euclaise/mathqa_programs huggingface dataset:
Problem: two trains start at same time from two stations and proceed towards each other at the rate of 20 km / hr and 25 km / hr respectively . when they meet , it is found that one train has traveled 50 km more than the other . what is the distance between the two stations ?
Options: a ) 540 km , b ) 767 km , c ) 276 km , d ) 450 km , e ) 176 km
Rationale: explanation : let us assume that trains meet after ' x ' hours distance = speed * time distance traveled by two trains = 20 x km and 25 x km resp . as one train travels 50 km more than the other , 25 x â € “ 20 x = 50 5 x = 50 x = 10 hours as the two trains are moving towards each other , relative speed = 20 + 25 = 45 km / hr therefore , total distance = 45 * 10 = 450 km . answer : d
Answer: d
Python program:
a = 20 + 25 
b = 25 - 20
c = 50 / b
d = a * c
Problem: a test has 150 questions . each question has 5 options , but only 1 option is correct . if test - takers mark the correct option , they are awarded 1 point . however , if an answer is incorrectly marked , the test - taker loses 0.25 points . no points are awarded or deducted if a question is not attempted . a certain group of test - takers attempted different numbers of questions , but each test - taker still received the same net score of 40 . what is the maximum possible number of such test - takers ?
Options: a ) 19 , b ) 21 , c ) 23 , d ) 25 , e ) 27
Rationale: "a correct answers get you 1 point , an incorrect answer gets you minus 1 / 4 point and a skipped question gets you 0 points . since there are 200 total questions , there are a variety of ways to get a total of 40 points . let c be the number of correct answers and let i be the number of incorrect answers . to get 40 points , a test taker must have at least 40 correct answers . then c = > 40 . for every correct question above 40 , the test taker has 4 incorrect answers . then , the i = 4 * ( c - 40 ) . also , i + c < = 150 . thus 5 c < = 310 and so c < = 62 . then 40 < = c < = 62 and c can have 23 possible values . the answer is c ."
Answer: c
Python program:
a = 150 - 40
b = a / 5
c = b + 1 
d = c + 1
Problem: the cost of 10 kg of mangos 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 $ 24 . find the total cost of 4 kg of mangos , 3 kg of rice and 5 kg of flour ?
Options: a ) 347.4 , b ) 987.4 , c ) 877.2 , d ) 1027.2 , e ) 1667.2
Rationale: "let the costs of each kg of mangos and each kg of rice be $ a and $ r respectively . 10 a = 24 r and 6 * 24 = 2 r a = 12 / 5 r and r = 72 a = 144 required total cost = 4 * 144 + 3 * 72 + 5 * 24 = 691.2 + 216 + 120 = $ 1027.20 d"
Answer: d
Python program:
a = 24 / 10
b = 24 * 6
c = b / 2
d = a * c
e = 4 * d
f = 24 * 6
g = f / 2
h = 3 * g
i = e + h 
j = 5 * 24
k = i + j
Problem: in one hour , a boat goes 11 km along the steram and 5 km against the stream . the speed of the boat in still waer ( in km / hr ) is :
Options: a ) 2 , b ) 4 , c ) 8 , d ) 12 , e ) 15
Rationale: sol . speed in still water = 1 / 2 ( 11 + 5 ) kmph = 8 kmph . answer c
Answer: c
Python program:
a = 11 + 5 
b = a / 2
Problem: if n is the product of integers from 1 to 20 inclusive what is the greatest integer k for which 2 ^ k is a factor of n ?
Options: a ) 10 , b ) 12 , c ) 15 , d ) 18 , e ) 20
Rationale: "given : n = 20 ! n = 20 ! . the highest power k for which 2 ^ k is a factor of n can be found with the above formula : k = 20 / 2 + 20 / 4 + 20 / 8 + 20 / 16 = 10 + 5 + 2 + 1 = 18 answer : d ."
Answer: d
Python program:
a = 20 / 2
b = 2 ** 2
c = 20 / b
d = a + c 
e = 2 ** 2
f = e ** 2
g = 20 / f
h = math.floor(g)
i = d + h 
j = 2 ** 3
k = 20 / j
l = math.floor(k)
m = i + l
Problem: a dog travelled for 2 hours . he covered the first half of the distance at 10 kmph and remaining half of the distance at 5 kmph . find the distance travelled by the dog ?
Options: a ) 20 km , b ) 16 km , c ) 6 km , d ) 3 km , e ) 61 km
Rationale: let the distance travelled be x km . total time = ( x / 2 ) / 10 + ( x / 2 ) / 5 = 2 = > x / 20 + x / 10 = 2 = > ( 1 x + 2 x ) / 20 = 2 = > x = 20 km answer : a
Answer: a
Python program:
a = 2 * 10
Problem: find the value of 72519 x 9999 = m ?
Options: a ) 455465473 , b ) 654676854 , c ) 667676753 , d ) 725117481 , e ) 764534522
Rationale: "72519 x 9999 = 72519 x ( 10000 - 1 ) = 72519 x 10000 - 72519 x 1 = 725190000 - 72519 = 725117481 d"
Answer: d
Python program:
a = 9999 - 4
b = a * 72519
Problem: 3 , 15 , x , 51 , 53 , 159161 value of x ?
Options: a ) 17 , b ) 34 , c ) 54 , d ) 64 , e ) 112
Rationale: 3 * 5 = 15 15 + 2 = 17 17 * 3 = 51 51 + 2 = 53 answer : a
Answer: a
Python program:
a = 15 + 2
Problem: a , b and c are partners . a receives 2 / 3 of profits , b and c dividing the remainder equally . a ' s income is increased by rs . 300 when the rate to profit rises from 5 to 7 percent . find the capital of a ?
Options: a ) 5000 , b ) 10000 , c ) 15000 , d ) 2778 , e ) 1991
Rationale: a : b : c = 2 / 3 : 1 / 6 : 1 / 6 = 4 : 1 : 1 x * 2 / 100 * 2 / 3 = 300 a ' s capital = 22500 * 2 / 3 = 15000 answer : c
Answer: c
Python program:
a = 300 * 100
b = a / 2
Problem: how many zeros does 100 ! end with ?
Options: a ) 20 , b ) 24 , c ) 25 , d ) 30 , e ) 32
Rationale: "according to above 100 ! has 100 / 5 + 100 / 25 = 20 + 4 = 24 trailing zeros . answer : b ."
Answer: b
Python program:
a = 4 + 1 
b = 100 / a
c = 4 + 1 
d = 100 - c
e = 4 + 1 
f = e ** 2
g = d / f
h = b + g 
i = 4 + 1 
j = 100 - i
k = 4 + 1 
l = k ** 3
m = j / l
n = h + m
Problem: how many two - digit numbers yield a remainder of 3 when divided by both 4 and 14 ?
Options: a ) 0 , b ) 1 , c ) 2 , d ) 3 , e ) 4
Rationale: "easier to start with numbers that are of the form 14 p + 3 - - - > 17,31 , 45,59 , 73,87 . out of these 3 ( 31 , 59,87 ) are also of the form 4 q + 3 . thus 3 is the answer . d is the correct answer ."
Answer: d
Python program:
a = 14 * 4
b = 3 + a 
c = 14 * 4
d = b - c
Problem: a squirrel can climb 5 metres of a pole in one minute but slips 2 metres in the next minute . how much time will the squirrel take to climb 26 metres ?
Options: a ) 15 minutes , b ) 18 minutes , c ) 12 minutes , d ) 58 minutes , e ) 10 minutes
Rationale: explanation : as the squirrel climbs 5 m in one minute and slips 2 metres in the next minute , it climbs 3 metres in 2 minute to climb 26 metres , the time required is : the squirrel will climb ( 26 – 5 ) = 21 metres = 7 * 3 metres in 7 * 2 = 14 minutes also , the last 5 metres it climbs in another 1 minute hence , total time required = 14 + 1 = 15 minutes answer : a
Answer: a
Python program:
a = 26 / 2
b = a + 2
Problem: a certain car dealership sells economy cars , luxury cars , and sport utility vehicles . the ratio of economy to luxury cars is 3 : 2 . the ratio of economy cars to sport utility vehicles is 4 : 2 . what is the ratio of luxury cars to sport utility vehicles ?
Options: a ) 9 : 8 , b ) 8 : 9 , c ) 3 : 2 , d ) 8 : 6 , e ) 1 : 2
Rationale: "the ratio of economy to luxury cars is 3 : 2 - - > e : l = 3 : 2 = 12 : 8 . the ratio of economy cars to sport utility vehicles is 4 : 2 - - > e : s = 4 : 2 = 12 : 6 . thus , l : s = 8 : 6 . answer : d ."
Answer: d
Python program:
a = 4 * 2
b = 3 * 0
c = a / b
d = 2 * 4
e = 2 * 4
f = d / e
g = c / f
Problem: a cycle is bought for rs . 900 and sold for rs . 1100 , find the gain percent ?
Options: a ) 11 , b ) 22 , c ) 99 , d ) 77 , e ) 18
Rationale: "900 - - - - 200 100 - - - - ? = > 22 % answer : b"
Answer: b
Python program:
a = 1100 - 900
b = a / 900
c = b * 100
Problem: two trains of length 120 m and 320 m are running towards each other on parallel lines at 42 kmph and 30 kmph respectively . in what time will they be clear of each other from the moment they meet ?
Options: a ) 10 sec , b ) 22 sec , c ) 82 sec , d ) 20 sec , e ) 89 sec
Rationale: "relative speed = ( 42 + 30 ) * 5 / 18 = 4 * 5 = 20 mps . distance covered in passing each other = 120 + 320 = 440 m . the time required = d / s = 440 / 20 = 22 sec . answer : b"
Answer: b
Python program:
a = 120 + 320 
b = 42 + 30 
c = b * const_0_2778
d = a / c
Problem: a man buys a cycle for rs . 1200 and sells it at a loss of 15 % . what is the selling price of the cycle ?
Options: a ) s . 1020 , b ) s . 1160 , c ) s . 1190 , d ) s . 1202 , e ) s . 1256
Rationale: "s . p . = 85 % of rs . 1200 = rs . 85 / 100 x 1200 = rs . 1020 answer : a"
Answer: a
Python program:
a = 100 - 15
b = a * 1200
c = b / 100
Problem: a wheel rotates 20 times every minute and moves 35 cm during each rotation . how many metres does the wheel move in one hour ?
Options: a ) 6 metre , b ) 120 metre , c ) 220 metre , d ) 1200 metre , e ) 420 metre
Rationale: number of times wheel moves in 1 hour = 20 * 60 = 1200 : . distance moves = ( 1200 * 35 ) cms = 42000 cms in metres = 420 metre answer : e
Answer: e
Python program:
a = 20 * const_60
b = a * 35
c = b / 100
Problem: a certain roller coaster has 2 cars , and a passenger is equally likely to ride in any 1 of the 2 cars each time that passenger rides the roller coaster . if a certain passenger is to ride the roller coaster 2 times , what is the probability that the passenger will ride in each of the 2 cars ?
Options: a ) 0 , b ) 1 / 2 , c ) 2 / 9 , d ) 1 / 3 , e ) 1
Rationale: "if he is to ride 2 times and since he can choose any of the 2 cars each time , total number of ways is = 2 * 2 = 4 now the number of ways if he is to choose a different car each time is = 2 * 1 = 2 so the probability is = 2 / 4 = 1 / 2 answer : b"
Answer: b
Python program:
a = math.factorial(2)
b = 1 / 2
c = b ** 2
d = a * c
Problem: if a rectangular room measures 12 meters by 6 meters by 4 meters , what is the volume of the room in cubic centimeters ? ( 1 meter = 100 centimeters )
Options: a ) 288 , 000,000 , b ) 240,000 , c ) 2 , 400,000 , d ) 24 , 000,000 , e ) 240 , 000,000
Rationale: "a . 288 , 000,000 12 * 100 * 6 * 100 * 4 * 100 = 288 , 000,000"
Answer: a
Python program:
a = 4 * 100
b = 1 / 10
c = a * b
d = 6 * 100
e = c * d
f = 12 * 100
g = e * f
Problem: a man invested rs . 4455 in rs . 10 shares quoted at rs . 8.25 . if the rate of dividend be 12 % , his annual income is :
Options: a ) rs . 207.40 , b ) rs . 534.60 , c ) rs . 648 , d ) rs . 655.60 , e ) rs . 685.60
Rationale: solution numbers of shares = ( 4455 / 825 ) = 540 face value = rs . ( 540 x 10 ) = rs . 5400 annual income = rs . ( 12 / 10 x 5400 ) = rs . 648 . answer c
Answer: c
Python program:
a = 12 / 100
b = 4455 / 8
c = b * 10
d = a * c
Problem: in a forest 160 deer were caught , tagged with electronic markers , then released . a week later , 50 deer were captured in the same forest . of these 50 deer , it was found that 5 had been tagged with the electronic markers . if the percentage of tagged deer in the second sample approximates the percentage of tagged deer in the forest , and if no deer had either left or entered the forest over the preceding week , what is the approximate number of deer in the forest ?
Options: a ) 150 , b ) 750 , c ) 1,250 , d ) 1,600 , e ) 2,500
Rationale: "the percentage of tagged deer in the second sample = 5 / 50 * 100 = 10 % . so , 160 tagged deers comprise 10 % of total # of deers - - > total # of deers = 160 * 10 = 1,600 . answer : d ."
Answer: d
Python program:
a = 50 * 5
Problem: mike drives his new corvette from san francisco to las vegas , a journey of 640 miles . he drives the first half of the trip at an average rate of 80 miles per hour , but has to slow down for the second half of his journey . if the second half of the trip takes him 200 percent longer than the first half , what is his average rate w in miles per hour for the entire trip ?
Options: a ) w = 26.7 , b ) w = 30.0 , c ) w = 40.0 , d ) w = 53.3 , e ) 60.0
Rationale: "veritas prepofficial solution correct answer : c using the formula : time = distance / rate , we find that mike takes 4 hours to cover the first 320 miles of his trip . since the 2 nd 320 miles take 200 % longer than the first , it takes mike 8 hours longer , or 12 hours . ( note : 200 % longer than the first half is not 200 % of the first half . ) the overall time is 4 hours + 12 hours or 16 hours . since the definition of average rate = total distance traveled / total time of travel , mike ' s average rate = 640 / 16 or 40 miles per hour . answer choice c is correct ."
Answer: c
Python program:
a = 640 / 2
b = a / 80
c = b * 2
d = 640 / 2
e = d / 80
f = c + e 
g = 640 / 2
h = g / 80
i = f + h 
j = 640 / i
Problem: the prices of tea and coffee per kg were the same in june . in july the price of coffee shot up by 20 % and that of tea dropped by 10 % . if in july , a mixture containing equal quantities of tea and coffee costs 50 / kg . how much did a kg of coffee cost in june ?
Options: a ) 45 , b ) 40 , c ) 35 , d ) 47.61 , e ) 30
Rationale: let the price of tea and coffee be x per kg in june . price of tea in july = 1.2 x price of coffee in july = 0.9 x . in july the price of 1 / 2 kg ( 500 gm ) of tea and 1 / 2 kg ( 500 gm ) of coffee ( equal quantities ) = 50 1.2 x ( 1 / 2 ) + 0.9 x ( 1 / 2 ) = 50 = > x = 47.61 d
Answer: d
Python program:
a = 10 / 100
b = 1 - a
c = 20 / 100
d = c + 1 
e = b * d
f = 50 / e
Problem: 1398 x 1398
Options: a ) 1954404 , b ) 1981709 , c ) 18362619 , d ) 2031719 , e ) none of these
Rationale: "1398 x 1398 = ( 1398 ) 2 = ( 1400 - 2 ) 2 = ( 1400 ) 2 + ( 2 ) 2 - ( 2 x 1400 x 2 ) = 1954404 . answer : option a"
Answer: a
Python program:
a = 1398 / 1398
b = a * 100
Problem: a man can swim in still water at 7.5 km / h , but takes twice as long to swim upstream than downstream . the speed of the stream is ?
Options: a ) 3 , b ) 2.5 , c ) 2.25 , d ) 1.5 , e ) 4
Rationale: "m = 7.5 s = x ds = 7.5 + x us = 7.5 - x 7.5 + x = ( 7.5 - x ) 2 7.5 + x = 15 - 2 x 3 x = 7.5 x = 2.5 answer : b"
Answer: b
Python program:
a = 7 / 5
Problem: two alloys a and b are composed of two basic elements . the ratios of the compositions of the two basic elements in the two alloys are 5 : 3 and 1 : 5 , respectively . a new alloy x is formed by mixing the two alloys a and b in the ratio 4 : 3 . what is the ratio of the composition of the two basic elements in alloy x ?
Options: a ) 1 : 1 , b ) 3 : 4 , c ) 5 : 2 , d ) 4 : 3 , e ) 7 : 9
Rationale: "mixture a has a total of 5 + 3 = 8 parts . if in the final mixture this represents 4 parts , then the total number of parts in mixture b should be ( 8 / 4 ) * 3 = 6 . so , we should take of mixture b a quantity with 1 and 5 parts , respectively . this will give us in the final mixture ( 5 + 1 ) : ( 3 + 5 ) , which means 6 : 8 , or 3 : 4 . answer b ."
Answer: b
Python program:
a = 4 * 5
b = 5 + 3 
c = b / 2
d = 3 * c
e = a + d 
f = 4 * 3
g = 5 + 3 
h = g / 2
i = 3 * h
j = f + i 
k = e / j
Problem: in a express train passengers traveling in a . c . sleeper class , first class and sleeper class are in the ratio 1 : 2 : 3 , and fare to each class in the ratio 5 : 4 : 2 . if the income from this train is rs . 57000 , the income of a . c . sleeper class is
Options: a ) rs . 8000 , b ) rs . 12000 , c ) rs . 15000 , d ) rs . 6000 , e ) none
Rationale: income is divided in the ratio 1 × 5 : 2 × 4 : 3 × 2 = 5 : 8 : 6 . now 5 x + 8 x + 6 x = 19 x = 57000 . ∴ x = 3000 . therefore income from a . c . sleeper class = 30005 = 15000 . answer : c .
Answer: c
Python program:
a = 57000 / 4
b = 3 * 5
c = b * 10
d = a + c
Problem: how many positive factors do 150 and 90 have in common ?
Options: a ) 8 , b ) 12 , c ) 16 , d ) 18 , e ) 24
Rationale: the number of common factors will be same as number of factors of the highest common factor ( hcf ) hcf of 150 and 90 is 30 number of factors of 30 = 8 answer : a
Answer: a
Python program:
a = 90 - 10
b = a / 10
Problem: mona and sona go around a circular track of length 400 m on a bike 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 , b ) 80 , c ) 60 , d ) 136 , e ) 150
Rationale: time taken to meet for the first time at the starting point = lcm { length of the track / speed of mona , length of the track / speed of sona } = lcm { 400 / ( 18 * 5 / 18 ) , 400 / ( 36 * 5 / 18 ) } = lcm ( 80 , 40 ) = 80 sec . answer : b
Answer: b
Python program:
a = 36 - 18
b = a * const_0_2778
c = 400 / b
Problem: the rate of interest on a sum of money is 11 % p . a . for the first 3 years , 4 % p . a . for the next 4 years , and 5 % for the period beyond 7 years . if the s . i , occured on the sum for the total period of 8 years is rs . 540 / - , the sum is
Options: a ) 1,000 , b ) 2,000 , c ) 2,100 , d ) 2,250 , e ) 2,540
Rationale: "explanation : i 1 = ( p x 3 x 11 ) / 100 = p / 3 i 2 = ( p x 4 x 4 ) / 100 = 4 p / 25 i 3 = ( p x 1 x 5 ) / 100 = p / 20 p / 3 + 4 p / 25 + p / 20 = 540 27 p / 50 = 540 p = 1000 answer : option a"
Answer: a
Python program:
a = 540 / 540
Problem: a cube of edge 10 cm is immersed completely in a rectangular vessel containing water . if the dimensions of the base of vessel are 20 cm * 15 cm , find the rise in water level ?
Options: a ) 6 cm
b ) 8.25 cm
c ) 11.25 cm
d ) 15.12 cm
e ) 3.33 cm
Rationale: increase in volume = volume of the cube = 10 * 10 * 10 cm ^ 3 rise in water level = volume / area = 10 * 10 * 10 / 20 * 15 = 3.33 cm answer is e
Answer: e
Python program:
a = volume_cube / (
Problem: a can contains a mixture of liquids a and b is the ratio 7 : 5 . when 12 litres of mixture are drawn off and the can is filled with b , the ratio of a and b becomes 7 : 9 . how many liter of liquid a was contained by the can initially ?
Options: a ) 25 , b ) 27 , c ) 29 , d ) 28 , e ) 31
Rationale: "ci * vi = cf * vf ( 7 / 12 ) * ( v 1 - 12 ) = ( 7 / 16 ) * v 1 ( v 1 - 12 ) / v 1 = 3 / 4 12 accounts for the difference of 1 on ratio scale so initial volume = v 1 = 4 * 12 = 48 litres . 7 / 12 of the initial mixture was liquid a so liquid a was ( 7 / 12 ) * 48 = 28 litres . answer : d"
Answer: d
Python program:
a = 7 + 12 
b = 7 + 5 
c = 5 / b
d = c * 12
e = 12 - d
f = a * e
g = 12 * 7
h = 7 * 5
i = g - h
j = f / i
k = 7 * j
Problem: a bag marked at $ 200 is sold for $ 120 . the rate of discount is ?
Options: a ) 10 % , b ) 25 % , c ) 20 % , d ) 50 % , e ) 40 %
Rationale: "rate of discount = 80 / 200 * 100 = 40 % answer is e"
Answer: e
Python program:
a = 200 - 120
b = a / 200
c = b * 100
Problem: the sale price of a trolley bag including the sale tax is rs . 1120 . the rate of sale tax is 12 % . if the shopkeeper has made a profit of 25 % , the cost price of the trolley bag is :
Options: a ) rs 1000 , b ) rs 1515 , c ) rs 800 , d ) rs 900 , e ) none of these
Rationale: "explanation : 112 % of s . p . = 1120 s . p . = rs . ( 1120 x 100 / 112 ) = rs . 1000 . c . p . = rs ( 100 / 125 x 1000 ) = rs 800 . answer : c"
Answer: c
Python program:
a = 12 / 100
b = 1120 * a
c = 1120 - b
d = 25 / 100
e = d + 1 
f = c / e
Problem: a train 125 m long passes a man , running at 10 km / hr in the same direction in which the train is going , in 10 sec . the speed of the train is ?
Options: a ) 65 km / hr , b ) 17 km / hr , c ) 55 km / hr , d ) 50 km / hr , e ) 15 km / hr
Rationale: "speed of the train relative to man = 125 / 10 = 25 / 2 m / sec . = 25 / 2 * 18 / 5 = 45 km / hr let the speed of the train be x km / hr . then , relative speed = ( x - 10 ) km / hr . x - 10 = 45 = > x = 55 km / hr . answer : c"
Answer: c
Python program:
a = 10 * const_0_2778
b = a * 10
c = 125 - b
d = c / 10
e = d / const_0_2778
Problem: the distance between west - town to east - town is 14 kilometers . two birds start flying simultaneously towards one another , the first leaving from west - town at a speed of 5 kilometers per minute and the second bird , leaving from east - town , at a speed of 2 kilometers per minute . what will be the distance , in kilometers , between the meeting point and west - town ?
Options: a ) 3 . , b ) 7 . , c ) 10 . , d ) 12 . , e ) 15 .
Rationale: "time taken by the birds to meet = 14 / ( 5 + 2 ) = 2 mins distance traveled by the bird traveling from west - town = 5 * 2 = 10 answer : c"
Answer: c
Python program:
a = 5 * 5
Problem: a rectangular room has the rectangular shaped rug shown as above figure such that the rug ’ s area is 220 square feet and its length is 12 feet longer than its width . if the uniform width between the rug and room is 12 feet , what is the area of the region uncovered by the rug ( shaded region ) , in square feet ?
Options: a ) 32 , b ) 1136 , c ) 40 , d ) 1344 , e ) 104
Rationale: "rug ' s area = 220 which is ( x ) x ( 12 + x ) = 220 so x = 10 rug maintains a uniform distance of 12 feet so room has dimension 10 + 24 and 22 + 24 i . e . 34 and 46 area of room 34 x 46 = 1564 area covered is 120 so uncovered area is 1564 - 220 = 1344 ( answer d )"
Answer: d
Python program:
a = 220 / 10
b = a - 2
c = b + 10 
d = 220 / 10
e = 220 / 10
f = e - 2
g = d + f 
h = c * g
i = h - 220
Problem: little john had $ 10.10 . he spent $ 3.25 on sweets and gave to his two friends $ 2.20 each . how much money was left ?
Options: a ) $ 2.45 , b ) $ 2.54 , c ) $ 2.35 , d ) $ 2.48 , e ) $ 2.49
Rationale: "john spent and gave to his two friends a total of 3.25 + 2.20 + 2.20 = $ 7.65 money left 10.10 - 7.65 = $ 2.45 answer : a"
Answer: a
Python program:
a = 2 + 20 
b = 3 + 25 
c = 10 - 10
Problem: evaluate : 37 x 181 + 37 x 319
Options: a ) 22500 , b ) 15500 , c ) 18500 , d ) 25000 , e ) none of them
Rationale: "37 x 181 + 37 x 319 = 37 x ( 181 + 319 ) = 37 x 500 = 18500 . answer is c ."
Answer: c
Python program:
a = 181 * 37
b = a * 319
c = 37 - b
Problem: the size of a television screen is given as the length of the screen ' s diagonal . if the screens were flat , then the area of a square 22 - inch screen would be how many square inches greater than the area of a square 20 - inch screen ?
Options: a ) 2 , b ) 4 , c ) 16 , d ) 42 , e ) 40
Rationale: "pythogoras will help here ! let the sides be x and diagonal be d then d ^ 2 = 2 x ^ 2 and area = x ^ 2 now plug in the given diagonal values to find x values and then subtract the areas ans will be 22 ^ 2 / 2 - 20 ^ 2 / 2 = 84 / 2 = 42 ans d ."
Answer: d
Python program:
a = 22 ** 2
b = 20 ** 2
c = a - b
d = c / 2
Problem: how many positive integers less than 600 can be formed using the numbers 1 , 2 , 3 , 5 and 6 for the digits ?
Options: a ) 48 , b ) 130 , c ) 66 , d ) 68 , e ) 84
Rationale: "notice that we can find the number of 2 and 3 digit numbers by just assuming the first digit can also be zero : 0 1 1 1 2 2 2 3 3 3 5 5 5 6 6 number of possibilities = 5 * 5 * 5 = 125 . then , just add up the number of 1 digits numbers = 5 , so total is 125 + 5 = 130 . answer : b"
Answer: b
Python program:
a = 600 - 1
b = a - 4
c = b - 1
Problem: if a and b are the roots of the equation x 2 - 5 x + 5 = 0 , then the value of a 2 + b 2 is :
Options: a ) 36 , b ) 24 , c ) 15 , d ) 6 , e ) 5
Rationale: "sol . ( b ) the sum of roots = a + b = 5 product of roots = ab = 5 now , a 2 + b 2 = ( a + b ) 2 - 2 ab = 25 - 10 = 15 answer c"
Answer: c
Python program:
a = 5 ** 2
b = 4 * 5
c = a - b
d = math.sqrt(c)
e = 5 - d
f = e / 2
g = f ** 2
h = 5 ** 2
i = 4 * 5
j = h - i
k = math.sqrt(j)
l = 5 + k 
m = l / 2
n = m ** 2
o = g + n
Problem: two cars a and b are running towards each other from different places 88 km apart . if the ratio of the speeds of the cars a and b is 5 : 6 and the speed of the car b is 90 km per hour then after how long will the two meet each other ?
Options: a ) 2263 minutes , b ) 24 minutes , c ) 32 minutes , d ) 36 minutes , e ) none of these
Rationale: speed of the car a = 5 ⁄ 6 × 90 = 75 km / hr \ reqd time = 88 / 90 + 75 × 60 = 32 minutes answer c
Answer: c
Python program:
a = 5 / 6
b = 90 * a
c = b + 90 
d = 88 / c
e = d * const_60
Problem: find the angle between the hour hand and the minute hand of a clock when 3.25 .
Options: a ) 47.5 , b ) 46.5 , c ) 45.5 , d ) 48.5 , e ) 44.5
Rationale: angle = 30 ( hours ) - ( 11 / 2 ) ( minutes ) = 30 * 3 - ( 5.5 * 25 ) ( hour = 3 and minutes = 25 ) = 90 - 137.5 = 47.5 answer : a
Answer: a
Python program:
a = const_60 / 2
b = 3 - 25
c = b * 100
d = a * c
e = d / const_60
f = const_60 - e