euclaise/mathqa_programs huggingface dataset:
Problem: two consultants can type up a report in 12.5 hours and edit it in 7.5 hours . if mary needs 30 hours to type the report and jim needs 12 hours to edit it alone , how many w hours will it take if jim types the report and mary edits it immediately after he is done ?
Options: a ) 41.4 , b ) 34.1 , c ) 13.4 , d ) 12.4 , e ) 10.8
Rationale: "break down the problem into two pieces : typing and editing . mary needs 30 hours to type the report - - > mary ' s typing rate = 1 / 30 ( rate reciprocal of time ) ( point 1 in theory below ) ; mary and jim can type up a report in 12.5 and - - > 1 / 30 + 1 / x = 1 / 12.5 = 2 / 25 ( where x is the time needed for jim to type the report alone ) ( point 23 in theory below ) - - > x = 150 / 7 ; jim needs 12 hours to edit the report - - > jim ' s editing rate = 1 / 12 ; mary and jim can edit a report in 7.5 and - - > 1 / y + 1 / 12 = 1 / 7.5 = 2 / 15 ( where y is the time needed for mary to edit the report alone ) - - > y = 20 ; how many w hours will it take if jim types the report and mary edits it immediately after he is done - - > x + y = 150 / 7 + 20 = ~ 41.4 answer : a ."
Answer: a
Python program:
a = 1 / 12
b = 1 / 30
c = a - b
d = 1/(c)
e = 1 / 7
f = 1 / 12
g = e - f
h = 1/(g)
i = d + h
Problem: a scuba diver descends at a rate of 35 feet per minute . a diver dive from a ship to search for a lost ship at the depth of 3500 feet below the sea level . . how long will he take to reach the ship ?
Options: a ) 160 minutes , b ) 120 minutes , c ) 100 minutes , d ) 76 minutes , e ) 77 minutes
Rationale: "time taken to reach = 3500 / 35 = 100 minutes answer : c"
Answer: c
Python program:
a = 3500 / 35
Problem: a snail , climbing a 42 feet high wall , climbs up 4 feet on the first day but slides down 2 feet on the second . it climbs 4 feet on the third day and slides down again 2 feet on the fourth day . if this pattern continues , how many days will it take the snail to reach the top of the wall ?
Options: a ) 20 , b ) 26 , c ) 32 , d ) 39 , e ) 51
Rationale: "total transaction in two days = 4 - 2 = 2 feet in 38 days it will climb 38 feet on the 39 th day , the snail will climb 4 feet , thus reaching the top therefore , total no of days required = 39 d"
Answer: d
Python program:
a = 42 - 4
Problem: at what rate percent on simple interest will rs . 900 amount to rs . 950 in 5 years ?
Options: a ) 1.11 % , b ) 5.93 % , c ) 4.33 % , d ) 5.33 % , e ) 6.33 %
Rationale: "50 = ( 900 * 5 * r ) / 100 r = 1.11 % answer : a"
Answer: a
Python program:
a = 950 - 900
b = a / 900
c = b / 5
d = c * 100
Problem: if the price of sugar rises from rs . 10 per kg to rs . 12 per kg , a person , to have no increase in the expenditure on sugar , will have to reduce his consumption of sugar by
Options: a ) 17 % , b ) 20 % , c ) 25 % , d ) 30 % , e ) none
Rationale: "sol . let the original consumption = 100 kg and new consumption = x kg . so , 100 x 10 = x × 12 = x = 83 kg . ∴ reduction in consumption = 17 % . answer a"
Answer: a
Python program:
a = 1 * 10
b = a / 12
c = 1 - b
d = c * 100
Problem: initially , the men and women in a room were in the ratio of 4 : 5 . then , 2 men entered the room and 3 women left the room . then , the number of women doubled . now there are 14 men in the room . how many e women are currently in the room ?
Options: a ) 12 , b ) 14 , c ) 15 , d ) 24 , e ) 36
Rationale: "the number of women doubled means that they have become 24 from 12 . . and we have to tell the current strength so 24 is the answer . . let the number be 4 x and 5 x . . given 4 x + 2 = 14 . . so x = 3 . . women number = 5 * 3 - 3 = 12 , then doubled = 24 . . ans d"
Answer: d
Python program:
a = 14 - 2
b = 5 * a
c = b / 4
d = c - 3
e = 2 * d
Problem: find the compound ratio of ( 2 : 3 ) , ( 3 : 4 ) and ( 1 : 4 ) is
Options: a ) 1 : 2 , b ) 2 : 3 , c ) 1 : 8 , d ) 4 : 5 , e ) 3 : 2
Rationale: "required ratio = 2 / 3 * 3 / 4 * 1 / 4 = 1 / 8 = 1 : 8 answer is c"
Answer: c
Python program:
a = 2 / 3
b = 2 / 3
c = 3 / 3
d = b * c
e = a * d
Problem: in a neighborhood having 90 households , 11 did not have either a car or a bike . if 16 households had a both a car and a bike and 44 had a car , how many had bike only ?
Options: a ) 30 , b ) 35 , c ) 20 , d ) 18 , e ) 10
Rationale: "{ total } = { car } + { bike } - { both } + { neither } - - > 90 = 44 + { bike } - 16 + 11 - - > { bike } = 51 - - > # those who have bike only is { bike } - { both } = 51 - 16 = 35 . answer : b ."
Answer: b
Python program:
a = 90 - 11
b = a + 16 
c = b - 44
d = c - 16
Problem: a bag marked at $ 150 is sold for $ 120 . the rate of discount is ?
Options: a ) 10 % , b ) 25 % , c ) 20 % , d ) 50 % , e ) 45 %
Rationale: "rate of discount = 30 / 150 * 100 = 20 % answer is c"
Answer: c
Python program:
a = 150 - 120
b = a / 150
c = b * 100
Problem: a man swims downstream 70 km and upstream 30 km taking 10 hours each time ; what is the speed of the current ?
Options: a ) 1 , b ) 4 , c ) 2 , d ) 6 , e ) 8
Rationale: "70 - - - 10 ds = 7 ? - - - - 1 30 - - - - 10 us = 3 ? - - - - 1 s = ? s = ( 7 - 3 ) / 2 = 2 answer : c"
Answer: c
Python program:
a = 30 / 10
b = 70 / 10
c = a + b 
d = c / 2
Problem: a certain university will select 1 of 7 candidates eligible to fill a position in the mathematics department and 2 of 8 candidates eligible to fill 2 identical positions in the computer science department . if none of the candidates is eligible for a position in both departments , how many different sets of 3 candidates are there to fill the 3 positions ?
Options: a ) 42 , b ) 70 , c ) 140 , d ) 196 , e ) 315
Rationale: "ans : 196 7 c 1 * 8 c 2 answer d )"
Answer: d
Python program:
a = 8 * 3
b = a * 7
Problem: if an object travels at three feet per second , how many feet does it travel in one hour ?
Options: a ) 3488 , b ) 10800 , c ) 12788 , d ) 1800 , e ) 2881
Rationale: explanation : if an object travels at 2 feet per second it covers 3 x 60 feet in one minute , and 3 x 60 x 60 feet in one hour . answer = 10800 answer : b ) 10800
Answer: b
Python program:
a = 3 * const_60
b = a * const_60
Problem: the length of a rectangle is twice its breadth . if its length is decreased by 5 cm and breadth is increased by 5 cm , the area of the rectangle is increased by 55 sq . cm . find the length of the rectangle .
Options: a ) 16 cm , b ) 18 cm , c ) 15 cm , d ) 20 cm , e ) 23 cm
Rationale: "explanation : let breadth = x . then , length = 2 x . then , ( 2 x - 5 ) ( x + 5 ) - 2 x * x = 55 = > 5 x - 25 = 55 = > x = 16 . length of the rectangle = 16 cm . answer : option a"
Answer: a
Python program:
a = 100 / 3
Problem: a cylindrical container with 6 meters diameter and a height of 8 meters is filled to capacity with water . if the water is then used to fill several smaller cylinders ( 2 meters radius and 5 meters height ) , how many smaller cylinders can be filled to capacity before the larger cylinder becomes empty ?
Options: a ) 5
b ) 4
c ) 3
d ) 2
e ) 1
Rationale: calculate the volume of the larger cylinder and divide it by the volume of the smaller cylinder . volume of cylinder = π r 2 h larger cylinder volume = 226.19 smaller cylinder volume = 62.83 therefore the number of smaller cylinders can be filled to capacity = 226.19 / 62.83 = 3.6 answer is c only 3 smaller cylinders can be filled to capacity .
Answer: c
Python program:
a = 6 / 2
b = volume_cylinder / (
c = b - volume_cylinder
Problem: four circular cardboard pieces , each of radius 7 cm are placed in such a way that each piece touches two other pieces . the area of the space encosed by the four pieces is. four circular cardboard pieces , each of radius 7 cm are placed in such a way that each piece touches two other pieces . the area of the space encosed by the four pieces is
Options: a ) 12
b ) 32
c ) 42
d ) 52
e ) 58
Rationale: required area = 14 * 14 - ( 4 * 1 / 4 * 22 / 7 * 7 * 7 ) sq cm = 196 - 154 = 42 sq cm . answer : c
Answer: c
Python program:
a = 7 * 2
b = a ** 2
c = 7 ** 2
d = c * math.pi
e = b - d
Problem: the roof of an apartment building is rectangular and its length is 5 times longer than its width . if the area of the roof is 720 feet squared , what is the difference between the length and the width of the roof ?
Options: a ) 38 . , b ) 40 . , c ) 42 . , d ) 44 . , e ) 48 .
Rationale: "answer is e : 48 let w be the width , so length is 5 w . therefore : w * 5 w = 720 , solving for , w = 12 , so 5 w - w = 4 w = 4 * 12 = 48"
Answer: e
Python program:
a = 720 / 5
b = math.sqrt(a)
c = b * 5
d = 720 / 5
e = math.sqrt(d)
f = c - e
Problem: jaclyn buys $ 10 000 worth of debentures in a company . she earns 9.5 % p . a . simple interest , paid to her quarterly ( that is , every 3 months ) . if the agreed period of the debenture was 18 months : calculate the amount of interest jaclyn will earn for each quarter
Options: a ) 237.5 , b ) 234 , c ) 289.5 , d ) 345 , e ) none of these
Rationale: explanation : i = ( p x r x t ) / 100 = 10000 * 9.5 / 100 * ( 18 / 12 ) ^ 1 / 6 = 237.5 answer : a
Answer: a
Python program:
a = 100 * 100
b = a * 9
c = b / 100
d = c / 4
Problem: two trains each 250 m in length are running on the same parallel lines in opposite directions with the speed of 80 kmph and 40 kmph respectively . in what time will they cross each other completely ?
Options: a ) 15 sec , b ) 19 sec , c ) 12 sec , d ) 10 sec , e ) 11 sec
Rationale: "explanation : d = 250 m + 250 m = 500 m rs = 80 + 40 = 120 * 5 / 18 = 100 / 3 t = 500 * 3 / 100 = 15 sec answer : option a"
Answer: a
Python program:
a = 80 * const_0_2778
b = 250 / a
Problem: at garage sale , all of the prices of the items sold were different . if the price of a radio sold at the garage sale was both the 15 th highest price and the 25 th lowest price among the prices of the items sold , how many items were sold at the garage sale ?
Options: a ) 33 , b ) 34 , c ) 35 , d ) 39 , e ) 37
Rationale: "14 + 24 + 1 = 39 answer : d"
Answer: d
Python program:
a = 15 + 25 
b = a - 1
Problem: in a division sum , the quotient is 20 , the divisor 66 and the remainder 55 , find the dividend ?
Options: a ) 1375 , b ) 1376 , c ) 1875 , d ) 1365 , e ) 1345
Rationale: "explanation : 20 * 66 + 55 = 1375 answer : a"
Answer: a
Python program:
a = 20 * 66
b = a + 55
Problem: a and b are two partially filled buckets of water . if 6 liters are transferred from a to b , then a would contain one - third of the amount of water in b . alternatively , if 6 liters are transferred from b to a , b would contain one - half of the amount of water in a . bucket a contains how many liters of water ?
Options: a ) 66 / 5 , b ) 13 , c ) 17 , d ) 21 , e ) 23
Rationale: let bucket a be a and bucket b be b scenario 1 a - 6 = 1 / 3 ( b + 6 ) - - - - > 3 a - 18 = b + 6 scenario 2 b - 6 = 1 / 2 ( a + 6 ) - - - - - > 2 b - 12 = a + 6 from scenario 1 , b = 3 a - 24 substitute b with this information in stmt 2 2 ( 3 a - 24 ) - 12 = a + 6 - - - - - - > 6 a - 48 - 12 = a + 6 - - - - - - > 6 a - a = 60 + 6 - - - > 5 a = 66 a = 66 / 5 , answer choice a
Answer: a
Python program:
a = 6 + 3 
b = a + 2 
c = 6 / 2
d = b * c
e = 1 / 2
f = 2 + e 
g = d / f
Problem: what is the total cost of 2 sandwiches at $ 2.49 each and 4 sodas at $ 1.87 each ?
Options: a ) $ 3.36 , b ) $ 6.85 , c ) $ 8.46 , d ) $ 10.08 , e ) $ 12.46
Rationale: "answer = e 2 * 2.49 + 4 * 1.87 = 2 ( 2.50 - 0.01 ) + 4 ( 2.00 - 0.13 ) = 5 + 8 - 0.02 - 0.52 = 13 - 0.54 = 12.46"
Answer: e
Python program:
a = 2 * 2
b = 4 * 1
c = a + b
Problem: the sum of ages of 4 children born 1 years different each is 38 years . what is the age of the elder child ?
Options: a ) 8 , b ) 11 , c ) 10 , d ) 16 , e ) 17
Rationale: "let the ages of children be x , ( x + 1 ) , ( x + 2 ) , ( x + 3 ) years . then , x + ( x + 1 ) + ( x + 2 ) + ( x + 3 ) = 38 4 x = 32 x = 8 . x + 3 = 8 + 3 = 11 answer : b"
Answer: b
Python program:
a = 2 + 0 
b = 1 + 4 
c = a + b 
d = 4 + 4 
e = c + d 
f = e + 38 
g = f / 4
Problem: what is the positive integer that can be added by 595 to make it a perfect square ?
Options: a ) 2 * 3 * 6
b ) 3 * 2 * 5
c ) 5 * 3 * 3
d ) 2 * 3
e ) 3 * 5 * 4
Rationale: 596 is added to a number that gives a perfect square nearest perfect square is 625 . so , 625 - 596 = 30 30 = 2 * 3 * 5 option b is answer
Answer: b
Python program:
a = math.sqrt(595)
b = math.floor(a)
c = b + 1 
d = c ** 2
e = d - 595
Problem: after a storm deposits 110 billion gallons of water into the city reservoir , the reservoir is 60 % full . if the original contents of the reservoir totaled 220 billion gallons , the reservoir was approximately what percentage full before the storm ?
Options: a ) 40 % , b ) 48 % , c ) 54 % , d ) 58 % , e ) 65 %
Rationale: when the storm deposited 110 billion gallons , volume of water in the reservoir = 220 + 110 = 360 billion gallons if this is only 60 % of the capacity of the reservoir , the total capacity of the reservoir = 330 / 0.6 = 550 billion gallons therefore percentage of reservoir that was full before the storm = ( 220 / 550 ) * 100 = 40 % option a
Answer: a
Python program:
a = 110 + 220 
b = 60 / 100
c = a / b
d = 220 / c
e = d * 100
Problem: ( 6 ) 6.5 × ( 36 ) 4.5 ÷ ( 216 ) 4.5 = ( 6 ) ?
Options: a ) 1 , b ) 2 , c ) 4 , d ) 6 , e ) 8
Rationale: "explanation : ( 6 ) 6.5 × ( 36 ) 4.5 ÷ ( 216 ) 4.5 = ( 6 ) 6.5 × [ ( 6 ) 2 ] 4.5 ÷ [ ( 6 ) 3 ] 4.5 = ( 6 ) 6.5 × ( 6 ) 9 ÷ ( 6 ) 13.5 = ( 6 ) ( 6.5 + 9 - 13.5 ) = ( 6 ) 2 answer : option b"
Answer: b
Python program:
a = const_60 ** 0
b = 6 ** 6
c = 36 ** 4
d = b * c
e = a * d
Problem: a rectangular grass field is 75 m * 55 m , it has a path of 3.2 m wide all round it on the outside . find the area of the path and the cost of constructing it at rs . 2 per sq m ?
Options: a ) s . 1350 , b ) s . 1327 , c ) s . 1328 , d ) s . 1364 , e ) s . 1927
Rationale: "area = ( l + b + 2 d ) 2 d = ( 75 + 55 + 3.2 * 2 ) 2 * 2.5 = > 682 682 * 2 = rs . 1364 answer : d"
Answer: d
Python program:
a = 3 * 2
b = 75 + a 
c = 3 * 2
d = 55 + c 
e = rectangle_area - (
f = e * rectangle_area
Problem: a fill pipe can fill 1 / 2 of cistern in 20 minutes . in how many minutes , it can fill 1 / 2 of the cistern ?
Options: a ) 5 min , b ) 10 min , c ) 15 min , d ) 20 min , e ) 25 min
Rationale: required time = 20 * 2 * 1 / 2 = 20 minutes answer is d
Answer: d
Python program:
a = 20 / 1
Problem: what is the average of 120 , 130 , 140 , 510 , 520 , 530 , 1115 , 1120 , and 1125 ?
Options: a ) 419 , b ) 551 , c ) 601 , d ) 590 , e ) 721
Rationale: "add 120 , 130 , 140 , 510 , 520 , 530 , 1115 , 1120 , and 1125 grouping numbers together may quicken the addition sum = 5310 5310 / 9 = 590 . d"
Answer: d
Python program:
a = 1115 + 130 
b = a + 140 
c = b + 510 
d = c + 520 
e = d + 530 
f = e + 1115 
g = 3 + 4 
h = f / g
Problem: a bus travels from town a to town b . if the bus ' s speed is 50 km / hr , it will arrive in town b 42 min later than scheduled . if the bus increases its speed by 509509 m / sec , it will arrive in town b 30 min earlier than scheduled . find : a ) the distance between the two towns ; b ) the bus ' s scheduled time of arrival in b ; c ) the speed of the bus when it ' s on schedule .
Options: a ) 60 , b ) 37 , c ) 26 , d ) 28 , e ) 11
Rationale: first we will determine the speed of the bus following its increase . the speed is increased by 509509 m / sec = 50 ⋅ 60 ⋅ 6091000 = 50 ⋅ 60 ⋅ 6091000 km / hr = 20 = 20 km / hr . therefore , the new speed is v = 50 + 20 = 70 v = 50 + 20 = 70 km / hr . if xx is the number of hours according to the schedule , then at the speed of 50 km / hr the bus travels from a to b within ( x + 4260 ) ( x + 4260 ) hr . when the speed of the bus is v = 70 v = 70 km / hr , the travel time is x − 3060 x − 3060 hr . then 50 ( x + 4260 ) = 70 ( x − 3060 ) 50 ( x + 4260 ) = 70 ( x − 3060 ) 5 ( x + 710 ) = 7 ( x − 12 ) 5 ( x + 710 ) = 7 ( x − 12 ) 72 + 72 = 7 x − 5 x 72 + 72 = 7 x − 5 x 2 x = 72 x = 7 x = 72 x = 72 hr . so , the bus is scheduled to make the trip in 33 hr 3030 min . the distance between the two towns is 70 ( 72 − 12 ) = 70 ⋅ 3 = 21070 ( 72 − 12 ) = 70 ⋅ 3 = 210 km and the scheduled speed is 210 / 7 / 2 = 60 km / hr . answer : a
Answer: a
Python program:
a = 30 / const_60
b = 509509 * const_3_6
c = a * b
d = 42 / const_60
e = 50 * d
f = c - e
g = 509509 * const_3_6
h = g - 50
i = f / h
j = 42 / const_60
k = i + j 
l = 50 * k
Problem: how many numbers from 10 to 100000 are exactly divisible by 9 ?
Options: a ) 900 , b ) 11110 , c ) 1100 , d ) 1200 , e ) 1400
Rationale: "10 / 9 = 1 and 100000 / 9 = 11111 = = > 11111 - 1 = 11110 . answer : b"
Answer: b
Python program:
a = 100000 / 9
b = math.floor(a)
c = b * 9
d = 10 / 9
e = math.floor(d)
f = e + 1 
g = f * 9
h = c - g
i = h / 9
j = i + 1
Problem: if 10 litres of an oil of rs . 40 per litres be mixed with 5 litres of another oil of rs . 66 per litre then what is the rate of mixed oil per litre ?
Options: a ) rs . 48.66 , b ) rs . 51.03 , c ) rs . 54.17 , d ) rs . 55.33 , e ) none of the above
Rationale: "40 * 10 = 400 66 * 5 = 330 730 / 15 = 48.66 answer : a"
Answer: a
Python program:
a = 10 * 40
b = 5 * 66
c = a + b 
d = 10 + 5 
e = c / d
Problem: tom wants to buy items costing $ 25.35 , $ 70.69 , and $ 85.96 . he earns $ 6.50 an hour doing odd jobs . if ten percent of his income is put aside for other purposes , how many hours must he work to earn the money he needs for his purchases ? round your answer to the nearest whole hour .
Options: a ) 8 hours , b ) 48 hours , c ) 31 hours , d ) 18 hours , e ) 28 hours
Rationale: $ 6.50 x . 10 = $ . 65 is 10 % of his hourly income $ 6.50 - . 65 = $ 5.85 hourly amount available to spend $ 25.35 + $ 70.69 + $ 85.96 = $ 182 total needed $ 182 ÷ $ 5.85 = 31.11 . . . rounds to 31 hours correct answer c
Answer: c
Python program:
a = 25 + 35 
b = a + 85 
c = 1 / 10
d = 1 - c
e = 6 * 5
f = b / e
g = math.floor(f)
Problem: a small college reduced its faculty by approximately 13 percent to 195 professors . what was the original number of faculty members ?
Options: a ) 182 , b ) 208 , c ) 224 , d ) 254 , e ) 302
Rationale: "f x is the original number of faculty members , then after 13 % reduction in faculty members number is . 87 x but we are given . 87 x = 195 x = 224 so the original number of faculty members is 224 correct answer - c"
Answer: c
Python program:
a = 100 - 13
b = a / 100
c = 195 / b
Problem: the probability that a man will be alive for 10 more yrs is 3 / 4 & the probability that his wife will alive for 10 more yrs is 1 / 5 . the probability that none of them will be alive for 10 more yrs , is
Options: a ) 1 / 2 , b ) 1 , c ) 2 / 3 , d ) 1 / 5 , e ) 2
Rationale: "sol . required probability = pg . ) x p ( b ) = ( 1 — d x ( 1 — i ) = : x 1 = 1 / 5 ans . ( d )"
Answer: d
Python program:
a = 3 / 4
b = 1 - a
c = 3 / 5
d = 3 - c
e = b * d
Problem: a reduction of 20 % in the price of salt enables a lady to obtain 10 kgs more for rs . 100 , find the original price per kg ?
Options: a ) 2.9 , b ) 2.2 , c ) 2.5 , d ) 2.1 , e ) 2.3
Rationale: "100 * ( 20 / 100 ) = 20 - - - 10 ? - - - 1 = > rs . 2 100 - - - 80 ? - - - 2 = > rs . 2.5 answer : c"
Answer: c
Python program:
a = 20 / 100
b = a * 100
c = b / 10
d = 20 / 100
e = d * 100
f = c / e
g = f * 100
Problem: a company that ships boxes to a total of 12 distribution centers uses color coding to identify each center . if either a single color or a pair of two different colors is chosen to represent each center and if each center is uniquely represented by that choice of one or two colors , what is the minimum number of colors needed for the coding ? ( assume that the order of the colors in a pair does not matter . )
Options: a ) 4 , b ) 5 , c ) 6 , d ) 12 , e ) 24
Rationale: "let ' s start with 4 minimum number of colors so single color code we can make 4 nos . now if we need to make 2 color combination out of 4 we can do so in 4 ! / 2 ! * 2 ! or 4 * 3 / 2 or 6 so total we can make 4 + 6 = 10 color combinations but we have 12 boxes so let ' s look at 5 we get 5 single color codes and out 5 color choices , we can choose 2 in 5 ! / 2 ! * 3 ! ways or 10 ways . so total we can have 5 + 10 = 15 color combinations . so , minimum number we need will be 5 ans is b . . . . . . ."
Answer: b
Python program:
a = 12 / 2
b = a - 1
c = math.factorial(b)
d = math.factorial(3)
e = math.factorial(2)
f = d * e
g = c / f
h = 12 / 2
i = h - 1
j = g - i
Problem: the present worth of a sum due sometime hence is rs . 576 and the banker ’ s gain is rs . 16 . the true discount is
Options: a ) rs . 36 , b ) rs . 72 , c ) rs . 48 , d ) rs . 96 , e ) none
Rationale: solution t . d = √ p . w xb . g = √ 576 x 16 = 96 . answer d
Answer: d
Python program:
a = 576 * 16
b = math.sqrt(a)
Problem: two trains are moving in the same direction at 90 kmph and 36 kmph . the faster train crosses a man in the slower train in 29 seconds . find the length of the faster train ?
Options: a ) 425 , b ) 435 , c ) 445 , d ) 455 , e ) 465
Rationale: "relative speed = ( 90 - 36 ) * 5 / 18 = 3 * 5 = 15 mps . distance covered in 29 sec = 29 * 15 = 435 m . the length of the faster train = 435 m . answer : b"
Answer: b
Python program:
a = 90 - 36
b = a / const_3_6
c = b * 29
Problem: the value of a machine depreciates at the rate of 10 % every year . it was purchased 3 years ago . if its present value is rs . 8748 , its purchase price was :
Options: a ) 12003 , b ) 12000 , c ) 12002 , d ) 12289 , e ) 12019
Rationale: "explanation : = rs . 12000 answer : b ) 12000"
Answer: b
Python program:
a = 10 / 100
b = a * 3
c = 1 - b
d = 8748 / c
Problem: solve for x the equation log 9 ( x 3 ) = log 2 ( 8 )
Options: a ) 9 , b ) 8 , c ) 7 , d ) 6 , e ) 5
Rationale: log 9 ( x 3 ) = log 2 ( 8 ) : given log 2 ( 23 ) = 3 : simplify right hand side of given equation . log 9 ( x 3 ) = 3 : rewrite the above equation log 9 ( x 3 ) = log 9 ( 93 ) : rewite 3 as a log base 9 . x 3 = 93 : obtain algebraic equation from eqaution d . x = 9 : solve above for x correct answer a
Answer: a
Python program:
a = math.log(8)
b = math.log(9)
c = a * b
d = c / 3
e = 2 ** d
Problem: there are 6 more women than there are men on a local co - ed softball team . if there are a total of 16 players on the team , what is the ratio of men to women ?
Options: a ) 10 / 16 , b ) 6 / 16 , c ) 4 / 16 , d ) 5 / 11 , e ) 4 / 10
Rationale: "w = m + 6 w + m = 16 m + 6 + m = 16 2 m = 10 m = 5 w = 11 ratio : 5 : 11 ans : d"
Answer: d
Python program:
a = 16 - 6
b = 1 + 1 
c = a / b
d = 16 - 6
e = 1 + 1 
f = d / e
g = f + 6 
h = c / g
Problem: salad dressing p is made up of 30 % vinegar and 70 % oil , and salad dressing q contains 10 % vinegar and 90 % oil . if the two dressings are combined to produce a salad dressing that is 25 % vinegar , dressing p comprises what percentage of the new dressing ?
Options: a ) 75 % , b ) 60 % , c ) 40 % , d ) 25 % , e ) 20 %
Rationale: "let x be the percentage of dressing p in the new dressing . 0.3 x + 0.1 ( 1 - x ) = 0.25 0.2 x = 0.15 x = 0.75 = 75 % the answer is a ."
Answer: a
Python program:
a = 30 - 10
b = 25 - 10
c = a / b
Problem: water consists of hydrogen and oxygen , and the approximate ratio , by mass , of hydrogen to oxygen is 2 : 16 . approximately how many grams of oxygen are there in 135 grams of water ?
Options: a ) 120 , b ) 116 , c ) 112 , d ) 108 , e ) 104
Rationale: "( 16 / 18 ) * 144 = 120 grams the answer is a ."
Answer: a
Python program:
a = 2 + 16 
b = 135 / a
c = 2 * b
Problem: a boat can travel with a speed of 16 km / hr in still water . if the rate of stream is 5 km / hr , then find the time taken by the boat to cover distance of 63 km downstream .
Options: a ) 3 hours , b ) 5 hours , c ) 6 hours , d ) 7 hours , e ) 8 hours
Rationale: "explanation : it is very important to check , if the boat speed given is in still water or with water or against water . because if we neglect it we will not reach on right answer . i just mentioned here because mostly mistakes in this chapter are of this kind only . lets see the question now . speed downstream = ( 16 + 5 ) = 21 kmph time = distance / speed = 63 / 21 = 3 hours option a"
Answer: a
Python program:
a = 16 + 5 
b = 63 / a