euclaise/mathqa_programs huggingface dataset:
Problem: the length of a rectangular field is 7 / 5 its width . if the perimeter of the field is 384 meters , what is the width of the field ?
Options: a ) 50 , b ) 60 , c ) 11 , d ) 80 , e ) 90
Rationale: "let l be the length and w be the width . l = ( 7 / 5 ) w perimeter : 2 l + 2 w = 384 , 2 ( 7 / 5 ) w + 2 w = 384 solve the above equation to find : w = 80 m and l = 112 m . correct answer d ) 80"
Answer: d
Python program:
a = 7 / 5
b = 7 / 5
c = a + b 
d = c + 2 
e = 384 / d
Problem: speed of a boat in standing water is 16 kmph and the speed of the stream is 2 kmph . a man rows to a place at a distance of 7740 km and comes back to the starting point . the total time taken by him is :
Options: a ) 914.2 hours , b ) 900 hours , c ) 915 hours , d ) 982.9 hours , e ) 915 hours
Rationale: "explanation : speed downstream = ( 16 + 2 ) = 18 kmph speed upstream = ( 16 - 2 ) = 14 kmph total time taken = 7740 / 18 + 7740 / 14 = 430 + 552.9 = 982.9 hours answer : option d"
Answer: d
Python program:
a = 16 + 2 
b = 7740 / a
c = 16 - 2
d = 7740 / c
e = b + d
Problem: 72 67 66 61 60 . . . ?
Options: a ) 52 , b ) 53 , c ) 54 , d ) 55 , e ) 56
Rationale: "sequence = 72 67 66 61 60 55 there is 2 series : 1 st series = 72 66 60 ( decreasing by 6 ) 2 nd series = 67 61 55 ( decreasing by 6 ) answer : d"
Answer: d
Python program:
a = 67 / 66
b = 72 + a 
c = b * 61
d = c / 100
Problem: a train is running at a speed of 40 km / hr and it crosses a post in 25.2 seconds . what is the length of the train ?
Options: a ) 190 metres , b ) 160 metres , c ) 280 metres , d ) 120 metres , e ) 250 metres
Rationale: "speed of the train , v = 40 km / hr = 40000 / 3600 m / s = 400 / 36 m / s time taken to cross , t = 25.2 s distance covered , d = vt = ( 400 / 36 ) ã — 25.2 = 280 m distance covered is equal to the length of the train = 280 m correct answer is 280 metres c"
Answer: c
Python program:
a = 40 * const_0_2778
b = 25 * 2
Problem: speed of a boat in standing water is 8 kmph and the speed of the stream is 6 kmph . a man rows to place at a distance of 210 km and comes back to the starting point . the total time taken by him is :
Options: a ) 120 hours , b ) 240 hours , c ) 160 hours , d ) 480 hours , e ) none
Rationale: "sol . speed upstream = 2 kmph ; speed downstream = 14 kmph . ∴ total time taken = [ 210 / 2 + 210 / 2 ] hours = 120 hours . answer a"
Answer: a
Python program:
a = 8 + 6 
b = 210 / a
c = 8 - 6
d = 210 / c
e = b + d
Problem: a rectangular garden is to be twice as long as it is wide . if 300 yards of fencing , including the gate , will completely enclose the garden , what will be the length of the garden , in yards ?
Options: a ) 40 , b ) 50 , c ) 60 , d ) 70 , e ) 100
Rationale: "alternate approach backsolving ( using answer options to reach the correct answer ) can work wonders here if one is fast in calculations . given perimeter is 300 so , 2 ( l + b ) = 300 or , l + b = 150 now use the answer options ( given length ; breath will be half the length ) ( a ) 40 l = 40 ; b = 20 l + b = 60 ( b ) 50 l = 50 ; b = 25 l + b = 75 ( c ) 60 l = 60 ; b = 30 l + b = 90 ( d ) 70 l = 70 ; b = 35 l + b = 105 ( e ) 100 l = 100 ; b = 50 l + b = 150 thus you see no , need of any calculations , u can reach the correct option only by checking options ; correct answer will be ( e )"
Answer: e
Python program:
a = 2 + 1 
b = a * 2
c = 300 / b
d = c * 2
Problem: the average age of 35 students in a class is 16 years . the average age of 21 students is 14 . what is the average age of remaining 19 students ?
Options: a ) 14 years , b ) 17 years , c ) 19 years , d ) 21 years , e ) none
Rationale: "solution sum of the ages of 14 students = ( 16 x 35 ) - ( 14 x 21 ) = 560 - 294 . = 266 . ∴ required average = 266 / 19 = 14 years . answer a"
Answer: a
Python program:
a = 35 * 16
b = a + 21 
c = b + 35 
d = 35 * 16
e = c - d
Problem: if each side of a right triangle is increased by 10 % and the base ( b ) is half of the height , find the percentage change in its area ?
Options: a ) 26 %
b ) 21 %
c ) 15 %
d ) 18 %
e ) 12 %
Rationale: a = 1 / 2 x b x h or 1 / 2 x 2 a x a ( for simplification ) new h = 220 a / 100 = 22 a / 10 new b = ( 110 a x 100 ) = = 11 a / 10 new area = 1 / 2 ( 22 a x 11 a ) / ( 10 x 10 ) = ( 121 a ² / 100 ) increased area = = ( 121 a ² / 100 ) - a ² increase % = [ ( 21 a ² / 100 ) x ( 1 / a ² ) x 100 ] % = 21 % answer : b
Answer: b
Python program:
a = 100 + 10 
b = a / 100
c = b ** 2
d = c - 1
e = d * 100
Problem: the calendar of the year 2032 can be used again in the year ?
Options: a ) 2060 , b ) 2050 , c ) 2040 , d ) 2033 , e ) 2034
Rationale: explanation : given year 2032 when divided by 4 , leaves a remainder 0 . note : when remainder is 0 , 28 is added to the given year to get the result . so , 2032 + 28 = 2060 answer : a
Answer: a
Python program:
a = 4 * 4
b = a - 2
c = b * 2
d = c + 2032
Problem: a sum of money at simple interest amounts to rs . 825 in 3 years and to rs . 840 in 4 years . the sum is ?
Options: a ) s . 738 , b ) s . 638 , c ) s . 777 , d ) s . 730 , e ) s . 735
Rationale: "s . i . for 1 year = ( 841 - 825 ) = rs . 16 s . i . for 3 years = 16 * 3 = rs . 48 principal = ( 825 - 48 ) = rs . 777 . answer : c"
Answer: c
Python program:
a = 840 - 825
b = a * 3
c = b / 4
d = 825 - c
Problem: if p is the product of the integers from 1 to 35 , inclusive , what is the greatest integer k for which 3 ^ k is a factor of p ?
Options: a ) 11 , b ) 13 , c ) 15 , d ) 17 , e ) 19
Rationale: "35 ! has 3 , 6 , 9 , . . . . 30 , 33 as factors , which are 11 multiples of 3 . we need to add 4 more to these 11 because of 9 , 18 , and 27 . the greatest integer of k is 15 . the answer is c ."
Answer: c
Python program:
a = 3 * 4
b = a + 3
Problem: the simple form of the ratio 4 / 5 : 8 / 9 is ?
Options: a ) 5 : 8 , b ) 4 : 9 , c ) 5 : 9 , d ) 5 : 3 , e ) 9 : 10
Rationale: 4 / 5 : 8 / 9 = 9 : 10 answer : e
Answer: e
Python program:
a = 8 / 9
Problem: what is the difference between the c . i . on rs . 6000 for 1 1 / 2 years at 4 % per annum compounded yearly and half - yearly ?
Options: a ) s . 2.04 , b ) s . 2.08 , c ) s . 2.02 , d ) s . 2.83 , e ) s . 2.45
Rationale: "c . i . when interest is compounded yearly = [ 6000 * ( 1 + 4 / 100 ) * ( 1 + ( 1 / 2 * 4 ) / 100 ] = 6000 * 26 / 25 * 51 / 50 = rs . 6364.8 c . i . when interest is compounded half - yearly = [ 6000 * ( 1 + 2 / 100 ) 2 ] = ( 6000 * 51 / 50 * 51 / 50 * 51 / 50 ) = rs . 6367.25 difference = ( 6367.25 - 6364.8 ) = rs . 2.45 . answer : e"
Answer: e
Python program:
a = 2 / 100
b = 1 + a 
c = 2 / 100
d = 1 + c 
e = b * d
f = 2 / 100
g = 1 + f 
h = e * g
i = 6000 * h
j = 2 / 100
k = 1 + j 
l = 4 / 100
m = 1 + l 
n = k * m
o = 6000 * n
p = i - o
Problem: in a village there are 150 men and 90 women in present time . if in next year population will be p = ( a ^ 2 + b ^ 2 ) ^ 1 / 2 , and in every year men are reduces 8 % . what is population of after 2 year .
Options: a ) 140 , b ) 141 , c ) 142 , d ) 143 , e ) 144
Rationale: "next year total population = [ 150 ^ 2 + 90 ^ 2 ] ^ . 5 = 174.92 = 175 man decreased by 8 % so total man = 150 * . 92 = 138 women will be = 175 - 138 = 37 so population after two years = [ 135 ^ 2 + 37 ^ 2 ] ^ . 5 = 142.87 = 143 so population after two year = 143 answer : d"
Answer: d
Python program:
a = 1 / 8
b = 1 - a
c = b * 150
d = c ** 2
e = 150 ** 2
f = 90 ** 2
g = e + f 
h = 1 / 2
i = g ** h
j = 1 / 8
k = 1 - j
l = k * 150
m = i - l
n = m ** 2
o = d + n 
p = 1 / 2
q = o ** p
Problem: i chose a number and divide it by 9 . then i subtracted 100 from the result and got 10 . what was the number i chose ?
Options: a ) 600 , b ) 700 , c ) 990 , d ) 900 , e ) none
Rationale: "solution : let x be the number i chose , then x / 9 â ˆ ’ 100 = 10 x / 9 = 110 x = 990 answer c"
Answer: c
Python program:
a = 100 + 10 
b = a * 9
Problem: the length of a rectangular plot is 20 metres more than its breadth . if the cost of fencing the plot @ rs . 26.50 per metre is rs . 6625 , what is the length of the plot in metres ?
Options: a ) 333 , b ) 250 , c ) 288 , d ) 276 , e ) 1999
Rationale: "let length of plot = l meters , then breadth = l - 20 meters and perimeter = 2 [ l + l - 20 ] = [ 4 l - 40 ] meters [ 4 l - 40 ] * 26.50 = 6625 [ 4 l - 40 ] = 6625 / 26.50 = 250 4 l = 290 l = 240 / 4 = 72.5 meters . answer : b"
Answer: b
Python program:
a = 6625 / 26
b = a / 2
c = 2 * 20
d = b - c
Problem: after giving a discount of rs . 50 the shopkeeper gets a profit of 20 % , if the cost price is rs . 500 . find the marked price % ?
Options: a ) 450 , b ) 500 , c ) 650 , d ) 600 , e ) 650
Rationale: "cost price = 500 s . p = 500 * 120 / 100 = 600 disc = 50 so . . . mark price = 600 + 50 = 650 . . . . . . answer : e"
Answer: e
Python program:
a = 100 / 20
b = 500 / a
c = 500 + b 
d = c + 50 
e = d - 500
f = e / 500
Problem: find the value of 2.5 x [ ( 3.6 x 0.48 x 2.50 ) / ( 0.12 x 0.09 x 0.5 ) ]
Options: a ) 2000 , b ) 500 , c ) 900 , d ) 1600 , e ) none
Rationale: "answer 2.5 x [ ( 3.6 x 0.48 x 2.50 ) / ( 0.12 x 0.09 x 0.5 ) ] = 2.5 x [ ( 36 x 48 x 250 ) / ( 12 x 9 x 5 ) ] = 2.5 x 4 x 4 x 50 = 2000 correct option : a"
Answer: a
Python program:
a = 3 * 6
b = a * 2
c = 0 * 12
d = c * 0
e = b / d
f = e * 2
Problem: on an order of 3 dozen boxes of a consumer product , a retailer receives an extra dozen free . this is equivalent to allowing him a discount of :
Options: a ) 20 % , b ) 25 % , c ) 30 % , d ) 35 % , e ) 40 %
Rationale: clearly , the retailer gets 1 dozen out of 4 dozens free . equivalent discount = 1 / 4 * 100 = 25 % . answer b ) 25 %
Answer: b
Python program:
a = 3 / 4
b = a * 100
c = 100 - b
Problem: if bill can buy 3 pairs of jeans and 2 shirts for $ 69 or 2 pairs of jeans and 3 shirts for $ 61 , how much does one shirt cost ?
Options: a ) $ 9 , b ) $ 12 , c ) $ 13.20 , d ) $ 15 , e ) $ 16.80
Rationale: 3 j + 2 s = 69 2 j + 3 s = 61 - - - - - - - - - - - - - - - - 5 j + 5 s = 130 - - - - ( divide by 5 ) - - - > j + s = 26 3 j + 2 s = j + 2 ( j + s ) = j + 52 = 69 - - - > j = 17 3 * 17 + 2 s = 69 51 + 2 s = 69 2 s = 18 s = 9 answer : a
Answer: a
Python program:
a = 61 * 3
b = 69 * 2
c = a - b
d = 3 * 3
e = 2 * 2
f = d - e
g = c / f
Problem: 30 square stone slabs of equal size were needed to cover a floor area of 50.7 sq . m . find the length of each stone slab ?
Options: a ) 130 cm , b ) 767 cm , c ) 88 cm , d ) 666 cm , e ) 776 cm
Rationale: "area of each slab = 50.7 / 30 m 2 = 1.69 m 2 length of each slab √ 1.69 = 1.3 m = 130 cm"
Answer: a
Python program:
a = 50 / 7
b = math.sqrt(a)
c = b * 100
Problem: the cost of 10 kg of apples is equal to the cost of 24 kg of rice . the cost of 6 kg of flour equals the cost of 2 kg of rice . the cost of each kg of flour is rs . 20.50 . find the total cost of 4 kg of apples , 3 kg of rice and 5 kg of flour ?
Options: a ) rs . 849.40 , b ) rs . 877.40 , c ) rs . 901.60 , d ) rs . 815.20 , e ) none of these
Rationale: let the costs of each kg of apples and each kg of rice be rs . a and rs . r respectively . 10 a = 24 r and 6 * 20.50 = 2 r a = 12 / 5 r and r = 61.5 a = 147.6 required total cost = 4 * 147.6 + 3 * 61.5 + 5 * 20.5 = 590.4 + 184.5 + 102.5 = rs . 877.40 answer : b
Answer: b
Python program:
a = 6 * 20
b = a / 2
c = 24 * b
d = c / 10
e = d * 4
f = 6 * 20
g = f / 2
h = g * 3
i = 5 * 20
j = h + i 
k = e + j
Problem: the shopkeeper increased the price of a product by 25 % so that customer finds it difficult to purchase the required amount . but somehow the customer managed to purchase only 70 % of the required amount . what is the net difference in the expenditure on that product ?
Options: a ) 12.5 % , b ) 13 % , c ) 13.15 % , d ) 14 % , e ) 15 %
Rationale: "quantity x rate = price 1 x 1 = 1 0.7 x 1.25 = 0.875 decrease in price = ( 0.125 / 1 ) × 100 = 12.5 % a )"
Answer: a
Python program:
a = 100 * 100
b = 100 + 25 
c = b * 70
d = a - c
e = d * 100
f = 100 * 100
g = e / f
Problem: how many positive integers less than 100 have a remainder of 5 when divided by 13 ?
Options: a ) 5 , b ) 7 , c ) 8 , d ) 9 , e ) 10
Rationale: "we have to include 5 also . as 13 * 0 + 5 = 5 if somebody says to divide 5 by 13 , we will be telling we have 0 quotient and remainder as 5 . answer is a"
Answer: a
Python program:
a = 4 + 5 
b = a - 1
c = math.factorial(b)
d = math.factorial(5)
e = 4 - 1
f = math.factorial(e)
g = d * f
h = c / g
Problem: a spirit and water solution is sold in a market . the cost per liter of the solution is directly proportional to the part ( fraction ) of spirit ( by volume ) the solution has . a solution of 1 liter of spirit and 1 liter of water costs 80 cents . how many cents does a solution of 1 liter of spirit and 2 liters of water cost ?
Options: a ) 53 , b ) 66 , c ) 60 , d ) 85 , e ) 80
Rationale: "yes , ensure that you understand the relation thoroughly ! cost per liter = k * fraction of spirit 80 cents is the cost of 2 liters of solution ( 1 part water , 1 part spirit ) . so cost per liter is 40 cents . fraction of spirit is 1 / 2 . 40 = k * ( 1 / 2 ) k = 80 cost per liter = 80 * ( 1 / 3 ) ( 1 part spirit , 2 parts water ) cost for 3 liters = 80 * ( 1 / 3 ) * 3 = 80 cents e . 80 cents"
Answer: e
Python program:
a = 1 + 2 
b = 1 / a
c = 80 * b
d = 1 + 2 
e = c * d
Problem: two pipes can fill a tank in 10 minutes and 15 minutes . an outlet pipe can empty the tank in 45 minutes . if all the pipes are opened when the tank is empty , then how many minutes will it take to fill the tank ?
Options: a ) 30 minutes , b ) 8 minutes , c ) 15 minutes , d ) 10 minutes , e ) 12 minutes
Rationale: "part of the filled by all the three pipes in one minute = 1 / 10 + 1 / 15 - 1 / 45 = ( 9 + 6 - 2 ) / 90 = 13 / 90 so , the tank becomes full in 8 minutes . answer : b"
Answer: b
Python program:
a = 1 / 10
b = 1 / 15
c = a + b 
d = 1 / 45
e = c - d
Problem: dean winchester has got a long wooden stock of size 60 feet , he need to cut small stock of size 1 feet long using his axe . he takes 5 minutes to cut one small stock ( 1 feet ) , how long will he take to make 60 such small stocks ?
Options: a ) 296 minutes . , b ) 297 minutes . , c ) 295 minutes . , d ) 294 minutes . , e ) none
Rationale: solution : 295 minutes . when he cut 59 stocks , the 60 th stock will remain . 59 * 5 = 295 minutes . answer c
Answer: c
Python program:
a = 60 * 5
Problem: the difference between the squares of two consecutive odd integers is a square < 1000 whose root equals the combined sum of the digits of the two integers . what is the sum of the digits x of the larger integer ?
Options: a ) x = 2 , b ) x = 5 , c ) x = 8 , d ) 10 , e ) 11
Rationale: really hard . but let ' s start with few concepts : 1 . square of an odd integer will be odd . 2 . difference of odd and odd will be even . 3 . any odd integer can be expressed as difference of two squares . 4 . an even integer can be expressed as difference of two squares only if that even integer is a multiple of 4 . assume two odd integers to be ( 2 x - 1 ) and ( 2 x + 1 ) . difference of their squares = ( 2 x + 1 ) ^ 2 - ( 2 x - 1 ) ^ 2 = 4 x ^ 2 + 1 + 4 x - ( 4 x ^ 2 + 1 - 4 x ) = 4 x ^ 2 + 1 + 4 x - 4 x ^ 2 - 1 + 4 x = 8 x now root of 8 x needs to be an integer such that it is equal to the sum of the digits of the two odd integers . 8 = 2 ^ 3 , so x needs to be such that itcompletesa perfect square . if we find x , we can find the value of 2 x + 1 ( larger integer ) and then sum of its digits . let ' s check the options , starting with c . for sum to be 8 , few possibilities are : 17 , 35 , 53 , 71 if we take 17 , the pair is 15 and 17 , meaning x = 8 . 8 x = 64 root of 64 = 4 but 4 is not equal to 1 + 5 + 1 + 7 . reject . if we take 35 , the pair is 33 and 35 , meaning x = 17 . 8 x = 8 * 17 reject since perfect square is not possible . if we take 53 , the pair is 51 and 53 , meaning x = 26 . 8 x = 8 * 26 reject since perfect square is not possible . if we take 71 , the pair is 69 and 71 , meaning x = 35 . 8 x = 8 * 35 reject since perfect square is not possible . i tried each option and the possibilities and then got lost . then , it occurred to me that i was only checking 2 - digit integers . what about 3 - digits ? starting with option a , only 2 - digit odd integer whose sum is 2 is 101 . if we take 101 , the pair is 99 and 101 , meaning x = 50 . 8 x = 8 * 50 = 400 root of 400 = 20 which is indeed equal to 9 + 9 + 1 + 1 . answer ( a ) .
Answer: a
Python program:
a = math.sqrt(1000)
b = a + 1 
c = math.floor(b)
d = c - 12
e = d ** 2
f = 2 ** 3
g = e / f
h = g * 2
i = h / 100
j = i + 1
Problem: if c is 25 % of a and 50 % of b , what percent of a is b ?
Options: a ) 2.5 % , b ) 50 % , c ) 25 % , d ) 35 % , e ) 250 %
Rationale: "answer = b 25 a / 100 = 50 b / 100 b = 25 a / 50 = 50 a / 100 = 50 %"
Answer: b
Python program:
a = 25 / 100
b = 50 / 100
c = a / b
d = c * 100
Problem: a teacher grades students ’ tests by subtracting twice the number of incorrect responses from the number of correct responses . if student a answers each of the 100 questions on her test and receives a score of 61 , how many questions did student a answer correctly ?
Options: a ) 55 , b ) 60 , c ) 73 , d ) 81 , e ) 87
Rationale: "let the number of correct responses be x then the number of incorrect responses = 100 - x according to question x - 2 ( 100 - x ) = 61 ( subtracting twice of incorrect from correct ) 3 x = 261 x = 87 answer : e"
Answer: e
Python program:
a = 100 - 61
b = a / 3
c = 100 - b
Problem: if x is invested in a bank at a rate of simple interest of y % p . a . for two years , then the interest earned is 600 . if x is invested at y % p . a . , for two years when the interest is compounded annually , the interest is 615 . what is the value of x ?
Options: a ) 8000 , b ) 6000 , c ) 5000 , d ) 4000 , e ) 3000
Rationale: "simple way to solve this question is to use options . from si , we know that x * y = 30,000 . now , put the value of x = 6000 , we will have y = 5 % to calculate ci , now , we know 1 st year amount = 6000 + 5 % of 6000 = 6300 . 2 nd year , amount = 6300 + 5 % of 6300 = 6615 we can see after 2 years interest = 6615 - 6000 = 615 . hence , it satisfies the question . hence b is the correct answer"
Answer: b
Python program:
a = 600 / 2
b = a ** 2
c = 615 - 600
d = b / c
Problem: a store purchased a pair of pants for $ 210 and was selling it at a price that equaled the purchase price of the pants plus a markup that was 25 percent of the selling price . after some time a store owner decided to decrease the selling price by 20 percent . what was the store ' s gross profit on this sale ?
Options: a ) $ 14 , b ) $ 2 , c ) $ 10 , d ) $ 6 , e ) $ 8
Rationale: sale price ( sp ) = 210 + markup ( mp ) - - > mp = sp - 210 and given mp = sp / 4 ( 25 % is 1 / 4 th ) so sp / 4 = sp - 210 3 sp / 4 = 210 sp = 280 now a discount of 20 % is given so new sp is . 8 * 280 = 224 profit = 224 - 210 = 14 answer is a
Answer: a
Python program:
a = 210 * 20
b = a / 100
c = b / 3
Problem: the length of a room is 5.5 m and width is 3.75 m . find the cost of paving the floor by slabs at the rate of rs . 400 per sq . metre .
Options: a ) rs . 15000 , b ) rs . 8250 , c ) rs . 15600 , d ) rs . 16500 , e ) none of these
Rationale: "solution area of the floor = ( 5.5 × 3.75 ) m 2 = 20.625 m 2 ∴ cost of paving = rs . ( 400 × 20.625 ) = 8250 . answer b"
Answer: b
Python program:
a = 5 * 5
b = 400 * a
Problem: find 125 / 14 * 6
Options: a ) 2.4658 , b ) 6.398 , c ) 1.488 , d ) 5.687 , e ) 9.652
Rationale: "answer = 125 / 14 * 6 = 125 / 84 = 1.488 option c is correct"
Answer: c
Python program:
a = 125 / 14
Problem: if a 2 - b 2 = 5 and a * b = 2 , find a 4 + b 4 .
Options: a ) 50 , b ) 72 , c ) 25 , d ) 92 , e ) 33
Rationale: "a 2 - b 2 = 5 : given a 4 + b 4 - 2 a 2 b 2 = 52 : square both sides and expand . a * b = 2 : given a 2 b 2 = 22 : square both sides . a 4 + b 4 - 2 ( 4 ) = 25 : substitute a 4 + b 4 = 33 correct answer e"
Answer: e
Python program:
a = 5 ** 2
b = 2 ** 2
c = b * 2
d = a + c
Problem: if 1 + 2 + 3 + . . . + n = n ( n + 1 ) , then 3 ( 1 + 3 + 5 + . . . . + 79 ) = ?
Options: a ) 4500 , b ) 4250 , c ) 4350 , d ) 4800 , e ) 4150
Rationale: "explanation : to solve this use the formula of ap , sn = ( n / 2 ) ( a + l ) . . . . . . . . . . . . . . . . ( 1 ) to find n , use = > tn = a + ( n - 1 ) d = > 79 = 1 + ( n - 1 ) 2 = > n = 40 use value of n in ( 1 ) then , sn = ( 40 / 2 ) ( 1 + 79 ) = 1600 ans : - 3 ( sn ) = 4800 answer : d"
Answer: d
Python program:
a = 79 + 1 
b = 79 * a
c = b / 2
d = 79 - 1
e = d / 2
f = 79 - 1
g = f / 2
h = g + 1 
i = e * h
j = c - i
k = j * 3
Problem: a river boat leaves silver town and travels upstream to gold town at an average speed of 4 kilometers per hour . it returns by the same route at an average speed of 7 kilometers per hour . what is the average speed for the round - trip in kilometers per hour ?
Options: a ) 5.1 , b ) 7.1 , c ) 7.2 , d ) 7.5 , e ) 8.0
Rationale: "pick a number which is lcm of 7 and 4 = 18 . upstream time = 28 / 4 = 7 hrs downstream time = 28 / 7 = 4 hrs total time = 11 hrs total distance = 56 average speed = 56 / 11 = 5.1 km / hr"
Answer: a
Python program:
a = 4 * 7
b = a * 2
c = 4 + 7 
d = b / c
Problem: a certain car traveled twice as many miles from town a to town b as it did from town b to town c . from town a to town b , the car averaged 25 miles per gallon , and from town b to town c , the car averaged 30 miles per gallon . what is the average miles per gallon that the car achieved on its trip from town a through town b to town c ?
Options: a ) 24 , b ) 25 , c ) 23 , d ) 22 , e ) 26.5
Rationale: step 1 ) took lcm of 25 and 30 . . came as 150 . step 2 ) 150 distance between b to c . . . do 150 / 30 hence 5 gallons used step 3 ) twice distance . . hence 150 * 2 = 300 . . . do as above . . 300 / 25 = 12 gallons used step 4 ) total gallons . . 5 + 12 = 17 gallons step ) total miles = 150 + 300 = 450 miles hence . . average of whole journey = 450 / 17 which comes to 26.5 answer : e
Answer: e
Python program:
a = 30 * 10
b = 30 * 10
c = b / 2
d = a + c 
e = 30 * 10
f = e / 25
g = 30 * 10
h = g / 2
i = h / 30
j = f + i 
k = d / j
Problem: if w , x , y and z are distinct odd positive integers , then the maximum value of the expression ( w ^ 2 + x ^ 2 ) * ( y ^ 2 + z ^ 2 ) can be divisible by ?
Options: a ) 2 , b ) 3 , c ) 5 , d ) 8 , e ) 10
Rationale: any odd number square will give odd number only . . similarly wen we add 2 odd numbers we will get even number . . wen we multiply 2 even owe will get even nuber . . so the result of the above expression is an even number only . . hence it is divisible by 2 . . . answer : a
Answer: a
Python program:
a = 2 + 2 
b = a * 2
c = 2 * 2
d = b / c
Problem: john found that the average of 15 numbers is 40 . if 10 is added to each number then the mean of number is ?
Options: a ) 50 , b ) 60 , c ) 75 , d ) 80 , e ) 85
Rationale: "( x + x 1 + . . . x 14 ) / 15 = 40 50 option a"
Answer: a
Python program:
a = 40 + 10
Problem: if a ' s salary is 20 % less than b ' s salary , by how much percent is b ' s salary more than a ' s ?
Options: a ) 5 % , b ) 10 % , c ) 15 % , d ) 25 % , e ) none
Rationale: solution required percentage ‹ = › [ 20 / ( 100 - 20 ) x 100 ] % ‹ = › 25 % answer d
Answer: d
Python program:
a = 100 - 20
b = 100 - a
c = 100 - 20
d = c / 100
e = b / d
Problem: what will be the difference between simple interest and compound interest @ 10 % per annum on a sum of rs . 1000 after 3 years ?
Options: a ) 22 , b ) 77 , c ) 26 , d ) 19 , e ) 31
Rationale: "explanation : s . i . = rs . [ ( 1000 x 10 x 3 ) / 100 ] = rs . 300 c . i . = rs . [ 1000 x ( 1 + ( 10 / 100 ) ) 3 - 1000 ] = rs . 331 difference = rs . ( 331 - 300 ) = rs . 31 answer : e"
Answer: e
Python program:
a = 10 / 100
b = a + 1 
c = b ** 3
d = c * 1000
e = d - 1000
f = 10 * 1000
g = 3 * f
h = g / 100
i = e - h
Problem: the mean of 25 values was 190 . it was detected on rechecking that one value 165 was wrongly copied as 130 for the computation of the mean . find the correct mean .
Options: a ) 151 , b ) 149 , c ) 152 , d ) 191.4 , e ) none of the above
Rationale: "corrected mean = 190 × 25 − 130 + 165 / 25 = 4750 + 35 / 25 = 4785 / 25 = 191.4 answer d"
Answer: d
Python program:
a = 25 * 190
b = 165 - 130
c = a + b 
d = c / 25