euclaise/mathqa_programs huggingface dataset:
Problem: the dimensions of a rectangular solid are 4 inches , 6 inches , and 8 inches . if a cube , a side of which is equal to one of the dimensions of the rectangular solid , is placed entirely within thespherejust large enough to hold the cube , what the ratio of the volume of the cube to the volume within thespherethat is not occupied by the cube ?
Options: a ) 10 : 17 , b ) 2 : 5 , c ) 5 : 16 , d ) 25 : 7 , e ) 2 : 3
Rationale: answer : e .
Answer: e
Python program:
a = 8 * 2
b = a + 2 
c = b + 1 
d = 10 / c
Problem: annika hikes at a constant rate of 12 minutes per kilometer . she has hiked 2.75 kilometers east from the start of a hiking trail when she realizes that she has to be back at the start of the trail in 51 minutes . if annika continues east , then turns around and retraces her path to reach the start of the trail in exactly 51 minutes , for how many kilometers total did she hike east ?
Options: a ) 3.625 , b ) 3 , c ) 4.5 , d ) 4 , e ) 3.5
Rationale: "set up two r x t = d cases . 1 . 1 / 12 km / min x t = 2.75 from which t = 33 mins . we know total journey time now is 51 + 33 = 84 . the rate is the same ie 1 / 12 km / min . set up second r x t = d case . 1 / 12 km / min x 84 = 7 km now the total journey would be halved as distance would be same in each direction . 7 / 2 = 3.5 e ."
Answer: e
Python program:
a = 51 / 12
b = a - 2
c = b / 2
d = c + 2
Problem: if y is the smallest positive integer such that 1,260 multiplied by y is the square of an integer , then y must be
Options: a ) 23 , b ) 51 , c ) 38 , d ) 35 , e ) 37
Rationale: "1260 = 2 * 2 * 3 * 3 * 7 * 5 , so we need one 7 and one 5 to make it a square of a number . so 7 * 5 = 35 ans : d"
Answer: d
Python program:
a = 2 + 3 
b = a * 2
Problem: if sharon ' s weekly salary increased by 16 percent , she would earn $ 348 per week . if instead , her weekly salary were to increase by 25 percent , how much would she earn per week ?
Options: a ) $ 374 , b ) $ 382 , c ) $ 385 , d ) $ 392 , e ) $ 375
Rationale: "( 348 / 116 ) 125 = 375 in this case long division does not take much time . ( 348 / 116 ) = 3 3 * 125 = 375 ( 300 + 75 ) answer e"
Answer: e
Python program:
a = 16 / 100
b = 1 + a 
c = 348 / b
d = 25 / 100
e = 16 / 100
f = 1 + e 
g = 348 / f
h = d * g
i = c + h
Problem: how many books each of volume 250 meter cube can be packed into a crate of volume 4500 meter cube
Options: a ) 25 , b ) can not be determined , c ) 10 , d ) 15 , e ) 20
Rationale: "gud question with a simple concept . in geo if we want to insert one shape into another we need to know the dimensions of the two shapes . in above with volume given , we can come up with different shapes , so we cant know the answer for ex : 4500 m 3 can be 450 * 10 or 45 * 100 or just 4500 * 1 we do n ' t know , so we cant calculate answer : b"
Answer: b
Python program:
a = 4500 * 1
Problem: how long does a train 90 m long traveling at 60 kmph takes to cross a bridge of 170 m in length ?
Options: a ) sec , b ) sec , c ) sec , d ) sec , e ) sec
Rationale: "d = 90 + 170 = 260 m s = 60 * 5 / 18 = 50 / 3 t = 260 * 3 / 50 = 15.6 sec answer : d"
Answer: d
Python program:
a = 90 + 170 
b = 60 * const_0_2778
c = a / b
Problem: a certain hospital has a policy that for every 50 patients there should be 2 doctors . if the number of patients visiting the hospital every day is 400 , how many doctors are there in the hospital ?
Options: a ) 4 , b ) 16 , c ) 5 , d ) 14 , e ) 11
Rationale: 2 / 50 = x / 400 x = 16 answer is b
Answer: b
Python program:
a = 400 / 50
b = a * 2
Problem: what will be the compound interest on rs . 30000 after 3 years at the rate of 12 % per annum
Options: a ) rs 10123.20 , b ) rs 12147.84 , c ) rs 10123.40 , d ) rs 10123.50 , e ) none of these
Rationale: "explanation : ( 30000 × ( 1 + 12 / 100 ) 3 ) = > 30000 × 28 / 25 × 28 / 25 × 28 / 25 = > 42147.84 so compound interest will be 42147.84 - 30000 = rs 12147.84 option b"
Answer: b
Python program:
a = 4 * 100
b = a * 100
c = 12 / 100
d = 1 + c 
e = d ** 3
f = b * e
g = 4 * 100
h = g * 100
i = f - h
Problem: 5 % people of a village in sri lanka died by bombardment , 15 % of the remainder left the village on account of fear . if now the population is reduced to 2553 , how much was it in the beginning ?
Options: a ) 2988 , b ) 2776 , c ) 4400 , d ) 2871 , e ) 3162
Rationale: "x * ( 95 / 100 ) * ( 85 / 100 ) = 2553 x = 3162 answer : e"
Answer: e
Python program:
a = 100 - 5
b = a / 100
c = 100 - 15
d = c / 100
e = b * d
f = 2553 / e
g = math.floor(f)
Problem: a rectangular block 6 cm by 12 cm by 15 cm is cut into an exact number of equal cubes . find the least possible number of cubes ?
Options: a ) 20 , b ) 25 , c ) 40 , d ) 50 , e ) 35
Rationale: "volume of the block = 6 * 12 * 15 = 1080 cm ^ 3 side of the largest cube = h . c . f of 6 , 12,15 = 3 cm volume of the cube = 3 * 3 * 3 = 27 cm ^ 3 number of cubes = 1080 / 27 = 40 answer is c"
Answer: c
Python program:
a = rectangle_area / (
b = a - 10
c = 3 * 2
d = 1000 * c
e = b + d 
f = 3 * 1000
g = 15 * 10
h = f + g 
i = e / h
Problem: a cistern 4 m long and 8 m wide contains water up to a depth of 1 m 25 cm . the total area of the wet surface is :
Options: a ) 49 m 2 , b ) 50 m 2 , c ) 52 m 2 , d ) 62 m 2 , e ) 55 m 2
Rationale: "area of the wet surface = [ 2 ( lb + bh + lh ) - lb ] = 2 ( bh + lh ) + lb = [ 2 ( 8 x 1.25 + 4 x 1.25 ) + 8 x 4 ] m 2 = 62 m 2 . answer : d"
Answer: d
Python program:
a = 25 / 100
b = a + 1 
c = b * 8
d = 25 / 100
e = d + 1 
f = e * 4
g = c + f 
h = 2 * g
i = 8 * 4
j = h + i
Problem: in measuring the sides of a rectangle , one side is taken 12 % in excess and other 5 % in deficit . find the error percentage in the area calculated from these measurements .
Options: a ) 3.5 % , b ) 6.4 % , c ) 3 % , d ) 5 % , e ) 2.6 %
Rationale: "say both sides of the rectangle are equal to 100 ( so consider that we have a square ) . in this case the area is 100 * 100 = 10,000 . now , the area obtained with wrong measurements would be 112 * 95 = 10,640 , which is 6.4 % greater than the actual area . answer : b ."
Answer: b
Python program:
a = 12 - 5
b = 12 * 5
c = b / 100
d = a - c
Problem: in an election between two candidates a and b , the number of valid votes received by a exceeds those received by b by 15 % of the total number of votes polled . if 20 % of the votes polled were invalid and a total of 7720 votes were polled , then how many valid votes did b get ?
Options: a ) 1888 , b ) 2999 , c ) 2834 , d ) 2509 , e ) 2991
Rationale: let the total number of votes polled in the election be 100 k . number of valid votes = 100 k - 20 % ( 100 k ) = 80 k let the number of votes polled in favour of a and b be a and b respectively . a - b = 15 % ( 100 k ) = > a = b + 15 k = > a + b = b + 15 k + b now , 2 b + 15 k = 80 k and hence b = 32.5 k it is given that 100 k = 7720 32.5 k = 32.5 k / 100 k * 7720 = 2509 the number of valid votes polled in favour of b is 2834 . answer : d
Answer: d
Python program:
a = 20 / 100
b = 1 - a
c = b * 7720
d = 15 * 7720
e = d / 100
f = c - e
g = f / 2
Problem: a 180 meter long train crosses a man standing on the platform in 9 sec . what is the speed of the train ?
Options: a ) 72 , b ) 108 , c ) 1266 , d ) 188 , e ) 211
Rationale: "s = 180 / 9 * 18 / 5 = 72 kmph answer : a"
Answer: a
Python program:
a = 180 / 9
b = a * const_3_6
Problem: 3 candidates in an election and received 3000 , 5000 and 15000 votes respectively . what % of the total votes did the winningcandidate got in that election ?
Options: a ) 65.21 % , b ) 50.16 % , c ) 57 % , d ) 60 % , e ) 65.24 %
Rationale: "total number of votes polled = ( 3000 + 5000 + 15000 ) = 23000 so , required percentage = 15000 / 23000 * 100 = 65.21 % a"
Answer: a
Python program:
a = 3000 + 5000 
b = a + 15000 
c = 15000 / b
d = c * 100
Problem: lisa and robert have taken the same number of photos on their school trip . lisa has taken 3 times as many photos as claire and robert has taken 16 more photos than claire . how many photos has claire taken ?
Options: a ) 6 , b ) 8 , c ) 10 , d ) 12 , e ) 14
Rationale: "l = r l = 3 c r = c + 16 3 c = c + 16 c = 8 the answer is b ."
Answer: b
Python program:
a = 3 - 1
b = 16 / a
Problem: in the fifth grade at parkway elementary school there are 420 students . 296 students are boys and 250 students are playing soccer . 86 % of the students that play soccer are boys . how many girl student are in parkway that is not playing soccer ?
Options: a ) 69 . , b ) 73 . , c ) 81 , d ) 91 , e ) 89
Rationale: "total students = 420 boys = 296 , girls = 124 total playing soccer = 250 86 % of 250 = 215 are boys who play soccer . girls who play soccer = 35 . total girls who do not play soccer = 124 - 35 = 89 . correct option : e"
Answer: e
Python program:
a = 420 - 296
b = 250 * 86
c = b / 100
d = 250 - c
e = a - d
Problem: the percentage increase in the area of a rectangle , if each of its sides is increased by 20 %
Options: a ) 33 , b ) 37 , c ) 44 , d ) 99 , e ) 277
Rationale: "explanation : let original length = x metres and original breadth = y metres . original area = xy increased length = and increased breadth = new area = the difference between the original area and new area is : increase % = = 44 % ] answer : c ) 44 %"
Answer: c
Python program:
a = 100 + 20 
b = a / 100
c = 100 + 20 
d = c / 100
e = b * d
f = e - 1
g = f * 100
Problem: a sum was put at simple interest at certain rate for 3 years . had it been put at 1 % higher rate it would have fetched rs . 69 more . the sum is : a . rs . 2,400 b . rs . 2,100 c . rs . 2,200 d . rs . 2,480
Options: a ) 2000 , b ) 2100 , c ) 2200 , d ) 2300 , e ) 2400
Rationale: "1 percent for 3 years = 69 1 percent for 1 year = 23 = > 100 percent = 2300 answer : d"
Answer: d
Python program:
a = 69 / 3
b = a * 100
Problem: if 5 x = 6 y = z , what is x + y , in terms of z ?
Options: a ) z / 2 , b ) 2 z , c ) z / 3 , d ) 11 z / 30 , e ) z / 9
Rationale: "5 x = 6 y = z x = z / 5 and y = z / 6 x + y = z / 5 + z / 6 = 11 z / 30 answer is d"
Answer: d
Python program:
a = 5 * 100
b = a / 2
c = b - 2
d = 5 * 100
e = d / 2
f = e + 2 
g = c / f
Problem: if the mean of numbers 38 , x , 70 , 88 and 110 is 69 , what is the mean of 50 , 72 , 97 , 125,147 and x ?
Options: a ) 73.5 , b ) 77.86 , c ) 86.67 , d ) 66.69 , e ) 70.56
Rationale: "mean = ( sum of all no . in series ) / ( no . in series ) m 1 = 69 = ( x + 38 + 70 + 88 + 110 ) / ( 5 ) 69 x 5 = 290 + x x = 39 therefore mean of 2 nd series m 2 = ( x + 50 + 62 + 97 + 125 + 147 ) / 6 m 2 = 86.67 answer = c"
Answer: c
Python program:
a = 4 + 1 
b = 69 * a
c = 38 + 70 
d = c + 88 
e = d + 110 
f = b - e
g = f + 50 
h = g + 72 
i = h + 97 
j = i + 125 
k = 4 + 1 
l = j / k
Problem: a train 200 m long running at 54 kmph crosses a platform in 25 sec . what is the length of the platform ?
Options: a ) 175 , b ) 266 , c ) 350 , d ) 277 , e ) 232
Rationale: length of the platform = 54 * 5 / 18 * 25 = 375 – 200 = 175 answer : a
Answer: a
Python program:
a = 54 * const_0_2778
b = 25 * a
c = b - 200
Problem: liam is pulled over for speeding just as he is arriving at work . he explains to the police officer that he could not afford to be late today , and has arrived at work only four minutes before he is to start . the officer explains that if liam had driven 5 mph slower for his whole commute , he would have arrived at work exactly on time . if liam ' s commute is 60 miles long , how fast was he actually driving ? ( assume that liam drove at a constant speed for the duration of his commute . )
Options: a ) 50 mph , b ) 45 mph , c ) 48 mph , d ) 52 mph , e ) 70 mph
Rationale: "let t be the number of hours he would need to reach office on time . when he is driving with over speed , he reached office 4 min earlier ! so the equation for this is s ( t - 4 / 60 ) = 60 where s is the speed and 30 is the distance . if he decreases his speed by 5 mph then he would have reached his office on time : ( s - 5 ) t = 60 if you solve above equations , you will arrive at t = 2 / 3 hr and s = 70 mph therefore answer is e"
Answer: e
Python program:
a = 5 * 4
b = 60 + a
Problem: a merchant has selected two items to be placed on sale , one of which currently sells for 35 percent less than the other . if he wishes to raise the price of the cheaper item so that the two items are equally priced , by what percentage must he raise the price of the less expensive item ?
Options: a ) 30 % , b ) 40 % , c ) 50 % , d ) 60 % , e ) 70 %
Rationale: "expensive item = $ 100 ; cheap item = $ 65 ; we must increase $ 65 to $ 100 , so by $ 35 , which is approximately 50 % increase : ( 100 - 65 ) / 65 = ~ 0.53 . answer : c ."
Answer: c
Python program:
a = 35 / 100
b = 35 / 100
c = 1 - b
d = a / c
e = d * 100
Problem: the population of a bacteria colony doubles every day . if it was started 11 days ago with 2 bacteria and each bacteria lives for 12 days , how large is the colony today ?
Options: a ) 512 , b ) 768 , c ) 1024 , d ) 2048 , e ) 4096
Rationale: "2 ^ 11 ( 2 ) = 2 ^ 12 = 4096 the answer is e ."
Answer: e
Python program:
a = 11 + 1 
b = 2 ** a
c = b - 1
Problem: the unit digit in the product 7858 * 1086 * 4582 * 9783 is ?
Options: a ) 0 , b ) 1 , c ) 8 , d ) 3 , e ) 4
Rationale: "unit digit in the given product = unit digit in 8 * 6 * 2 * 3 = 8 answer is c"
Answer: c
Python program:
a = 7858 * 1086
b = a * 4582
c = b * 9783
d = 7858 * 1086
e = d * 4582
f = e * 9783
g = 4 + 4 
h = f - g
i = c - h
Problem: a train speeds past a pole in 20 seconds and passes through a tunnel 500 m long in 40 seconds . its length is :
Options: a ) 200 m , b ) 400 m , c ) 500 m , d ) 700 m , e ) none of the above
Rationale: sol . let the length of the train be x metres and its speed be y m / sec . then , x / y = 20 ⇒ y = x / 20 ∴ ( x + 500 ) / 40 = x / 20 ⇔ x = 500 m . answer c
Answer: c
Python program:
a = 2 - 1
b = 500 * a
Problem: yesterday ' s closing prices of 1,980 different stocks listed on a certain stock exchange were all different from today ' s closing prices . the number of stocks that closed at a higher price today than yesterday was 20 percent greater than the number that closed at a lower price . how many of the stocks closed at a higher price today than yesterday ?
Options: a ) 484 , b ) 1080 , c ) 1,100 , d ) 1,320 , e ) 1,694
Rationale: lets consider the below - the number of stocks that closed at a higher price = h the number of stocks that closed at a lower price = l we understand from first statement - > h + l = 1980 - - - - ( 1 ) we understand from second statement - > h = ( 120 / 100 ) l = > h = 1.2 l - - - - ( 2 ) solve eq ( 1 ) ( 2 ) to get h = 1080 . b is my answer .
Answer: b
Python program:
a = 20 * 100
b = a - 10
c = b - 10
d = 20 / 100
e = 1 + d 
f = e + 1 
g = c / f
h = 20 / 100
i = 1 + h 
j = g * i
Problem: 20 - 8 percent of the programmers in a startup company weigh 200 pounds or more . 20 - 5 percent of the programmers that are under 200 pounds in that same company weigh 100 pounds or less . what percent of the programmers in the startup company weigh between 100 and 200 pounds ?
Options: a ) 15 % , b ) 20 % , c ) 25 % , d ) 54 % , e ) 75 %
Rationale: initially 72 % and 28 % split 80 % is further divided as 25 % and 75 % q is asking about that 75 % let total be ' 100 ' then that 75 % is ( 3 / 4 ) ∗ 72 so , the required % is [ ( 3 / 4 ) ∗ 72 / 100 ] ∗ 100 = 54 % answer : d
Answer: d
Python program:
a = 20 + 8 
b = 100 - a
c = 20 + 5 
d = 100 - c
e = d / 100
f = b * e
Problem: the racing magic takes 90 seconds to circle the racing track once . the charging bull makes 40 rounds of the track in an hour . if they left the starting point together , how many minutes will it take for them to meet at the starting point for the second time ?
Options: a ) 3 , b ) 6 , c ) 9 , d ) 12 , e ) 15
Rationale: "time taken by racing magic to make one circle = 90 seconds time taken bycharging bullto make one circle = 60 mins / 40 = 1.5 mins = 90 seconds lcm of 90 and 90 seconds = 90 seconds time taken for them to meet at the starting point for the second time = 2 * 90 sec = 180 seconds = 3 mins answer a"
Answer: a
Python program:
a = 90 / 40
b = 90 * a
c = b * 2
d = c / 90
e = d * 2
Problem: a lent rs . 5000 to b for 2 years and rs . 3000 to c for 4 years on simple interest at the same rate of interest and received rs . 3300 in all from both of them as interest . the rate of interest per annum is ?
Options: a ) 16 % , b ) 12 % , c ) 74 % , d ) 10 % , e ) 15 %
Rationale: "let the rate be r % p . a . then , ( 5000 * r * 2 ) / 100 + ( 3000 * r * 4 ) / 100 = 3300 100 r + 120 r = 3300 r = 15 % answer : e"
Answer: e
Python program:
a = 5000 * 2
b = 3000 * 4
c = a + b 
d = 3300 / c
e = d * 100
Problem: in the first 10 overs of a cricket game , the run rate was only 3.2 . what should be the run rate in the remaining 40 overs to reach the target of 282 runs ?
Options: a ) 6.25 , b ) 7.25 , c ) 7.75 , d ) 7.35 , e ) 8.25
Rationale: "runs scored in the first 10 overs = 10 × 3.2 = 32 total runs = 282 remaining runs to be scored = 282 - 32 = 250 remaining overs = 40 run rate needed = 25040 = 6.25 answer : a"
Answer: a
Python program:
a = 10 * 3
b = 282 - a
c = b / 40
Problem: a can finish a work in 4 days and b can do same work in half the time taken by a . then working together , what part of same work they can finish in a day ?
Options: a ) 1 / 4 , b ) 1 / 6 , c ) 1 / 7 , d ) 3 / 4 , e ) none of these
Rationale: explanation : please note in this question , we need to answer part of work for a day rather than complete work . it was worth mentioning here because many do mistake at this point in hurry to solve the question so lets solve now , a ' s 1 day work = 1 / 4 b ' s 1 day work = 1 / 2 [ because b take half the time than a ] ( a + b ) ' s one day work = ( 1 / 4 + 1 / 2 ) = 3 / 4 so in one day 3 / 4 work will be done answer : d
Answer: d
Python program:
a = 1 / 4
b = 1 / 4
c = b * 2
d = a + c
Problem: two pipes a and b can separately fill a tank in 16 and 10 minutes respectively . a third pipe c can drain off 60 liters of water per minute . if all the pipes are opened , the tank can be filled in 10 minutes . what is the capacity of the tank ?
Options: a ) 590 liters , b ) 960 liters , c ) 740 liters , d ) 560 liters , e ) 580 liters
Rationale: "1 / 16 + 1 / 10 - 1 / x = 1 / 10 x = 12 16 * 60 = 960 answer : b"
Answer: b
Python program:
a = 1 / 16
b = 1 / 10
c = a + b 
d = 1 / 60
e = c + d 
f = 1 / 10
g = e - f
h = 1/(g)
i = h * 3
j = i * 10
Problem: a train speeds past a pole in 15 sec and a platform 110 m long in 25 sec , its length is ?
Options: a ) 100 , b ) 150 , c ) 160 , d ) 165 , e ) 180
Rationale: "let the length of the train be x m and its speed be y m / sec . then , x / y = 15 = > y = x / 15 ( x + 110 ) / 25 = x / 15 = > x = 165 m . answer : option d"
Answer: d
Python program:
a = 2 - 1
b = 110 * a
Problem: if ( t - 8 ) is a factor of t ^ 2 - kt - 47 , then k =
Options: a ) 16 , b ) 12 , c ) 2 , d ) 6 , e ) 14
Rationale: "t ^ 2 - kt - 48 = ( t - 8 ) ( t + m ) where m is any positive integer . if 48 / 8 = 6 , then we know as a matter of fact that : m = + 6 and thus k = 8 - 6 = 6 t ^ 2 - kt - m = ( t - a ) ( t + m ) where a > m t ^ 2 + kt - m = ( t - a ) ( t + m ) where a < m t ^ 2 - kt + m = ( t - a ) ( t - m ) t ^ 2 + kt + m = ( t + a ) ( t + m ) d"
Answer: d
Python program:
a = 10 + 2
Problem: during a special promotion , a certain filling station is offering a 10 percent discount on gas purchased after the first 10 gallons . if kim purchased 15 gallons of gas , and isabella purchased 25 gallons of gas , then isabella ‟ s total per - gallon discount is what percent of kim ‟ s total per - gallon discount ?
Options: a ) 80 % , b ) 100 % , c ) 116.7 % , d ) 120 % , e ) 180 %
Rationale: "kim purchased 15 gallons of gas . she paid for 10 + 0.9 * 5 = 14.5 gallons , so the overall discount she got was 0.5 / 15 = 3.33 % . isabella purchased 25 gallons of gas . she paid for 10 + 0.9 * 15 = 23.5 gallons , so the overall discount she got was 1.5 / 25 = 6 % . 6 is 6 / 3.33 * 100 = 180 % of 3.33 . answer : e ."
Answer: e
Python program:
a = 10 - 1
b = 10 + a 
c = 100 - 10
d = b * c
e = d / 100
f = e + 10 
g = f / 25
h = 1 - g
i = h * 100
j = 10 + 4 
k = 100 - 10
l = j * k
m = l / 100
n = 10 + m 
o = n / 15
p = 1 - o
q = p * 100
r = i / q
s = r * 100
Problem: a man can row downstream at the rate of 16 km / hr and upstream at 6 km / hr . find man ' s rate in still water and the rate of current ?
Options: a ) 9,6 , b ) 11,5 , c ) 9,3 , d ) 6,6 , e ) none of these
Rationale: "explanation : rate of still water = 1 / 2 ( 16 + 6 ) = 11 km / hr rate of current = 1 / 2 ( 16 - 6 ) = 5 km / hr answer : option b"
Answer: b
Python program:
a = 16 - 6
b = a / 2
Problem: a rectangular lawn of dimensions 100 m * 60 m has two roads each 10 m wide running in the middle of the lawn , one parallel to the length and the other parallel to the breadth . what is the cost of traveling the two roads at rs . 3 per sq m ?
Options: a ) a ) 3820 , b ) b ) 930 , c ) c ) 9309 , d ) d ) 4500 , e ) e ) 8302
Rationale: "explanation : area = ( l + b – d ) d ( 100 + 60 – 10 ) 10 = > 1500 m 2 1500 * 3 = rs . 4500 answer : option d"
Answer: d
Python program:
a = 100 + 60 
b = a - 10
c = b * 10
d = c * 3
Problem: find avrg speed if a man travels at speed of 18 km / hr up and 24 km / hr dawn at an altitude of 300 m .
Options: a ) 25.8 , b ) 26.8 , c ) 27.8 , d ) 20.5 , e ) 21.8
Rationale: "avg speed = 2 * x * y / ( x + y ) = 2 * 18 * 24 / ( 18 + 24 ) = 20.5 answer : d"
Answer: d
Python program:
a = 2 * 18
b = a * 24
c = 18 + 24 
d = b / c
Problem: nitin ranks 27 th in a class of 89 students . what is rank from the last ?
Options: a ) 63 , b ) 65 , c ) 67 , d ) 87 , e ) 89
Rationale: "explanation : number students behind the nitin in rank = ( 89 - 27 ) = 62 nitin is 63 th from the last answer : a ) 63"
Answer: a
Python program:
a = 89 - 27
Problem: set a consists of the integers from 3 to 12 , inclusive , while set b consists of the integers from 6 to 20 , inclusive . how many distinct integers do belong to the both sets at the same time ?
Options: a ) 5 , b ) 7 , c ) 8 , d ) 9 , e ) 10
Rationale: "a = { 3,4 , 5,6 , 7,8 , 9,10 , 11,12 } b = { 6 , 7,8 , 9,10 , 11,12 . . . } thus we see that there are 7 distinct integers that are common to both . b is the correct answer ."
Answer: b
Python program:
a = 6 + 3
Problem: what is the units digit of the expression 14 ^ 7 − 20 ^ 4 ?
Options: a ) 8 , b ) 3 , c ) 4 , d ) 6 , e ) 0
Rationale: i think answer on this one should be a too . since we know that 14 ^ 7 > 20 ^ 4 , as will said one should always check if the number is positive .
Answer: a
Python program:
a = 4 + 3 
b = a + 2
Problem: the telephone company wants to add an area code composed of 2 letters to every phone number . in order to do so , the company chose a special sign language containing 424 different signs . if the company used 422 of the signs fully and two remained unused , how many additional area codes can be created if the company uses all 424 signs ?
Options: a ) 246 , b ) 248 , c ) 1692 , d ) 15,128 , e ) 30,256
Rationale: "# of 2 - letter codes possible from 424 different signs = 424 * 424 . # of 2 - letter codes possible from 422 different signs = 422 * 422 . the difference = 424 ^ 2 - 422 ^ 2 = ( 424 - 422 ) ( 424 + 422 ) = 1692 . answer : c ."
Answer: c
Python program:
a = 424 - 422
b = 422 * a
c = 424 - 422
d = b * c
Problem: thin rectangular slab of potato was cut into two pieces for an osmosis lab . one piece is 50 mm greater than the other . if the original uncut slab is 600 mm , what is the length of the other piece of the potato after it is cut .
Options: a ) 550
b ) 275
c ) 50
d ) 300
e ) 250
Rationale: piece one as p 1 , and piece two as p 2 . p 2 + 50 = p 1 as eq . a p 1 + p 2 = 600 as eq . b substitute eq . a into eq . b , resulting in ( p 2 + 50 ) + p 2 = 600 mm . group like terms , p 2 + p 2 = 600 - 50 ( 2 * p 2 / 2 ) = 550 / 2 solves to p 2 = 275 . ansewr is b .
Answer: b
Python program:
a = 600 - 50
b = a / 2