euclaise/mathqa_programs huggingface dataset:
Problem: 1297 x 1297 = ?
Options: a ) a ) 1682209 , b ) b ) 1951601 , c ) c ) 1951602 , d ) d ) 1951603 , e ) e ) 1951604
Rationale: "1297 x 1297 = ( 1297 ) 2 = ( 1300 - 3 ) 2 = ( 1300 ) 2 + ( 3 ) 2 - ( 2 x 1300 x 3 ) = 1690000 + 9 - 7800 = 1690009 - 7800 = 1682209 . answer : a"
Answer: a
Python program:
a = 1297 / 1297
b = a * 100
Problem: 80 percent of the members of a study group are women , and 40 percent of those women are lawyers . if one member of the study group is to be selected at random , what is the probability that the member selected is a woman lawyer ?
Options: a ) 0.45 , b ) 0.55 , c ) 0.65 , d ) 0.32 , e ) 0.35
Rationale: say there are 100 people in that group , then there would be 0.8 * 0.40 * 100 = 32 women lawyers , which means that the probability that the member selected is a woman lawyer is favorable / total = 32 / 100 . answer : d
Answer: d
Python program:
a = 5 * 5
b = a * 4
c = 80 / b
d = 5 * 5
e = d * 4
f = 40 / e
g = c * f
Problem: if a and b are positive integers and ( 2 ^ a ) ^ b = 2 ^ 5 , what is the value of 2 ^ a * 2 ^ b ?
Options: a ) 8 , b ) 64 , c ) 16 , d ) 32 , e ) 4
Rationale: "2 ^ ab = 2 ^ 5 therefore ab = 5 either a = 1 or 5 or b = 5 or 1 therefore 2 ^ a * 2 ^ b = 2 ^ ( a + b ) = 2 ^ 6 = 64 b"
Answer: b
Python program:
a = 2 ** 2
b = a * 2
Problem: if money is invested at r percent interest , compounded annually , the amount of investment will double in approximately 70 / r years . if pat ' s parents invested $ 8000 in a long term bond that pays 8 percent interest , compounded annually , what will be the approximate total amount of investment 18 years later , when pat is ready for college ?
Options: a ) $ 20000 , b ) $ 15000 , c ) $ 32000 , d ) $ 10000 , e ) $ 9000
Rationale: "since investment doubles in 70 / r years then for r = 8 it ' ll double in 70 / 8 = ~ 9 years ( we are not asked about the exact amount so such an approximation will do ) . thus in 18 years investment will double twice and become ( $ 8,000 * 2 ) * 2 = $ 32,000 ( after 9 years investment will become $ 8,000 * 2 = $ 16,000 and in another 9 years it ' ll become $ 16,000 * 2 = $ 32,000 ) . answer : c ."
Answer: c
Python program:
a = 8000 * 2
b = a * 2
Problem: the average ( arithmetic mean ) of the even integers from 0 to 120 inclusive is how much greater than the average ( arithmetic mean ) of the even integers from 0 to 60 inclusive ?
Options: a ) 10 , b ) 15 , c ) 20 , d ) 30 , e ) 60
Rationale: "the sum of even numbers from 0 to n is 2 + 4 + . . . + n = 2 ( 1 + 2 + . . . + n / 2 ) = 2 ( n / 2 ) ( n / 2 + 1 ) / 2 = ( n / 2 ) ( n / 2 + 1 ) the average is ( n / 2 ) ( n / 2 + 1 ) / ( n / 2 + 1 ) = n / 2 the average of the even numbers from 0 to 120 is 120 / 2 = 60 the average of the even numbers from 0 to 60 is 60 / 2 = 30 the answer is d ."
Answer: d
Python program:
a = 60 + 0 
b = a / 2
c = 120 + 0 
d = c / 2
e = b - d
Problem: a batsman scored 120 runs which included 3 boundaries and 8 sixes . what percent of his total score did he make by running between the wickets ?
Options: a ) 45 ( 4 / 11 ) % , b ) 50 % , c ) 45 ( 5 / 11 ) % , d ) 44 ( 5 / 11 ) % , e ) none of these
Rationale: "explanation : total runs scored = 120 total runs scored from boundaries and sixes = 3 x 4 + 8 x 6 = 60 total runs scored by running between the wickets = 120 - 60 = 60 required % = ( 60 / 120 ) × 100 = 50 % answer : option b"
Answer: b
Python program:
a = 3 * 8
b = 8 * 3
c = a + b 
d = 120 - c
e = d / 120
f = e * 100
Problem: the average age of 6 men increases by 3 years when two women are included in place of two men of ages 24 and 26 years . find the average age of the women ?
Options: a ) 37 , b ) 26 , c ) 34 , d ) 18 , e ) 11
Rationale: explanation : 24 + 26 + 6 * 3 = 68 / 2 = 34 answer : c
Answer: c
Python program:
a = 24 + 26 
b = 6 * 3
c = a + b 
d = c / 2
Problem: | 9 - 4 | - | 12 - 14 | = ?
Options: a ) 3 , b ) 2 , c ) 1 , d ) 0 , e ) 4
Rationale: "| 9 - 4 | - | 12 - 14 | = | 5 | - | - 2 | = 5 - 2 = 3 correct answer a"
Answer: a
Python program:
a = 9 - 4
b = 14 - 12
c = a - b
Problem: a school has received 80 % of the amount it needs for a new building by receiving a donation of $ 600 each from people already solicited . people already solicited represent 40 % of the people from whom the school will solicit donations . how much average contribution is requited from the remaining targeted people to complete the fund raising exercise ?
Options: a ) $ 200 , b ) 100 , c ) $ 105 , d ) $ 250 , e ) $ 300
Rationale: "let us suppose there are 100 people . 40 % of them donated $ 24000 ( 600 * 40 ) $ 24000 is 80 % of total amount . so total amount = 24000 * 100 / 80 remaining amount is 20 % of total amount . 20 % of total amount = 24000 * ( 100 / 80 ) * ( 20 / 100 ) = 6000 this amount has to be divided by 60 ( remaining people are 60 ) so per head amount is 6000 / 60 = $ 100 answer : b"
Answer: b
Python program:
a = 40 / 100
b = a * 600
c = 80 / 100
d = b / c
e = 40 / 100
f = d * e
g = 80 / 100
h = f / g
Problem: if 4 ^ k = 5 , then 4 ^ ( 2 k + 2 ) =
Options: a ) 400 , b ) 540 , c ) 100 , d ) 830 , e ) 420
Rationale: "4 ^ k = 5 4 ^ 2 k = 5 ^ 2 4 ^ 2 k = 25 4 ^ ( 2 k + 2 ) = 4 ^ 2 k * 4 ^ 2 = 25 * 16 = 400 answer : a"
Answer: a
Python program:
a = 5 ** 2
b = 4 ** 2
c = a * b
Problem: there are 16 stations between hyderabad and bangalore . how many second class tickets have to be printed , so that a passenger can travel from any station to any other station ?
Options: a ) 288 , b ) 267 , c ) 261 , d ) 211 , e ) 306
Rationale: the total number of stations = 18 from 18 stations we have to choose any two stations and the direction of travel ( i . e . , hyderabad to bangalore is different from bangalore to hyderabad ) in 18 p ₂ ways . 18 p ₂ = 18 * 17 = 306 . answer : e
Answer: e
Python program:
a = 16 + 1 
b = 16 + 1 
c = b + 1 
d = a * c
Problem: an auction house charges a commission of 15 % on the first $ 50,000 of the sale price of an item , plus 10 % on the amount of of the sale price in excess of $ 50,000 . what was the price of a painting for which the house charged a total commission of $ 24,000 ?
Options: a ) $ 115,000 , b ) $ 160,000 , c ) $ 215,000 , d ) $ 240,000 , e ) $ 365,000
Rationale: say the price of the house was $ x , then 0.15 * 50,000 + 0.1 * ( x - 50,000 ) = 24,000 - - > x = $ 215,000 ( 15 % of $ 50,000 plus 10 % of the amount in excess of $ 50,000 , which is x - 50,000 , should equal to total commission of $ 24,000 ) . answer : c
Answer: c
Python program:
a = 15 * 10
b = a + 10
Problem: a man travelled for 13 hours . he covered the first half of the distance at 20 kmph and remaining half of the distance at 25 kmph . find the distance travelled by the man ?
Options: a ) 168 km , b ) 864 km , c ) 200 km , d ) 240 km , e ) 460 km
Rationale: let the distance travelled be x km . total time = ( x / 2 ) / 20 + ( x / 2 ) / 25 = 13 = > x / 40 + x / 50 = 13 = > ( 5 x + 4 x ) / 200 = 13 = > x = 200 km answer : c
Answer: c
Python program:
a = 13 / 3
b = a * 20
c = 13 / 3
d = c * 25
e = b + d
Problem: in the storage room of a certain bakery , the ratio of sugar to flour is 5 to 4 , and the ratio of flour to baking soda is 10 to 1 . if there were 60 more pounds of baking soda in the room , the ratio of flour to baking soda would be 8 to 1 . how many pounds of sugar are stored in the room ?
Options: a ) 600 , b ) 1200 , c ) 1500 , d ) 1600 , e ) 3000
Rationale: sugar : flour = 5 : 4 = 25 : 20 ; flour : soda = 10 : 1 = 20 : 2 ; thus we have that sugar : flour : soda = 25 x : 20 x : 2 x . also given that 20 x / ( 2 x + 60 ) = 8 / 1 - - > x = 120 - - > sugar = 25 x = 3,000 answer : e .
Answer: e
Python program:
a = 5 / 4
b = 8 * 60
c = 10 - 8
d = b / c
e = 10 * d
f = a * e
Problem: a can do a work in 2 days . b can do the same work in 3 days . both a & b together will finish the work and they got $ 500 from that work . find their shares ?
Options: a ) 100,200 , b ) 400,100 , c ) 300,150 , d ) 300,200 , e ) 250,250
Rationale: "ratio of their works a : b = 2 : 3 ratio of their wages a : b = 3 : 2 a ' s share = ( 3 / 5 ) 500 = 300 b ' s share = ( 2 / 5 ) 500 = 200 correct option is d"
Answer: d
Python program:
a = 2 * 3
b = 2 + 3 
c = a / b
Problem: the cost price of a radio is rs . 1890 and it was sold for rs . 1500 , find the loss % ?
Options: a ) 18 , b ) 20 , c ) 77 , d ) 66 , e ) 41
Rationale: "1890 - - - - 390 100 - - - - ? = > 20 % answer : b"
Answer: b
Python program:
a = 1890 - 1500
b = a / 1890
c = b * 100
Problem: if the price of petrol increases by 44 , by how much must a user cut down his consumption so that his expenditure on petrol remains constant ?
Options: a ) 25 % , b ) 20 % , c ) 16.67 % , d ) 33.33 % , e ) none of these
Rationale: "explanation : let us assume before increase the petrol will be rs . 100 . after increase it will be rs ( 100 + 44 ) i . e 144 . now , his consumption should be reduced to : - = ( 144 − 100 ) / 144 ∗ 100 . hence , the consumption should be reduced to 30.6 % . answer : e"
Answer: e
Python program:
a = 100 + 44 
b = 100 / a
c = 1 - b
d = c * 100
Problem: a certain sum is invested at simple interest at 15 % p . a . for two years instead of investing at 12 % p . a . for the same time period . therefore the interest received is more by rs . 840 . find the sum ?
Options: a ) rs . 7000 , b ) rs . 9000 , c ) rs . 14000 , d ) rs . 17000 , e ) rs . 27000
Rationale: let the sum be rs . x . ( x * 15 * 2 ) / 100 - ( x * 12 * 2 ) / 100 = 840 = > 30 x / 100 - 24 x / 100 = 840 = > 6 x / 100 = 840 = > x = 14000 . answer : c
Answer: c
Python program:
a = 15 - 12
b = a * 2
c = b / 100
d = 840 / c
Problem: what is 35 % of 4 / 13 of 715 ?
Options: a ) 44 , b ) 55 , c ) 66 , d ) 77 , e ) 88
Rationale: "this problem can be solved easily if we just use approximation : 35 % is a little over 1 / 3 , while 4 / 13 is a little less than 4 / 12 , which is 1 / 3 . thus , the answer is about 1 / 3 of 1 / 3 of 715 , or 1 / 9 of 715 . since the first 1 / 3 is a slight underestimate and the second 1 / 3 is a slight overestimate , the errors will partially cancel each other out . our estimate will be relatively accurate . the number 715 is about 720 , so ( 1 / 9 ) * 715 will be a bit less than 80 . keeping track not only of your current estimate , but also of the degree to which you have overestimated or underestimated , can help you pinpoint the correct answer more confidently . the closest answer is 77 , so this is the answer to choose . the answer is d ."
Answer: d
Python program:
a = 3 + 2 
b = a * 2
c = 3 * 4
d = c * 100
e = b * d
f = 3 + 4 
g = 3 + 2 
h = f * g
i = 3 + 2 
j = i * 2
k = h * j
l = e + k 
m = 3 + 3 
n = l + m 
o = 35 * n
p = o / 100
Problem: 16 welders work at a constant rate they complete an order in 8 days . if after the first day , 9 welders start to work on the other project , how many more days the remaining welders will need to complete the rest of the order ?
Options: a ) 5 , b ) 2 , c ) 8 , d ) 4 , e ) 16
Rationale: "1 . we need to find out the time taken by 7 workers after day 1 . 2 . total no . of wokers * total time taken = time taken by 1 worker 3 . time taken by 1 worker = 16 * 8 = 128 days 4 . but on day 1 sixteen workers had already worked finishing 1 / 8 of the job . so 7 workers have to finish only 7 / 8 of the job . 5 . total time taken by 7 workers can be got from formula used at ( 2 ) . i . e . , 7 * total time taken = 128 . total time taken by 7 workers to finish the complete job is 128 / 7 = 18.286 days . 6 . time taken by 7 workers to finish 7 / 8 of the job is 7 / 8 * 18.286 = 16 days . the answer is choice e"
Answer: e
Python program:
a = 16 * 8
b = 1 / a
c = b * 16
d = 1 - c
e = 16 - 9
f = d / e
g = 16 * 8
h = 1 / g
i = f / h
Problem: if the radius of a circle is decreased by 50 % , find the percentage decrease in its area .
Options: a ) 25 % , b ) 50 % , c ) 75 % , d ) 95 % , e ) none of them
Rationale: "let original radius = r . new radius = ( 50 / 100 ) r = ( r / 2 ) original area = 22 / 7 ( r ) 2 = and new area =  ( ( r / 2 ) ) 2 = (  ( r ) 2 ) / 4 decrease in area = ( ( 3 ( 22 / 7 ) ( r ) 2 ) / 4 x ( 1 / ( 22 / 7 ) ( r ) 2 ) x 100 ) % = 75 % answer is c ."
Answer: c
Python program:
a = 100 / 100
b = 100 / 100
c = 50 / 100
d = b - c
e = d ** 2
f = a - e
g = f * 100
Problem: what is the least number of squares tiles required to pave the floor of a room 8 m 82 cm long and 2 m 52 cm broad ?
Options: a ) 14 , b ) 20 , c ) 40 , d ) 44 , e ) 48
Rationale: "length of largest tile = h . c . f . of 882 cm and 252 cm = 126 cm . area of each tile = ( 126 x 126 ) cm 2 . required number of tiles = 882 x 252 / ( 126 ^ 2 ) = 14 . answer : a"
Answer: a
Python program:
a = 8 * 100
b = 82 * 100
c = rectangle_area / (
Problem: a coin is tossed 8 times . what is the probability of getting exactly 7 heads ?
Options: a ) 1 / 8 , b ) 1 / 16 , c ) 1 / 32 , d ) 1 / 64 , e ) 1 / 128
Rationale: "the number of possible outcomes is 2 ^ 8 = 256 there are 8 ways to get exactly 7 heads . p ( exactly 7 heads ) = 8 / 256 = 1 / 32 the answer is c ."
Answer: c
Python program:
a = 1 / 2
b = a ** 7
c = math.comb(8, 7)
d = 1 / 2
e = c * d
f = b * e
Problem: the price of a jacket is reduced by 25 % . during a special sale the price of the jacket is reduced another 30 % . by approximately what percent must the price of the jacket now be increased in order to restore it to its original amount ?
Options: a ) 105 , b ) 45 , c ) 85 , d ) 95 , e ) 90.5
Rationale: "1 ) let the price of jacket initially be $ 100 . 2 ) then it is decreased by 25 % , therefore bringing down the price to $ 75 . 3 ) again it is further discounted by 30 % , therefore bringing down the price to $ 52.5 . 4 ) now 52.5 has to be added byx % in order to equal the original price . 52.5 + ( x % ) 52.5 = 100 . solving this eq for x , we get x = 90.5 ans is e"
Answer: e
Python program:
a = 100 - 25
b = 100 - 25
c = 30 / 100
d = b * c
e = a - d
f = 100 - e
g = 100 - 25
h = 100 - 25
i = 30 / 100
j = h * i
k = g - j
l = f / k
m = 100 * l
Problem: tough and tricky questions : word problems . mike , sarah and david decided to club together to buy a present . each of them gave equal amount of money . luckily sarah negotiated a 20 % discount for the present so that each of them paid 4 dollars less . how much did they pay for a present ?
Options: a ) 20 , b ) 36 , c ) 48 , d ) 60 , e ) 72
Rationale: answer c . we know that sarah negotiated a discount of 20 % , so each of them paid $ 4 less . since there are three people , the 20 % of the original price amounts to $ 12 . 5 times 12 $ is 60 $ , so the original price , before sarah negotiated the discount , had been $ 60 . they paid $ 12 less than the base price , so they spent $ 48 .
Answer: c
Python program:
a = 4 * 3
b = a * 100
c = b / 20
d = 20 * 4
e = c * d
f = e / 100
Problem: if each digit in the set a = { 1 , 2 , 3 , 4 , 5 , 6 , 7 , 8 , 9 } is used exactly once , in how many ways can the digits be arranged ?
Options: a ) 356,580 , b ) 358,680 , c ) 360,780 , d ) 362,880 , e ) 364,980
Rationale: "9 ! = 362,880 the answer is d ."
Answer: d
Python program:
a = math.factorial(6)
Problem: 8 ^ 100 is divisible by 17 . find the remainder ?
Options: a ) 10 , b ) 12 , c ) 16 , d ) 18 , e ) 20
Rationale: "this is an extremely difficult problem to solve with out fermat ' s little theorem . by applying fermat ' s little theorem , we know that 816 when divided by 17 , the remainder is 1 . so divide 100 by 16 and find the remainder . remainder = 4 therefore , 100 = ( 16 × 6 ) + 4 now this problem can be written as 810017 = 816 × 6 + 417 = ( 816 ) 6 × 8417 now this problem simply boils down to ( 1 ) 6 × 8417 = 8417 84 = 82 × 82 , we need to find the remainder when 64 × 64 is divisible by 17 . or 13 × 13 = 169 . when 169 is divided by 17 , remainder is 16 . c"
Answer: c
Python program:
a = 17 - 8
Problem: in a competitive examination in a state a , 6 % candidates got selected from the total appeared candidates . state b had an equal number of candidates appeared and 7 % candidates got selected with 80 more candidates got selected than a . what was the number of candidates appeared from each state ?
Options: a ) 8000 , b ) 7540 , c ) 6500 , d ) 9100 , e ) 6000
Rationale: let the number of candidates appeared be x then , 7 % of x - 6 % of x = 80 1 % of x = 80 x = 80 * 100 = 8000 answer is a
Answer: a
Python program:
a = 7 - 6
b = a * 100
c = b * 80
Problem: how many natural numbers are there between 23 and 100 which are exactly divisible by 6 ?
Options: a ) 13 , b ) 25 , c ) 87 , d ) 49 , e ) 63
Rationale: explanation : required numbers are 24 , 30 , 36 , 42 , . . . , 96 this is an a . p . in which a = 24 , d = 6 and l = 96 let the number of terms in it be n . then tn = 96 a + ( n - 1 ) d = 96 24 + ( n - 1 ) x 6 = 96 ( n - 1 ) x 6 = 72 ( n - 1 ) = 12 n = 13 required number of numbers = 13 . a )
Answer: a
Python program:
a = 100 - 4
b = 23 + 1 
c = a - b
d = c / 6
e = d + 1
Problem: at a loading dock , each worker on the night crew loaded 3 / 4 as many boxes as each worker on the day crew . if the night crew has 4 / 9 as many workers as the day crew , what fraction of all the boxes loaded by the two crews did the day crew load ?
Options: a ) 1 / 2 , b ) 2 / 5 , c ) 3 / 4 , d ) 4 / 5 , e ) 5 / 8
Rationale: "method : x = no . of boxes loaded by day crew . boxes by night crew = 3 / 4 * 4 / 9 x = 1 / 3 x % loaded by day crew = x / ( x + 1 / 3 x ) = 3 / 4 answer c"
Answer: c
Python program:
a = 9 * 4
b = 9 * 4
c = 3 * 4
d = b + c 
e = a / d
Problem: a bowl was filled with 10 ounces of water , and 0.0008 ounce of the water evaporated each day during a 50 - day period . what percent of the original amount of water evaporated during this period ?
Options: a ) 0.004 % , b ) 0.04 % , c ) 0.40 % , d ) 4 % , e ) 40 %
Rationale: total amount of water evaporated each day during a 50 - day period = . 0008 * 50 = . 0008 * 100 / 2 = . 08 / 2 = . 04 percent of the original amount of water evaporated during this period = ( . 04 / 10 ) * 100 % = 0.4 % answer c
Answer: c
Python program:
a = 50 * 0
b = a / 10
c = b * 100
Problem: if x ¤ y = ( x + y ) ^ 2 - ( x - y ) ^ 2 . then √ 5 ¤ √ 5 =
Options: a ) 0 , b ) 5 , c ) 10 , d ) 15 , e ) 20
Rationale: "x = √ 5 and y also = √ 5 applying the function ( √ 5 + √ 5 ) ^ 2 - ( √ 5 - √ 5 ) ^ 2 = ( 2 √ 5 ) ^ 2 - 0 = 4 x 5 = 20 . note : alternative approach is the entire function is represented as x ^ 2 - y ^ 2 = ( x + y ) ( x - y ) which can be simplified as ( x + y + x - y ) ( x + y - ( x - y ) ) = ( 2 x ) ( 2 y ) = 4 xy . substituting x = √ 5 and y = √ 5 you get the answer 20 answer is e ."
Answer: e
Python program:
a = math.sqrt(5)
b = math.sqrt(5)
c = a + b 
d = c ** 2
Problem: 31 of the scientists that attended a certain workshop were wolf prize laureates , and 16 of these 31 were also nobel prize laureates . of the scientists that attended that workshop and had not received the wolf prize , the number of scientists that had received the nobel prize was 3 greater than the number of scientists that had not received the nobel prize . if 50 of the scientists attended that workshop , how many of them were nobel prize laureates ?
Options: a ) a ) 11 , b ) b ) 18 , c ) c ) 24 , d ) d ) 27 , e ) d ) 36
Rationale: lets solve by creating equation . . w = 31 . . total = 50 . . not w = 50 - 31 = 19 . . now let people who were neither be x , so out of 19 who won nobel = x + 3 . . so x + x + 3 = 19 or x = 8 . . so who won nobel but not wolf = x + 3 = 11 . . but people who won both w and n = 13 . . so total who won n = 11 + 16 = 27 . . d
Answer: d
Python program:
a = 50 - 31
b = a - 3
c = b / 2
d = 3 + c 
e = d + 16
Problem: which number should replace both the asterisks in ( * / 20 ) x ( * / 180 ) = 1 ?
Options: a ) 20 , b ) 40 , c ) 60 , d ) 90 , e ) 120
Rationale: "let ( y / 20 ) x ( y / 180 ) = 1 y ^ 2 = 20 x 180 = 20 x 20 x 9 y = ( 20 x 3 ) = 60 the answer is c ."
Answer: c
Python program:
a = 180 * 20
b = math.sqrt(a)
Problem: how many seconds will a train 100 meters long take to cross a bridge 150 meters long if the speed of the train is 18 kmph ?
Options: a ) 80 sec , b ) 20 sec , c ) 40 sec , d ) 50 sec , e ) 60 sec
Rationale: "d = 100 + 150 = 250 s = 18 * 5 / 18 = 5 mps t = 250 / 5 = 50 sec d ) 50 sec"
Answer: d
Python program:
a = 150 + 100 
b = 18 * const_0_2778
c = a / b
Problem: what is the sum of all even numbers from 1 to 701 ?
Options: a ) 122821 , b ) 281228 , c ) 281199 , d ) 122850 , e ) 128111
Rationale: "explanation : 700 / 2 = 350 350 * 351 = 122850 answer : d"
Answer: d
Python program:
a = 1 * 701
b = a / 4
Problem: two numbers have a h . c . f of 11 and a product of two numbers is 1991 . find the l . c . m of the two numbers ?
Options: a ) 140 , b ) 181 , c ) 160 , d ) 170 , e ) 180
Rationale: "l . c . m of two numbers is given by ( product of the two numbers ) / ( h . c . f of the two numbers ) = 1991 / 11 = 181 . answer : b"
Answer: b
Python program:
a = 1991 / 11
Problem: at what price must an book costing $ 47.50 be marked in order that after deducting 15 % from the list price . it may be sold at a profit of 25 % on the cost price ?
Options: a ) 72.85 , b ) 69.85 , c ) 62.85 , d ) 82.85 , e ) 60.85
Rationale: "c $ 62.50 cp = 47.50 sp = 47.50 * ( 125 / 100 ) = 59.375 mp * ( 85 / 100 ) = 59.375 mp = 69.85 b"
Answer: b
Python program:
a = 100 + 25 
b = 47 * 50
c = b / 100
d = 100 - 15
e = c / d
f = e * 100
Problem: 16.02 × 0.001 = ?
Options: a ) 0.1602 , b ) 0.001602 , c ) 1.6021 , d ) 0.01602 , e ) none of these
Rationale: "16.02 × 0.001 = ? or , ? = 0.01602 answer d"
Answer: d
Python program:
a = 16 / 2
b = a * 100
Problem: find the numbers which are in the ratio 3 : 2 : 3 such that the sum of the first and the second added to the difference of the third and the second is 24 ?
Options: a ) 4 , 3,22 , b ) 4 , 4,22 , c ) 9 , 3,32 , d ) 9 , 6,12 , e ) 18 , 12,18
Rationale: "let the numbers be a , b and c . a : b : c = 3 : 2 : 3 given , ( a + b ) + ( c - b ) = 24 = > a + c = 24 = > 3 x + 3 x = 24 = > x = 6 a , b , c are 3 x , 2 x , 3 x a , b , c are 18 , 12 , 18 . answer : e"
Answer: e
Python program:
a = 3 * 3
b = a / 3
Problem: in one hour , a boat goes 13 km along the stream and 5 km against the stream . the speed of the boat in still water ( in km / hr ) is :
Options: a ) 2 , b ) 4 , c ) 9 , d ) 12 , e ) 15
Rationale: "sol . speed in still water = 1 / 2 ( 13 + 5 ) kmph = 9 kmph . answer c"
Answer: c
Python program:
a = 13 + 5 
b = a / 2
Problem: a library has an average of 510 visitors on sundays and 240 on other days . what is the average number of visitors per day in a month of 30 days beginning with a sunday ?
Options: a ) 290 , b ) 304 , c ) 285 , d ) 270 , e ) 275
Rationale: "in a month of 30 days beginning with a sunday , there will be 4 complete weeks and another two days which will be sunday and monday . hence there will be 5 sundays and 25 other days in a month of 30 days beginning with a sunday average visitors on sundays = 510 total visitors of 5 sundays = 510 × 5 average visitors on other days = 240 total visitors of other 25 days = 240 × 25 total visitors = ( 510 × 5 ) + ( 240 × 25 ) total days = 30 average number of visitors per day = ( ( 510 × 5 ) + ( 240 × 25 ) ) / 30 = ( ( 51 × 5 ) + ( 24 × 25 ) ) / 3 = ( 17 × 5 ) + ( 8 × 25 ) = 85 + 200 = 285 answer is c ."
Answer: c
Python program:
a = 3 + 4 
b = 30 / a
c = math.floor(b)
d = c + 1 
e = d * 510
f = 3 + 4 
g = 30 / f
h = math.floor(g)
i = h + 1 
j = 30 - i
k = j * 240
l = e + k 
m = l / 30
Problem: if each participant of a chess tournament plays exactly one game with each of the remaining participants , then 231 games will be played during the tournament . what is the number of participants ?
Options: a ) 16 , b ) 18 , c ) 20 , d ) 22 , e ) 24
Rationale: "let n be the number of participants . the number of games is nc 2 = n * ( n - 1 ) / 2 = 231 n * ( n - 1 ) = 462 = 22 * 21 ( trial and error ) the answer is d ."
Answer: d
Python program:
a = 231 * 2
b = a * 4
c = b + 1 
d = math.sqrt(c)
e = d + 1 
f = e / 2