euclaise/mathqa_programs huggingface dataset:
Problem: a multiple choice test consists of 4 questions , and each question has 5 answer choices . in how many q ways can the test be completed if every question is unanswered ?
Options: a ) 24 , b ) 120 , c ) 625 , d ) 720 , e ) 1024
Rationale: 5 choices for each of the 4 questions , thus total q of 5 * 5 * 5 * 5 = 5 ^ 4 = 625 ways to answer all of them . answer : c .
Answer: c
Python program:
a = 5 ** 4
Problem: two numbers are in the ratio 3 : 5 . if 9 be subtracted from each , they are in the ratio of 3 : 2 . the first number is :
Options: a ) a ) 3 , b ) b ) 98 , c ) c ) 34 , d ) d ) 35 , e ) e ) 62
Rationale: "( 3 x - 9 ) : ( 5 x - 9 ) = 3 : 2 x = 1 = > 3 x = 3 answer : a"
Answer: a
Python program:
a = 3 * 5
b = 9 / a
c = 3 * b
d = 3 * 5
e = 9 / d
f = 5 * e
g = c + f
Problem: at a speed of 60 miles per hour , a certain car uses 1 gallon of gasoline every 30 miles . if the car starts with a full 12 gallon tank of gasoline and travels for 5 hours at 60 miles per hour , the amount of gasoline used would be what fraction of a full tank ?
Options: a ) 3 / 25 , b ) 11 / 36 , c ) 7 / 12 , d ) 2 / 3 , e ) 5 / 6
Rationale: "gas used = ( 5 hours ) * ( 60 miles / hour ) * ( 1 gallon / 30 miles ) = 10 gallons portion used = ( 10 ) / 12 = 5 / 6 ans e"
Answer: e
Python program:
a = 60 * 5
b = a / 30
c = b / 12
Problem: on a map , 2 inches represent 30 miles . how many miles approximately is the distance if you measured 38 centimeters assuming that 1 - inch is 2.54 centimeters ?
Options: a ) 226 , b ) 228 , c ) 230 , d ) 224 , e ) 232
Rationale: "1 inch = 2.54 cm 2 inch = 2.54 * 2 cm 5.08 cm = 30 miles 38 cms = 30 / 5.08 * 38 = 224 miles answer : d"
Answer: d
Python program:
a = 38 / 2
b = 30 / 2
c = a * b
Problem: a is an integer greater than 49 but less than 61 , b is an integer greater than 59 but less than 71 , what is the range of a / b ?
Options: a ) 2 / 7 , b ) 1 / 2 , c ) 3 / 4 , d ) 1 , e ) 5 / 4
Rationale: "min value of a / b will be when b is highest and a is lowest - - - > a = 50 and b = 70 so , a / b = 5 / 7 max value of a / b will be when b is lowest and a is highest - - - > a = 60 and b = 60 so , a / b = 1 range is 1 - ( 5 / 7 ) = 2 / 7 . answer should be a ."
Answer: a
Python program:
a = 61 - 1
b = 59 + 1 
c = a / b
d = 49 + 1 
e = 71 - 1
f = d / e
g = c - f
Problem: find the value of x , y by solving the below equations x + y = 15 x - y = 5
Options: a ) 10 , 5 , b ) 8 , 7 , c ) 9 , 6 , d ) 11 , 4 , e ) 12 , 3
Rationale: x + y = 15 - - - ( i ) x - y = 5 - - - - - ( ii ) by adding ( i ) and ( ii ) - - - - - - - - - - - - 2 x = 20 = = > x = 20 / 2 = 10 by replacing the value of x in ( i ) we get 10 + y = 15 = = > y = 15 - 10 = 5 . so , x = 10 , y = 5 answer a ) 10 , 5
Answer: a
Python program:
a = 15 - 5
b = a / 2
c = 15 - b
Problem: in a urban village of india named ` ` owlna ' ' , 90 % people have refrigerator , 86 % people have television , 80 % people got computers and 80 % got air - conditionor . how many people ( minimum ) got all these luxury .
Options: a ) 23 % , b ) 36 % , c ) 30 % , d ) 34 % , e ) 42 %
Rationale: "b 10 % 100 - [ ( 100 - 90 ) + ( 100 - 86 ) + ( 100 - 80 ) + ( 100 - 80 ) ] = 100 - ( 10 + 14 + 20 + 20 ) = 100 - 64"
Answer: b
Python program:
a = 100 - 90
b = 100 - 86
c = a + b 
d = 100 - 80
e = c + d 
f = 100 - 80
g = e + f 
h = 100 - g
Problem: the annual interest rate earned by an investment increased by 8 percent from last year to this year . if the annual interest rate earned by the investment this year was 27 percent , what was the annual interest rate last year ?
Options: a ) 22 % , b ) 20 % , c ) 25 % , d ) 23 % , e ) 21 %
Rationale: "let i = interest rate i ( this year ) = i ( last year ) + 0.08 i ( last year ) = 1.08 i ( last year ) 27 = 1.08 x i ( last year ) i ( last year ) = 27 / 1.08 = 2700 / 108 = 25 % answer : c"
Answer: c
Python program:
a = 27 * 100
b = 27 + 100 
c = a / b
Problem: if a and b are positive numbers , and a ^ 3 + b ^ 3 = 140 , then the greatest possible value of a is between :
Options: a ) 0 and 2 , b ) 2 and 3 , c ) 3 and 4 , d ) 4 and 5 , e ) 5 and 8
Rationale: if a = 5.1 and b is a bit less than 2 , then a ^ 3 + b ^ 3 can equal 140 . if a > 8 , then a ^ 3 + b ^ 3 > 140 . the answer is e .
Answer: e
Python program:
a = 1/(3)
b = 140 ** a
c = math.floor(b)
d = c * 10
e = 1/(3)
f = 140 ** e
g = math.floor(f)
h = g + 1 
i = d + h
Problem: a train 160 m long is running at a speed of 45 km / hr . in what time will it pass a bridge 140 m long ?
Options: a ) 40 sec , b ) 50 sec , c ) 44 sec , d ) 24 sec , e ) 60 sec
Rationale: "speed = 45 * 5 / 18 = 25 / 2 m / sec total distance covered = 160 + 140 = 300 m required time = 300 * 2 / 25 = 24 sec answer : d"
Answer: d
Python program:
a = 45 - 140
b = a * const_0_2778
c = 160 / b
Problem: the proportion of water to alcohol in solution a is 4 : 1 and the proportion of water to alcohol in solution b is 2 : 3 . if an equal amount of each solution is mixed together , what is the concentration of alcohol in the new solution ?
Options: a ) 39 % , b ) 40 % , c ) 41 % , d ) 42 % , e ) 43 %
Rationale: let v be the total volume of the new solution . then a volume of v / 2 was added from each solution a and b . the amount of alcohol added to the new solution was : ( 1 / 5 ) ( v / 2 ) + ( 3 / 5 ) ( v / 2 ) = v / 10 + 3 v / 10 = 4 v / 10 = 2 v / 5 . the concentration of alcohol is 2 / 5 = 40 % the answer is b .
Answer: b
Python program:
a = 1 + 3 
b = 4 + 2 
c = 1 + 3 
d = b + c 
e = a / d
f = e * 100
Problem: at what rate percent on simple interest will rs . 750 amount to rs . 900 in 4 years ?
Options: a ) 6 % , b ) 2 % , c ) 4 % , d ) 5 % , e ) 3 %
Rationale: "150 = ( 750 * 4 * r ) / 100 r = 5 % answer : d"
Answer: d
Python program:
a = 900 - 750
b = a / 750
c = b / 4
d = c * 100
Problem: if m is not equal to zero , and m + 1 / m = 1 , then what is the value of m ^ 4 + ( 1 / m ) ^ 4 ?
Options: a ) - 5 , b ) - 4 , c ) - 3 , d ) - 2 , e ) - 1
Rationale: m + 1 / m = 1 we square both sides so we have m ^ 2 + 1 / m ^ 2 + 2 = 1 or m ^ 2 + 1 / m ^ 2 = - 1 squaring again we have m ^ 4 + 1 / m ^ 4 + 2 = 1 or m ^ 4 + 1 / m ^ 4 = - 1 answer = - 1 ( e )
Answer: e
Python program:
a = 1 - 2
Problem: the ratio of money with ram and gopal is 7 : 17 and that with gopal and krishan is 7 : 17 . if ram has rs . 539 , krishan has ?
Options: a ) s . 2890 , b ) s . 2330 , c ) s . 1190 , d ) s . 1620 , e ) s . 3179
Rationale: "ram : gopal = 7 : 17 = 49 : 119 gopal : krishan = 7 : 17 = 119 : 289 ram : gopal : krishan = 49 : 119 : 289 ram : krishan = 49 : 289 thus , 49 : 289 = 539 : n & there n = 289 x 539 / 49 = rs . 3179 answer : e"
Answer: e
Python program:
a = 539 / 7
b = a * 17
c = b / 7
d = c * 17
Problem: the price of a cycle is reduced by 25 per cent . the new price is reduced by a further 20 per cent . the two reductions together are equal to a single reduction of
Options: a ) 33 , b ) 40 , c ) 99 , d ) 28 , e ) 72
Rationale: "explanation : let the original price of the cycle be 100 . after the first reduction the price will be 75 . this new price is then reduced by 20 % = 0.8 x 75 = 60 60 represents a reduction of 40 percent on the original . answer : b ) 40 %"
Answer: b
Python program:
a = 100 - 20
b = a / 100
c = 100 - 25
d = b * c
e = 100 - d
Problem: suresh started a business , investing rs . 18000 . after 3 months and 4 months respectively , rohan and sudhir joined him with capitals of 12000 and 9000 . at the end of the year the total profit was rs . 3960 . what is the difference between rohan ’ s and sudhir ’ s share in the profit ?
Options: a ) s . 345 , b ) s . 350 , c ) s . 352 , d ) s . 360 , e ) s . 368
Rationale: "suresh : rohan : sudhir ratio of their investments = 18000 × 12 : 12000 × 9 : 9000 × 8 = 6 : 3 : 2 the difference between rohan ’ s and sudhir ’ s share = 1 share : . i . e . = rs . 3960 × 1 / 11 = rs . 360 . d"
Answer: d
Python program:
a = 3 * 4
b = a - 3
c = 3 * 4
d = b / c
e = 12000 * d
f = 3 * 4
g = f - 4
h = 3 * 4
i = g / h
j = 9000 * i
k = e - j
l = 3 * 4
m = l - 3
n = 3 * 4
o = m / n
p = 12000 * o
q = 18000 + p 
r = 3 * 4
s = r - 4
t = 3 * 4
u = s / t
v = 9000 * u
w = q + v 
x = 3960 / w
y = k * x
Problem: in a ratio which is equal to 7 : 9 , if the antecedent is 56 , then the consequent is ?
Options: a ) 72 , b ) 85 , c ) 64 , d ) 51 , e ) 45
Rationale: "we have 7 / 9 = 56 / x 7 x = 56 * 9 x = 72 consequent = 72 answer is a"
Answer: a
Python program:
a = 56 / 2
b = 56 + a
Problem: if 20 % of a certain number is 60 , then what is 80 % of that number ?
Options: a ) 220 , b ) 210 , c ) 240 , d ) 250 , e ) 260
Rationale: "explanation : 20 % = 20 * 3 = 60 80 % = 80 * 3 = 240 answer : option c"
Answer: c
Python program:
a = 20 / 100
b = 60 / a
c = 80 / 100
d = b * c
Problem: if 2 men or 3 women can reap a field in 5 days how long will 5 men and 6 women take to reap it ?
Options: a ) 2 / 24 , b ) 6 / 18 , c ) 2 / 22 , d ) 5 / 12 , e ) 9 / 10
Rationale: "explanation : 2 men reap 2 / 5 field in 1 day 1 man reap 1 / ( 2 x 5 ) 3 women reap 1 / 43 field in 1 day 1 woman reap 1 / ( 5 x 3 ) 5 men and 6 women reap ( 5 / ( 2 x 5 ) + 6 / ( 3 x 5 ) ) = 9 / 10 in 1 day 5 men and 6 women will reap the field in 9 / 10 days answer : option e"
Answer: e
Python program:
a = 5 / 2
b = 5 * a
c = 5 / 3
d = 6 * c
e = b + d 
f = 5 / e
Problem: a customer went to a shop and paid a total of $ 30 , out of which $ 1.28 was for sales tax on taxable purchases . if the tax rate was 8 % , then what was the cost of the tax free items ?
Options: a ) $ 9.84 , b ) $ 10.68 , c ) $ 11.26 , d ) $ 12.72 , e ) $ 13.54
Rationale: the total cost was $ 30 . the tax was $ 1.28 let the original price of the taxable items = x given that tax rate = 8 % 0.08 x = 1.28 x = $ 16 the cost of the tax free items was $ 30 - $ 16 - $ 1.28 = $ 12.72 the answer is d .
Answer: d
Python program:
a = 30 - 1
b = 8 * 2
c = a - b
Problem: 2 + 2 + 2 ² + 2 ³ . . . + 2 ^ 11
Options: a ) 2 ^ 9 , b ) 2 ^ 10 , c ) 2 ^ 16 , d ) 2 ^ 12 , e ) 2 ^ 37
Rationale: "2 + 2 = 2 ^ 2 2 ^ 2 + 2 ^ 2 = ( 2 ^ 2 ) * ( 1 + 1 ) = 2 ^ 3 2 ^ 3 + 2 ^ 3 = ( 2 ^ 3 ) * ( 1 + 1 ) = 2 ^ 4 so you can notice the pattern . . . in the end you will have 2 ^ 11 + 2 ^ 11 , which will give you 2 ^ 12 answer d"
Answer: d
Python program:
a = 2 + 2 
b = 2 * a
c = b / 2
Problem: if a number p is prime , and 2 p + 5 = q , where q is also prime , then the decimal expansion of 1 / q will produce a decimal with q - 1 digits . if this method produces a decimal with 166 digits , what is the units digit of the product of p and q ?
Options: a ) 1 , b ) 3 , c ) 5 , d ) 7 , e ) 9
Rationale: 1 / 7 = 014285 . . . ( a repeating pattern one digit long ) a
Answer: a
Python program:
a = 166 + 1 
b = a - 5
c = b / 2
d = 166 + 1 
e = d - 5
f = e / 2
g = f - 1
h = c - g
Problem: walking at 25 % of his usual speed a man takes 24 minutes more to cover a distance . what is his usual time to cover this distance ?
Options: a ) 8 , b ) 16 , c ) 42 , d ) 48 , e ) 54
Rationale: "speed is inversly proprtional to time walking at 25 % of speed meand 1 / 4 s takes 4 t . it takes 24 minutes extra to cover the distance . then 4 t = t + 24 3 t = 24 t = 8 . option a is correct"
Answer: a
Python program:
a = 25 / 100
b = 1 / a
c = b - 1
d = 24 / c
Problem: the lowest number which should be added to 1277 so that the sum is exactly divisible by 3 , 2 , 5 , 4 and 7 is :
Options: a ) 303 , b ) 403 , c ) 203 , d ) 453 , e ) 203
Rationale: "l . c . m . of 5 , 6 , 4 and 3 = 420 . on dividing 1277 by 420 , the remainder is 17 . number to be added = ( 420 - 17 ) = 403 . answer : option ' b '"
Answer: b
Python program:
a = 1277 / 2
Problem: father is aged 3 times more than his son ronit . after 8 years , he would be two and half times if ronit ' s age . after further 8 years , how many times would he be of ronit ' s age ?
Options: a ) 2 times , b ) 2.5 times , c ) 3 times , d ) 3.8 times , e ) 4 times
Rationale: ronit ' s present age be x years . then , father ' s present age = ( x + 3 x ) years = 4 x years therefore ( 4 x + 8 ) = 5 / 2 ( x + 8 ) 8 x + 16 = 5 x + 40 3 x = 24 , x = 8 , ratio = ( 4 x + 16 ) / ( x + 16 ) = 48 / 24 = 2 , correct answer ( a )
Answer: a
Python program:
a = 4 * 8
b = 8 + 8 
c = a + b 
d = 8 + 8 
e = 8 + d 
f = c / e
Problem: due to construction , the speed limit along an 12 - mile section of highway is reduced from 55 miles per hour to 35 miles per hour . approximately how many minutes more will it take to travel along this section of highway at the new speed limit than it would have taken at the old speed limit ?
Options: a ) 4 , b ) 5 , c ) 6 , d ) 7 , e ) 8
Rationale: "12 / 35 - 12 / 55 = 12 / 5 * ( 11 - 7 ) / 77 = 12 / 5 * 4 / 77 * 60 min = 12 * 12 * 4 / 77 = 576 / 77 ~ 7.4 answer - d"
Answer: d
Python program:
a = 55 + 12 
b = a - 1
c = 12 / 35
d = 12 / 55
e = c - d
f = b * e
g = max(f)
Problem: the area of sector of a circle whose radius is 12 metro and whose angle at the center is 54 â ° is ?
Options: a ) 52.6 , b ) 52.9 , c ) 67.9 , d ) 52.1 , e ) 52.2
Rationale: "54 / 360 * 22 / 7 * 12 * 12 = 67.9 m 2 answer : c"
Answer: c
Python program:
a = 12 ** 2
b = 2 * 10
c = b + 2 
d = 4 + 3 
e = c / d
f = a * e
g = 3600 / 10
h = 54 / g
i = f * h
Problem: by selling 10 pens for a rupee a woman loses 18 % . how many for a rupee should he sell in order to gain 30 % ?
Options: a ) 12 , b ) 14 , c ) 45 , d ) 6 , e ) 7
Rationale: "d 82 % - - - 10 130 % - - - ? 82 / 130 * 10 = 6"
Answer: d
Python program:
a = 100 - 18
b = 100 / a
c = b / 10
d = 100 - 18
e = 100 / d
f = e / 10
g = f * 30
h = g / 100
i = c + h 
j = 1/(i)
Problem: what is the greatest number of 4 digits which is divisible by 15 , 25 , 40 and 75 ?
Options: a ) 9800 , b ) 9600 , c ) 9400 , d ) 9500 , e ) 9200
Rationale: greatest number of four digits = 9999 lcm of 15 , 25 , 40 and 75 = 600 9999 ÷ 600 = 16 , remainder = 399 hence , greatest number of four digits which is divisible by 15 , 25 , 40 and 75 = 9999 - 399 = 9600 answer : b
Answer: b
Python program:
a = 100 * 100
b = math.lcm(15, 25)
c = math.lcm(b, 40)
d = math.lcm(c, 75)
e = a / d
f = math.floor(e)
g = math.lcm(15, 25)
h = math.lcm(g, 40)
i = math.lcm(h, 75)
j = f * i
Problem: a one - foot stick is marked in 1 / 3 and 1 / 4 portion . how many total markings will there be , including the end points ?
Options: a ) 8 , b ) 9 , c ) 7 , d ) 6 , e ) 5
Rationale: "lcm of 12 = 12 1 / 3 marking are ( table of 4 ) 0 . . . . . . 4 . . . . . . 8 . . . . . 12 ( total = 4 ) 1 / 4 marking are ( table of 3 ) 0 . . . . . . . 3 . . . . . . 6 . . . . . . 9 . . . . . . . . 12 ( total = 5 ) overlapping markings are 0 . . . . . . . . 12 ( total = 2 ) total markings = 4 + 5 - 2 = 7 answer = c"
Answer: c
Python program:
a = 3 + 4
Problem: a company has a hierarchical system where for every 10 workers , there is one team lead , and for every 3 teams leads , there is one supervisor . if the company has 13 supervisors , how many workers does it have ?
Options: a ) 140 , b ) 321 , c ) 390 , d ) 500 , e ) 130
Rationale: some students may initially answer 130 to this question , especially if answering similar problems . however , that would be incorrect , as this is not a straight - forward ratio of 1 : 3 : 10 . the ratio of supervisors to team leads is 1 : 3 , and the ratio of team leads to workers is 1 : 10 . therefore , the ratio of supervisors to workers is 1 : 30 . therefore , 13 * 30 = 390 answer : c )
Answer: c
Python program:
a = 13 * 3
b = a * 10
Problem: a train 120 m long is running with a speed of 66 km / hr . in what time will it pass a man who is roller skating at 12 km / hr in the direction opposite to that in which the train is going ?
Options: a ) 4.92 , b ) 6.92 , c ) 7.92 , d ) 4.92 , e ) 2.92
Rationale: "speed of train relative to man = 66 + 12 = 78 km / hr . = 78 * 5 / 18 = 65 / 3 m / sec . time taken to pass the man = 150 * 3 / 65 = 6.92 sec . answer : b"
Answer: b
Python program:
a = const_60 + 0 
b = a * const_0_2778
c = 120 / b
Problem: paul ' s income is 20 % less than rex ' s income , quentin ' s income is 20 % less than paul ' s income , and sam ' s income is 40 % less than paul ' s income . if rex gave 60 % of his income to sam and 40 % of his income to quentin , quentin ' s new income would be what fraction of sam ' s new income ?
Options: a ) 26 / 27 , b ) 13 / 17 , c ) 13 / 19 , d ) 12 / 19 , e ) 11 / 19
Rationale: "make r = 10 p = 0.8 r = 8 q = 0.8 p = 6.4 s = 0.6 p = 4.8 for that we get s = 10.8 and q 10.4 so 10.4 / 10.8 = 2.6 / 2.7 ans : a"
Answer: a
Python program:
a = 40 * 100
b = 100 - 20
c = 40 * b
d = a + c 
e = 20 * 100
f = 20 + 20 
g = f * 40
h = e + g 
i = d / h
Problem: if a * b denotes the greatest common divisor of a and b , then ( ( 20 * 16 ) * ( 18 * 24 ) ) = ?
Options: a ) 24 , b ) 12 , c ) 6 , d ) 4 , e ) 2
Rationale: "the greatest common divisor of 20 and 16 is 4 . hence 20 * 16 = 4 ( note that * here denotes the function not multiplication ) . the greatest common divisor of 18 and 24 is 6 . hence 18 * 24 = 6 . hence ( ( 20 * 16 ) * ( 18 * 24 ) ) = 4 * 6 . the greatest common divisor of 4 and 6 is 2 . answer ; e ."
Answer: e
Python program:
a = 18 / 3
b = a / 3
Problem: how many quarters are equal to 2 dollars ?
Options: a ) 1 , b ) 8 , c ) 12 , d ) 9 , e ) 7
Rationale: b . 8 quarters
Answer: b
Python program:
a = 2 * 4
Problem: a person borrows 7000 for 3 years at 6 % p . a . simple interest . he immediately lends it to another person at 31 % p . a . for 3 years . find his gain in the transaction per year .
Options: a ) 1600 , b ) 1700 , c ) 1550 , d ) 1650 , e ) 1750
Rationale: "gain in 3 years = [ ( 7000 ã — 31 ã — 3 / 100 ) â ˆ ’ ( 7000 ã — 6 ã — 3 / 100 ) ] = ( 6510 â € “ 1260 ) = 5250 . â ˆ ´ gain in 1 year = ( 5250 â  „ 3 ) = 1750 answer e"
Answer: e
Python program:
a = 1 / 100
b = 7000 * a
Problem: david obtained 86 , 85 , 82 , 87 and 85 marks ( out of 100 ) in english , mathematics , physics , chemistry and biology what are his average marks ?
Options: a ) 75 , b ) 276 , c ) 87 , d ) 85 , e ) 11
Rationale: "explanation : average = ( 86 + 85 + 82 + 87 + 85 ) / 5 = 425 / 5 = 85 . answer : d"
Answer: d
Python program:
a = 86 + 85 
b = a + 82 
c = b + 87 
d = c + 85 
e = 2 + 3 
f = d / e
Problem: how many of the positive factors of 56 , 96 and how many common factors are there in numbers ?
Options: a ) 2 , b ) 4 , c ) 3 , d ) 5 , e ) 1
Rationale: "factors of 56 - 1 , 2 , 4 , 7 , 8 , 14 , 28 , 56 factors of 96 - 1 , 2 , 3 , 4 , 6 , 8 , 12 , 16 , 24 , 32 , 48 , 96 comparing both , we have three common factors of 56 and 96 - 1 , 2,4 answer ( c )"
Answer: c
Python program:
a = 96 / 56
Problem: it takes joey the postman 1 hours to run a 4 mile long route every day . he delivers packages and then returns to the post office along the same path . if the average speed of the round trip is 5 mile / hour , what is the speed with which joey returns ?
Options: a ) 6 2 / 3 , b ) 12 , c ) 13 , d ) 14 , e ) 15
Rationale: "let his speed for one half of the journey be 4 miles an hour let the other half be x miles an hour now , avg speed = 5 mile an hour 2 * 4 * x / 4 + x = 5 8 x = 5 x + 20 = > 3 x = 20 = > x = 6 2 / 3 a"
Answer: a
Python program:
a = 2 * 4
b = a / 5
c = b - 1
d = 4 / c
Problem: a business executive and his client are charging their dinner tab on the executive ' s expense account . the company will only allow them to spend a total of 50 $ for the meal . assuming that they will pay 7 % in sales tax for the meal and leave a 15 % tip , what is the most their food can cost ?
Options: a ) 39.55 $ , b ) 40.63 $ , c ) 41.63 $ , d ) 42.15 $ , e ) 43.15 $
Rationale: "let x be the amount the most their food can cost . x + 0.07 x + 0 . 15 x = 50 solving for x , x = 40.98 $ , this is the maximum amount that can be used for food . hence 40.63 $ is the maximum value less than 40.98 $ hence option b"
Answer: b
Python program:
a = 7 + 15 
b = a / 100
c = b + 1 
d = 50 / c
Problem: the sum of present age of abe and the age before 7 years is 37 . find the present age of abe . what will be his age after 7 years ?
Options: a ) 25 , b ) 26 , c ) 27 , d ) 28 , e ) 29
Rationale: "present age = x before 7 yrs , y = x - 7 after 7 yrs , z = x + 7 by the qn , x + ( x - 7 ) = 37 2 x - 7 = 37 2 x = 37 + 7 x = 44 / 2 x = 22 z = x + 7 = 22 + 7 = 29 answer : e"
Answer: e
Python program:
a = 37 + 7 
b = a / 2
c = b + 7
Problem: a retailer bought a machine at a wholesale price of $ 90 and later on sold it after a 10 % discount of the retail price . if the retailer made a profit equivalent to 20 % of the whole price , what is the retail price w of the machine ?
Options: a ) 81 , b ) 100 , c ) 120 , d ) 135 , e ) 160
Rationale: "since the wholesale price was $ 90 and the profit was 20 % of the wholesale price ( [ . 2 ] [ 90 ] = $ 18 ) , the retail price would have to be above $ 108 , but not that much greater than that . let ' s start by testing answer c : $ 120 . . . . if . . . . . retail price w = $ 120 10 % discount off = $ 120 - ( . 1 ) ( 120 ) = 120 - 12 = 108 20 % profit on wholesale price = 90 + ( . 2 ) ( 90 ) = 90 + 18 = 108 these two numbers match , so this must be the answer ! final answer : [ reveal ] spoiler : c"
Answer: c
Python program:
a = 90 * 20
b = a / 100
c = 90 + b 
d = c * 100
e = 3 * 3
f = e * 10
g = d / f
Problem: how many kg of pure salt must be added to 100 kg of 10 % solution of salt and water to increase it to a 12 % solution ?
Options: a ) a ) 6.7 , b ) b ) 2.3 , c ) c ) 9.6 , d ) d ) 12.5 , e ) e ) 7.9
Rationale: "amount salt in 100 kg solution = 10 * 100 / 100 = 10 kg let x kg of pure salt be added then ( 10 + x ) / ( 100 + x ) = 12 / 100 250 + 25 x = 300 + 3 x 22 x = 50 x = 2.3 answer is b"
Answer: b
Python program:
a = 12 - 10
b = 12 / 100
c = 1 - b
d = a / c
Problem: what is the total number of integers between 111 and 222 that are divisible by 9 ?
Options: a ) 12 , b ) 10 , c ) 11 , d ) 14 , e ) 13
Rationale: "117 , 126 , 135 , . . . , 207,216 this is an equally spaced list ; you can use the formula : n = ( largest - smallest ) / ( ' space ' ) + 1 = ( 216 - 117 ) / ( 9 ) + 1 = 99 / 9 + 1 = 11 + 1 = 12 answer is a"
Answer: a
Python program:
a = 222 - 111
b = a / 9
c = b + 1
Problem: 350 is increased by 50 % . find the final number .
Options: a ) 725 , b ) 625 , c ) 225 , d ) 525 , e ) 425
Rationale: explanation final number = initial number + 50 % ( original number ) = 350 + 50 % ( 350 ) = 350 + 175 = 525 . answer d
Answer: d
Python program:
a = 50 / 100
b = 350 * a
c = 350 + b
Problem: a train 240 m in length crosses a telegraph post in 16 seconds . the speed of the train is ?
Options: a ) 77 kmph , b ) 55 kmph , c ) 54 kmph , d ) 58 kmph , e ) 76 kmph
Rationale: "s = 240 / 16 * 18 / 5 = 54 kmph answer : c"
Answer: c
Python program:
a = 240 / 16
b = const_3_6 * a
Problem: a can do a particular work in 6 days . b can do the same work in 8 days . a and b signed to do it for rs . 2400 . they completed the work in 3 days with the help of c . how much is to be paid to c ?
Options: a ) s . 300 , b ) s . 600 , c ) s . 420 , d ) s . 400 , e ) s . 480
Rationale: "explanation : amount of work a can do in 1 day = 1 / 6 amount of work b can do in 1 day = 1 / 8 amount of work a + b can do in 1 day = 1 / 6 + 1 / 8 = 7 / 24 amount of work a + b + c can do = 1 / 3 amount of work c can do in 1 day = 1 / 3 - 7 / 24 = 1 / 24 work a can do in 1 day : work b can do in 1 day : work c can do in 1 day = 1 / 6 : 1 / 8 : 1 / 24 = 4 : 3 : 1 amount to be paid to c = 2400 × ( 1 / 8 ) = 300 answer : option a"
Answer: a
Python program:
a = 1 / 3
b = 1 / 6
c = 1 / 8
d = b + c 
e = a - d
f = 3 * e
g = f * 2400
Problem: because he ’ s taxed by his home planet , mork pays a tax rate of 45 % on his income , while mindy pays a rate of only 15 % on hers . if mindy earned 4 times as much as mork did , what was their combined tax rate ?
Options: a ) 19 % , b ) 21 % , c ) 23 % , d ) 25 % , e ) 27 %
Rationale: "let x be mork ' s income , then mindy ' s income is 4 x . the total tax paid is 0.45 x + 0.6 x = 1.05 x 1.05 x / 5 x = 0.21 the answer is b ."
Answer: b
Python program:
a = 45 / 100
b = 15 / 100
c = 4 * b
d = a + c 
e = 1 + 4 
f = d / e
g = 100 * f