euclaise/mathqa_programs huggingface dataset:
Problem: the unit digit in the product 784 * 618 * 917 * 463 is ?
Options: a ) 3 , b ) 2 , c ) 4 , d ) 5 , e ) 6
Rationale: "unit digit in the given product = unit digit in 4 * 8 * 7 * 3 = 2 answer is b"
Answer: b
Python program:
a = 784 * 618
b = a * 917
c = b * 463
d = 784 * 618
e = d * 917
f = e * 463
g = 4 + 4 
h = f - g
i = c - h
Problem: how many liters of a 40 % iodine solution need to be mixed with 35 liters of a 20 % iodine solution to create a 35 % iodine solution ?
Options: a ) 35 , b ) 49 , c ) 100 , d ) 105 , e ) 140
Rationale: "solution 1 : assume the iodine solution to be mixed = x lts . iodine = 0.4 x lts , water = 0.6 x lts . solution 2 : 35 liters of a 20 % iodine solution iodine = 7 lts , water = 28 lts . total iodine = 0.4 x + 7 total water = 0.6 x + 28 the resultant is a 35 % iodine solution . hence ( 0.4 x + 7 ) / ( x + 35 ) = 35 / 100 40 x + 700 = 35 x + 1225 5 x = 525 x = 105 lts correct option : d"
Answer: d
Python program:
a = 35 * 20
b = a / 100
c = b * 35
d = 35 * 20
e = d / 100
f = e * 20
g = c - f
h = 40 / 100
i = 20 * h
j = 35 * 20
k = j / 100
l = i - k
m = g / l
n = m + 35
Problem: if 8 men do a work in 80 days , in how many days will 20 men do it ?
Options: a ) 18 days , b ) 32 days , c ) 42 days , d ) 48 days , e ) 44 days
Rationale: "8 * 80 = 20 * x x = 32 days answer : b"
Answer: b
Python program:
a = 8 * 80
b = a / 20
Problem: in 2008 , the profits of company n were 10 percent of revenues . in 2009 , the revenues of company n fell by 20 percent , but profits were 18 percent of revenues . the profits in 2009 were what percent of the profits in 2008 ?
Options: a ) 80 % , b ) 105 % , c ) 120 % , d ) 144 % , e ) 138 %
Rationale: "x = profits r = revenue x / r = 0,1 x = 10 r = 100 2009 : r = 80 x / 80 = 0,18 = 18 / 100 x = 80 * 18 / 100 x = 14.4 14.4 / 10 = 1,44 = 144 % , answer d"
Answer: d
Python program:
a = 20 / 100
b = 1 - a
c = 18 * b
d = c / 10
e = d * 100
Problem: a courtyard is 30 meter long and 16 meter board is to be paved with bricks of dimensions 20 cm by 10 cm . the total number of bricks required is ?
Options: a ) 22877 , b ) 24000 , c ) 20000 , d ) 27999 , e ) 17799
Rationale: "number of bricks = courtyard area / 1 brick area = ( 3000 × 1600 / 20 × 10 ) = 24000 answer : b"
Answer: b
Python program:
a = 30 * 100
b = 16 * 100
c = a * b
d = 20 * 10
e = c / d
Problem: what is the smallest positive integer that leaves a remainder of 1 when divided by 2 , remainder of 2 when divided by 3 , a remainder of 3 when divided by 4 , and a remainder of 9 when divided by 10 ?
Options: a ) 58 , b ) 59 , c ) 60 , d ) 61 , e ) 62
Rationale: remainder of 1 when divided by 2 : ( 2 - 1 = 1 ) remainder of 2 when divided by 3 : ( 3 - 2 = 1 ) remainder of 3 when divided by 4 : ( 4 - 3 = 1 ) remainder of 9 when divided by 10 : ( 2 - 1 = 1 ) so n + 1 should be divisible by 23 , 410 ( where n is desired number ) l . c . m . of 23 , 410 = 60 ( = n + 1 ) n = 59 answer : b
Answer: b
Python program:
a = math.lcm(2, 3)
b = math.lcm(a, 4)
c = math.lcm(b, 10)
d = c - 1
Problem: find the fraction which has the same ratio to 2 / 6 that 3 / 4 has to 1 / 2
Options: a ) 1 / 2 , b ) 2 / 5 , c ) 6 / 8 , d ) 9 / 4 , e ) 7 / 5
Rationale: "p : 2 / 6 = 3 / 4 : 1 / 2 as the product of the means is equal to the product of the extremes . p * 1 / 2 = 2 / 6 * 3 / 4 p * 1 / 2 = 6 / 24 p = 1 / 2 = > p = 1 / 2 answer : a"
Answer: a
Python program:
a = 3 / 4
b = 1 / 2
c = a / b
d = 2 / 6
e = c * d
Problem: if 13 lions can kill 13 deers in 13 minutes how long will it take 100 lions to kill 100 deers ?
Options: a ) 1 minutes , b ) 13 minute , c ) 100 minutes , d ) 10000 minutes , e ) 1000 minutes
Rationale: "we can try the logic of time and work , our work is to kill the deers so 13 ( lions ) * 13 ( min ) / 13 ( deers ) = 100 ( lions ) * x ( min ) / 100 ( deers ) hence answer is x = 13 answer : b"
Answer: b
Python program:
a = 13 / 13
b = a * 13
Problem: if bill can buy 3 pairs of jeans and 2 shirts for $ 69 or 2 pairs of jeans and 3 shirts for $ 66 , how much does one shirt cost ?
Options: a ) $ 10 , b ) $ 12 , c ) $ 13.20 , d ) $ 15 , e ) $ 16.80
Rationale: "let the price of one shirt be ss and of jeans be j : 3 j + 2 s = 69 2 j + 3 s = 66 subtracting the second from the first gives : j − s = 3 or j = s + 3 plug j in either of the equations and solve for s , which is $ 12 answer : b ."
Answer: b
Python program:
a = 66 * 3
b = 69 * 2
c = a - b
d = 3 * 3
e = 2 * 2
f = d - e
g = c / f
Problem: each day a man meets his wife at the train station after work , and then she drives him home . she always arrives exactly on time to pick him up . one day he catches an earlier train and arrives at the station an hour early . he immediately begins walking home along the same route the wife drives . eventually his wife sees him on her way to the station and drives him the rest of the way home . when they arrive home the man notices that they arrived 30 minutes earlier than usual . how much time did the man spend walking ?
Options: a ) 45 minutes , b ) 50 minutes , c ) 40 minutes , d ) 55 minutes , e ) 35 minutes
Rationale: "as they arrived 30 minutes earlier than usual , they saved 30 minutes on round trip from home to station ( home - station - home ) - - > 15 minutes in each direction ( home - station ) - - > wife meets husband 15 minutes earlier the usual meeting time - - > husband arrived an hour earlier the usual meeting time , so he must have spent waking the rest of the time before their meeting , which is hour - 15 minutes = 45 minutes . answer : a"
Answer: a
Python program:
a = 30 / 2
b = const_60 - a
Problem: the speed of a car is 145 km in the first hour and 60 km in the second hour . what is the average speed of the car ?
Options: a ) 89 kmph , b ) 92 kmph , c ) 75 kmph , d ) 102.5 kmph , e ) 77 kmph
Rationale: "s = ( 145 + 60 ) / 2 = 102.5 kmph d"
Answer: d
Python program:
a = 145 + 60 
b = a / 2
Problem: the greatest number which on dividing 1657 and 2037 leaves remainders 10 and 7 respectively , is :
Options: a ) 123 , b ) 1 , c ) 235 , d ) 305 , e ) 505
Rationale: "explanation : required number = h . c . f . of ( 1657 - 10 ) and ( 2037 - 7 ) = h . c . f . of 1647 and 2030 = 1 . answer : b"
Answer: b
Python program:
a = 2037 - 7
b = 1657 - 10
c = math.gcd(a, b)
Problem: a grocer has 400 pounds of coffee in stock , 40 percent of which is decaffeinated . if the grocer buys another 100 pounds of coffee of which 60 percent is decaffeinated , what percent , by weight , of the grocer ’ s stock of coffee is decaffeinated ?
Options: a ) 28 % , b ) 30 % , c ) 32 % , d ) 34 % , e ) 44 %
Rationale: "1 . 40 % of 400 = 160 pounds of decaffeinated coffee 2 . 60 % of 100 = 60 pounds of decaffeinated coffee 3 . wt have 220 pounds of decaffeinated out of 500 pounds , that means 220 / 500 * 100 % = 44 % . the correct answer is e ."
Answer: e
Python program:
a = 40 / 100
b = a * 400
c = 60 / 100
d = 100 * c
e = b + d 
f = 400 + 100 
g = e / f
h = g * 100
Problem: if @ is a binary operation defined as the difference between an integer n and the product of n and 5 , then what is the largest positive integer n such that the outcome of the binary operation of n is less than 21 ?
Options: a ) 1 , b ) 2 , c ) 3 , d ) 4 , e ) 5
Rationale: "@ ( n ) = 5 n - n we need to find the largest positive integer such that 5 n - n < 21 . then 4 n < 21 and n < 5.25 . the largest possible integer is n = 5 . the answer is e ."
Answer: e
Python program:
a = 5 - 1
b = 21 / a
c = math.floor(b)
Problem: each factor of 290 is inscribed on its own plastic ball , and all of the balls are placed in a jar . if a ball is randomly selected from the jar , what is the probability that the ball is inscribed with a multiple of 42 ?
Options: a ) 1 / 16 , b ) 5 / 42 , c ) 16 , d ) 3 / 16 , e ) 1 / 4
Rationale: "290 = 2 * 3 * 5 * 7 , so the # of factors 210 has is ( 1 + 1 ) ( 1 + 1 ) ( 1 + 1 ) ( 1 + 1 ) = 16 ( see below ) ; 42 = 2 * 3 * 7 , so out of 16 factors only two are multiples of 42 : 42 and 210 , itself ; so , the probability is 2 / 16 = 1 / 6 answer : c ."
Answer: c
Python program:
a = math.comb(42, 1)
b = a / 42
c = 3 ** 2
d = b / c
Problem: the average runs of a cricket player of 13 innings was 22 . how many runs must he make in his next innings so as to increase his average of runs by 5 ?
Options: a ) 92 , b ) 42 , c ) 64 , d ) 76 , e ) 84
Rationale: explanation : average after 14 innings = 27 required number of runs = ( 27 * 14 ) – ( 22 * 13 ) = 378 – 286 = 92 answer a
Answer: a
Python program:
a = 13 + 1 
b = 22 + 5 
c = a * b
d = 22 * 13
e = c - d
Problem: in a certain candy store , 22 % of the customers are caught sampling the candy and are charged a small fine , but 20 % of the customers who sample the candy are not caught . what is the total percent of all customers who sample candy ?
Options: a ) 22 % , b ) 23 % , c ) 24 % , d ) 25 % , e ) 27.5 %
Rationale: "since 20 % of the customers who sample the candyare notcaught , then 80 % of the customers who sample the candyarecaught : { % of customers who sample candy } * 0.80 = 0.22 ; { % of customers who sample candy } = 0.275 answer : e ."
Answer: e
Python program:
a = 100 - 20
b = a / 100
c = 22 / b
Problem: if the selling price of 50 articles is equal to the cost price of 40 articles , then the loss or gain percent is ?
Options: a ) 20 % , b ) 80 % , c ) 90 % , d ) 22 % , e ) 24 %
Rationale: "let c . p . of each article be re . 1 . then , c . p . of 50 articles = rs . 50 ; s . p . of 50 articles = rs . 40 . loss % = 10 / 50 * 100 = 20 % . answer : a"
Answer: a
Python program:
a = 50 - 40
Problem: 3 students appear at an examination of mathematics . the probability of their success are 1 / 2 , 1 / 4 , 1 / 5 respectively . find the probability of success of at least two .
Options: a ) 1 / 60 , b ) 2 / 50 , c ) 9 / 40 , d ) 3 / 40 , e ) 4 / 50
Rationale: the probability of success of at least two students will involve the following possibilities . the first two students are successful , the last two students are successful , the first and third students are successful and all the three students are successful . therefore , the required probability = 1 / 2 x 1 / 4 x 4 / 5 + 1 / 4 x 1 / 5 x 1 / 2 + 1 / 2 x 1 / 5 x 3 / 4 + 1 / 2 x 1 / 4 x 1 / 5 = 9 / 40 answer : c
Answer: c
Python program:
a = 1 / 2
b = 1 / 4
c = a * b
d = 1 / 5
e = c * d
f = 1 / 2
g = 1 / 5
h = f * g
i = 1 / 4
j = 1 - i
k = h * j
l = 1 / 2
m = 1 / 5
n = l * m
o = k + n 
p = 1 / 4
q = 1 / 5
r = p * q
s = 1 / 2
t = 1 - s
u = r * t
v = o + u 
w = e + v
Problem: if a / b = 1 / 3 , b / c = 2 , c / d = 1 / 2 , d / e = 3 and e / f = 1 / 2 , then what is the value of abc / def ?
Options: a ) 27 / 4 , b ) 27 / 8 , c ) 3 / 4 , d ) 3 / 8 , e ) 1 / 4
Rationale: "say a = 3 . then : a / b = 1 / 3 - - > b = 9 ; b / c = 2 - - > c = 9 / 2 ; c / d = 1 / 2 - - > d = 9 ; d / e = 3 - - > e = 3 ; e / f = 1 / 2 - - > f = 6 . abc / def = ( 3 * 9 * 9 / 2 ) / ( 9 * 3 * 6 ) = 3 / 4 . answer : c ."
Answer: c
Python program:
a = 3 * 3
b = 3 * 2
c = 2 * b
d = a / c
Problem: a train leaves delhi at 9 a . m . at a speed of 30 kmph . another train leaves at 2 p . m . at a speed of 42 kmph on the same day and in the same direction . how far from delhi , will the two trains meet ?
Options: a ) 229 , b ) 288 , c ) 787.5 , d ) 888 , e ) 121
Rationale: "d = 30 * 5 = 150 rs = 42 – 30 = 8 t = 150 / 8 = 18.75 d = 42 * 18.75 = 787.5 km answer : c"
Answer: c
Python program:
a = 3 + 2 
b = 30 * a
c = 42 - 30
d = b / c
e = d * 42
Problem: a man performs 1 / 2 of the total journey by rail , 1 / 3 by bus and the remaining 2 km on foot . his total journey is
Options: a ) 16 km , b ) 10 km , c ) 12 km , d ) 24 km , e ) 25 km
Rationale: "explanation : let the journey be x km then , 1 x / 2 + 1 x / 3 + 2 = x 5 x + 12 = 6 x x = 12 km answer : option c"
Answer: c
Python program:
a = 3 * 2
Problem: the average of 7 consecutive numbers is 33 . the highest of these numbers is :
Options: a ) 28 , b ) 30 , c ) 33 , d ) 36 , e ) 28
Rationale: "the average of 7 consecutive numbers will be the 4 th number which is given to be = 33 5 th number = 34 , 6 th number = 35 , 7 th number = 36 answer : d ."
Answer: d
Python program:
a = 33 * 7
b = 1 + 2 
c = b + 1 
d = c + 1 
e = d + 1 
f = e + 1 
g = 1 + f 
h = g + 1 
i = h + 1 
j = 1 + 2 
k = j + 1 
l = k + 1 
m = l + 1 
n = m + 1 
o = 1 + n 
p = o + 1 
q = p + 1 
r = q + 1 
s = i + r 
t = a - s
u = t / 7
v = 1 + 2 
w = v + 1 
x = w + 1 
y = x + 1 
z = u + y
Problem: in a certain animal population , for each of the first 3 months of life , the probability that an animal will die during that month is 1 / 6 . for a group of 200 newborn members of the population , approximately how many would be expected to survive the first 3 months of life ?
Options: a ) 116 , b ) 146 , c ) 152 , d ) 162 , e ) 170
Rationale: "the probability of survival for each of the first 3 months of life is 1 - 1 / 6 = 5 / 6 , so of 200 newborn 200 * 5 / 6 * 5 / 6 * 5 / 6 = ~ 116 is expected to survive . answer : a ."
Answer: a
Python program:
a = 1 / 6
b = 1 - a
c = 200 * b
d = 1 / 6
e = 1 - d
f = c * e
g = 1 / 6
h = 1 - g
i = f * h
Problem: in what time will a train 50 m long cross an electric pole , it its speed be 144 km / hr ?
Options: a ) 1.25 sec , b ) 2.75 sec , c ) 3.5 sec , d ) 2.39 sec , e ) 9.5 sec
Rationale: "speed = 144 * 5 / 18 = 40 m / sec time taken = 50 / 40 = 1.25 sec . answer : a"
Answer: a
Python program:
a = 144 * const_0_2778
b = 50 / a
Problem: a square carpet with an area 169 m 2 must have 2 metres cut - off one of its edges in order to be a perfect fit for a rectangular room . what is the area of rectangular room ?
Options: a ) 180 m 2
b ) 164 m 2
c ) 152 m 2
d ) 143 m 2
e ) none of these
Rationale: side of square carpet = √ area = √ 169 = 13 m after cutting of one side , measure of one side = 13 – 2 = 11 m and other side = 13 m ( remain same ) ∴ area of rectangular room = 13 × 11 = 143 m 2 answer d
Answer: d
Python program:
a = math.sqrt(169)
b = math.sqrt(169)
c = b - 2
d = a * c
Problem: a “ sophie germain ” prime is any positive prime number p for which 2 p + 1 is also prime . the product of all the possible units digits of sophie germain primes greater than 3 is
Options: a ) 3 , b ) 189 , c ) 221 , d ) 227 , e ) 230
Rationale: "in that case , the sophie prime numbers greater than 5 are 7 , 11,23 , 47,59 , . . which yields units digit as 1 , 3,7 and 9 product would be 1 x 3 x 7 x 9 = 189 answer should be b ."
Answer: b
Python program:
a = 3 - 1
b = 2 + 1 
c = a + b 
d = 2 + 1 
e = c + d 
f = e - 10
g = 3 - 1
h = 2 + 1 
i = g + h 
j = 2 * i
k = j + 1 
l = k - 10
m = f * l
n = 2 + 1 
o = m * n
p = 3 - 1
q = 2 + 1 
r = p + q 
s = 2 + 1 
t = r + s 
u = 2 + 1 
v = t + u 
w = 2 * v
x = w + 1 
y = 2 * 10
z = x - y
A = o * z
Problem: a number x is multiplied by 5 , and this product is then divided by 7 . if the positive square root of the result of these two operations equals x , what is the value of x if x ≠ 0 ?
Options: a ) 25 / 9 , b ) 9 / 5 , c ) 5 / 7 , d ) 3 / 5 , e ) 9 / 25
Rationale: "sqrt ( 5 x / 7 ) to be perfect square x has to 5 / 7 ans : c"
Answer: c
Python program:
a = 5 / 7
Problem: the center of a circle lies on the origin of the coordinate plane . if a point ( x , y ) is randomly selected inside of the circle , what is the probability that y > 0 or y > x ?
Options: a ) 5 / 8 , b ) 1 / 6 , c ) 3 / 8 , d ) 1 / 2 , e ) 3 / 4
Rationale: "the line y = x divides the circle into two equal areas . all the points above the line y = x satisfy the condition that y > x . all the points above the x - axis satisfy the condition that y > 0 . the union of these two areas is 5 / 8 of the circle . the answer is a ."
Answer: a
Python program:
a = 2 * 4
b = 3 / a
Problem: in a kilometer race , a beats b by 25 meters or 10 seconds . what time does a take to complete the race ?
Options: a ) 167 sec , b ) 190 sec , c ) 390 sec , d ) 716 sec , e ) 123 sec
Rationale: "time taken by b run 1000 meters = ( 1000 * 10 ) / 25 = 400 sec . time taken by a = 400 - 10 = 390 sec . answer : c"
Answer: c
Python program:
a = 1 * 1000
b = 25 / 10
c = a / b
d = c - 10
Problem: one week , a certain truck rental lot had a total of 26 trucks , all of which were on the lot monday morning . if 50 % of the trucks that were rented out during the week were returned to the lot on or before saturday morning of that week , and if there were at least 14 trucks on the lot that saturday morning , what is the greatest number of different trucks that could have been rented out during the week ?
Options: a ) 18 , b ) 16 , c ) 12 , d ) 24 , e ) 4
Rationale: "n - not rented trucks ; r - rented trucks n + r = 26 n + r / 2 = 14 r = 24 d"
Answer: d
Python program:
a = 50 / 100
b = 26 * a
c = 14 + b
Problem: each week , harry is paid x dollars per hour for the first 15 hours and 1.5 x dollars for each additional hour worked that week . each week , james is paid x dollars per per hour for the first 40 hours and 2 x dollars for each additional hour worked that week . last week james worked a total of 41 hours if harry and james were paid the same amount last week , how many hours did harry work last week ?
Options: a ) 33 , b ) 36 , c ) 37 , d ) 38 , e ) 39
Rationale: 42 x = 15 x + 1.5 x ( h - 15 ) = = > 42 = 15 + 1.5 ( h - 15 ) = = > h - 15 = 27 / 1.5 = 18 = = > h = 33 answer is a
Answer: a
Python program:
a = 40 + 2 
b = a - 15
c = b / 1
d = c + 15
Problem: shawn invested one half of his savings in a bond that paid simple interest for 2 years and received $ 200 as interest . he invested the remaining in a bond that paid compound interest , interest being compounded annually , for the same 2 years at the same rate of interest and received $ 245 as interest . what was the value of his total savings before investing in these two bonds ?
Options: a ) 4000 , b ) 3500 , c ) 2500 , d ) 3000 , e ) 2000
Rationale: "so , we know that shawn received 20 % of the amount he invested in a year . we also know that in one year shawn received $ 100 , thus 0.2 x = $ 100 - - > x = $ 1,000 . since , he invested equal sums in his 2 bonds , then his total savings before investing was 2 * $ 1,000 = $ 2,000 answer e"
Answer: e
Python program:
a = 200 / 2
b = 200 / 2
c = a * b
d = 245 - 200
e = c / d
f = e * 2
Problem: how many seconds will a train 100 meters long take to cross a bridge 160 meters long if the speed of the train is 36 kmph ?
Options: a ) 26 , b ) 72 , c ) 25 , d ) 82 , e ) 27
Rationale: "explanation : d = 100 + 160 = 260 s = 36 * 5 / 18 = 10 mps t = 260 / 10 = 26 sec answer : option a"
Answer: a
Python program:
a = 160 + 100 
b = 36 * const_0_2778
c = a / b
Problem: at a bank , the service charges for transactions were us dollar 1 for every 5 transactions . the bank recently revised the charges to us dollar 0.75 for every 3 transactions . by approximately what percent did the ratio of price to transactions increase from the previous charge ?
Options: a ) 28 , b ) 24 , c ) 23 , d ) 22 , e ) 25
Rationale: initial charge / transaction ratio = 1 / 5 = 3 / 15 revised charge / transaction ratio = . 75 / 3 = 3.75 / 15 answer : e
Answer: e
Python program:
a = 0 / 75
b = 1 / 5
c = a / b
d = c * 100
e = d - 100
Problem: convert 800 miles into meters ?
Options: a ) 1287472 , b ) 845796 , c ) 804670 , d ) 784596 , e ) 864520
Rationale: "1 mile = 1609.34 meters 800 mile = 800 * 1609.34 = 1287472 meters answer is a"
Answer: a
Python program:
a = 3 + 2 
b = a * 2
c = 3 + 2 
d = c * 2
e = b * d
f = e * 800
g = 3 + 2 
h = g * 2
i = 3 + 2 
j = i * 2
k = h * j
l = f / k
Problem: nil and ethan are brothers . they left their home at the same time and drove to the same beach . nil drove at a speed of 80 miles per hour . ethan drove at a speed of 20 miles per hour . nil arrived at the beach 0.5 hour earlier than ethan . what is the distance between their home and the beach ?
Options: a ) 70 miles , b ) 80 miles , c ) 90 miles , d ) 100 miles , e ) 110 miles
Rationale: every hour , nil gets ahead of ethan 80 - 20 = 60 miles . when nil arrived at the beach , ethan is only 20 × 0.5 = 10 miles behind . that tells us they only drove 1 hour when nil arrived at the beach . the distance between their home and the beach is nil ’ s speed × nil ’ s time = 80 × 1 = 80 miles . correct answer b
Answer: b
Python program:
a = 1/(20)
b = 1/(80)
c = a - b
d = 0 / 5
Problem: if m = 3 ^ n , what is the greatest value of n for which m is a factor of 19 !
Options: a ) 8 , b ) 10 , c ) 12 , d ) 14 , e ) 16
Rationale: solution - consider multiples of 25 ! = > 3,6 , 9,12 , 15,18 count no . of 3 in each multiple . 3 = 3 x 1 - > 1 6 = 3 x 2 - > 1 9 = 3 x 3 - > 2 12 = 3 x 4 - > 1 15 = 3 x 5 - > 1 18 = 3 x 3 x 2 - > 2 - - - - count 3 ' s = 8 so answer is 8 answer : a
Answer: a
Python program:
a = 19 / 3
b = math.floor(a)
c = 3 ** 2
d = 19 / c
e = math.floor(d)
f = b + e
Problem: a reduction of 15 % in the price of oil enables a house wife to obtain 4 kgs more for rs . 1200 , what is the reduced price for kg ?
Options: a ) 43 , b ) 55 , c ) 35 , d ) 45 , e ) 40
Rationale: "1200 * ( 15 / 100 ) = 180 - - - - 4 ? - - - - 1 = > rs . 45 answer : d"
Answer: d
Python program:
a = 1200 * 15
b = a / 100
c = b / 4
Problem: x , y , and z are different prime numbers . the product x ^ 2 * y ^ 2 * z is divisible by how many different positive numbers ?
Options: a ) 6 , b ) 8 , c ) 12 , d ) 18 , e ) 24
Rationale: "the exponents of x ^ 2 * y ^ 2 * z are 2 , 2 , and 1 . the number of factors is ( 2 + 1 ) ( 2 + 1 ) ( 1 + 1 ) = 18 the answer is d ."
Answer: d
Python program:
a = 2 ** 4
b = a - 4
Problem: a car travels from point a to point b . the average speed of the car is 60 km / hr and it travels the first half of the trip at a speed of 48 km / hr . what is the speed of the car in the second half of the trip ?
Options: a ) 72 , b ) 75 , c ) 80 , d ) 84 , e ) 90
Rationale: "let d be the distance and let v be the speed in the second half . the total time = t 1 + t 2 d / 60 = d / 96 + ( d / 2 ) / v 8 d / 480 - 5 d / 480 = ( d / 2 ) / v d / 160 = d / 2 v and so v = 80 km / hr the answer is c ."
Answer: c
Python program:
a = 48 * 60
b = 48 - 60
c = b * 60
d = a / c
e = 60 * d
f = 60 / 10
g = e / f
Problem: a soccer store typically sells replica jerseys at a discount of 60 percent to 50 percent off list price . during the annual summer sale , everything in the store is an additional 20 percent off the original list price . if a replica jersey ' s list price is $ 80 , approximately what percent of the list price is the lowest possible sale price ?
Options: a ) 20 , b ) 25 , c ) 30 , d ) 40 , e ) 50
Rationale: "let the list price be 2 x for min sale price , the first discount given should be 50 % , 2 x becomes x here now , during summer sale additional 20 % off is given ie sale price becomes 0.8 x it is given lise price is $ 80 = > 2 x = 80 = > x = 50 and 0.8 x = 32 so lowest sale price is 32 , which is 40 % of 80 hence , e is the answer"
Answer: e
Python program:
a = 80 / 2
Problem: how many real solutions does the equation x 5 + 2 x 3 + 8 x 2 + 16 = 0 have ?
Options: a ) 0 , b ) 1 , c ) 2 , d ) 3 , e ) 5
Rationale: note that x 5 + 2 x 3 + 8 x 2 + 16 = ( x 3 + 8 ) ( x 2 + 2 ) = ( x + 2 ) ( x 2 - 2 x + 4 ) ( x 2 + 2 ) . since the quadratic equations x 2 - 2 x + 4 = 0 and x 2 + 2 = 0 have no real solutions , the original equation has just one real solution , x = - 2 . correct answer b
Answer: b
Python program:
a = 5 * 1
b = a - 1
c = b - 1
d = c - 1
e = d - 1
Problem: a man is 20 years older than his son . in two years , his age will be twice the age of his son . what is the present age of his son ?
Options: a ) 23 years , b ) 22 years , c ) 21 years , d ) 20 years , e ) 18 years
Rationale: "let present age of the son = x years then , present age the man = ( x + 20 ) years given that , in 2 years , man ' s age will be twice the age of his son â ‡ ’ ( x + 20 ) + 2 = 2 ( x + 2 ) â ‡ ’ x = 18 answer : e"
Answer: e
Python program:
a = 2 * 2
b = a - 2
c = 20 - b
d = 2 - 1
e = c / d
Problem: a man can row downstream at the rate of 10 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 ) 8,2 , c ) 9,3 , d ) 6,6 , e ) none of these
Rationale: "explanation : rate of still water = 1 / 2 ( 10 + 6 ) = 8 km / hr rate of current = 1 / 2 ( 10 - 6 ) = 2 km / hr answer : option b"
Answer: b
Python program:
a = 10 - 6
b = a / 2