euclaise/mathqa_programs huggingface dataset:
Problem: two trains 200 m and 300 m long run at the speed of 70 kmph and 50 kmph in opposite directions in parallel tracks . the time which they take to cross each other is ?
Options: a ) 10 sec , b ) 15 sec , c ) 18 sec , d ) 20 sec , e ) 22 sec
Rationale: "relative speed = 70 + 50 = 120 kmph * 5 / 18 = 100 / 3 m / s distance covered in crossing each other = 200 + 300 = 500 m required time = 500 * 3 / 100 = 15 sec answer is b"
Answer: b
Python program:
a = 200 + 300 
b = 70 + 50 
c = b * const_0_2778
d = a / c
Problem: find the area of a parallelogram with base 12 cm and height 10 cm ?
Options: a ) 297 cm 2 , b ) 384 cm 2 , c ) 120 cm 2 , d ) 267 cm 2 , e ) 186 cm 2
Rationale: "area of a parallelogram = base * height = 12 * 10 = 120 cm 2 answer : c"
Answer: c
Python program:
a = 12 * 10
Problem: 6 lights begin to flash together at 12 : 00 noon and flash respectively at intervals of 3 , 4 , 5 , 6 , 7 , and 8 seconds . not including the flash at 12 : 00 noon , how many more times will all 6 lights flash together before 1 : 00 pm ( i . e . one hour later ) ?
Options: a ) 4 , b ) 6 , c ) 8 , d ) 10 , e ) 12
Rationale: the least common multiple is 2 * 2 * 2 * 3 * 5 * 7 = 840 . 3600 seconds / 840 = 4 + remainder . the answer is a .
Answer: a
Python program:
a = 1 * 3600
b = math.lcm(7, 8)
c = math.lcm(3, 4)
d = math.lcm(5, 6)
e = math.lcm(c, d)
f = math.lcm(b, e)
g = a / f
h = math.floor(g)
Problem: a is the hundreds digit of the 3 digit integer x , b is the tens digit of x , and c is the units digit of x . 2 a = b = 4 c , and a > 0 . what is the difference between the two greatest possible values of x ? tip : dont stop till you have exhausted all answer choices to arrive at the correct one .
Options: a ) 124 , b ) 241 , c ) 394 , d ) 421 , e ) 842
Rationale: ratio of a : b : c = 2 : 4 : 1 two possible greatest single digit values for b are 8 and 4 if b is 8 , then x = 482 if b is 4 , then x = 241 difference = 482 - 241 = 241 b is the answer
Answer: b
Python program:
a = 4 * 1
b = a * 100
c = 4 * 2
d = c * 10
e = b + d 
f = 4 * 1
g = f / 2
h = e + g 
i = 4 * 1
j = i / 2
k = j * 100
l = 4 * 1
m = l * 10
n = k + m 
o = n + 1 
p = h - o
Problem: find the slope of the line perpendicular to the line y = ( 1 / 2 ) x - 7
Options: a ) 1 , b ) 2 , c ) - 2 , d ) 4 , e ) 5
Rationale: "two lines are perpendicular if the product of their slopes is equal to - 1 . the slope of the given line is equal to 1 / 2 . if m is the slope of the line perpendicular to the given line , then m × ( 1 / 2 ) = - 1 solve for m m = - 2 correct answer c ) - 2"
Answer: c
Python program:
a = 1 / 2
Problem: the sale price of an article including the sales tax is rs . 616 . the rate of sales tax is 10 % . if the shopkeeper has made a profit of 25 % , then the cost price of the article is :
Options: a ) 500 , b ) 277 , c ) 222 , d ) 448 , e ) 111
Rationale: "explanation : 110 % of s . p . = 616 s . p . = ( 616 * 100 ) / 110 = rs . 560 c . p = ( 100 * 560 ) / 125 = rs . 448 answer : d"
Answer: d
Python program:
a = 616 * 100
b = 100 + 10 
c = a / b
d = 100 + 10 
e = c * d
f = 100 + 25 
g = e / f
Problem: the triplicate ratio of 1 : 2 is ?
Options: a ) 1 : 7 , b ) 1 : 8 , c ) 1 : 3 , d ) 1 : 1 , e ) 1 : 2
Rationale: "13 : 23 = 1 : 8 answer : b"
Answer: b
Python program:
a = 1 ** 2
b = 3 ** 0
c = a / b
Problem: a number with an interesting property : when i divide it by 2 , the remainder is 1 . when i divide it by 3 , the remainder is 2 . when i divide it by 4 , the remainder is 3 . when i divide it by 5 , the remainder is 4 . when i divide it by 6 , the remainder is 5 . when i divide it by 7 , the remainder is 6 . when i divide it by 8 , the remainder is 7 . when i divide it by 9 , the remainder is 8 . when i divide it by 10 , the remainder is 9 . it ' s not a small number , but it ' s not really big , either . when i looked for a smaller number with this property i could n ' t find one . can you find it ?
Options: a ) 2588 , b ) 2474 , c ) 2254 , d ) 2519 , e ) 8725
Rationale: d 2519 the number has to end in 9 . looked brute force for small numbers . 59 and 119 were promising , but no cigar . then looked for agreement among 39 + multiples of 40 , 69 + multiples of 70 and 89 + multiples of 90 smallest one was 2519 .
Answer: d
Python program:
a = math.lcm(9, 10)
b = math.lcm(a, 7)
c = b * 2
d = c * 2
e = d - 1
Problem: 65 % of a number is 21 less than 4 / 5 th of that number . what is the number ?
Options: a ) 100 , b ) 120 , c ) 140 , d ) 130 , e ) 115
Rationale: let the number be x then , 4 x / 5 - ( 65 % of x ) = 21 4 x / 5 - 65 x / 100 = 21 x = 140 answer is c
Answer: c
Python program:
a = 21 * 5
b = 100 / 5
c = a * b
d = 100 / 5
e = d * 4
f = e - 65
g = c / f
Problem: what is the sum of the integers 45 through 175 inclusive ?
Options: a ) 12,295 , b ) 13,000 , c ) 14,300 , d ) 14,410 , e ) 28,820
Rationale: "sum of n consecutive positive integers = n ( n + 1 ) / 2 . . in one case n = 44 and other 175 . . . subtract the sum to get the answer sum of first 175 + ive numbers = 175 * 176 / 2 = 15400 . . sum of first 45 + i ' ve numbers = 45 * 44 / 2 = 990 . . answer = 15400 - 990 = 14410 answer : d"
Answer: d
Python program:
a = 45 * 175
b = a / 4
Problem: the ratio of males to females in a class is 2 : 3 . the career preferences of the students in the class are represented in a circle graph . if the area of the graph allocated to each career preference is proportional to the number of students who have that career preference , how many degrees of the circle should be used to represent a career that is preferred by one - half of the males and one - fourth of the females in the class ?
Options: a ) 120 , b ) 126 , c ) 132 , d ) 138 , e ) 144
Rationale: "1 / 2 * 2 / 5 + 1 / 4 * 3 / 5 = 4 / 20 + 3 / 20 = 7 / 20 the number of degrees is 7 / 20 * 360 = 126 degrees the answer is b ."
Answer: b
Python program:
a = 2 * 360
b = 2 + 3 
c = a / b
Problem: a vendor sells 60 percent of the apples he had and throws away 40 percent of the remainder . the next day , the vendor sells 50 percent of the remaining apples and throws away the rest . in total , what percent of his apples does the vendor throw away ?
Options: a ) 24 , b ) 26 , c ) 28 , d ) 30 , e ) 32
Rationale: "let x be the original number of apples . on day one , the vendor throws away ( 0.4 ) ( 0.4 ) x = 0.16 x . the remaining apples are ( 0.6 ) ( 0.4 ) x = 0.24 x . on day two , the vendor throws away ( 0.5 ) ( 0.24 ) x = 0.12 x . the vendor throws away a total of 0.16 x + 0.12 x = 0.28 x . the vendor throws away 28 percent of the apples . the answer is c ."
Answer: c
Python program:
a = 100 - 60
b = 40 / 100
c = 100 - 60
d = b * c
e = a - d
f = e / 2
g = 40 / 100
h = 100 - 60
i = g * h
j = f + i
Problem: a vendor sells 80 percent of the pears he had and throws away 50 percent of the remainder . the next day , the vendor sells 80 percent of the remaining pears and throws away the rest . in total , what percent of his pears does the vendor throw away ?
Options: a ) 6 , b ) 8 , c ) 10 , d ) 12 , e ) 14
Rationale: "let x be the original number of pears . on day one , the vendor throws away ( 0.5 ) ( 0.2 ) x = 0.1 x . the remaining pears are ( 0.5 ) ( 0.2 ) x = 0.1 x . on day two , the vendor throws away ( 0.2 ) ( 0.1 ) x = 0.02 x . the vendor throws away a total of 0.1 x + 0.02 x = 0.12 x . the vendor throws away 12 percent of the pears . the answer is d ."
Answer: d
Python program:
a = 80 / 100
b = 1 - a
c = 50 / 100
d = 80 / 100
e = 1 - d
f = c * e
g = b - f
h = 80 / 100
i = 1 - h
j = 50 / 100
k = 80 / 100
l = 1 - k
m = j * l
n = i - m
o = 80 / 100
p = n * o
q = g - p
r = 50 / 100
s = 80 / 100
t = 1 - s
u = r * t
v = q + u 
w = 100 * v
Problem: a train 700 m long can cross an electric pole in 20 sec and then find the speed of the train ?
Options: a ) 117 kmph , b ) 178 kmph , c ) 126 kmph , d ) 118 kmph , e ) 119 kmph
Rationale: "length = speed * time speed = l / t s = 700 / 20 s = 35 m / sec speed = 35 * 18 / 5 ( to convert m / sec in to kmph multiply by 18 / 5 ) speed = 126 kmph answer : c"
Answer: c
Python program:
a = 700 / 1000
b = 20 / 3600
c = a / b
Problem: the average weight of 8 persons increases by 3.5 kg when a new person comes in place of one of them weighing 65 kg . what might be the weight of the new person ?
Options: a ) 75 kg , b ) 65 kg , c ) 55 kg , d ) 85 kg , e ) 93 kg
Rationale: "total weight increased = ( 8 x 3.5 ) kg = 28 kg . weight of new person = ( 65 + 28 ) kg = 93 kg . answer : e"
Answer: e
Python program:
a = 8 * 3
b = 65 + a
Problem: an industrial loom weaves 1.14 meters of cloth every second . approximately , how much time will it take to weave 52 meters of cloth ?
Options: a ) 29.32 sec , b ) 42.51 sec , c ) 39.25 sec , d ) 45.61 sec , e ) none of these
Rationale: explanation : given loom weaves 1.14 mts of cloth in one second then 52 mts of cloth can be weaved by loom in , 1.14 - - - - - 1 52.0 - - - - - - ? = > 52 / 1.14 = 45.61 sec answer is d
Answer: d
Python program:
a = 52 / 1
Problem: one pipe can fill a tank three times as fast as another pipe . if together the two pipes can fill tank in 37 min , then the slower pipe alone will be able to fill the tank in ?
Options: a ) 229 , b ) 787 , c ) 144 , d ) 148 , e ) 121
Rationale: "let the slower pipe alone fill the tank in x min . then , faster pipe will fill it in x / 3 min . 1 / x + 3 / x = 1 / 37 4 / x = 1 / 37 = > x = 148 min . answer : d"
Answer: d
Python program:
a = 1 + 4 
b = a * 37
Problem: if 10 machines can produce 20 units in 10 hours , how long would it take 40 machines to produce 100 units ?
Options: a ) 9.5 , b ) 6.4 , c ) 2.3 , d ) 8.9 , e ) 12.5
Rationale: "10 machines would produce 100 units in 50 hours . increasing the amount of machines by 4 would mean dividing 50 hours by 4 . 50 / 4 = 12.5 answer : e"
Answer: e
Python program:
a = 20 / 10
b = a / 10
c = b * 20
d = 100 / c
Problem: when positive integer n is divided by positive integer j , the remainder is 14 . if n / j = 134.07 , what is value of j ?
Options: a ) 22 , b ) 56 , c ) 78 , d ) 200 , e ) 175
Rationale: "1 ) we know that decimal part of decimal quotient = { remainder / divisor } so 0.07 , the decimal part of the decimal quotient , must equal the remainder , 14 , divided by the divisor j . 0.07 = 14 / j 0.07 * j = 14 j = 14 / 0.07 = 1400 / 7 = 200 so j = 200 , answer = d ."
Answer: d
Python program:
a = 4 * 10
b = a + 2 
c = 100 + b 
d = 134 - 7
e = 14 / d
Problem: if m : n is 2 : 9 and n : p is 9 : 4 then m : p is equal to
Options: a ) 1 : 4 , b ) 1 : 3 , c ) 5 : 2 , d ) 3 : 2 , e ) 1 : 2
Rationale: the two ratios given are having the same number 9 for n in both the ratios . hence - m : n = 2 : 9 n : p = 9 : 4 = > m : p = 2 : 4 = > 1 : 2 answer e
Answer: e
Python program:
a = 2 / 4
Problem: the product of two numbers is 1320 and their h . c . f is 6 . the l . c . m of the numbers is
Options: a ) 220 , b ) 1314 , c ) 1326 , d ) 7920 , e ) none
Rationale: "solution l . c . m = product of numbers / h . c . f ‹ = › 1320 / 6 ‹ = › 220 . answer a"
Answer: a
Python program:
a = 2 * 1320
b = 6 - a
c = math.sqrt(b)
d = c ** 2
e = 4 * 1320
f = d + e 
g = math.sqrt(f)
Problem: a certain taxi company charges $ 2.80 for the first 1 / 5 of a mile plus $ 0.40 for each additional 1 / 5 of a mile . what would this company charge for a taxi ride that was 8 miles long ?
Options: a ) 15.6 , b ) 16.0 , c ) 18.4 , d ) 18.7 , e ) 19.1
Rationale: "a certain taxi company charges $ 2.80 for the first 1 / 5 of a mile plus $ 0.40 for each additional 1 / 5 of a mile . what would this company charge for a taxi ride that was 8 miles long ? a . 15.60 b . 16.00 c . 17.50 d . 18.70 e . 19.10 1 / 5 miles = 0.2 miles . the cost of 8 miles long ride would be $ 2.80 for the first 0.2 miles plus ( 8 - 0.2 ) / 0.2 * 0.4 = $ 2.8 + $ 15.6 = $ 18.4 . answer : c ."
Answer: c
Python program:
a = 1 / 5
b = 8 / a
c = b - 1
d = c * 0
e = 2 + 80
Problem: the average of first five multiples of 4 is
Options: a ) 3 , b ) 6 , c ) 9 , d ) 12 , e ) 15
Rationale: "solution average = 4 ( 1 + 2 + 3 + 4 + 5 ) / 5 = 60 / 5 . = 12 answer d"
Answer: d
Python program:
a = 4 + 1
Problem: of the 3 - digit integers greater than 200 , how many have two digits that are equal to each other and the remaining digit different from the other two ?
Options: a ) 90 , b ) 82 , c ) 80 , d ) 45 , e ) 36
Rationale: let the three digit number be represented as x y z . there are 3 cases : case i . [ x = y ] z is not equal to xy : xxzoryyz x can be either 7 , 8 or 9 , so digit at x can be chosen in 3 ways after x is chosen , y can be chosen in 1 way after xy are chosen , z can be chosen in 9 ways thus , possible no of digits = ( 3 ways ) * ( 1 way ) * ( 9 ways ) = 27 . . . . ( 1 ) [ example numbers : 774,779 , 882,993 etc ] case ii . [ x = z ] y is not equal to xz : xyxorzyz x can be either 7 , 8 or 9 , so digit at x can be chosen in 3 ways after x is chosen , z can be chosen in 1 way after xz are chosen , z can be chosen in 9 ways thus , possible no of digits = ( 3 ways ) * ( 9 ways ) * ( 1 way ) = 27 . . . . ( 2 ) [ example numbers : 747,797 , 828,939 etc ] case iii . [ y = z ] x is not equal to yz : xyyorxzz x can be either 7 , 8 or 9 , so digit at x can be chosen in 3 ways after x is chosen , y can be chosen in 9 ways after y is chosen , z can have 1 way thus , possible no of digits = ( 3 ways ) * ( 1 way ) * ( 9 ways ) = 27 . . . . ( 3 ) [ example numbers : 744,799 , 822,933 etc ] therefore , total numbers of possible digits [ sum of case ( 1 ) , ( 2 ) ( 3 ) above ] = 27 + 27 + 27 - 1 = 80 one digit is subtracted from total number of possible digits to eliminate one possibility of xyz = 700 to satisfy the condition that digit > 200 . answer : ( e )
Answer: e
Python program:
a = 200 / 2
b = a - 1
c = b / 3
d = c + 3
Problem: a rectangular mat has an area of 120 sq . metres and perimeter of 46 m . the length of its diagonal is :
Options: a ) 19 m
b ) 17 m
c ) 15 m
d ) 16 m
e ) 20 m
Rationale: rectangular area = l × b = 120 and perimeter = 2 ( l + b ) = 46 l + b = 23 ( l - b ) power 2 - 4 lb = ( 23 ) power 2 - 4 × 120 = ( 529 - 480 ) = 49 = l - b = 7 l + b = 23 , l - b = 7 , we get l = 15 , b = 8 diagonal = √ 152 + 82 √ 225 + 64 = > √ 289 = 17 m answer is b .
Answer: b
Python program:
a = 46 / 2
b = a ** 2
c = 120 * 2
d = b - c
e = math.sqrt(d)
Problem: a farmer used 1,034 acres of land for beans , wheat , and corn in the ratio of 5 : 2 : 4 , respectively . how many r acres were used for corn ?
Options: a ) 188 , b ) 258 , c ) 376 , d ) 470 , e ) 517
Rationale: "consider 5 x acres of land used for bean consider 2 x acres of land used for wheat consider 4 x acres of land used for corn total given is 1034 acres 11 x = 1034 x = 94 land used for corn r = 4 * 94 = 376 correct option - c"
Answer: c
Python program:
a = 1000 * 1
b = 10 * 3
c = b + 4 
d = a + c 
e = 5 + 2 
f = e + 4 
g = d / f
h = g * 4
Problem: the tax on a commodity is diminished by 40 % but its consumption is increased by 25 % . find the decrease percent in the revenue derived from it ?
Options: a ) 18 % , b ) 72 % , c ) 25 % , d ) 12 % , e ) 52 %
Rationale: "100 * 100 = 10000 60 * 125 = 7500 10000 - - - - - - - 2500 100 - - - - - - - ? = 25 % answer : c"
Answer: c
Python program:
a = 100 + 25 
b = 100 - 40
c = a * b
d = c / 100
e = 100 - d
Problem: a lady grows cabbage in her garden that is in the shape of a square . each cabbage takes 1 square foot of area in her garden . this year , she has increased her output by 127 cabbages when compared to last year . the shape of the area used for growing the cabbage has remained a square in both these years . how many cabbages did she produce this year ?
Options: a ) 4096 , b ) 4098 , c ) 5000 , d ) 5096 , e ) can not be determined
Rationale: "explanatory answer the shape of the area used for growing cabbage has remained a square in both the years . let the side of the square area used for growing cabbage this year be x ft . therefore , the area of the ground used for cultivation this year = x 2 sq . ft . let the side of the square area used for growing cabbage last year be y ft . therefore , the area of the ground used for cultivation last year = y 2 sq . ft . as the number of cabbage grown has increased by 127 , the area would have increased by 127 sq ft because each cabbage takes 1 sq ft space . hence , x 2 - y 2 = 127 ( x + y ) ( x - y ) = 127 . 127 is a prime number and hence it will have only two factors . i . e . , 127 and 1 . therefore , 127 can be expressed as product of 2 numbers in only way = 127 * 1 i . e . , ( x + y ) ( x - y ) = 127 * 1 so , ( x + y ) should be 127 and ( x - y ) should be 1 . solving the two equations we get x = 64 and y = 63 . therefore , number of cabbage produced this year = x 2 = 642 = 4096 . alternative approach : use answer choices the area in both the years are squares of two numbers . that rules out choice b , c and d . as 4098,5000 and 5096 are not the square of any number . check choice a : if this year ' s produce is 4096 , last year ' s produce would have been 4096 - 127 = 3969 3969 is the square of 63 . so , 4096 is the answer . choice a"
Answer: a
Python program:
a = 127 - 1
b = a / 2
c = b + 1 
d = c ** 2
Problem: a snail , climbing a 20 feet high wall , climbs up 8 feet on the first day but slides down 4 feet on the second . it climbs 8 feet on the third day and slides down again 4 feet on the fourth day . if this pattern continues , how many days will it take the snail to reach the top of the wall ?
Options: a ) 7 , b ) 16 , c ) 17 , d ) 20 , e ) 21
Rationale: "total transaction in two days = 8 - 4 = 4 feet in 7 days it will climb 20 feet thus reaching the top therefore , total no of days required = 7 a"
Answer: a
Python program:
a = 20 - 8
Problem: out of 40 applicants to a law school , 15 majored in political science , 20 had a grade point average higher than 3.0 , and 10 did not major in political science and had a gpa equal to or lower than 3.0 . how many of q applicants majored in political science and had a gpa higher than 3.0 ?
Options: a ) 5 , b ) 10 , c ) 15 , d ) 25 , e ) 35
Rationale: total applicants = 40 political science = 15 and non political science = 40 - 15 = 25 gpa > 3.0 = 20 and gpa < = 3.0 = 20 10 non political science students had gpa < = 3.0 - - > 15 non political science students had gpa > 3.0 gpa > 3.0 in political science = total - ( gpa > 3.0 in non political science ) q = 20 - 15 = 5 answer : a
Answer: a
Python program:
a = 10 + 15 
b = 40 - a
c = 20 - b
Problem: the sum of the squares of the first 15 positive integers ( 1 ^ 2 + 2 ^ 2 + 3 ^ 2 + . . . + 15 ^ 2 ) is equal to 1270 . what is the sum of the squares of the second 15 positive integers ( 16 ^ 2 + 17 ^ 2 + 18 ^ 2 + . . . + 30 ^ 2 ) ?
Options: a ) 2480 , b ) 3490 , c ) 6785 , d ) 8245 , e ) 9255
Rationale: "you ' ll never need a formula for the sums of squares on the actual gmat . you do n ' t need to use that formula here , though it ' s not all that straightforward to solve without one . two different approaches : 16 ^ 2 + 17 ^ 2 + 18 ^ 2 + . . . + 30 ^ 2 = ( 15 + 1 ) ^ 2 + ( 15 + 2 ) ^ 2 + ( 15 + 3 ) ^ 2 + . . . + ( 15 + 15 ) ^ 2 now we can expand each square ; they are all in the ( x + y ) ^ 2 = x ^ 2 + 2 xy + y ^ 2 pattern . = ( 15 ^ 2 + 2 * 15 + 1 ^ 2 ) + ( 15 ^ 2 + 4 * 15 + 2 ^ 2 ) + ( 15 ^ 2 + 6 * 15 + 3 ^ 2 ) + . . . + ( 15 ^ 2 + 30 * 15 + 15 ^ 2 ) now we have fifteen 15 ^ 2 terms , so adding these gives 15 * 15 ^ 2 = 15 ^ 3 = 3375 . we also have the entire sum 1 ^ 2 + 2 ^ 2 + . . . + 15 ^ 2 , which we know is equal to 1240 . finally adding the middle terms , we have : 2 * 15 + 4 * 15 + 6 * 15 + . . . + 30 * 15 = 15 ( 2 + 4 + 6 + . . . . + 30 ) = 15 * 2 * ( 1 + 2 + 3 + . . . + 15 ) = 15 * 2 * 8 * 15 = 3600 so the sum must be 3375 + 1240 + 3600 = 8215 alternatively , we can use a different factoring pattern . we want to find the value of 30 ^ 2 + 29 ^ 2 + . . . + 17 ^ 2 + 16 ^ 2 . well if we subtract 15 ^ 2 + 14 ^ 2 + . . . . + 2 ^ 2 + 1 ^ 2 from this , the answer will be 1240 less than what we want to find . so if we can find the value of 30 ^ 2 + 29 ^ 2 + . . . + 17 ^ 2 + 16 ^ 2 - ( 15 ^ 2 + 14 ^ 2 + . . . . + 2 ^ 2 + 1 ^ 2 ) then we can add 1240 to get the answer . now grouping the terms above to get differences of squares , we have = ( 30 ^ 2 - 15 ^ 2 ) + ( 29 ^ 2 - 14 ^ 2 ) + . . . + ( 16 ^ 2 - 1 ^ 2 ) and factoring each of these using x ^ 2 - y ^ 2 = ( x + y ) ( x - y ) , we have = 45 * 15 + 43 * 15 + 41 * 15 + . . . + 17 * 15 = 15 ( 45 + 43 + 41 + . . . + 17 ) in brackets we have an equally spaced sum with fifteen terms , which we can evaluate using the familiar formula . so the above equals 15 * 15 * 62 / 2 = 6975 and adding back the 1270 , we get the answer of 8245 . ( ans d )"
Answer: d
Python program:
a = 30 + 1 
b = 30 * a
c = 2 * 30
d = c + 1 
e = b * d
f = 3 + 3 
g = e / f
h = g - 1270
Problem: last week vartan spent 15 percent of his wages on recreation . this week , his wages are 10 percent less than last week ʼ s wages and he spent 30 percent of his wages on recreation . the amount he spends on recreation this week is what percent of the amount he spent on recreation last week ?
Options: a ) 100 % , b ) 160 % , c ) 180 % , d ) 200 % , e ) 220 %
Rationale: say vartan ' s wages last week were $ 100 , so he spent 0.15 * 100 = $ 15 on recreation ; this week ' s wages is 0.9 * 100 = $ 90 , so he spends 0.3 * 90 = $ 27 on recreation ; 27 / 15 = 1.8 , hence the amount he spends on recreation this week is 180 % of the amount he spent on recreation last week : 15 * 1.8 = 27 . answer : c .
Answer: c
Python program:
a = 100 - 10
b = 30 * a
c = b / 15
Problem: the circumferences of two circles are 528 meters and 704 meters . find the difference between the areas of the larger and the smaller circles ?
Options: a ) 29963 sq m , b ) 28937 sq m , c ) 43162 sq m , d ) 27688 sq m , e ) 17248 sq m
Rationale: "let the radii of the smaller and the larger circles be s m and l m respectively . 2 ∏ s = 528 and 2 ∏ l = 704 s = 528 / 2 ∏ and l = 704 / 2 ∏ difference between the areas = ∏ l ^ 2 - ∏ s ^ 2 = ∏ { 264 ^ 2 / ∏ ^ 2 - 352 ^ 2 / ∏ ^ 2 } = 264 ^ 2 / ∏ - 352 ^ 2 / ∏ = ( 264 - 352 ) ( 264 + 352 ) / ∏ = ( 88 ) ( 616 ) / ( 22 / 7 ) = 17248 sq m answer : e"
Answer: e
Python program:
a = 2 * math.pi
b = 704 / a
c = circle_area - (
Problem: if 15 % of a is the same as 25 % of b , then a : b is :
Options: a ) 5 : 3 , b ) 4 : 3 , c ) 7 : 16 , d ) 12 : 17 , e ) 11 : 13
Rationale: "expl : 15 % of a i = 25 % of b = 15 a / 100 = 25 b / 100 = 5 / 3 = 5 : 3 answer : a"
Answer: a
Python program:
a = 25 / 100
b = 15 / 100
c = a / b
Problem: the ages of old and young total 48 . old is twice as old as young was when old was half as old as young will be when young is 3 times as old was when old was 3 times as old as young . how old is old ?
Options: a ) 23 , b ) 27 , c ) 12 , d ) 43 , e ) 37
Rationale: explanation : from the options itself , we can see that option c old = 30 young = 18 30 + 18 = 48 by reducing this years only by one before 6 years old = 24 ( half of young ) young = 12 ( twice of old ) answer : c
Answer: c
Python program:
a = 3 + 3 
b = a * 2
Problem: the percentage profit earned by selling an article for rs . 1520 is equal to the percentage loss incurred by selling the same article for rs . 1280 . at what price should the article be sold to make 25 % profit ?
Options: a ) 3000 , b ) 1230 , c ) 1750 , d ) 5600 , e ) 3400
Rationale: "c . p . be rs . x . then , ( 1520 - x ) / x * 100 = ( x - 1280 ) / x * 100 1520 - x = x - 1280 2 x = 2800 = > x = 1400 required s . p . = 125 % of rs . 1400 = 125 / 100 * 1400 = rs . 1750 . answer c"
Answer: c
Python program:
a = 100 + 25 
b = a / 100
c = 1520 + 1280 
d = c / 2
e = b * d
Problem: convert 2.5 hectares in ares
Options: a ) 130 ares . , b ) 160 ares . , c ) 180 ares . , d ) 230 ares . , e ) 250 ares .
Rationale: "2.5 hectares in ares 1 hectare = 100 ares therefore , 2.5 hectares = 2.5 × 100 ares = 250 ares . answer - e"
Answer: e
Python program:
a = 3 + 2 
b = a * 2
c = 3 + 2 
d = c * 2
e = b * d
f = e * 2
g = 3 + 2 
h = g * 2
i = 3 + 2 
j = i * 2
k = h * j
l = f / k