euclaise/mathqa_programs huggingface dataset:
Problem: linda spent 5 / 6 of her savings on furniture and the rest on a tv . if the tv cost her $ 500 , what were her original savings ?
Options: a ) $ 9000 , b ) $ 3000 , c ) $ 6000 , d ) $ 7000 , e ) $ 8000
Rationale: "if linda spent 5 / 6 of her savings on furniture , the rest 6 / 6 - 5 / 6 = 1 / 6 on a tv but the tv cost her $ 500 . so 1 / 6 of her savings is $ 500 . so her original savings are 6 times $ 500 = $ 3000 correct answer b"
Answer: b
Python program:
a = 5 / 6
b = 1 - a
c = 500 / b
Problem: how many bricks , each measuring 40 cm x 11.25 cm x 6 cm , will be needed to build a wall of 8 m x 6 m x 22.5 cm ?
Options: a ) 1400 , b ) 2400 , c ) 4000 , d ) 7000 , e ) 3400
Rationale: "number of bricks = volume of the wall / volume of 1 brick = ( 800 x 600 x 22.5 ) / ( 40 x 11.25 x 6 ) = 4000 answer : c"
Answer: c
Python program:
a = 8 * 100
b = 6 * 100
c = a * b
d = c * 22
e = 40 * 11
f = e * 6
g = d / f
Problem: find the simple interest on rs . 64,000 at 16 2 / 3 % per annum for 9 months .
Options: a ) s . 8500 , b ) s . 8000 , c ) s . 7500 , d ) s . 7000 , e ) s . 6500
Rationale: "p = rs . 64000 , r = 50 / 3 % p . a and t = 9 / 12 years = 3 / 4 years . s . i . = ( p * r * t ) / 100 = rs . ( 64,000 * ( 50 / 3 ) * ( 3 / 4 ) * ( 1 / 100 ) ) = rs . 8000 answer is b ."
Answer: b
Python program:
a = 2 * 3
b = a * 100
c = b * 100
d = 3 * 3
e = d * 100
f = 3 + 2 
g = f * 2
h = e * g
i = c + h 
j = 16 * 3
k = j + 2 
l = k / 3
m = i * l
n = 3 * 3
o = 2 * 3
p = 2 * o
q = n / p
r = m * q
s = 1 / 100
t = r * s
Problem: the average height of 15 girls out of a class of 60 is 138 cm . and that of the remaining girls is 142 cm . the average height of the whole class is :
Options: a ) 132 cms , b ) 141 cms , c ) 142 cms , d ) 152 cms , e ) 161 cms
Rationale: "explanation : average height of the whole class = ( 15 × 138 + 45 × 142 / 60 ) = 141 cms answer b"
Answer: b
Python program:
a = 138 * 15
b = 142 * 10
c = a + b 
d = c / 60
Problem: a cistern can be filled by a tap in 2 hours while it can be emptied by another tap in 9 hours . if both the taps are opened simultaneously , then after how much time will the cistern get filled ?
Options: a ) 2.57 hrs , b ) 5 hrs , c ) 6.57 hrs , d ) 7.2 hrs , e ) 9.27 hrs
Rationale: "net part filled in 1 hour = 1 / 2 - 1 / 9 = 7 / 18 therefore the cistern will be filled in 18 / 7 hours or 2.57 hours . answer : a"
Answer: a
Python program:
a = 1 / 2
b = 1 / 9
c = a - b
d = 1 / c
Problem: a began business with rs . 45000 and was joined afterwards by b with rs . 27000 . when did b join if the profits at the end of the year were divided in the ratio of 2 : 1 ?
Options: a ) 1 , b ) 6 , c ) 7 , d ) 8 , e ) 2
Rationale: "45 * 12 : 27 * x = 2 : 1 x = 10 12 - 10 = 2 answer : e"
Answer: e
Python program:
a = 4 * 3
b = 4 * 3
c = 45000 * b
d = c / 27000
e = d / 2
f = a - e
Problem: 1 / 3 + 1 / 2 - 5 / 6 + 1 / 5 + 1 / 4 - 9 / 20 - 9 / 20 =
Options: a ) 0 , b ) 2 / 15 , c ) 2 / 5 , d ) 9 / 20 , e ) 5 / 6
Rationale: "we need to determine the result of 1 / 3 + 1 / 2 - 5 / 6 + 1 / 5 + 1 / 4 - 9 / 20 let ’ s add the given fractions in two groups . in the group of the first three fractions , notice that 1 / 3 and 1 / 2 share a common denominator of 6 with 5 / 6 . 1 / 2 + 1 / 3 = 3 / 6 + 2 / 6 = 5 / 6 thus , 5 / 6 – 5 / 6 = 0 looking at the 2 nd group of the fractions ( 1 / 5 , 1 / 4 , and 9 / 20 ) , notice that 1 / 5 and 1 / 4 share a common denominator of 20 with 9 / 20 . 1 / 5 + 1 / 4 = 4 / 20 + 5 / 20 = 9 / 20 thus , 9 / 20 – 9 / 20 = 0 . thus , the result of 1 / 3 + 1 / 2 – 5 / 6 + 1 / 5 + 1 / 4 – 9 / 20 is 9 / 20 . answer : d"
Answer: d
Python program:
a = 9 / 20
Problem: a certain car dealership sells economy cars , luxury cars , and sport utility vehicles . the ratio of economy to luxury cars is 4 : 3 . the ratio of economy cars to sport utility vehicles is 6 : 5 . what is the ratio of luxury cars to sport utility vehicles ?
Options: a ) 9 : 10 , b ) 8 : 9 , c ) 3 : 2 , d ) 2 : 3 , e ) 1 : 2
Rationale: "the ratio of economy to luxury cars is 4 : 3 - - > e : l = 4 : 3 = 24 : 18 . the ratio of economy cars to sport utility vehicles is 6 : 5 - - > e : s = 6 : 5 = 24 : 20 . thus , l : s = 18 : 20 = 9 : 10 . answer : a ."
Answer: a
Python program:
a = 4 * 3
b = 5 * 5
c = a / b
d = 5 * 4
e = 3 * 4
f = d / e
g = c / f
Problem: which digits should come in place of @ and # if the number 62684 @ # is divisible by both 8 and 5 ?
Options: a ) 4,0 , b ) 0,4 , c ) 4,4 , d ) 0,0 , e ) none
Rationale: explanation : since the given number is divisible by 5 , so 0 or 5 must come in place of # . but , a number ending with 5 is never divisible by 8 . so , 0 will replace # . now , the number formed by the last three digits is 4 @ 0 , which becomes divisible by 8 , if @ is replaced by 4 . hence , digits in place of @ and # are 4 and 0 respectively . answer : a
Answer: a
Python program:
a = math.lcm(8, 5)
b = a * 2
c = b / 10
d = c / 2
Problem: a invested $ 300 in a business after 6 months b invested $ 200 in the business . end of the year if they got $ 100 as profit . find b ' s shares ?
Options: a ) $ 100 , b ) $ 75 , c ) $ 25 , d ) $ 120 , e ) $ 50
Rationale: "a : b = 300 * 12 : 200 * 6 a : b = 1 : 1 b ' s share = 100 * 1 / 4 = $ 25 answer is c"
Answer: c
Python program:
a = 200 / 2
b = 200 / 2
c = 300 + b 
d = a / c
e = 1 - d
f = 100 * e
Problem: ashok secured average of 76 marks in 6 subjects . if the average of marks in 5 subjects is 74 , how many marks did he secure in the 6 th subject ?
Options: a ) 38 , b ) 27 , c ) 99 , d ) 17 , e ) 86
Rationale: "explanation : number of subjects = 6 average of marks in 6 subjects = 76 therefore total marks in 6 subjects = 76 * 6 = 456 now , no . of subjects = 5 total marks in 5 subjects = 74 * 5 = 370 therefore marks in 6 th subject = 456 – 370 = 86 answer : e"
Answer: e
Python program:
a = 76 * 6
b = 74 * 5
c = a - b
Problem: a man has a certain number of small boxes to pack into parcles . if he packs 3 , 4 , 5 or 6 in a parcel , he is left with one over ; if he packs 7 in a parcle , none is left over . what is the number of boxes , he may have to pack ?
Options: a ) 106 , b ) 301 , c ) 309 , d ) 400 , e ) 450
Rationale: explanation : clearly , the required number would be such that it leaves a remainder of 1 when divided by 3 , 4 , 5 , or 6 and no remainder when divided by 7 . thus , the number must be of the form ( l . c . m of 3 , 4 , 5 , 6 ) x + 1 i . e . , ( 60 x + 1 ) and a multiple of 7 . clearly , for x = 5 , the number is a multiple of 7 . so the number is 301 . answer : b ) 301
Answer: b
Python program:
a = math.lcm(3, 4)
b = math.lcm(a, 5)
c = math.lcm(b, 6)
d = c * 5
e = d + 1
Problem: find b and c so that the parabola with equation y = 4 x 2 - bx - c has a vertex at ( 2 , 4 ) ?
Options: a ) - 10 , b ) - 20 , c ) - 30 , d ) - 40 , e ) - 50
Rationale: h = b / 8 = 2 : formula for x coordinate of vertex b = 16 : solve for b y = 4 for x = 2 : the vertex point is a solution to the equation of the parabola 4 ( 2 ) 2 - 16 ( 2 ) - c = 4 c = - 20 : solve for c correct answer b
Answer: b
Python program:
a = 2 * 4
b = 2 * a
Problem: pipe a can fill a tank in 8 minutes and pipe b cam empty it in 24 minutes . if both the pipes are opened together after how many minutes should pipe b be closed , so that the tank is filled in 30 minutes ?
Options: a ) 18 , b ) 27 , c ) 98 , d ) 27 , e ) 66
Rationale: let the pipe b be closed after x minutes . 30 / 8 - x / 24 = 1 = > x / 24 = 30 / 8 - 1 = 11 / 4 = > x = 11 / 4 * 24 = 66 . answer : e
Answer: e
Python program:
a = 30 / 8
b = a - 1
c = b * 24
Problem: a call center has two teams . each member of team a was able to process 2 / 5 calls as compared to each member of team b . if team a has 5 / 8 as many number of call center agents as team b , what fraction of the total calls was processed by team b ?
Options: a ) 3 / 2 , b ) 3 / 4 , c ) 4 / 5 , d ) 1 / 2 , e ) 1 / 5
Rationale: let team b has 8 agents , so team a has 5 agents let each agent of team b picked up 5 calls , so total calls by team b = 40 so , each agent in team a picked up 2 calls , so total calls for team a = 10 fraction for team b = 40 / ( 40 + 10 ) = 4 / 5 = answer = c
Answer: c
Python program:
a = 8 * 5
b = 8 * 5
c = 5 * 2
d = b + c 
e = a / d
Problem: if the wheel is 15 cm then the number of revolutions to cover a distance of 1056 cm is ?
Options: a ) 18 , b ) 11.2 , c ) 14 , d ) 12 , e ) 91
Rationale: "2 * 22 / 7 * 15 * x = 1056 = > x = 11.2 answer : b"
Answer: b
Python program:
a = 3 * 100
b = 1 * 10
c = a + b 
d = c + 4 
e = d / 100
f = 2 * e
g = f * 15
h = 1056 / g
Problem: a sum of rs . 1190 has been divided among a , b and c such that a gets of what b gets and b gets of what c gets . b ’ s share is :
Options: a ) rs . 120 , b ) rs . 210 , c ) rs . 240 , d ) rs . 300 , e ) none
Rationale: explanation let c ’ s share = rs . x then , b ’ s share = rs . x / 4 , a ’ s share = rs . ( 2 / 3 x x / 4 ) = rs . x / 6 = x / 6 + x / 4 + x = 1190 = > 17 x / 12 = 1190 = > 1190 x 12 / 17 = rs . 840 hence , b ’ s share = rs . ( 840 / 4 ) = rs . 210 . answer b
Answer: b
Python program:
a = 1190 / 10
b = a * 2
c = b - 12
d = c - 12
Problem: a number increased by 40 % gives 1680 . the number is ?
Options: a ) 1680 , b ) 1600 , c ) 1200 , d ) 1500 , e ) 600
Rationale: "formula = total = 100 % , increase = ` ` + ' ' decrease = ` ` - ' ' a number means = 100 % that same number increased by 40 % = 140 % 140 % - - - - - - - > 1680 ( 140 ã — 12 = 1680 ) 100 % - - - - - - - > 1200 ( 100 ã — 12 = 1200 ) option ' c '"
Answer: c
Python program:
a = 40 / 100
b = 1 + a 
c = 1680 / b
Problem: if each digit in the set a = { 1 , 2 , 3 , 4 , 5 } is used exactly once , in how many ways can the 5 digits be arranged ?
Options: a ) 6 , b ) 24 , c ) 72 , d ) 96 , e ) 120
Rationale: "use the slot method for all the possible arrangements : we have 5 options for the 1 st slot , 4 for the 2 nd , 3 for 3 rd , 2 for 4 th and 1 for the 5 th , giving the total number of arrangements = 5 * 4 * 3 * 2 * 1 = 120 , e is the correct answer ."
Answer: e
Python program:
a = math.factorial(5)
Problem: two pipes a and b can fill a tank in 12 hours and 15 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 ) 10 hours , d ) 12 hours , e ) 7 4 / 9 hours
Rationale: "part filled by a in 1 hour = 1 / 12 part filled by b in 1 hour = 1 / 15 part filled by ( a + b ) in 1 hour = 1 / 12 + 1 / 15 = 9 / 60 both the pipes together fill the tank in 60 / 9 = 7 4 / 9 hours answer is e"
Answer: e
Python program:
a = 1 / 12
b = 1 / 15
c = a + b 
d = 1 / c
Problem: the sides of the triangle are in the ratio 5 : 6 : 7 and its perimeter is 720 cm . the length of the longest side is ?
Options: a ) 150 cm
b ) 200 cm
c ) 162 cm
d ) 220 cm
e ) 280 cm
Rationale: ratio of sides = 5 : 6 : 7 largest side = 720 * 7 / 18 = 280 cm answer is e
Answer: e
Python program:
a = 7 * 720
b = 5 + 6 
c = 7 + b 
d = a / c
Problem: jackie has two solutions that are 2 percent sulfuric acid and 12 percent sulfuric acid by volume , respectively . if these solutions are mixed in appropriate quantities to produce 60 liters of a solution that is 10 percent sulfuric acid , approximately how many liters of the 2 percent solution will be required ?
Options: a ) 18 , b ) 12 , c ) 24 , d ) 36 , e ) 42
Rationale: "let a = amount of 2 % acid and b = amount of 12 % acid . now , the equation translates to , 0.02 a + . 12 b = . 1 ( a + b ) but a + b = 60 therefore . 02 a + . 12 b = . 1 ( 60 ) = > 2 a + 12 b = 600 but b = 60 - a therefore 2 a + 12 ( 60 - a ) = 600 = > 10 a = 120 hence a = 12 . answer : b"
Answer: b
Python program:
a = 60 / 10
b = 3 * a
Problem: a man saves 20 % of his monthly salary . if an account of dearness of things he is to increase his monthly expenses by 20 % , he is only able to save rs . 220 per month . what is his monthly salary ?
Options: a ) 5500 , b ) 2999 , c ) 2878 , d ) 2990 , e ) 2771
Rationale: "income = rs . 100 expenditure = rs . 80 savings = rs . 20 present expenditure 80 * ( 20 / 100 ) = rs . 96 present savings = 100 â € “ 96 = rs . 4 100 - - - - - - 4 ? - - - - - - - - - 220 = > 5500 answer : a"
Answer: a
Python program:
a = 220 * 100
b = 100 - 20
c = 100 - 20
d = 20 / 100
e = c * d
f = b + e 
g = 100 - f
h = a / g
Problem: triangle atriangle b are similar triangles with areas 1536 units square and 2166 units square respectively . the ratio of there corresponding height would be
Options: a ) 9 : 10
b ) 17 : 19
c ) 23 : 27
d ) 13 : 17
e ) 16 : 19
Rationale: let x be the height of triangle a and y be the height of triangle of b . since triangles are similar , ratio of area of a and b is in the ratio of x ^ 2 / y ^ 2 therefore , ( x ^ 2 / y ^ 2 ) = 1536 / 2166 ( x ^ 2 / y ^ 2 ) = ( 16 * 16 * 6 ) / ( 19 * 19 * 6 ) ( x ^ 2 / y ^ 2 ) = 17 ^ 2 / 19 ^ 2 x / y = 16 / 19 ans = e
Answer: e
Python program:
a = 1536 / 2166
b = math.sqrt(a)
Problem: the megatek corporation is displaying its distribution of employees by department in a circle graph . the size of each sector of the graph representing a department is proportional to the percentage of total employees in that department . if the section of the circle graph representing the manufacturing department takes up 108 ° of the circle , what percentage of megatek employees are in manufacturing ?
Options: a ) 20 % , b ) 25 % , c ) 30 % , d ) 35 % , e ) 72 %
Rationale: "answer : c 108 ° divided by 360 ° equals 0.3 , therefore the sector is equal to 30 % of the total"
Answer: c
Python program:
a = 3600 / 10
b = 108 / a
c = b * 100
Problem: the toll t , in dollars , for a truck using a certain bridge is given by the formula t = 2.50 + 0.50 ( x − 2 ) , where x is the number of axles on the truck . what is the toll for an 18 - wheel truck that has 2 wheels on its front axle and 4 wheels on each of its other axles ?
Options: a ) $ 2.50 , b ) $ 3.00 , c ) $ 3.50 , d ) $ 4.00 , e ) $ 5.00
Rationale: "number of wheels in truck = 18 number of wheels on its front axle = 2 number of wheels remaining = 16 number of axles remaining axles = 16 / 4 = 4 total number of axles = 5 t = 2.50 + 0.50 ( x − 2 ) = 2.50 + . 5 * 3 = 2.5 + 1.5 = 4 $ answer d"
Answer: d
Python program:
a = 18 - 2
b = a / 4
c = b + 1 
d = c - 2
e = 0 * 50
f = 2 + 50
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 20 percent of revenues . the profits in 2009 were what percent of the profits in 2008 ?
Options: a ) 80 % , b ) 105 % , c ) 120 % , d ) 124.2 % , e ) 160 %
Rationale: "x = profits r = revenue x / r = 0,1 x = 10 r = 100 2009 : r = 80 x / 80 = 0,2 = 15 / 100 x = 80 * 20 / 100 x = 16 16 / 10 = 1,6 = 160 % , answer e"
Answer: e
Python program:
a = 20 / 100
b = 1 - a
c = 20 * b
d = c / 10
e = d * 100
Problem: a man walking at a constant rate of 6 miles per hour is passed by a woman traveling in the same direction along the same path at a constant rate of 12 miles per hour . the woman stops to wait for the man 10 minutes after passing him , while the man continues to walk at his constant rate . how many minutes must the woman wait until the man catches up ?
Options: a ) 5 , b ) 15 , c ) 10 , d ) 20 , e ) 25
Rationale: "when the woman passes the man , they are aligned ( m and w ) . they are moving in the same direction . after 5 minutes , the woman ( w ) will be ahead the man ( m ) : m - - - - - - m - - - - - - - - - - - - - - - w w in the 5 minutes , after passing the man , the woman walks the distance mw = ww , which is 10 * 12 / 60 = 2 miles and the man walks the distance mm , which is 10 * 6 / 60 = 1 mile . the difference of 2 - 1 = 1 miles ( mw ) will be covered by the man in ( 1 ) / 6 = 1 / 6 of an hour , which is 10 minutes . answer c ."
Answer: c
Python program:
a = 10 / const_60
b = 12 - 6
c = a * b
d = c / 6
e = const_60 * d
Problem: a number when divided by 219 gives a remainder 32 , what remainder will be obtained by dividing the same number 12 ?
Options: a ) 7 , b ) 11 , c ) 9 , d ) 2 , e ) 3
Rationale: "explanation : 219 + 32 = 251 / 12 = 9 ( remainder ) answer : b"
Answer: b
Python program:
a = 12 * 2
b = 32 - a
Problem: what is the difference between the c . i . on rs . 7000 for 1 1 / 2 years at 4 % per annum compounded yearly and half - yearly ?
Options: a ) s . 2.04 , b ) s . 2.08 , c ) s . 2.02 , d ) s . 2.86 , e ) s . 2.42
Rationale: "c . i . when interest is compounded yearly = [ 7000 * ( 1 + 4 / 100 ) * ( 1 + ( 1 / 2 * 4 ) / 100 ] = 7000 * 26 / 25 * 51 / 50 = rs . 7425.6 c . i . when interest is compounded half - yearly = [ 7000 * ( 1 + 2 / 100 ) 2 ] = ( 7000 * 51 / 50 * 51 / 50 * 51 / 50 ) = rs . 7428.46 difference = ( 7428.46 - 7425.6 ) = rs . 2.86 . answer : d"
Answer: d
Python program:
a = 2 / 100
b = 1 + a 
c = 2 / 100
d = 1 + c 
e = b * d
f = 2 / 100
g = 1 + f 
h = e * g
i = 7000 * h
j = 2 / 100
k = 1 + j 
l = 4 / 100
m = 1 + l 
n = k * m
o = 7000 * n
p = i - o
Problem: mary ' s income is 70 percent more than tim ' s income , and tim ' s income is 40 percent less than juan ' s income . what percent of juan ' s income is mary ' s income ?
Options: a ) 124 % , b ) 102 % , c ) 96 % , d ) 80 % , e ) 64 %
Rationale: juan ' s income = 100 ( assume ) ; tim ' s income = 60 ( 40 percent less than juan ' s income ) ; mary ' s income = 102 ( 70 percent more than tim ' s income ) . thus , mary ' s income ( 102 ) is 102 % of juan ' s income ( 100 ) . answer : b .
Answer: b
Python program:
a = 40 / 100
b = 1 - a
c = 70 / 100
d = 1 + c 
e = b * d
f = e * 100
Problem: a sum of money lent out at s . i . amounts to a total of $ 480 after 2 years and to $ 680 after a further period of 5 years . what was the initial sum of money that was invested ?
Options: a ) $ 360 , b ) $ 380 , c ) $ 400 , d ) $ 420 , e ) $ 440
Rationale: "s . i for 5 years = $ 680 - $ 480 = $ 200 the s . i . is $ 40 / year s . i . for 2 years = $ 80 principal = $ 480 - $ 80 = $ 400 the answer is c ."
Answer: c
Python program:
a = 680 - 480
b = 2 / 5
c = a * b
d = 480 - c
Problem: 5.005 / 2.002 =
Options: a ) 2.05 , b ) 2.50025 , c ) 2.501 , d ) 2.5025 , e ) 2.5
Rationale: "5.005 / 2.002 = 5005 / 2002 = 5 ( 1001 ) / 2 ( 1001 ) = 5 / 2 = 2.5 the answer is e ."
Answer: e
Python program:
a = 5 / 5
b = a * 100
Problem: irin , ingrid and nell bake chocolate chip cookies in the ratio of 9.18 : 5.17 : 2.05 . if altogether they baked a batch of 148 cookies , what percent of the cookies did irin bake ?
Options: a ) 0.125 % , b ) 1.25 % , c ) 56 % , d ) 125 % , e ) 0.152 %
Rationale: "9.18 x + 5.17 x + 2.05 x = 16.4 x = 150 cookies x = 150 / 16.4 = 9.14 ( approx ) so , irin baked 9.14 * 9.18 cookies or 84 cookies ( approx ) % share = 84 / 150 = 56 approx hence , answer is c ."
Answer: c
Python program:
a = 148 * 5
b = 9 + 18 
c = b + 2 
d = a / c
e = d / 148
f = e * 100
Problem: a man is 24 years older than his son . in two years , his age will be twice the age of his son . the present age of the son is ?
Options: a ) 11 , b ) 25 , c ) 27 , d ) 22 , e ) 91
Rationale: "let the son ' s present age be x years . then , man ' s present age = ( x + 24 ) years . ( x + 24 ) + 2 = 2 ( x + 2 ) x + 26 = 2 x + 4 = > x = 22 . answer : d"
Answer: d
Python program:
a = 2 * 2
b = a - 2
c = 24 - b
d = 2 - 1
e = c / d
Problem: a dress on sale in a shop is marked at $ d . during the discount sale its price is reduced by 55 % . staff are allowed a further 50 % reduction on the discounted price . if a staff member buys the dress what will she have to pay in terms of d ?
Options: a ) 0.275 d , b ) 0.225 d , c ) 0.265 d , d ) 0.245 d , e ) 0.205 d
Rationale: "effective discount = a + b + ab / 100 = - 55 - 50 + ( - 55 ) ( - 50 ) / 100 = 77.5 sale price = d * ( 1 - 77.5 / 100 ) sale price = . 225 * d answer ( b )"
Answer: b
Python program:
a = 100 - 55
b = a / 100
c = 100 - 55
d = c / 100
e = 50 / 100
f = d * e
g = b - f
Problem: if 100 < x < 190 and 10 < y < 100 , then the product xy can not be equal to :
Options: a ) 18,104 , b ) 18,303 , c ) 18 , 356.732 , d ) 19,502 , e ) 18,909
Rationale: "correct answer : ( d ) determine the range of xy by multiplying the two extremes of each individual range together . the smallest value of xy must be greater than 100 * 10 . the largest value must be less than 190 * 100 . this means that 1000 < xy < 19,000 . ( d ) is outside of this range , so it is not a possible product of xy ."
Answer: d
Python program:
a = 100 + 1
Problem: if the cost price of 20 articles is equal to the selling price of 40 articles , what is the % profit or loss made by the merchant ?
Options: a ) 25 % loss , b ) 25 % profit , c ) 20 % loss , d ) 20 % profit , e ) 50 % loss
Rationale: "let the cost price of 1 article be $ 1 . therefore , cost price of 20 articles = 20 * 1 = $ 20 the selling price of 40 articles = cost price of 40 articles = $ 40 . now , we know the selling price of 40 articles . let us find the cost price of 40 articles . cost price of 40 articles = 40 * 1 = $ 40 . therefore , profit made on sale of 40 articles = selling price of 40 articles - cost price of 40 articles = 20 - 40 = - $ 20 . as the profit is in the negative , the merchant has made a loss of $ 20 . therefore , % loss = loss / cp * 100 % loss = - 20 / 40 * 100 = 50 % loss . e"
Answer: e
Python program:
a = 100 * 40
b = a / 20
c = 100 - b
d = 100 * 40
e = d / 20
f = c / e
g = 100 * f
Problem: if x < y < z and y - x > 5 , where x is an even integer and y and z are odd integers , what is the least possible value of z - x ?
Options: a ) 6 , b ) 7 , c ) 8 , d ) 9 , e ) 10
Rationale: "we want to minimize z − xz − x , so we need to maximize xx . say z = 11 = oddz = 11 = odd , then max value of yy will be 9 ( as yy is also odd ) . now , since y − 5 > xy − 5 > x - - > 9 − 5 > x 9 − 5 > x - - > 4 > x 4 > x , then max value of xx is 2 ( as xx is even ) . hence , the least possible value of z − xz − x is 11 - 2 = 9 . answer : d ."
Answer: d
Python program:
a = 5 + 2 
b = a + 2
Problem: reeya obtained 65 , 67 , 76 , 82 and 85 out of 100 in different subjects , what will be the average
Options: a ) 70 , b ) 75 , c ) 80 , d ) 85 , e ) 60
Rationale: "explanation : ( 65 + 67 + 76 + 82 + 855 ) = 75 answer : option b"
Answer: b
Python program:
a = 65 + 67 
b = a + 76 
c = b + 82 
d = c + 85 
e = 4 + 1 
f = d / e
Problem: a certain bus driver is paid a regular rate of $ 15 per hour for any number of hours that does not exceed 40 hours per week . for any overtime hours worked in excess of 40 hours per week , the bus driver is paid a rate that is 75 % higher than his regular rate . if last week the bus driver earned $ 982 in total compensation , how many total hours did he work that week ?
Options: a ) 56 , b ) 40 , c ) 44 , d ) 48 , e ) 52
Rationale: "for 40 hrs = 40 * 15 = 600 excess = 982 - 600 = 382 for extra hours = . 75 ( 15 ) = 11.25 + 16 = 27.25 number of extra hrs = 382 / 27.25 = 14 total hrs = 40 + 14 = 56 answer a 56"
Answer: a
Python program:
a = 15 * 40
b = 982 - a
c = 100 + 75 
d = 15 * c
e = d / 100
f = b / e
g = 40 + f
Problem: how long does a train 165 meters long running at the rate of 54 kmph take to cross a bridge 720 meters in length ?
Options: a ) 28 , b ) 27 , c ) 55 , d ) 59 , e ) 12
Rationale: "t = ( 720 + 165 ) / 54 * 18 / 5 t = 59 answer : d"
Answer: d
Python program:
a = 165 + 720 
b = 54 * const_0_2778
c = a / b
Problem: 90 students represent x percent of the boys at jones elementary school . if the boys at jones elementary make up 30 % of the total school population of x students , what is x ?
Options: a ) 125 , b ) 173 , c ) 225 , d ) 250 , e ) 500
Rationale: "90 = x / 100 * 30 / 100 * x = > x ^ 2 = 9 * 10000 / 3 = > x = 173 b"
Answer: b
Python program:
a = 90 * 100
b = 30 / 100
c = a / b
d = math.sqrt(c)