euclaise/mathqa_programs huggingface dataset:
Problem: roja and pooja start moving in the opposite directions from a pole . they are moving at the speeds of 7 km / hr and 3 km / hr respectively . after 4 hours what will be the distance between them ?
Options: a ) 22 km , b ) 40 km , c ) 65 km , d ) 18 km , e ) 16 km
Rationale: "distance = relative speed * time = ( 7 + 3 ) * 4 = 40 km [ they are travelling in the opposite direction , relative speed = sum of the speeds ] . answer : b"
Answer: b
Python program:
a = 7 + 3 
b = a * 4
Problem: if xy denotes x is raised to the power y , find the last two digits of 19413846 + 19614181
Options: a ) 67 , b ) 74 , c ) 82 , d ) 98 , e ) 34
Rationale: 1941 ^ 3846 unit digit = 1 ^ 4 = 1 10 th digit = 4 * 6 = 24 = 2 means last two digit = 41 and 1972 ^ 4181 unit digit = 1 10 th digit = 7 * 2 = 14 mean last two digit = 41 hence , 41 + 41 = 82
Answer: c
Python program:
a = 100 ** 2
b = reminder - (
c = b - 100
d = c + 10 
e = d - 10
f = 100 ** 2
g = 19413846 / f
h = math.floor(g)
i = e - reminder
Problem: all the milk in container a which was filled to its brim was poured into two containers b and c . the quantity of milk in container b was 62.5 % less than the capacity of container a . if 156 liters was now transferred from c to b , then both the containers would have equal quantities of milk . what was the initial quantity of milk in container a ?
Options: a ) 1248 , b ) 1723 , c ) 1129 , d ) 2613 , e ) 1372
Rationale: "a b has 62.5 % or ( 5 / 8 ) of the milk in a . therefore , let the quantity of milk in container a ( initially ) be 8 k . quantity of milk in b = 8 k - 5 k = 3 k . quantity of milk in container c = 8 k - 3 k = 5 k container : a b c quantity of milk : 8 k 3 k 5 k it is given that if 156 liters was transferred from container c to container b , then both the containers would have equal quantities of milk . 5 k - 156 = 3 k + 156 = > 2 k = 312 = > k = 156 the initial quantity of milk in a = 8 k = 8 * 156 = 1248 liters ."
Answer: a
Python program:
a = 1/(2)
b = 62 / 5
c = 1 - b
d = a - c
e = 156 / d
Problem: the chance of rain on any given day in tel - aviv is 50 % . what is the probability a that it rained in tel - aviv on exactly 4 out of 6 randomly chosen days ?
Options: a ) 15 / 64 , b ) 30 / 64 , c ) 1 / 2 , d ) 1 / 4 , e ) 52 / 64
Rationale: "chances of rain on exactly 4 days and not rain on 2 days = ( 1 / 2 ) ^ 4 * ( 1 / 2 ) ^ 2 = 1 / 64 chosing 4 days out of 6 = 6 ! / ( 4 ! * 2 ! ) = 15 chances of rain on exactly 4 days out of 6 days a = 15 / 64 ans a it is ."
Answer: a
Python program:
a = math.comb(6, 4)
b = 1 / 2
c = b ** 4
d = 1 / 2
e = d ** 2
f = c * e
g = 1/(f)
h = a / g
Problem: a 300 m long train crosses a platform in 27 sec while it crosses a signal pole in 18 sec . what is the length of the platform ?
Options: a ) 286 m , b ) 350 m , c ) 277 m , d ) 278 m , e ) 150 m
Rationale: "speed = 300 / 18 = 50 / 3 m / sec . let the length of the platform be x meters . then , ( x + 300 ) / 27 = 50 / 3 x = 150 m . answer : e"
Answer: e
Python program:
a = speed * (
b = a - 27
Problem: of 67 players on a cricket team , 37 are throwers . the rest of the team is divided so one third are left - handed and the rest are right handed . assuming that all throwers are right handed , how many right - handed players are there total ?
Options: a ) 54 , b ) 55 , c ) 57 , d ) 71 , e ) 92
Rationale: "total = 67 thrower = 37 rest = 67 - 37 = 30 left handed = 30 / 3 = 10 right handed = 20 if all thrower are right handed then total right handed is 30 + 20 = 57 so c . 57 is the right answer"
Answer: c
Python program:
a = 1 / 3
b = 1 - a
c = 67 - 37
d = b * c
e = 37 + d
Problem: a can do a half of certain work in 70 days and b one third of the same in 35 days . they together will do the whole work in .
Options: a ) 88 days , b ) 27 days , c ) 78 days , d ) 60 days , e ) 17 days
Rationale: "a = 140 days b = 105 days 1 / 140 + 1 / 105 = 7 / 420 = 1 / 60 = > 60 days answer : d"
Answer: d
Python program:
a = 70 * 2
b = 1/(a)
c = 35 * 3
d = 1/(c)
e = b + d
Problem: when 1 / 10 percent of 4,000 is subtracted from 1 / 10 of 4,000 , the difference is
Options: a ) 0 , b ) 50 , c ) 396 , d ) 495 , e ) 500
Rationale: "we can break this problem into two parts : 1 ) what is 1 / 10 percent of 4,000 ? 2 ) what is 1 / 10 of 4,000 ? to calculate 1 / 10 percent of 4,000 we must first remember to divide 1 / 10 by 100 . so we have : ( 1 / 10 ) / ( 100 ) to divide a number by 100 means to multiply it by 1 / 100 , so we have : 1 / 10 x 1 / 100 = 1 / 1,000 thus , 1 / 10 percent of 4,000 = 1 / 1,000 x 4,000 = 4 . now let ' s concentrate on part 2 . we need to calculate 1 / 10 of 4,000 . to do this we simply multiply 1 / 10 by 4,000 . 1 / 10 x 4,000 = 400 the answer to part 1 is 4 , and the answer to part 2 is 400 . their difference is 400 – 4 = 396 . answer c ."
Answer: c
Python program:
a = 3 + 4 
b = a * 1000
c = 1 / 10
d = b * c
e = 1 / 10
f = e / 100
g = 3 + 4 
h = g * 1000
i = f * h
j = d - i
Problem: if n = 2.0823 and n * is the decimal obtained by rounding n to the nearest hundredth , what is the value of n * – n ?
Options: a ) - 0.0053 , b ) - 0.0023 , c ) 0.0007 , d ) 0.0047 , e ) 0.0153
Rationale: "n * = 2.08 n * - n = 2.08 - 2.0823 - 0.0023 answer : b"
Answer: b
Python program:
a = 2 * 10
b = a + 3 
c = b / 100
d = c / 100
e = 2 - 823
f = e - 2
Problem: if jack walked 7 miles in 1 hour and 15 minutes , what was his rate of walking in miles per hour ?
Options: a ) 4 , b ) 4.5 , c ) 5.6 , d ) 6.25 , e ) 15
Rationale: "distance walked in 1 hour and 15 mins = 7 miles speed per hour = distance / time = 7 / ( 5 / 4 ) = 5.6 miles per hour answer c"
Answer: c
Python program:
a = 7 * const_60
b = 15 + const_60 
c = a / b
Problem: a grocery shop has a sale of rs . 6635 , rs . 6927 , rs . 6855 , rs . 7230 and rs . 6562 for 5 consecutive months . how much sale must he have in the sixth month so that he gets an average sale of rs . 6500 ?
Options: a ) 4857 , b ) 4184 , c ) 4012 , d ) 4791 , e ) 5291
Rationale: let the sale in the sixth month = x then ( 6635 + 6927 + 6855 + 7230 + 6562 + x ) / 6 = 6500 = > 6635 + 6927 + 6855 + 7230 + 6562 + x = 6 × 6500 = > 34209 + x = 39000 = > x = 39000 − 34209 = 4791 answer : d
Answer: d
Python program:
a = 5 + 1 
b = 6500 * a
c = 6635 + 6927 
d = 6855 + c 
e = d + 7230 
f = e + 6562 
g = b - f
Problem: a car gets 40 kilometers per gallon of gasoline . how many gallons of gasoline would the car need to travel 150 kilometers ?
Options: a ) 3.5 gallons , b ) 2.7 gallons , c ) 5.75 gallons , d ) 3.75 gallons , e ) 7.50 gallons
Rationale: "each 40 kilometers , 1 gallon is needed . we need to know how many 40 kilometers are there in 150 kilometers ? 150 ã · 40 = 3.75 ã — 1 gallon = 3.75 gallons correct answer is d ) 3.75 gallons"
Answer: d
Python program:
a = 150 / 40
Problem: a fellow borrowed a certain sum of money at 5 % per annum at simple interest and in 5 years the interest amounted to rs . 2250 less than the sum lent . what was the sum lent ?
Options: a ) 1050 , b ) 1220 , c ) 1250 , d ) 1060 , e ) 3000
Rationale: "p - 2250 = ( p * 5 * 5 ) / 100 p = 3000 answer : e"
Answer: e
Python program:
a = 5 * 5
b = a / 100
c = 1 - b
d = 2250 / c
Problem: in a certain country 1 / 3 of 4 = 8 . assuming the same proportion , what would be the value of 1 / 8 of 4 ?
Options: a ) 2 , b ) 6 , c ) 5 , d ) 4 , e ) 3
Rationale: "e 3"
Answer: e
Python program:
a = 3 / 4
b = a * 4
Problem: the average age of a group of 12 students is 20 years . if 4 more students join the group , the average age increases by 1 year . the average age of the new students is
Options: a ) 22 , b ) 23 , c ) 24 , d ) 25 , e ) 26
Rationale: "total age of 12 std = 20 * 12 total age of 16 std = 21 * 16 total age of 4 std = ( 21 * 16 ) - 20 * 12 = 96 avg of 4 std = ( 96 ) / 4 = 24 answer : c"
Answer: c
Python program:
a = 20 + 1 
b = 20 + 1 
c = a * b
d = 20 * 12
e = c - d
f = e / 4
Problem: golu started from his house towards north . after covering a distance of 8 km . he turned towards left and covered a distance of 6 km . what is the shortest distance now from his house ?
Options: a ) 10 km . , b ) 16 km . , c ) 14 km , d ) 2 km . , e ) 4 km .
Rationale: c - - - - - - - - - - - - - b ! ! ! ! ! a ab = 8 km bc = 6 km ac = sqrtof ( 8 ^ 2 + 6 ^ 2 ) ac = 10 km answer : a
Answer: a
Python program:
a = 8 ** 2
b = 6 ** 2
c = a + b 
d = math.sqrt(c)
Problem: a tank can be filled by a tap in 20 minutes and by another tap in 60 minutes . both the taps are kept open for 10 minutes and then the first tap is shut off . after this , the tank will be completely filled in what time ?
Options: a ) 10 mins , b ) 15 mins , c ) 20 mins , d ) 25 mins , e ) 30 mins
Rationale: explanation : how we can solve this question ? first we will calculate the work done for 10 mins , then we will get the remaining work , then we will find answer with one tap work , as part filled by tap a in 1 min = 1 / 20 part filled by tap b in 1 min = 1 / 60 ( a + b ) ' s 10 mins work = 10 ∗ ( 1 / 20 + 1 / 60 ) = 10 ∗ 4 / 60 = 2 / 3 remaining work = 1 − 2 / 3 = 1 / 3 method 1 = > 1 / 60 : 1 / 3 = 1 : x = > x = 20 method 2 1 / 60 part filled by b in = 1 min 1 / 3 part will be filled in = 1 / 3 / 1 / 60 = 60 / 3 = 20 option c
Answer: c
Python program:
a = 1 / 20
b = 1 / 60
c = a + b 
d = 10 * c
e = 1 - d
f = 1 / 60
g = e / f
Problem: renu can do a piece of work in 6 days , but with the help of her friend suma , she can do it in 3 days . in what time suma can do it alone ?
Options: a ) 6 , b ) 12 , c ) 14 , d ) 15 , e ) 17
Rationale: "renu â € ™ s one day â € ™ s work = 1 / 6 suma â € ™ s one day â € ™ s work = 1 / 3 - 1 / 6 = 1 / 6 suma can do it alone in 6 days . answer : a"
Answer: a
Python program:
a = 1 / 3
b = 1 / 6
c = a - b
d = 1/(c)
Problem: an engineer undertakes a project to build a road 15 km long in 300 days and employs 50 men for the purpose . after 100 days , he finds only 2.5 km of the road has been completed . find the ( approximate ) number of extra men he must employ to finish the work in time .
Options: a ) a . 43 , b ) b . 45 , c ) c . 75 , d ) d . 68 , e ) e . 60
Rationale: "50 workers working already let x be the total men required to finish the task in next 200 days 2.5 km done hence remaining is 12.5 km also , work has to be completed in next 200 days ( 300 - 100 = 200 ) we know that , proportion of men to distance is direct proportion and , proportion of men to days is inverse proportion hence , x = ( 50 * 12.5 * 100 ) / ( 2.5 * 200 ) thus , x = 125 thus , more men needed to finish the task = 125 - 50 = 75 hence answer is c"
Answer: c
Python program:
a = 15 - 2
b = 50 * a
c = b * 100
d = 300 - 100
e = 2 * 5
f = c / e
g = f - 50
Problem: a train running at the speed of 60 km / hr crosses a pole in 12 seconds . what is the length of the train ?
Options: a ) 187 m , b ) 278 m , c ) 876 m , d ) 200 m , e ) 267 m
Rationale: "speed = ( 60 * 5 / 18 ) m / sec = ( 50 / 3 ) m / sec length of the train = ( speed x time ) = ( 50 / 3 * 12 ) m = 200 m . answer : d"
Answer: d
Python program:
a = 60 * 1000
b = a / 3600
c = b * 12
Problem: a is twice as fast as b . if b alone can do a piece of work in 24 days , in what time can a and b together complete the work ?
Options: a ) 10 , b ) 12 , c ) 6 , d ) 2 , e ) 8
Rationale: a can do the work in 24 / 2 i . e . , 12 days . a and b ' s one day ' s work = 1 / 12 + 1 / 24 = ( 2 + 1 ) / 24 = 1 / 8 so a and b together can do the work in 8 days . answer : e
Answer: e
Python program:
a = 1 / 24
b = 1 / 24
c = b * 2
d = a + c 
e = 1/(d)
Problem: the owner of a furniture shop charges his customer 32 % more than the cost price . if a customer paid rs . 5400 for a computer table , then what was the cost price of the computer table ?
Options: a ) rs . 4090 , b ) rs . 4067 , c ) rs . 6290 , d ) rs . 6725 , e ) rs . 6708
Rationale: "cp = sp * ( 100 / ( 100 + profit % ) ) = 5400 ( 100 / 132 ) = rs . 4090 . answer : a"
Answer: a
Python program:
a = 32 / 100
b = 1 + a 
c = 5400 / b
Problem: city a and city b are 140 miles apart . train c departs city a , heading towards city b , at 4 : 00 and travels at 40 miles per hour . train d departs city b , heading towards city a , at 5 : 00 and travels at 20 miles per hour . the trains travel on parallel tracks . at what time do the two trains meet ?
Options: a ) 5 : 00 , b ) 5 : 30 , c ) 6 : 00 , d ) 6 : 30 , e ) 7 : 00
Rationale: "train c has traveled 20 mi in the half hour before train d has started its journey . 140 - 20 = 120 40 + 20 = 60 mph 120 mi / 60 mph = 2 hrs 5 : 00 pm + 2 hrs = 7 : 00 pm answer : e . 7 : 00"
Answer: e
Python program:
a = 5 + 2 
b = a / 0
Problem: a vendor buys 10 t - shirts at an average price of $ 14 per t - shirt . he then buys 15 more t - shirts at an average price of $ 11 per t - shirt . what is the average price b per t - shirt that the vendor paid for these purchases ?
Options: a ) $ 12.20 , b ) $ 12.50 , c ) $ 12.55 , d ) $ 12.70 , e ) $ 13.00
Rationale: correct answer : a explanation : the relevant formula for this problem is average b = ( sum ) / ( number of terms ) . another way to look at the formula is sum = average x number of terms . for the first purchase , the vendor ' s sum ( total cost ) was $ 140 , since 14 x 10 = 140 . for the second purchase , the vendor ' s cost was $ 165 , since 11 x 15 = 165 . the grand sum is then $ 140 + $ 165 , which equals $ 305 . the total number of shirts purchased was 25 , so to get the average price per shirt , we divide 305 by 25 , which equals $ 12.20 . as a result , the correct answer is a . note : a relative understanding of weighted average offers a shortcut to this problem . because the true average of 11 and 14 is 12.5 , but the vendor sells more shirts at the lower price than at the higher price , the weighted average must be less than $ 12.50 ; only answer choice a is a possibility .
Answer: a
Python program:
a = 10 + 14 
b = a / 2
c = const_0_25 + const_0_25 
d = b + c
Problem: a cylinder is 6 cms in diameter and 6 cms in height . if spheres of the same size are made from the material obtained , what is the diameter of each sphere ?
Options: a ) 5 cms
b ) 2 cms
c ) 3 cms
d ) 4 cms
e ) 6 cms
Rationale: since the sphere is made out of the cylinder material their volume will be same volume of cylinder = pi * 3 ^ 2 * 6 volume of one sphere = 4 / 3 * pi * r ^ 3 ( where r is radius of sphere ) so if there are n such sphere ' s equating the volumes , pi * r ^ 2 * h = n * ( 4 / 3 ) * pi * r ^ 3 n is the number of spheres , substituting the , r and h 9 * 6 = n * ( 4 / 3 ) * ( d / 2 ) ^ 3 d is the diameter of a sphere , n = ( 9 * 6 * 3 * 8 ) / ( 4 * d ^ 3 ) n = 324 / d ^ 3 now substitute the given answers for d and find the values for n , since a n has to be an integer only value fit for d is 3 , answer : c
Answer: c
Python program:
a = 3 * 3
b = a * 6
c = 4 / 3
d = 6 * 2
e = c * d
f = b / e
g = math.floor(f)
Problem: a number x is 8 times another number y . the percentage that y is less than x is
Options: a ) 12.5 % , b ) 87.5 % , c ) 80 % , d ) 11 % , e ) 1 %
Rationale: "say y = 1 and x = 8 . then y = 1 is less than x = 8 by ( 8 - 1 ) / 8 * 100 = 7 / 8 * 100 = 87.5 % . answer : b ."
Answer: b
Python program:
a = 8 - 1
b = a / 8
c = b * 100
Problem: if 20 typists can type 44 letters in 20 minutes , then how many letters will 30 typists working at the same rate complete in 1 hour ?
Options: a ) 63 , b ) 72 , c ) 198 , d ) 216 , e ) 400
Rationale: "20 typists can type 44 letters , so 30 typists can type = 44 * 30 / 20 44 * 30 / 20 letters can be typed in 20 mins . in 60 mins typist can type = 44 * 30 * 60 / 20 * 20 = 198 c is the answer"
Answer: c
Python program:
a = 44 * 3
b = a / 20
c = b * 30
Problem: if ( 1 / 5 ) ^ m * ( 1 / 2 ) ^ 5 = 1 / ( ( 10 ) ^ 5 ) , then m =
Options: a ) 1 , b ) 2 , c ) 3 , d ) 4 , e ) 5
Rationale: "( 1 / 5 ) ^ m ( 1 / 2 ) ^ 5 = 1 / { ( 10 ) ^ 5 } ( 10 ) ^ 5 / 2 ^ 5 = 5 ^ m [ ( 2 ^ 5 ) ( 5 ^ 5 ) ] / [ 2 ^ 5 ] = 5 ^ m 5 ^ 5 = 5 ^ m m = 5 e"
Answer: e
Python program:
a = 1 / 2
b = a * 10
c = 1 / 5
d = c * 10
e = b + d 
f = 5 / 10
g = e - f
Problem: amithab ' s average expenditure for the january to june is rs . 4200 and he spends rs . 1200 in january and rs . 1500 in july . the average expenditure for the months of febraury to july is :
Options: a ) rs . 4250 , b ) rs . 4288 , c ) rs . 4227 , d ) rs . 4218 , e ) rs . 4219
Rationale: "explanation : amithab ' s total expenditure for jan - june = 4200 x 6 = 25200 expenditure for feb - june = 25200 - 1200 = 24000 expenditure for the months of feb - july = 24000 + 1500 = 25500 the average expenditure = { 25500 } { 6 } = 4250 answer : a"
Answer: a
Python program:
a = 1500 - 1200
b = 2 * 3
c = a / b
d = 4200 + c
Problem: a doctor prescribed 18 cubic centimeters of a certain drug to a patient whose body weight was 105 pounds . if the typical dosage is 2 cubic centimeters per 15 pounds of the body weight , by what percent was the prescribed dosage greater than the typical dosage ?
Options: a ) 8 % , b ) 9 % , c ) 11 % , d ) 12.5 % , e ) 14.28 %
Rationale: "typical dosage is dose : weight : : 2 : 15 . now if weight is 105 ( multiplying factor is 7 : ( 105 / 15 ) ) then typical dosage would be 2 * 7 = 14 cc . dosage = 18 cc . dosage is greater by 2 cc . % dosage is greater : ( 2 / 14 ) * 100 = 14.28 % e is the answer ."
Answer: e
Python program:
a = 2 / 15
b = a * 105
c = b - 18
d = 2 / 15
e = d * 105
f = c / e
g = f * 100
Problem: a discount electronics store normally sells all merchandise at a discount of 5 percent to 45 percent off the suggested retail price . if , during a special sale , an additional 2 percent were to be deducted from the discount price , what would be the lowest possible price of an item costing $ 400 before any discount ?
Options: a ) $ 215.00 , b ) $ 200.00 , c ) $ 215.80 , d ) $ 182.00 , e ) $ 215.60
Rationale: "original price : 400 $ max first discount = - 45 % thus : 400 â ˆ — ( 1 â ˆ ’ 45 / 100 ) = 220 second discount on the discounted price = - 2 % thus : 220 â ˆ — ( 1 â ˆ ’ 2 / 100 ) = 215.60 answer e"
Answer: e
Python program:
a = 45 + 2 
b = a / 100
c = 400 * b
Problem: a man sold 20 articles for $ 40 and gained 20 % . how many articles should he sell for $ 90 to incur a loss 20 % ?
Options: a ) 45 , b ) 36 , c ) 40 , d ) 50 , e ) 67.5
Rationale: "production cost per article : $ 40 * ( 100 % - 20 % ) / 20 = $ 1.6 required production costs for a loss of 20 % : $ 90 * ( 100 % + 20 % ) = $ 108 number of articles to be sold for $ 108 to incur a 20 % loss : $ 108 / $ 1.6 = 67.5 thus , solution e is correct ."
Answer: e
Python program:
a = original_price_before_loss / (
Problem: two trains are moving in the same direction at 162 kmph and 18 kmph . the faster train crosses a man in the slower train in 33 seconds . find the length of the faster train ?
Options: a ) 1300 , b ) 1310 , c ) 1320 , d ) 1330 , e ) 1340
Rationale: "relative speed = ( 162 - 18 ) * 5 / 18 = 8 * 5 = 40 mps . distance covered in 33 sec = 33 * 40 = 1320 m . the length of the faster train = 1320 m . answer : c"
Answer: c
Python program:
a = 162 - 18
b = a / const_3_6
c = b * 33
Problem: a man engaged a servant on the condition that he would pay him rs . 900 and a uniform after 1 year service . he served only for 9 months and receiveduniform and rs . 650 , find the price of the uniform ?
Options: a ) rs . 90 , b ) rs . 100 , c ) rs . 130 , d ) rs . 170 , e ) rs . 190
Rationale: "9 / 12 = 3 / 4 * 900 = 675 650 - - - - - - - - - - - - - 25 1 / 4 - - - - - - - - 25 1 - - - - - - - - - ? = > rs . 100 b"
Answer: b
Python program:
a = 1 * 900
b = 3 * 4
c = b * 9
d = a - c
e = 3 * 4
f = e * 1
g = d / f
h = g * 4
Problem: 500 x 223 + 500 x 77 = ?
Options: a ) 2736900 , b ) 2738800 , c ) 150000 , d ) 2716740 , e ) none of them
Rationale: "= 8796 x ( 223 + 77 ) ( by distributive law ) = 500 x 300 = 150000 answer is c"
Answer: c
Python program:
a = 223 ** 500
b = 500 * a
Problem: how many factors of 220 are odd numbers greater than 1 ?
Options: a ) 3 , b ) 4 , c ) 5 , d ) 6 , e ) 7
Rationale: when factorized , 220 has 4 prime factors . of these prime factors 2 are odd and 2 are even . hence total number of odd factors is 2 * 2 ( 4 ) , which includes 1 . the total number of odd factors greater than 1 are 3 . ( option a )
Answer: a
Python program:
a = 10 * 2
b = const_60 / 0
Problem: in xyz business school , 88 % are taking their specialization as finance at the same time 76 % taking their specialization as marketing . if 90 % are taking their specialization as finance then , what is % of marketing specialization students ?
Options: a ) 55 , b ) 75 , c ) 43 , d ) 52 , e ) 45
Rationale: percentage of finance specialization = 88 ; percentage of marketing specialization = 75 % ; total = 90 * 100 ; percentage of finance specialization = 90 - 88 = 2 ; percentage of marketing specialization = 100 - 75 = 25 ; then percentage of marketing specialization = 0.75 * 24 = 18 . then total percentage of marketing specialization = 25 + 18 = 43 . answer : c
Answer: c
Python program:
a = 90 - 76
b = 88 - a
c = b / 3
d = 90 - 76
e = 88 - d
f = e / 3
g = c + f 
h = g - 3
i = 90 - 76
j = 88 - i
k = j / 3
l = 90 - 76
m = 88 - l
n = m / 3
o = k + n 
p = 90 - 76
q = 88 - p
r = q / 3
s = 90 - 76
t = 88 - s
u = t / 3
v = r + u 
w = v - 3
x = o - w
y = h - x
Problem: the figure above shows the dimensions of a semicircular cross section of a one - way tunnel . the single traffic lane is 12 feet wide and is equidistant from the sides of the tunnel . if vehicles must clear the top of the tunnel by at least ½ foot when they are inside the traffic lane , what should be the limit y on the height of vehicles that are allowed to use the tunnel ?
Options: a ) 5 ½ ft , b ) 7 ½ ft , c ) 8 ½ ft , d ) 9 ½ ft , e ) 10 ft
Rationale: "let ' s label the midpoint of the circle o . since the base of the semi - circle is 20 , we know that the diameter is 20 and , accordingly , the radius is 10 . we also know that the traffic lane is 12 feet long and there ' s an equal amount of space on either side , so the traffic lane extends 6 feet on either side of o . let ' s call the leftmost point on the base of the traffic lane a . so , the distance oa is 6 . now draw a line straight up from a to the top of the tunnel . let ' s label the point at which the line intersects the circle b . the answer to the question will , therefore , be the height ab - . 5 feet ( we need to leave . 5 feet of clearance ) . here ' s the key to solving the question : if we draw a line from o to b , that line is a radius of the circle and , therefore , has length 10 . we now have right triangle oab ( the right angle is at point a ) , with leg oa = 6 and hypotenuse ob = 10 . we can now solve for leg ab = 8 ( either by applying the pythagorean theorum or by applying the 3 / 4 / 5 special right triangle ratio ) . finally : ab = 8 , so the correct answer ybis 8 - . 5 = 7.5 . . . choose ( b ) ! from a strategic guessing point of view , as soon as we realize that the height of the tunnel is 10 in the middle , we should quickly eliminate ( d ) and ( e ) as too big ; worse case you have a 1 / 3 shot at picking up the points . b"
Answer: b
Python program:
a = 12 / 2
b = 1 / 2
c = a - b
Problem: in the rectangular coordinate system , points ( 4 , 0 ) and ( – 4 , 0 ) both lie on circle c . what is the maximum possible value of the radius of c
Options: a ) 2 , b ) 4 , c ) 8 , d ) 16 , e ) none of the above
Rationale: "it takes 3 distinct points to define a circle . only 2 are given here . the two points essentially identify a single chord of the circle c . since no other information is provided , however , the radius of the circle can essentially be anything . all this information tell us is that the radius isgreater 4 b"
Answer: b
Python program:
a = 4 ** 2
b = math.sqrt(a)
Problem: on a map , 3 centimeters represents 33 kilometers . two cities 209 kilometers apart would be separated on the map by how many centimeters ?
Options: a ) 19 , b ) 7 , c ) 13 , d ) 110 , e ) 180
Rationale: "1 centimeter represents 11 kilometers ( 33 / 3 ) x = 209 / 11 = 19 answer : a"
Answer: a
Python program:
a = 3 / 33
b = a * 209