euclaise/mathqa_programs huggingface dataset:
Problem: how many numbers from 10 to 100 are exactly divisible by 9 ?
Options: a ) 7 , b ) 8 , c ) 10 , d ) 12 , e ) 14
Rationale: "option ' c ' 10 / 9 = 1 and 100 / 9 = 11 = = > 11 - 1 = 10 . therefore 10 digits ."
Answer: c
Python program:
a = 100 / 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: what is the units digit of the expression 7 ^ 75 + 6 ?
Options: a ) 1 , b ) 3 , c ) 5 , d ) 7 , e ) 9
Rationale: "7 in power repeats pattern of 4 : 7 - 9 - 3 - 1 . as 75 = 4 * 18 + 3 then the last digit of 7 ^ 75 is the same as the last digit of 7 ^ 3 , which is 3 . units digit of 7 ^ 75 + 6 will be : 3 + 6 = 9 . answer is e"
Answer: e
Python program:
a = 4 + 3 
b = a + 2
Problem: a certain list consists of 21 different numbers . if n is in the list and n is 8 times the average ( arithmetic mean ) of the other 20 numbers in the list , then n is what fraction of the sum of the 21 numbers in the list ?
Options: a ) 1 / 20 , b ) 1 / 6 , c ) 2 / 7 , d ) 4 / 21 , e ) 5 / 21
Rationale: "series : a 1 , a 2 . . . . a 20 , n sum of a 1 + a 2 + . . . + a 20 = 20 * x ( x = average ) so , n = 8 * x hence , a 1 + a 2 + . . + a 20 + n = 28 x so , the fraction asked = 8 x / 28 x = 2 / 7 c"
Answer: c
Python program:
a = 1 * 1
b = 20 / 8
c = b + 21 
d = c / 8
e = d * 2
f = e - 8
g = f - 3
h = a / g
Problem: two tains of equal lengths take 10 seconds and 12 seconds respectively to cross a telegraph post . if the length of each train be 120 metres , in what time ( in seconds ) will they cross each other travelling in opposite direction ?
Options: a ) 12 , b ) 14 , c ) 10.9 , d ) 20 , e ) 18
Rationale: "sol . speed of the first train = [ 120 / 10 ] m / sec = 12 m / sec . speed of the second train = [ 120 / 12 ] m / sec = 10 m / sec . relative speed = ( 12 + 10 ) = m / sec = 22 m / sec . ∴ required time = ( 120 + 120 ) / 22 secc = 10.9 sec . answer c"
Answer: c
Python program:
a = 120 + 120 
b = 120 / 12
c = 120 / 10
d = b + c 
e = a / d
Problem: 108 . triangle a ’ s base is 8 % greater than the base of triangle b , and a ’ s height is 8 % less than the height of triangle b . the area of triangle a is what percent less or more than the area of triangle b ?
Options: a ) 9 % less , b ) 1 % less , c ) equal to each other , d ) 1.6 % more , e ) 9 % more
Rationale: "wish the question specified that we are talking about corresponding height . base of a = 9 / 8 * base of b height of a = 7 / 8 * height of b area of a = ( 1 / 2 ) * base of a * height of a = 9 / 8 * 7 / 8 * area of b = 63 / 64 * area of b area of a is 1.6 % more than the area of b . answer ( d )"
Answer: d
Python program:
a = 100 * 100
b = 100 + 8 
c = 100 - 8
d = b * c
e = a - d
f = 100 / e
Problem: an agent , gets a commission of 4 % on the sales of cloth . if on a certain day , he gets rs . 12.50 as commission , the cloth sold through him on that day is worth
Options: a ) 312 , b ) 500 , c ) 887 , d ) 299 , e ) 132
Rationale: "explanation : let the total sale be rs . x . then , 4 % . of x = 12.50 = ( 4 / 100 * x ) = 12.5 < = > x = 312.5 . answer : a"
Answer: a
Python program:
a = 4 / 100
b = 12 / 50
Problem: a certain university will select 3 of 7 candidates eligible to fill a position in the mathematics department and 5 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 ) 42232 , b ) 42170 , c ) 14008 , d ) 16510 , e ) 41160
Rationale: "7 c 3 * 8 c 5 = 35 * 56 = 41160 the answer is ( e )"
Answer: e
Python program:
a = 8 * 3
b = a * 7
Problem: a and b can do a work in 10 days and 15 days respectively . a starts the work and b joins him after 2 days . in how many days can they complete the remaining work ?
Options: a ) 6 days , b ) 2 days , c ) 4 4 / 5 days , d ) 3 days , e ) 9 days
Rationale: "work done by a in 2 days = 2 / 10 = 1 / 5 remaining work = 4 / 5 work done by both a and b in one day = 1 / 10 + 1 / 15 = 5 / 30 = 1 / 6 remaining work = 4 / 5 * 6 / 1 = 24 / 5 = 4 4 / 5 days . answer : c"
Answer: c
Python program:
a = 1/(15)
b = 1/(10)
c = a + b 
d = 1/(c)
e = d + 10 
f = e - 3
Problem: the breadth of a rectangular field is 60 % of its length . if the perimeter of the field is 800 m . what is the area of the field ?
Options: a ) 18750 sq . m
b ) 37500 sq . m
c ) 40000 sq . m
d ) 48000 sq . m
e ) none of these
Rationale: solution so length = 250 m ; breadth = 150 m area = ( 250 x 150 ) m ² = 37500 m ² answer b
Answer: b
Python program:
a = 800 / 2
b = 60 / 100
c = b + 1 
d = a / c
e = 800 / 2
f = 800 / 2
g = 60 / 100
h = g + 1 
i = f / h
j = e - i
k = d * j
Problem: if | 20 x - 10 | = 170 , then find the product of the values of x ?
Options: a ) - 45 , b ) 50 , c ) - 72 , d ) 35 , e ) - 30
Rationale: "| 20 x - 10 | = 170 20 x - 10 = 170 or 20 x - 10 = - 170 20 x = 180 or 20 x = - 160 x = 9 or x = - 8 product = - 8 * 9 = - 72 answer is c"
Answer: c
Python program:
a = 170 - 10
b = 170 + 10 
c = a - b
d = c - 10
Problem: 5 liters of a 20 percent solution of alcohol in water are mixed with 3 liters of a 12 percent alcohol in water solution . what is the percentage of alcohol in the new solution ?
Options: a ) 16.7 % , b ) 17.0 % , c ) 17.3 % , d ) 17.6 % , e ) 17.9 %
Rationale: "the total amount of alcohol is 0.2 ( 5 ) + 0.12 ( 3 ) = 1.36 liters . the percentage is 1.36 / 8 = 136 / 800 = 17 / 100 which is 17 % the answer is b ."
Answer: b
Python program:
a = 20 / 100
b = 5 * a
c = 12 / 100
d = 20 / 100
e = 5 * d
f = c * e
g = b + f 
h = 5 + 3 
i = g / h
j = i * 100
Problem: a shop owner professes to sell his articles at certain cost price but he uses false weights with which he cheats by 20 % while buying and by 20 % while selling . what is his percentage profit ?
Options: a ) 10.22 % , b ) 20.22 % , c ) 21.22 % , d ) 50 % , e ) ca n ' t be calculated
Rationale: "the owner buys 100 kg but actually gets 120 kg ; the owner sells 100 kg but actually gives 80 kg ; profit : ( 120 - 80 ) / 80 * 100 = ~ 50 % answer : d ."
Answer: d
Python program:
a = 100 + 20 
b = 100 - 20
c = a - b
d = c * 100
e = 100 - 20
f = d / e
Problem: compare the rates of two trains , one travelling at 45 km / hr and other is at 10 m / s ?
Options: a ) 5 : 4 , b ) 3 : 2 , c ) 1 : 5 , d ) 2 : 7 , e ) 3 : 5
Rationale: "speed of the 1 st train = 45 km / hr speed of the 2 nd train = 10 m / s = 10 * 18 / 5 = 36 km / hr ratio of the speeds of the train = 45 : 36 = 5 : 4 answer is a"
Answer: a
Python program:
a = 10 / 1000
b = a * 3600
c = 45 / b
Problem: a scuba diver descends at a rate of 32 feet per minute . a diver dive from a ship to search for a lost ship at the depth of 6400 feet below the sea level . . how long will he take to reach the ship ?
Options: a ) 200 minutes , b ) 240 minutes , c ) 220 minutes , d ) 210 minutes , e ) 77 minutes
Rationale: "time taken to reach = 6400 / 32 = 200 minutes answer : a"
Answer: a
Python program:
a = 6400 / 32
Problem: a clock shows the time as 9 a . m . if the minute hand gains 5 minutes every hour , how many minutes will the clock gain by 6 p . m . ?
Options: a ) 30 min , b ) 35 min , c ) 45 min , d ) 50 min , e ) 55 min
Rationale: "there are 9 hours in between 9 a . m . to 6 p . m . 9 * 5 = 45 minutes . answer : c"
Answer: c
Python program:
a = 3 + 6 
b = a * 5
Problem: three numbers are in the ratio of 2 : 3 : 4 and their l . c . m . is 300 . what is their h . c . f . ?
Options: a ) 20 , b ) 25 , c ) 30 , d ) 60 , e ) 75
Rationale: "let the numbers be 2 x , 3 x , and 4 x . lcm of 2 x , 3 x and 4 x is 12 x . 12 x = 300 x = 25 hcf of 2 x , 3 x and 4 x = x = 25 the answer is b ."
Answer: b
Python program:
a = 2 * 4
Problem: for what values of k will the pair of equations 3 x + 4 y = 12 and ( kx + 12 y ) / 2 = 15 does not have a unique solution ?
Options: a ) 12 , b ) 9 , c ) 3 , d ) 7.5 , e ) 2.5
Rationale: "we have 2 equations 1 . 3 x + 4 y = 12 - - > 9 x + 12 y = 36 2 . ( kx + 12 y ) / 2 = 15 - - > kx + 12 y = 30 substract 1 - 2 , we get ( 9 - k ) x = 6 i . e . x = 6 / ( 9 - k ) then , by looking at options , we get some value of x except for b . when we put k = 9 , x becomes 6 / 0 and hence answer is b"
Answer: b
Python program:
a = 2 * 4
b = a / 3
Problem: what will be the compound interest on a sum of rs . 30,000 after 3 years at the rate of 12 % p . a . ?
Options: a ) s : 10123.19 , b ) s : 10123.29 , c ) s : 10123.20 , d ) s : 10123.28 , e ) s : 12147.84
Rationale: "amount = [ 30000 * ( 1 + 12 / 100 ) 3 ] = 30000 * 28 / 25 * 28 / 25 * 28 / 25 = rs . 42147.84 c . i . = ( 42147.84 - 30000 ) = rs : 12147.84 answer : e"
Answer: e
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: a box contains either blue or red flags . the total number of flags in the box is an even number . a group of children are asked to pick up two flags each . if all the flags are used up in the process such that 60 % of the children have blue flags , and 65 % have red flags , what percentage of children have flags of both the colors ?
Options: a ) 5 % , b ) 10 % , c ) 15 % , d ) 20 % , e ) 25 %
Rationale: "solution : let the total number of flags be 100 ( even number ) let the total number of ' blue ' flags alone be ' a ' let the total number of ' red ' flags alone be ' b ' let the total number of ' both ' flags be ' c ' we have given , total number of blue flags = 60 % = 60 = a + c total number of red flags = 65 % = 65 = b + c total number of flags = a + b + c = 100 ( since all the flags have been utilized ) so , substituting for c in the third equation , we have , 60 - c + c + 65 - c = 100 c = 25 option e ."
Answer: e
Python program:
a = 60 + 65 
b = a - 100
Problem: how many multiples of 6 are less than 3600 , and also multiples of 36 ?
Options: a ) 94 , b ) 100 , c ) 625 , d ) 832 , e ) 833
Rationale: the lcm of 6 and 36 is 36 . divide 3600 / 36 = 100 . xxx . so b is your answer .
Answer: b
Python program:
a = 36 - 3600
b = a / 6
c = b + 1
Problem: 17 times a positive integer is more than its square by 70 , then the positive integer is
Options: a ) 13 , b ) 10 , c ) 11 , d ) 12 , e ) 14
Rationale: "explanation : let the number be x . then , 17 x = x 2 + 70 = > x 2 - 17 x + 70 = 0 = > ( x - 7 ) ( x - 10 ) = 0 = > x = 7 or 10 answer : b"
Answer: b
Python program:
a = 17 ** 2
b = 70 * 4
c = a - b
d = 17 + c 
e = d / 2
Problem: the profit earned by selling an article for rs . 832 is equal to the loss incurred when the same article is sold for rs . 448 . what should be the sale price for making 80 % profit ?
Options: a ) 1152 , b ) 230 , c ) 960 , d ) 780 , e ) 400
Rationale: "c . p . = rs . x . then , 832 - x = x - 448 2 x = 1280 = > x = 640 required s . p . = 180 % of rs . 640 = 180 / 100 * 640 = rs . 1152 . a"
Answer: a
Python program:
a = 832 - 448
b = a / 2
c = 832 - b
d = 80 / 100
e = 1 + d 
f = c * e
Problem: find the distance covered by a man walking for 30 min at a speed of 5 km / hr ?
Options: a ) 1 km , b ) 3 km , c ) 4 km , d ) 2.5 km , e ) 6 km
Rationale: "distance = 5 * 30 / 60 = 2.5 km answer is d"
Answer: d
Python program:
a = 5 * 1000
b = a / const_60
c = 30 * b
d = c / 1000
Problem: dacid obtained 96 , 95 , 82 , 87 and 92 marks ( out of 100 ) in english , mathematics , physics , chemistry and biology . what are his average marks ?
Options: a ) 67 , b ) 26 , c ) 87 , d ) 26 , e ) 90
Rationale: "average = ( 96 + 95 + 82 + 87 + 92 ) / 5 = 452 / 5 = 90 . answer : e"
Answer: e
Python program:
a = 96 + 95 
b = a + 82 
c = b + 87 
d = c + 92 
e = 10 / 2
f = d / e
Problem: a person can row at 10 kmph in still water . if the velocity of the current is 2 kmph and it takes him 15 hour to row to a place and come back , how far is the place ?
Options: a ) 24 km , b ) 30 km , c ) 48 km , d ) 72 km , e ) 15 km
Rationale: "speed of down stream = 10 + 2 = 12 kmph speed of upstream = 10 - 2 = 8 kmph let the required distance be xkm x / 12 + x / 8 = 15 2 x + 3 x = 360 x = 72 km answer is d"
Answer: d
Python program:
a = 10 - 2
b = 10 + 2 
c = a * b
d = c * 15
e = 10 - 2
f = 10 + 2 
g = e + f 
h = d / g
Problem: of the 80 people in a room , 2 / 5 are women . if 1 / 2 of the people are married , what is the maximum number of women in the room who could be unmarried ?
Options: a ) 20 , b ) 22 , c ) 26 , d ) 30 , e ) 32
Rationale: "women = 2 / 5 * 80 = 32 married = 1 / 2 * 80 = 40 unmarried = 40 max ( un - married women ) = 32 e"
Answer: e
Python program:
a = 2 / 5
b = 80 * a
Problem: the value of x . 1234 - x = 4234 - 3361
Options: a ) 671 , b ) 371 , c ) 361 , d ) 248 , e ) 246
Rationale: "1234 - x = 4234 - 3361 x = 1234 - 4234 + 3361 = 361 x = 361 correct answer : c"
Answer: c
Python program:
a = 1234 * 1234
b = a * 1234
c = b + 1234
Problem: in a group of ducks and cows , the total number of legs are 32 more than twice the no . of heads . find the total no . of buffaloes .
Options: a ) 11 , b ) 12 , c ) 14 , d ) 16 , e ) 18
Rationale: "let the number of buffaloes be x and the number of ducks be y = > 4 x + 2 y = 2 ( x + y ) + 32 = > 2 x = 32 = > x = 16 d"
Answer: d
Python program:
a = 32 / 2
Problem: two pipes a and b can fill a tank in 24 hours and 36 hours respectively . if both the pipes are opened simultaneously , how much time will be taken to fill the tank ?
Options: a ) 20 hours , b ) 15 hours , c ) 14 2 / 5 hours , d ) 12 hours , e ) 8 hours
Rationale: "part filled by a in 1 hour = 1 / 24 part filled by b in 1 hour = 1 / 36 part filled by ( a + b ) in 1 hour = 1 / 24 + 1 / 36 = 5 / 72 both the pipes together fill the tank in 72 / 5 = 14 2 / 5 hours answer is c"
Answer: c
Python program:
a = 1 / 24
b = 1 / 36
c = a + b 
d = 1 / c
Problem: maxwell leaves his home and walks toward brad ' s house at the same time that brad leaves his home and runs toward maxwell ' s house . if the distance between their homes is 20 kilometers , maxwell ' s walking speed is 4 km / h , and brad ' s running speed is 6 km / h , what is the distance traveled by brad ?
Options: a ) 12 , b ) 18 , c ) 20 , d ) 24 , e ) 30
Rationale: "time taken = total distance / relative speed total distance = 20 kms relative speed ( opposite side ) ( as they are moving towards each other speed would be added ) = 6 + 4 = 10 kms / hr time taken = 20 / 10 = 2 hrs distance traveled by brad = brad ' s speed * time taken = 6 * 2 = 12 kms . . . answer - a"
Answer: a
Python program:
a = 4 + 6 
b = 20 / a
c = 4 * b
Problem: in 1 kg mixture of iron and manganese 20 % of manganese . how much iron should be added so that the proportion of manganese becomes 10 %
Options: a ) 1.5 kg , b ) 2 kg , c ) . 5 kg , d ) 1 kg , e ) none of these
Rationale: explanation : by the rule of alligation , we have percentage concentration of manganese in the mixture : 20 percentage concentration of manganese in pure iron : 0 percentage concentration of manganese in the final mixture 10 10 - 0 = 10 20 - 10 = 10 = > quantity of the mixture : quantity of iron = 10 : 10 = 1 : 1 given that quantity of the mixture = 1 kg hence quantity of iron to be added = 1 kg answer : option d
Answer: d
Python program:
a = 20 / 100
b = 10 / 100
c = a / b
d = c - 1
Problem: a recipe requires 2 1 / 2 ( mixed number ) cups of flour 2 3 / 4 ( mixed number ) cups of sugar and 1 1 / 3 ( mixed number ) cups of milk to make one cake . victor has 15 cups if flour , 16 cups of sugar and 8 cups of milk . what is the greatest number of cakes john can make using this recipe ?
Options: a ) 5 , b ) 6 , c ) 7 , d ) 8 , e ) 9
Rationale: "less work up front : go through each item and see what the greatest number of cakes you can make with each . the lowest of these will be the right answer . flour : 15 cups , we need 2.5 cups each . just keep going up the line to see how many cakes we can make : that means i can make 2 cakes with 5 cups , so 6 cakes overall with 15 cups . i ' ve already got the answer narrowed to either a or b . sugar : 16 cups , we need 2.75 cups each . same principle . i can make 2 cups with 5.5 cups , so to make 6 cakes i ' d need 16.5 cups . i do n ' t have that much sugar , so we ' re limited to 5 cakes . no need to even do milk because we ' re already at 5 . sugar will be the limiting factor . answer is a"
Answer: a
Python program:
a = 1 / 2
b = 2 + a 
c = 15 / b
d = 3 / 4
e = d + 2 
f = 16 / e
g = math.floor(f)
h = min(c)
i = 1 / 3
j = i + 1 
k = 8 / j
l = min(h)
Problem: a meal cost $ 36.50 and there was no tax . if the tip was more than 10 pc but less than 15 pc of the price , then the total amount paid should be :
Options: a ) 40 - 42 , b ) 39 - 41 , c ) 38 - 40 , d ) 37 - 39 , e ) 36 - 37
Rationale: "10 % ( 36.5 ) = 3.65 15 % ( 36.5 ) = 5.475 total amount could have been 36.5 + 3.65 and 36.5 + 5.475 = > could have been between 40.15 and 41.975 = > approximately between 40 and 42 answer is a ."
Answer: a
Python program:
a = 15 / 100
b = 36 * 50
c = b + 36
Problem: imagine an analog clock set to 12 o ' clock . note that the hour and minute hands overlap . how many times each day do both the hour and minute hands overlap ? how would you determine the exact times of the day that this occurs ?
Options: a ) 11 , b ) 12 , c ) 22 , d ) 24 , e ) 44
Rationale: 22 times in a day . 12,1 hours 60 / 11 minutes , 2 hours 120 / 11 minutes , . . . so on till 12 ( 11 hours 660 / 11 minutes ) answer : c
Answer: c
Python program:
a = 12 - 1
b = a * 2
Problem: a basketball is dropped from a height of 30 feet . if it bounces back up to a height that is exactly half of its previous height , and it stops bouncing after hitting the ground for the fourth time , then how many total feet will the ball have traveled after 2 full bounces .
Options: a ) 50 , b ) 55 , c ) 60 , d ) 75 , e ) 80
Rationale: "initial distance = 30 feet first bounce = 15 feet up + 15 feet down = 30 feet second bouche = 7.5 feet up + 7.5 feet down = 15 feet total distance covered = 30 + 30 + 15 = 75 answer : d"
Answer: d
Python program:
a = 30 / 2
b = a / 2
c = b / 2
d = c / 2
e = 30 / 2
f = 30 + e 
g = 30 / 2
h = f + g 
i = 30 / 2
j = i / 2
k = h + j 
l = 30 / 2
m = l / 2
n = k + m 
o = 30 / 2
p = o / 2
q = p / 2
r = n + q 
s = 30 / 2
t = s / 2
u = t / 2
v = r + u 
w = d + v 
x = w * 2
y = 30 / 2
z = y / 2
A = z / 2
B = x - A
C = 30 / 2
D = C / 2
E = D / 2
F = B - E
G = 30 / 2
H = G / 2
I = H / 2
J = F - I
K = 30 / 2
L = K / 2
M = L / 2
N = J - M
Problem: jamshid can paint a fence in 50 percent less time than taimour can when each works alone . when they work together , they can paint the fence in 7 hours . how long would it take taimour to paint the fence alone ?
Options: a ) 6 hours , b ) 8 hours , c ) 14 hours , d ) 21 hours , e ) 32 hours
Rationale: "i believe the answer is d . please see below for explanation . if jamshid can paint a dence in 50 percent less time then taimour we can infer the following rate j = 2 t if working together they can do the job in 8 hours we can infer 1 = 2 t + t * 7 = > 1 / 21 working alone taimour can do the job in 1 = 1 / 21 * hours = > 21 answer d"
Answer: d
Python program:
a = 7 * 3
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 1 / 5 of its present ?
Options: a ) 61.5 , b ) 60.5 , c ) 63.5 , d ) 62.5 , e ) 125
Rationale: "let capacity of 1 bucket = x capacity of the tank = 25 x new capacity of the bucket = 1 x / 5 hence , number of buckets needed = 25 x / ( 1 x / 5 ) = ( 25 × 5 ) / 1 = 125 answer is e ."
Answer: e
Python program:
a = 4 + 1 
b = 25 * a
c = b / 2
Problem: 12 buckets of water fill a tank when the capacity of each bucket is 81 litres . how many buckets will be needed to fill the same tank , if the capacity of each bucket is 9 litres ?
Options: a ) 96 , b ) 110 , c ) 100 , d ) 90 , e ) 108
Rationale: "capacity of the tank = ( 12 ã — 81 ) litre number of buckets required of capacity of each bucket is 17 litre = 12 ã — 81 / 9 = 12 ã — 9 = 108 answer is e"
Answer: e
Python program:
a = 81 * 12
b = a / 9
Problem: the number 83 can be written as the sum of the squares of 3 different positive integers . what is the sum of these 3 integers ?
Options: a ) 17
b ) 16
c ) 15
d ) 14
e ) 13
Rationale: 7 ^ 2 + 5 ^ 2 + 3 ^ 2 = 49 + 25 + 9 = 83 7 + 5 + 3 = 15 hence answer is c
Answer: c
Python program:
a = 4 + 3 
b = 3 + 2 
c = a + b 
d = c + 3
Problem: one side of a rectangle is 3 cm shorter than the other side . if we increase the length of each side by 1 cm , then the area of the rectangle will increase by 24 cm 2 . find the lengths of all sides .
Options: a ) 10 and 3
b ) 7 and 10
c ) 10 and 7
d ) 3 and 10
e ) 13 and 10
Rationale: let x be the length of the longer side x > 3 , then the other side ' s length is x − 3 cm . then the area is s 1 = x ( x - 3 ) cm 2 . after we increase the lengths of the sides they will become ( x + 1 ) and ( x − 3 + 1 ) = ( x − 2 ) cm long . hence the area of the new rectangle will be a 2 = ( x + 1 ) ⋅ ( x − 2 ) cm 2 , which is 24 cm 2 more than the first area . therefore a 1 + 24 = a 2 x ( x − 3 ) + 24 = ( x + 1 ) ( x − 2 ) x 2 − 3 x + 24 = x 2 + x − 2 x − 2 2 x = 26 x = 13 . so , the sides of the rectangle are 13 cm and ( 13 − 3 ) = 10 cm long . so answer is e .
Answer: e
Python program:
a = 24 / 2
b = a + 1 
c = b - 3
Problem: the amount of an investment will double in approximately 70 / p years , where p is the percent interest , compounded annually . if thelma invests $ 50,000 in a long - term cd that pays 5 percent interest , compounded annually , what will be the approximate total value of the investment when thelma is ready to retire 42 years later ?
Options: a ) $ 280,000 , b ) $ 320,000 , c ) $ 360,000 , d ) $ 400,000 , e ) $ 540,000
Rationale: "the amount of an investment will double in approximately 70 / p years , where p is the percent interest , compounded annually . if thelma invests $ 50,000 in a long - term cd that pays 5 percent interest , compounded annually , what will be the approximate total value of the investment when thelma is ready to retire 42 years later ? the investment gets doubled in 70 / p years . therefore , the investment gets doubled in 70 / 5 = every 14 years . after 42 years , the investment will get doubled 42 / 14 = 3 times . so the amount invested will get doubled thrice . so , 50000 * 2 ^ 3 = 400000 hence , the answer is d ."
Answer: d
Python program:
a = 3600 / 10
Problem: a man buys an article for $ 110 . and sells it for $ 125 . find the gain percent ?
Options: a ) 10 % , b ) 13.6 % , c ) 25 % , d ) 20 % , e ) 30 %
Rationale: "c . p . = $ 110 s . p . = $ 125 gain = $ 15 gain % = 15 / 110 * 100 = 13.6 % answer is b"
Answer: b
Python program:
a = 110 / 100
b = 125 / a
c = b - 100
Problem: the slant height of a cone is 10 cm and radius of the base is 5 cm , find the curved surface of the cone ?
Options: a ) 150 , b ) 155 , c ) 158 , d ) 157 , e ) 190
Rationale: "π * 10 * 5 = 157 answer : d"
Answer: d
Python program:
a = math.pi * 5
b = a * 10
Problem: excluding stoppages , the speed of a train is 54 kmph and including stoppages it is 36 kmph . of how many minutes does the train stop per hour ?
Options: a ) 20 , b ) 17 , c ) 15 , d ) 18 , e ) 12
Rationale: "t = 18 / 54 * 60 = 20 answer : a"
Answer: a
Python program:
a = 36 / 54
b = const_60 * a
c = const_60 - b
Problem: a rectangular region has a fence along three sides and a wall along the fourth side . the fenced side opposite the wall is twice the length of each of the other two fenced sides . if the area of the rectangular region is 200 square feet , what is the total length of the fence , in feet ?
Options: a ) 10
b ) 20
c ) 30
d ) 40
e ) 80
Rationale: two sides each = x the third = 2 x and the wall length is thus 2 x too x * 2 x = 2 x ^ 2 = 200 ie x ^ 2 = 100 ie x = 10 l = 20 w = 10 total lenght of fence = 2 * 10 + 20 = 40 my answer is d
Answer: d
Python program:
a = 1 + 1 
b = a * 2
c = b + 1 
d = 2 * c
e = 1 + 1 
f = e * 2
g = f + 1 
h = 2 * g
i = 1 + 1 
j = i * 2
k = j + 1 
l = 2 * k
m = h + l 
n = d + m 
o = 1 + 1 
p = o * 2
q = p + 1 
r = 1 + 1 
s = r * 2
t = s + 1 
u = 2 * t
v = q + u 
w = 1 + 1 
x = w * 2
y = x + 1 
z = v + y 
A = 200 / z
B = n + A