) 12 , d ) 17 , e ) 25
Rationale: 16 + 9 = 25 . answer is e .
Answer: e
Python program:
a = 16 + 9
Problem: seller selling an apple for rs . 20 , a seller loses 1 / 6 th of what it costs him . the cp of the apple is ?
Options: a ) 10 , b ) 12 , c ) 21 , d ) 18 , e ) 20
Rationale: "sp = 20 loss = cp 21 loss = cp − sp = cp − 20 ⇒ cp 21 = cp − 20 ⇒ 20 cp 21 = 20 ⇒ cp 21 = 1 ⇒ cp = 21 c"
Answer: c
Python program:
a = 20 + 1
Problem: what are the last two digits of ( 301 * 402 * 503 * 604 * 645 * 547 * 448 * 349 ) ^ 2
Options: a ) 96 , b ) 76 , c ) 56 , d ) 36 , e ) 00
Rationale: ( ( 301 * 402 * 503 * 604 * 645 ) * ( 547 * 448 * 349 ) ) ^ 2 if you observe above digits , last digit are : 1,2 , 3,4 , 5,7 , 8,9 ; 6 is missing ; so i have rearranged them so that multiplication will be easy for me as initial 4 digits have last two digits as 01 , 02,03 , 04,45 and final three as 47 * 48 * 49 . solving for only last two digits and multiplying them we get : ( ( 06 * 04 * 45 ) ( 56 * 49 ) ) ^ 2 = ( 00 * 44 ) ^ 2 = 00 ^ 2 = 00 hence answer is e
Answer: e
Python program:
a = 100 / 4
b = 2 * 3
c = 1 - 2
d = b * c
e = 1 - 2
f = d * e
g = 1 - 2
h = f * g
i = a + h 
j = i * 4
Problem: nina has exactly enough money to purchase 6 widgets . if the cost of each widget were reduced by $ 1.15 , then nina would have exactly enough money to purchase 8 widgets . how much money does nina have ?
Options: a ) $ 22 , b ) $ 27.6 , c ) $ 30 , d ) $ 36 , e ) $ 40
Rationale: "b its is . let price = x ( x - 1.15 ) 8 = 6 x x = 4.6 hence total money = 6 * 4.6 = 27.6"
Answer: b
Python program:
a = 1 * 15
b = 8 - 6
c = a / b
d = c * 6
Problem: a broker invested her own money in the stock market . during the first year , she increased her stock market wealth by 60 percent . in the second year , largely as a result of a slump in the stock market , she suffered a 30 percent decrease in the value of her stock investments . what was the net increase or decrease on her overall stock investment wealth by the end of the second year ?
Options: a ) − 5 % , b ) 5 % , c ) 12 % , d ) 20 % , e ) 80 %
Rationale: the actual answer is obtained by multiplying 160 % by 70 % and subtracting 100 % from this total . that is : 160 % × 70 % = 112 % ; 112 % − 100 % = 12 % . answer : c
Answer: c
Python program:
a = 60 / 100
b = 1 + a 
c = 30 / 100
d = 1 - c
e = b * d
f = e - 1
g = f * 100
Problem: a fair coin is tossed 3 times . what is the probability of getting at least 2 tails ?
Options: a ) 3 / 4 , b ) 3 / 2 , c ) 1 / 2 , d ) 3 / 4 , e ) 1 / 4
Rationale: "let ' s find the probability of 2 tails , 3 tails p ( ttt ) = ( ( 1 / 2 ) ^ 3 = 1 / 8 . p ( htt ) = ( 3 ! / 2 ! ) * ( 1 / 2 ) ^ 3 = 3 / 8 total probablity = 1 / 8 + 3 / 8 = 1 / 2 answer ( c )"
Answer: c
Python program:
a = math.comb(3, 2)
b = math.comb(3, 3)
c = a + b 
d = math.comb(3, 4)
e = c + d 
f = math.comb(3, 3)
g = e + f 
h = 2 ** 3
i = g / h
Problem: a 75 - liter solution of cool - drink is made from 10 % jasmine water . if 3.5 liters of jasmine and 9.5 liters of water were added to the solution , what percent of the solution is jasmine ?
Options: a ) 12.5 % , b ) 14 % , c ) 15.5 % , d ) 17 % , e ) 18.5 %
Rationale: "the percent of jasmine in the resulting solution is : ( amount of jasmine ) / ( total volume ) ( 0.1 ( 75 ) + 3.5 ) / 88 = 11 / 88 = 1 / 8 = 12.5 % the answer is a ."
Answer: a
Python program:
a = 10 / 100
b = a * 75
c = 3 + 5
Problem: a 1200 m long train crosses a tree in 120 sec , how much time will i take to pass a platform 1200 m long ?
Options: a ) 200 sec , b ) 240 sec , c ) 167 sec , d ) 197 sec , e ) 179 sec
Rationale: "l = s * t s = 1200 / 120 s = 10 m / sec . total length ( d ) = 2400 m t = d / s t = 2400 / 10 t = 240 sec answer : b"
Answer: b
Python program:
a = 1200 + 1200 
b = 1200 / 120
c = a / b
Problem: a 300 meter long train crosses a platform in 39 seconds while it crosses a signal pole in 18 seconds . what is the length of the platform .
Options: a ) 310 meter , b ) 335 meter , c ) 345 meter , d ) 350 meter , e ) none of these
Rationale: "explanation : speed = distance / time = 300 / 18 = 50 / 3 m / sec let the length of the platform be x meters then distance = speed ∗ time x + 300 = 50 / 3 ∗ 39 = > 3 ( x + 300 ) = 1950 = > x = 350 meters option d"
Answer: d
Python program:
a = 300 / 18
b = a * 39
c = b - 300
Problem: a and b go around a circular track of length 100 m on a cycle at speeds of 18 kmph and 36 kmph . after how much time will they meet for the first time at the starting point ?
Options: a ) 120 sec , b ) 198 sec , c ) 178 sec , d ) 665 sec , e ) 20 sec
Rationale: "time taken to meet for the first time at the starting point = lcm { length of the track / speed of a , length of the track / speed of b } = lcm { 100 / ( 18 * 5 / 18 ) , 100 / ( 36 * 5 / 18 ) } = lcm ( 20 , 10 ) = 20 sec . answer : e"
Answer: e
Python program:
a = 36 * const_0_2778
b = 18 * const_0_2778
c = a - b
d = 100 / c
Problem: zoey won the lottery and got $ 7 , 348340 . she wants to split it among herself and 5 friends evenly . how much money must she add if she wants to split it evenly ?
Options: a ) $ 3 , b ) $ 2 , c ) $ 9 , d ) $ 1 , e ) $ 4
Rationale: zoey and her 5 friends is 6 people in all . $ 7 , 348340 must be divisible by 6 if she wants to split it evenly . the money is divisible by 6 if it ' s divisible by 2 and 3 . 7 + 3 + 4 + 8 + 3 + 4 + 0 = 29 . 2 and 3 cant go into 29 . adding 1 dollar makes it 30 . 2 and 3 can go into 30 so 6 can also . the answer is d .
Answer: d
Python program:
a = 1000 * 1000
b = 7 * a
c = b + 348340 
d = 5 + 1 
e = reminder - (
Problem: in a certain code language , ' book ' is coded as ' pencil ' , ' pencil ' is coded as ' mirror ' , ' mirror ' is coded as ' board ' . then what is useful to write on a paper ?
Options: a ) 2 , b ) 6278 , c ) 277 , d ) 281 , e ) 22
Rationale: we use pencil to write on a paper but here pencil is coded as mirror . so , the answer is mirror . answer : a
Answer: a
Python program:
a = 2 * 1
Problem: what is the angle between the hands of a clock when time is 8 : 40 ?
Options: a ) 65 deg , b ) 75 deg , c ) 45 deg , d ) 15 deg , e ) 100 deg
Rationale: "angle between two hands = 40 h - 11 / 2 m = 40 * 8 - 40 * 11 / 2 = 320 - 220 = 100 deg answer : e"
Answer: e
Python program:
a = 3 * 2
b = 40 * a
c = b - 8
Problem: how many integers from 0 to 50 inclusive have a remainder of 3 when divided by 6 ?
Options: a ) 5 , b ) 6 , c ) 7 , d ) 8 , e ) 9
Rationale: "the numbers should be of the form 6 c + 3 . the minimum is 3 when c = 0 . the maximum is 45 when c = 7 . there are 8 such numbers . the answer is d ."
Answer: d
Python program:
a = 50 / 10
Problem: a box contains 4 red balls and 4 black balls . one by one , every ball is selected at random without replacement . what is the probability that the fourth ball selected is black ?
Options: a ) 1 / 4 , b ) 1 / 2 , c ) 1 / 2 , d ) 5 / 8 , e ) 2
Rationale: "my complicated version of your simple approach let the 4 black balls be bbbband 4 red balls be rrrr they can be arranged in 8 slots _ _ _ _ _ _ _ _ in ( 8 ! ) / ( 4 ! x 4 ! ) if the fourth slot is black ball then the arrangement will be to fill _ _ _ b _ _ _ _ we have 7 slots and 3 black ( bbb ) and 4 red ( rrrr ) they can be arranged in ( 7 ! ) / ( 4 ! x 3 ! ) hence required probability = [ ( 8 ! ) / ( 4 ! x 4 ! ) ] / [ ( 7 ! ) / ( 4 ! x 3 ! ) ] = 2 e"
Answer: e
Python program:
a = 4 + 4 
b = a / 4
Problem: if 50 % of ( x - y ) = 30 % of ( x + y ) , then what percent of x is y ?
Options: a ) 20 % , b ) 30 % , c ) 25 % , d ) 15 % , e ) 50 %
Rationale: "50 % of ( x - y ) = 30 % of ( x + y ) 50 / 100 ( x - y ) = 30 / 100 ( x + y ) x = 4 y required percentage = y / x * 100 = y / 4 y * 100 = 25 % answer is c"
Answer: c
Python program:
a = 50 - 30
b = 50 + 30 
c = a / b
d = c * 100
Problem: 30 ^ 10 / 180 ^ 5 = ?
Options: a ) 5 ^ 5 , b ) 5 ^ 6 , c ) 3 ^ 6 , d ) 6 ^ 3 , e ) 15 ^ 3
Rationale: "30 ^ 10 / 180 ^ 5 = ? a . 5 ^ 5 b . 5 ^ 6 c . 3 ^ 6 d . 6 ^ 3 e . 15 ^ 3 - > 30 ^ 10 / 180 ^ 5 = ( 30 ^ 10 ) / ( 6 ^ 5 ) ( 30 ^ 5 ) = ( 30 ^ 5 ) / ( 6 ^ 5 ) = ( 6 ^ 5 ) ( 5 ^ 5 ) / ( 6 ^ 5 ) = 5 ^ 5 . thus , a is the answer ."
Answer: a
Python program:
a = 30 ** 10
b = 30 ** 5
c = a / b
Problem: an army ’ s recruitment process included n rounds of selection tasks . for the first a rounds , the rejection percentage was 60 percent per round . for the next b rounds , the rejection percentage was 50 percent per round and for the remaining rounds , the selection percentage was 70 percent per round . if there were 100000 people who applied for the army and 245 were finally selected , what was the value of n ?
Options: a ) 4 , b ) 5 , c ) 6 , d ) 8 , e ) 9
Rationale: fastly i reduce 60 % till it gets closer to our required 2000 candidates step ( 1 ) 40000 accepted . step ( 2 ) another 40 % of 40000 = 16000 accepted . here it is quiet observable that if we further deduct candidate by 60 % it would change our probablity of easy going 2000 candidate . so i would get to second stage of recruitment where 50 % is accepted step ( 3 ) 50 % of 16000 = 8000 step ( 4 ) 50 % of 8000 = 4000 step ( 5 ) 50 % of 4000 = 2000 step ( 6 ) 50 % of 2000 = 1000 step ( 7 ) 50 % of 1000 = 500 step ( 8 ) 70 % of 500 = 350 step ( 9 ) 70 % of 350 = 245 ( our target ) total 9 steps required . ans e
Answer: e
Python program:
a = 1 + 4 
b = 2 + a 
c = b + 2
Problem: when the price of an article was reduced by 30 % its sale increased by 80 % . what was the net effect on the sale ?
Options: a ) 26 % increase , b ) 44 % decrease , c ) 60 % increase , d ) 66 % increase , e ) 66 % decrease
Rationale: "if n items are sold for $ p each , revenue is $ np . if we reduce the price by 30 % , the new price is 0.7 p . if we increase the number sold by 80 % , the new number sold is 1.8 n . so the new revenue is ( 0.7 p ) ( 1.8 n ) = 1.26 np , which is 1.26 times the old revenue , so is 26 % greater . answer : a"
Answer: a
Python program:
a = 80 + 100 
b = 100 - 30
c = a * b
d = c / 100
e = d - 100
Problem: if the simple interest on a certain sum of money for 4 years is one – fifth of the sum , then the rate of interest per annum is
Options: a ) 4 % , b ) 7 % , c ) 6 % , d ) 5 % , e ) 3 %
Rationale: "explanation : let the principal ( p ) be x then , simple interest ( si ) = x / 5 time ( t ) = 4 years rate of interest per annum ( r ) = ( 100 × si ) / pt = ( 100 × ( x / 5 ) / ( x × 4 ) = 20 / 4 = 5 % answer : option d"
Answer: d
Python program:
a = 1 + 4 
b = 100 / a
c = b / 4
Problem: the average of 11 results is 60 . if the average of first 6 results is 58 and that of the last 6 is 63 , find the sixth result ?
Options: a ) 50 , b ) 52 , c ) 65 , d ) 42 , e ) 66
Rationale: sixth result = 58 * 6 + 63 * 6 - 60 * 11 = 66 answer is e
Answer: e
Python program:
a = 6 * 58
b = 6 * 63
c = a + b 
d = 11 * 60
e = c - d
Problem: if a student loses 5 kilograms , he will weigh twice as much as his sister . together they now weigh 116 kilograms . what is the student ' s present weight in kilograms ?
Options: a ) 76 , b ) 77 , c ) 78 , d ) 79 , e ) 80
Rationale: "let x be the weight of the sister . then the student ' s weight is 2 x + 5 . x + ( 2 x + 5 ) = 116 3 x = 111 x = 37 kg then the student ' s weight is 79 kg . the answer is d ."
Answer: d
Python program:
a = 116 - 5
b = a / 3
c = 116 - b
Problem: a circular path of 13 m radius has marginal walk 2 m wide all round it . find the cost of leveling the walk at 25 p per m 2 ?
Options: a ) rs . 48 , b ) rs . 64 , c ) rs . 44 , d ) rs . 46 , e ) rs . 34
Rationale: "π ( 152 - 132 ) = 176 176 * 1 / 4 = rs . 44 answer : c"
Answer: c
Python program:
a = 13 + 2 
b = circle_area - (
c = 25 * b
Problem: tom drives from town q to town b , driving at a constant speed of 60 miles per hour . from town b tom immediately continues to town c . the distance between q and b is twice the distance between b and c . if the average speed of the whole journey was 36 mph , then what is tom ' s speed driving from b to c in miles per hour ?
Options: a ) 12 , b ) 20 , c ) 24 , d ) 30 , e ) 36
Rationale: let ' s assume that it takes 4 hours to go from point q to b . then the distance between them becomes 240 which makes distance between b and c 120 . ( 240 + 120 ) / ( 4 + x ) gives us the average speed which is 36 . you find x = 6 . so the question simplifies itself to 120 / 6 = 20 hence the answer is b .
Answer: b
Python program:
a = 60 * 36
b = 36 * 3
c = a / b
Problem: a watch was sold at a loss of 10 % . if it was sold for rs . 540 more , there would have been a gain of 8 % . what is the cost price ?
Options: a ) 1000 , b ) 2998 , c ) 3000 , d ) 2788 , e ) 2991
Rationale: "90 % 108 % - - - - - - - - 18 % - - - - 540 100 % - - - - ? = > rs . 3000 answer : c"
Answer: c
Python program:
a = 540 * 100
b = 100 + 8 
c = 100 - 10
d = b - c
e = a / d
Problem: a man took a loan from a bank at the rate of 8 % p . a . simple interest . after 3 years he had to pay rs . 5400 interest only for the period . the principal amount borrowed by him was :
Options: a ) rs . 2000 , b ) rs . 10,500 , c ) rs . 15,500 , d ) rs . 22,500 , e ) none
Rationale: solution principal = rs . ( 100 x 5400 / 8 x 3 ) = rs . 22,500 . answer d
Answer: d
Python program:
a = 5400 * 100
b = 3 * 8
c = a / b
d = const_60 / 4
e = d * 100
f = c / e
Problem: what is the remainder when the number q = 14 ^ 2 * 15 ^ 8 is divided by 5 ?
Options: a ) 0 , b ) 1 , c ) 2 , d ) 4 , e ) 5
Rationale: 14 ^ 2 has units digit 6 15 ^ 8 has units digit 5 thus q = 14 ^ 2 * 15 ^ 8 has units digit 0 and will be divisible by 5 . the remainder will be zero answer : ( a )
Answer: a
Python program:
a = 5 / 5
Problem: a jar contains 3 black , 3 white and 1 green balls . if you pick two balls at the same time , what ' s the probability that one ball is black and one is white ?
Options: a ) 2 / 7 , b ) 5 / 7 , c ) 4 / 7 , d ) 3 / 7 , e ) 1 / 2
Rationale: p ( 1 st black , 2 nd white ) = 3 / 7 * 3 / 6 = 9 / 42 ; p ( 1 st white , 2 nd black ) = 3 / 7 * 3 / 6 = 9 / 42 . p = 9 / 42 + 9 / 42 = 18 / 42 = 3 / 7 . answer : d .
Answer: d
Python program:
a = 3 + 3 
b = a + 1 
c = b - 1
d = 3 / c
e = 3 + 3 
f = 3 + 3 
g = f + 1 
h = e / g
i = d * h