euclaise/mathqa_programs huggingface dataset:
Problem: if a 10 percent deposit that has been paid toward the purchase of a certain product is $ 55 , how much more remains to be paid ?
Options: a ) $ 455 , b ) $ 495 , c ) $ 525 , d ) $ 550 , e ) $ 585
Rationale: "90 % remains to be paid so the remaining amount is 9 * 55 = $ 495 . the answer is b ."
Answer: b
Python program:
a = 100 / 10
b = 55 * a
c = b - 55
Problem: if two times of the daughter ’ s age in years is included to the mother ’ s age , the total is 70 and if two times of the mother ’ s age is included to the daughter ’ s age , the total is 95 . so the mother ’ s age is ,
Options: a ) 30 , b ) 40 , c ) 50 , d ) 60 , e ) 39
Rationale: b 40 let daughter ’ s age = a and mother ’ s age = b given : 2 a + b = 70 and , a + 2 b = 95 solving b , we will get b = 40 .
Answer: b
Python program:
a = 95 * 2
b = a - 70
c = b / 3
Problem: an auto assembly plant performs 6 functions with each frame that arrives : add axles , add wheels to the axles , install the windshield to the frame , install the instrument panel , install the steering wheel , and install the interior seating . once those 6 tasks are performed , each car goes to a separate building for finishing touches . if these tasks can be arranged along a linear assembly line in any order , except that the axles must be installed before the wheels can be added , how many r ways can the assembly line be arranged ?
Options: a ) 120 , b ) 240 , c ) 360 , d ) 480 , e ) 720
Rationale: c ) 360 short way : there are 6 c ! ways to do the six tasks . half will have wheels before axles and half will have axles before wheels . so we want r = 6 c ! / 2 - > 720 / 2 = 360
Answer: c
Python program:
a = math.factorial(6)
b = a / 2
Problem: a and b put in rs . 300 and rs . 400 respectively into a business . a reinvests into the business his share of the first year ' s profit of rs . 140 where as b does not . in what ratio should they divide the second year ' s profit ?
Options: a ) 8 : 7 , b ) 7 : 5 , c ) 1 : 3 , d ) 8 : 7 , e ) 9 : 10
Rationale: "explanation : 3 : 4 a = 3 / 7 * 140 = 60 360 : 400 39 : 40 answer : e"
Answer: e
Python program:
a = 400 - 100
b = a + 300 
c = 300 / b
d = 3 + 2 
e = 2 * d
f = 140 + e 
g = c * f
h = 300 + g 
i = 400 - 100
j = h / i
Problem: the difference between the compound interest and simple interest on a certain sum at 10 % per annum for 2 years is $ 631 . find the sum ?
Options: a ) $ 52000 , b ) $ 61000 , c ) $ 71540 , d ) $ 63100 , e ) $ 56210
Rationale: let the sum be $ x c . i . = x ( 1 + 10 / 100 ) ^ 2 - x = 21 x / 100 s . i . = ( x * 10 * 2 ) / 100 = x / 5 c . i . - s . i . = ( 21 x / 100 ) - ( x / 5 ) = x / 100 x / 100 = 631 x = 63100 answer is d
Answer: d
Python program:
a = 100 * 100
b = a * 631
c = b / 100
Problem: what is the smallest number which when diminished by 16 , is divisible 4 , 6 , 8 and 10 ?
Options: a ) 136 , b ) 192 , c ) 198 , d ) 122 , e ) 142
Rationale: required number = ( lcm of 4 , 6,8 , and 10 ) + 16 = 120 + 16 = 136 option a
Answer: a
Python program:
a = math.lcm(4, 6)
b = math.lcm(8, 10)
c = math.lcm(a, b)
d = c + 16
Problem: in a room with 10 people , 6 people have exactly 1 friend in the room and 5 people have exactly 2 friends in the room ( assuming that friendship is a mutual relationship , i . e . if jane is paul ' s friend , paul is jane ' s friend ) . if two individuals are selected from the room at random , what is the probability that those two individuals are not friends ?
Options: a ) 5 / 21 , b ) 3 / 7 , c ) 4 / 5 , d ) 5 / 7 , e ) 16 / 21
Rationale: ( 6 / 10 ) ( 7 / 9 ) + ( 5 / 10 ) ( 6 / 9 ) if you choose one of the 6 with one other friend , then you have a 7 / 9 chance of not picking their friend 2 nd . if you choose one of the 5 with 2 friends , you have a 6 / 9 chance of not picking one of their friends second . add them up . 42 / 90 + 30 / 90 72 / 90 = 4 / 5 c . 4 / 5
Answer: c
Python program:
a = 10 - 1
b = a - 1
c = b - 1
d = 10 - 1
e = c / d
Problem: there are 4 people of different heights standing in order of increasing height . the difference is 2 inches between the first person and the second person , and also between the second person and the third person . the difference between the third person and the fourth person is 6 inches and the average height is 79 . how tall is the fourth person ?
Options: a ) 85 , b ) 87 , c ) 89 , d ) 91 , e ) 93
Rationale: "let x be the height of the first person . then the heights are x , x + 2 , x + 4 , and x + 10 . 4 x + 16 = 4 ( 79 ) = 316 x = 75 and the fourth person has a height of 75 + 10 = 85 inches the answer is a ."
Answer: a
Python program:
a = 79 * 4
b = 4 + 6 
c = 6 + b 
d = a - c
e = d / 4
f = 4 + 6 
g = e + f
Problem: a not - so - good clockmaker has four clocks on display in the window . clock # 1 loses 17 minutes every hour . clock # 2 gains 15 minutes every hour relative to clock # 1 ( i . e . , as clock # 1 moves from 12 : 00 to 1 : 00 , clock # 2 moves from 12 : 00 to 1 : 15 ) . clock # 3 loses 20 minutes every hour relative to clock # 2 . finally , clock # 4 gains 20 minutes every hour relative to clock # 3 . if the clockmaker resets all four clocks to the correct time at 12 noon , what time will clock # 4 display after 6 actual hours ( when it is actually 6 : 00 pm that same day ) ?
Options: a ) 5 : 00 , b ) 5 : 34 , c ) 5 : 42 , d ) 6 : 00 , e ) 6 : 24
Rationale: c 1 loses 15 minutes every hour . so after 60 minutes have passed , c 1 displays that 60 - 15 = 45 minutes have passed . c 2 gains 15 minutes for every 60 minutes displayed on c 1 . thus , the time displayed on c 2 is 75 / 60 = 5 / 4 the time displayed on c 1 . so after 60 minutes have passed , c 2 displays the passing of ( 5 / 4 * 45 ) minutes . c 3 loses 20 minutes for every 60 minutes displayed on c 2 . thus , the time displayed on c 3 is 40 / 60 = 2 / 3 the time displayed on c 2 . so after 60 minutes have passed , c 3 displays the passing of ( 2 / 3 * 5 / 4 * 45 ) minutes . c 4 gains 20 minutes for every 60 minutes displayed on c 3 . thus , the time displayed on c 4 is 80 / 60 = 4 / 3 the time displayed on clock 3 . so after 60 minutes have passed , c 4 displays the passing of 4 / 3 * 2 / 3 * 5 / 4 * 45 = 50 minutes . c 4 loses 10 minutes every hour . in 6 hours , c 4 will lose 6 * 10 = 60 minutes = 1 hour . since the correct time after 6 hours will be 6 pm , c 4 will show a time of 6 - 1 = 5 : 34 pm . the correct answer is b .
Answer: b
Python program:
a = 6 * 10
b = const_60 + 15 
c = b / const_60
d = const_60 - 20
e = d / const_60
f = c * e
g = const_60 + 20 
h = g / const_60
i = f * h
j = const_60 - 17
k = i * j
l = a - k
Problem: if both 5 ^ 3 and 3 ^ 4 are factors of n x ( 2 ^ 5 ) x ( 12 ^ 2 ) x ( 7 ^ 3 ) x ( 10 ^ 2 ) , what is the smallest possible positive value of n ?
Options: a ) 15 , b ) 45 , c ) 75 , d ) 125 , e ) 150
Rationale: "( 2 ^ 5 ) x ( 12 ^ 2 ) x ( 7 ^ 3 ) x ( 10 ) has two appearances of 3 ( in 12 ^ 2 ) and two appearances of 5 ( in 10 ^ 2 ) . thus n must include at least 3 ^ 2 * 5 = 45 the answer is b ."
Answer: b
Python program:
a = 5 * 2
b = a * 3
c = 5 * 2
d = c * 3
e = b + d 
f = 5 * 2
g = f * 3
h = e + g 
i = h + 2 
j = i + 4 
k = j + 4
Problem: the profit earned by selling an article for 812 is equal to the loss incurred when the same article is sold for 448 . what should be the sale price of the article for making 50 per cent profit ?
Options: a ) 960 , b ) 1060 , c ) 1,200 , d ) 945 , e ) none of these
Rationale: "let the profit or loss be x and 812 – x = 448 + x or , x = 364 ⁄ 2 = 182 \ cost price of the article = 812 – x = 448 + x = 630 \ sp of the article = 630 × 150 ⁄ 100 = 945 answer d"
Answer: d
Python program:
a = 812 + 448 
b = a / 2
c = 50 / 100
d = 1 + c 
e = b * d
Problem: if w is 40 percent less than e , e is 40 percent less than y , and z is 46 percent less than y , then z is greater than w by what percent of w ?
Options: a ) 4 % , b ) 18 % , c ) 36 % , d ) 40 % , e ) 50 %
Rationale: given w = 0.6 e , e = 0.6 y , z = 0.54 y , substituting , w = 2 / 3 z - - - - > z = 1.5 w and thus z is 50 % greater than w . e is the correct answer .
Answer: e
Python program:
a = 46 / 100
b = 1 - a
c = 40 / 100
d = 1 - c
e = 40 / 100
f = 1 - e
g = d * f
h = b / g
i = h - 1
j = i * 100
Problem: what is the angle between the minute hand and the hour hand when the time is 1540 hours ?
Options: a ) 150 , b ) 160 , c ) 140 , d ) 130 , e ) none
Rationale: solution : the total angle made by the minute hand during an hour is 360 o . if it takes 360 o for an hour , it will take ( 40 / 60 ) * 360 = 240 o . the angle between the hour hand the minute hand will therefore , be somewhere between 240 - 90 = 150 o , as the hour hand is between 3 and 4 . the angle made by the hour hand when it moves from say 3 to 4 will be 30 o . that is the hour hand makes 30 o during the course of an hour . the hour hand will therefore , move ( 40 / 60 ) * 30 = 20 o . therefore , the net angle between the hour hand and the minute hand will be 150 - 20 = 130 o . answer d
Answer: d
Python program:
a = 1540 / 4
b = a / 3
Problem: what is the sum of the multiples of 3 from 33 to 60 , inclusive ?
Options: a ) 465 , b ) 470 , c ) 452 , d ) 450 , e ) 460
Rationale: "the formula we want to use in this type of problem is this : average * total numbers = sum first , find the average by taking the sum of the f + l number and divide it by 2 : a = ( f + l ) / 2 second , find the total numbers in our range by dividing our f and l numbers by 7 and add 1 . ( 60 / 3 ) - ( 33 / 3 ) + 1 multiply these together so what we show average * total numbers = sum ( 33 + 60 ) / 2 * ( 60 / 3 ) - ( 33 / 3 ) + 1 = sum 93 / 2 * 10 = 465 a"
Answer: a
Python program:
a = 60 - 3
b = 33 + 2 
c = a + b 
d = c / 2
e = 60 - 3
f = 33 + 2 
g = e - f
h = g / 3
i = h + 1 
j = d * i
Problem: 3 people each took 5 tests . if the ranges of their scores in the 5 practice tests were 15 , 25 and 30 , what is the minimum possible range in scores of the 3 test - takers ?
Options: a ) 25 , b ) 30 , c ) 35 , d ) 15 , e ) 10
Rationale: i simply looked at the 3 different possible scores for each individual test : 15 , 30,25 we have to find the minimum range : 30 - 15 = 15 30 - 25 = 5 25 - 15 = 10 the find the minimum range , you have to make the set of the 5 scores as small as possible . which means that 4 of the 5 scores of each individual person is zero . 5 * 5 = 25 . answer : a
Answer: a
Python program:
a = 30 - 5
Problem: a goods train runs at the speed of 72 kmph and crosses a 270 m long platform in 26 seconds . what is the length of the goods train ?
Options: a ) 230 m , b ) 250 m , c ) 643 m , d ) 832 m , e ) 270 m
Rationale: "speed = ( 72 x 5 / 18 ) m / sec = 20 m / sec . time = 26 sec . let the length of the train be x metres . then , x + 270 / 26 = 20 x + 270 = 520 x = 250 . answer : b"
Answer: b
Python program:
a = const_0_2778 * 72
b = 270 / a
c = 26 - b
d = const_0_2778 * 72
e = c * d
Problem: rebecca ' s annual income is $ 15000 and jimmy ' s annual income is $ 18000 . by how much must rebecca ' s annual income increase so that it constitutes 50 % of rebecca and jimmy ' s combined income ?
Options: a ) 7000 , b ) 6000 , c ) 5000 , d ) 4000 , e ) 3000
Rationale: total rebecca = x + 15000 ; total = x + 15000 + 18000 x + 15000 / x + 33000 = 50 / 100 therefore x = 3000 e
Answer: e
Python program:
a = 100 - 50
b = a / 100
c = 18000 / b
d = c - 18000
e = d - 15000
Problem: a cubic object 3 ' ' x 3 ' ' x 3 ' ' is painted blue on all the outside surfaces , including the top and bottom . if the cube is cut into 27 cubes of 1 ' ' x 1 ' ' x 1 ' ' , how many 1 ' ' cubes do have any painted surfaces ?
Options: a ) 15
b ) 22
c ) 26
d ) 33
e ) 44
Rationale: c 26 only the box in the very centre of the stack will not suffer the strokes of the paint brush , whereas all the other 26 boxes will have at least one side painted .
Answer: c
Python program:
a = 27 - 1
Problem: the ratio of ages of aman , bren , and charlie are in the ratio 5 : 8 : 7 respectively . if 8 years ago , the sum of their ages was 76 , what will be the age of charlie 10 years from now ?
Options: a ) 17 , b ) 25 , c ) 45 , d ) 47 , e ) 50
Rationale: "let the present ages of aman , bren , and charlie be 5 x , 8 x and 7 x respectively . 5 x - 8 + 8 x - 8 + 7 x - 8 = 76 x = 5 present age of charlie = 7 * 5 = 35 charlie ' s age 10 years hence = 35 + 10 = 45 answer = c"
Answer: c
Python program:
a = 8 * 3
b = a + 76 
c = 5 + 8 
d = c + 7 
e = b / d
f = e * 8
g = f + 10
Problem: how many of the positive factors of 17 are not factors of 34 ?
Options: a ) 0 , b ) 1 , c ) 2 , d ) 3 , e ) 4
Rationale: "factors of 17 - 1 , 17 factors of 34 - 1 , 2 , 17 , 34 , comparing both , we have three factors of 17 which are not factors of 34 - no factors the answer is a"
Answer: a
Python program:
a = 34 / 17
Problem: rectangle a has sides a and b , and rectangle b has sides c and d . if a / c = b / d = 3 / 5 , what is the ratio of rectangle a ’ s area to rectangle b ’ s area ?
Options: a ) 5 / 3
b ) 9 / 5
c ) 9 / 25
d ) 3 / 5
e ) 25 / 9
Rationale: the area of rectangle a is ab . c = 5 a / 3 and d = 5 b / 3 . the area of rectangle b is cd = 25 ab / 9 . the ratio of rectangle a ' s area to rectangle b ' s area is ab / ( 25 ab / 9 ) = 9 / 25 . the answer is c .
Answer: c
Python program:
a = 3 ** 2
b = 5 ** 2
c = a / b
Problem: j is faster than p . j and p each walk 24 km . sum of the speeds of j and p is 7 kmph . sum of time taken by them is 14 hours . then j speed is equal to
Options: a ) 22 , b ) 14 , c ) 6 , d ) 8 , e ) 16
Rationale: given j > p j + p = 7 , only options are ( 6 , 1 ) , ( 5 , 2 ) , ( 4 , 3 ) from the given options , if j = 4 the p = 3 . times taken by them = 244 + 243 = 14 answer : b
Answer: b
Python program:
a = 24 / 4
b = 24 / 3
c = a + b
Problem: 2 ^ 8 × 39 + 31 = ?
Options: a ) 34545 , b ) 65657 , c ) 65567 , d ) 45677 , e ) 56782
Rationale: "256 * 39 + 31 65567 c"
Answer: c
Python program:
a = 2 ** 8
b = 2 ** 31
c = a / b
Problem: a river 5 m deep and 35 m wide is flowing at the rate of 2 kmph , calculate the amount of water that runs into the sea per minute ?
Options: a ) 5832.75 , b ) 5839.75 , c ) 5837.75 , d ) 5222.75 , e ) 5835.75
Rationale: "rate of water flow - 2 kmph - - 2000 / 60 - - 33.33 m / min depth of river - - 5 m width of river - - 35 m vol of water per min - - 33.33 * 5 * 35 - - - 5832.75 answer a"
Answer: a
Python program:
a = 5 * 35
b = 2 * 1000
c = a * b
d = 1 * const_60
e = c / d
Problem: on a certain road 10 % of the motorists exceed the posted speed limit and receive speeding tickets , but 15 % of the motorists who exceed the posted speed limit do not receive speeding tickets . what percent of the motorists on the road exceed the posted speed limit ?
Options: a ) 11.7 % , b ) 12.5 % , c ) 15 % , d ) 22 % , e ) 30 %
Rationale: "answer is a . this question is in the og and thus well explained by ets . those who exceed : x so x = 10 % + 0,15 x id est x = 11,7 %"
Answer: a
Python program:
a = 10 / 100
b = 15 / 100
c = a * b
d = c * 100
e = 100 / d
Problem: a train passes a station platform in 36 sec and a man standing on the platform in 23 sec . if the speed of the train is 54 km / hr . what is the length of the platform ?
Options: a ) 288 , b ) 195 , c ) 881 , d ) 1277 , e ) 121
Rationale: "speed = 54 * 5 / 18 = 15 m / sec . length of the train = 15 * 23 = 345 m . let the length of the platform be x m . then , ( x + 345 ) / 36 = 15 = > x = 195 m . answer : b"
Answer: b
Python program:
a = 54 * const_0_2778
b = 23 * a
Problem: the area of a square field is 4802 m ( power ) 2 the length of its diagonal is :
Options: a ) 98 m
b ) 102 m
c ) 95 m
d ) 105 m
e ) 96 m
Rationale: let the diagonal be d metres , then 1 / 2 d ( power ) 2 = 4802 d 2 = 9604 d = √ 9604 d = 98 m answer is a .
Answer: a
Python program:
a = math.sqrt(4802)
b = math.sqrt(2)
c = a * b
Problem: for any positive number x , the function [ x ] denotes the greatest integer less than or equal to x . for example , [ 1 ] = 1 , [ 1.567 ] = 1 and [ 1.999 ] = 1 . if k is a positive integer such that k ^ 2 is divisible by 45 and 80 , what is the units digit of k ^ 3 / 4000 ?
Options: a ) 0 , b ) 1 , c ) 27 , d ) 0 , e ) can not be determined
Rationale: k = [ lcm of 80 and 45 ] * ( any integer ) however minimum value of k is sq . rt of 3 ^ 2 * 4 ^ 2 * 5 ^ 2 = 60 * any integer for value of k ( 60 ) * any integer unit value will be always zero . d
Answer: d
Python program:
a = 3 * 2
b = 3 * 2
c = a * b
d = 3 * 2
e = c * d
f = e / 4
Problem: in the faculty of reverse - engineering , 100 second year students study numeric methods , 100 second year students study automatic control of airborne vehicles and 25 second year students study them both . how many students are there in the faculty if the second year students are approximately 50 % of the total ?
Options: a ) 340 , b ) 335 , c ) 370 , d ) 360 , e ) 350
Rationale: "total number of students studying both are 100 + 100 - 25 = 175 ( subtracting the 25 since they were included in the both the other numbers already ) . so 50 % of total is 175 , so 100 % is 350 answer is e"
Answer: e
Python program:
a = 100 + 100
Problem: the probability that a computer company will get a computer hardware contract is 3 / 4 and the probability that it will not get a software contract is 3 / 5 . if the probability of getting at least one contract is 5 / 6 , what is the probability that it will get both the contracts ?
Options: a ) 7 / 30 , b ) 11 / 40 , c ) 17 / 50 , d ) 19 / 60 , e ) 33 / 80
Rationale: let , a ≡ event of getting hardware contract b ≡ event of getting software contract ab ≡ event of getting both hardware and software contract . p ( a ) = 3 / 4 , p ( ~ b ) = 5 / 9 = > p ( b ) = 1 - ( 3 / 5 ) = 2 / 5 . a and b are not mutually exclusive events but independent events . so , p ( at least one of a and b ) = p ( a ) + p ( b ) - p ( ab ) . = > 5 / 6 = ( 3 / 4 ) + ( 2 / 5 ) - p ( ab ) . = > p ( ab ) = 19 / 60 . hence , the required probability is 19 / 60 . the answer is d .
Answer: d
Python program:
a = 3 / 4
b = 3 / 5
c = 1 - b
d = a + c 
e = 5 / 6
f = d - e
Problem: a man sitting in a train which is travelling at 60 kmph observes that a goods train , travelling in opposite direction , takes 9 seconds to pass him . if the goods train is 280 m long , find its speed ?
Options: a ) 52 kmph . , b ) 62 kmph . , c ) 72 kmph . , d ) 80 kmph . , e ) none
Rationale: "solution relative speed = ( 280 / 9 ) m / sec = ( 280 / 9 x 18 / 5 ) = 112 kmph . speed of the train = ( 112 - 60 ) kmph = 52 kmph . answer a"
Answer: a
Python program:
a = 280 / 9
b = a * const_3_6
c = b - 60
Problem: a straight line in the xy - plane has slope 2 . on this line the x - coordinate of the point is 300 and y - coordinate is 900 then what is the y intercept of the plane ?
Options: a ) 200 , b ) 250 , c ) 100 , d ) 300 , e ) 220
Rationale: "eq of line = y = mx + c m = 2 x = 300 y = 300 * 2 + c , substitute y by 900 as given in question . 900 = 600 + c , c = 200 correct option is a"
Answer: a
Python program:
a = 300 * 2
b = 900 - a
Problem: a marketing survey of anytown found that the ratio of trucks to sedans to motorcycles was 3 : 7 : 2 , respectively . given that there are 11,200 sedans in anytown , how many motorcycles are there ?
Options: a ) 1260 , b ) 2100 , c ) 3600 , d ) 3200 , e ) 5200
Rationale: "let the total number of trucks = 3 x total number of sedans = 7 x total number of motorcycles = 2 x total number of sedans = 11200 = > 7 x = 11200 = > x = 1600 total number of motorcycles = 2 x = 2 * 1600 = 3200 answer d"
Answer: d
Python program:
a = 3 * 3
b = a * 1000
c = b + 100 
d = c / 7
e = d * 2
Problem: to fill a tank , 25 buckets of water is required . how many buckets of water will be required to fill the same tank if the capacity of the bucket is reduced to two - fifth of its present ?
Options: a ) 62.5 , b ) 65 , c ) 61 , d ) 64 , e ) 60
Rationale: "let the capacity of 1 bucket = x . then , the capacity of tank = 25 x . new capacity of bucket = 2 / 5 x therefore , required number of buckets = ( 25 x ) / ( 2 x / 5 ) = ( 25 x ) x 5 / 2 x = 125 / 2 = 62.5 answer is a ."
Answer: a
Python program:
a = 4 + 1 
b = 25 * a
c = b / 2
Problem: the walker walking at a constant rate of 4 miles per hour is passed by a cyclist traveling in the same direction along the same path at 20 miles per hour . the cyclist stops to wait for the hiker 5 minutes after passing her , while the walker continues to walk at her constant rate , how many minutes must the cyclist wait until the walker catches up ?
Options: a ) 16 , b ) 18 , c ) 20 , d ) 22 , e ) 24
Rationale: after passing the hiker the cyclist travels for 5 minutes at a rate of 20 miles / hour . in those 5 mins the cyclist travels a distance of 5 / 3 miles . in those 5 mins the hiker travels a distance of 1 / 3 miles . so the hiker still has to cover 4 / 3 miles to meet the waiting cyclist . the hiker will need 1 / 3 hours or 20 mins to cover the remaining 4 / 3 miles . so the answer is c .
Answer: c
Python program:
a = 20 / const_60
b = a * 5
c = 4 / const_60
d = c * 5
e = b - d
f = 4 / const_60
g = e / f
Problem: a train traveled the first d miles of its journey it an average speed of 60 miles per hour , the next d miles of its journey at an average speed of y miles per hour , and the final d miles of its journey at an average speed of 160 miles per hour . if the train ’ s average speed over the total distance was 94 miles per hour , what is the value of y ?
Options: a ) 98 , b ) 84 , c ) 90 , d ) 120 , e ) 135
Rationale: "average speed = total distance traveled / total time taken 3 d / d / 60 + d / y + d / 160 = 94 solving for d and y , 15 y = 11 y + 480 5 y = 480 y = 98 answer a"
Answer: a
Python program:
a = 4 * 2
b = a * 10
c = 100 * 4
d = b + c 
e = 4 * 2
f = e * 10
g = 100 * 4
h = f + g 
i = h * 3
j = i / 94
k = 4 * 2
l = k + 3 
m = j - l
n = d / m
Problem: what is the total number of positive integers that are less than 1000 and that have no positive factor in common with 1000 other than 1 ?
Options: a ) 100 , b ) 200 , c ) 300 , d ) 400 , e ) 500
Rationale: "since 1000 = 2 ^ 3 * 5 ^ 3 then a number can not have 2 and / or 5 as a factor . the odd numbers do not have 2 as a factor and there are 500 odd numbers from 1 to 1000 . we then need to eliminate the 100 numbers that end with 5 , that is 5 , 15 , 25 , . . . , 995 . there are a total of 500 - 100 = 400 such numbers between 1 and 1000 . the answer is d ."
Answer: d
Python program:
a = 1000 - 1
b = 1000 - 2
c = b - 2
d = c / 2
e = d + 1 
f = 1000 / 100
g = 1000 - f
h = 1000 / 100
i = g - h
j = 1000 / 100
k = i / j
l = k + 1 
m = e + l 
n = 1000 - 10
o = n - 10
p = o / 10
q = p + 1 
r = m - q
s = a - r
Problem: the monthly incomes of a and b are in the ratio 5 : 2 . b ' s monthly income is 12 % more than c ' s monthly income . if c ' s monthly income is rs . 13000 , then find the annual income of a ?
Options: a ) rs . 420000 , b ) rs . 180000 , c ) rs . 436800 , d ) rs . 504000 , e ) none of these
Rationale: "b ' s monthly income = 13000 * 112 / 100 = rs . 14560 b ' s monthly income = 2 parts - - - - > rs . 14560 a ' s monthly income = 5 parts = 5 / 2 * 14560 = rs . 36400 a ' s annual income = rs . 36400 * 12 = rs . 436800 answer : c"
Answer: c
Python program:
a = 12 / 100
b = 1 + a 
c = 13000 * b
d = 5 / 2
e = c * d
f = e * 12
Problem: 3 * 13 + 3 * 14 + 3 * 17 + 11 = ?
Options: a ) 125 , b ) 126 , c ) 130 , d ) 143 , e ) 151
Rationale: "3 * 13 + 3 * 14 + 3 * 17 + 11 = 39 + 42 + 51 + 11 = 143 the answer is d ."
Answer: d
Python program:
a = 3 * 13
b = 3 * 14
c = a + b 
d = 3 * 17
e = c + d 
f = e + 11
Problem: in mrs . susna ' s class , 1 / 4 of her students are getting an a , 1 / 2 are getting a b , 1 / 8 are getting a c , 1 / 12 are getting a d , and 1 / 24 are getting a f . what fraction of mrs . susna ' s class getting a passing grade of c or higher .
Options: a ) 5 / 6 , b ) 3 / 4 , c ) 7 / 8 , d ) 1 / 8 , e ) 1 / 2
Rationale: if mrs . susna ' s class has 24 students , the number of students receiving as , bs , or cs , are 6 , 12 , and 3 respectively . that means 21 / 24 of her students are receiving passing grades or 7 / 8 . ( answer : c )
Answer: c
Python program:
a = 1 / 4
b = 1 / 2
c = a + b 
d = 1 / 8
e = c + d