euclaise/mathqa_programs huggingface dataset:
Problem: there are 193 items that are members of set u . of these items , 47 are members of set b , 59 are not members of either of set a or set b , and 23 are members of both sets a and b . how many of the members of set u are members of set a ?
Options: a ) 72 , b ) 85 , c ) 94 , d ) 106 , e ) 108
Rationale: "you had the answer almost right . the x = 83 refers to only set a . however what ' s being asked is how many members are part of set a . this will include : 1 . only set a 2 . set a and set b so the answer is set a = 85 + set ab = 83 + 23 = 106 d"
Answer: d
Python program:
a = 193 - 59
b = a + 23 
c = b - 47
Problem: in a group of 800 people , 2 / 5 play at least one instrument , 96 play two or more . what is the probability that one student play exactly one instrument ?
Options: a ) 2 / 125 , b ) 3 / 125 , c ) c ) 2 / 25 , d ) 3 / 25 , e ) 7 / 25
Rationale: "p ( playing 2 or more instruments ) = 96 / 800 = 3 / 25 . then , the probability of playing exactly one instrument is given by : p ( playing 1 or more instruments ) - p ( playing 2 or more instruments ) = 2 / 5 - 3 / 25 = 7 / 25 . answer e ."
Answer: e
Python program:
a = 800 * 2
b = a / 5
c = b - 96
d = c / 800
Problem: a person can swim in still water at 16 km / h . if the speed of water 8 km / h , how many hours will the man take to swim back against the current for 12 km ?
Options: a ) 3 , b ) 1.5 , c ) 2.3 , d ) 1.8 , e ) 6
Rationale: "m = 16 s = 8 us = 16 - 8 = 8 d = 12 t = 12 / 8 = 1.5 answer : b"
Answer: b
Python program:
a = 16 - 8
b = 12 / a
Problem: the population of a town is 15000 . it decreases annually at the rate of 20 % p . a . what will be its population after 2 years ?
Options: a ) 4300 , b ) 4500 , c ) 5120 , d ) 9600 , e ) 5366
Rationale: 15000 × 80 / 100 × 80 / 100 = 9600 answer : d
Answer: d
Python program:
a = 20 / 100
b = 15000 * a
c = 15000 - b
d = 20 / 100
e = 15000 * d
f = 15000 - e
g = 20 / 100
h = f * g
i = c - h
Problem: what will be the compound interest on a sum of rs . 40,000 after 3 years at the rate of 11 p . c . p . a . ?
Options: a ) rs . 14705.24 , b ) rs . 14602.25 , c ) rs . 14822.26 , d ) rs . 14322.10 , e ) rs . 15350.23
Rationale: explanation : amount after 3 years = p ( 1 + r / 100 ) t = 40000 ( 1 + 11 / 100 ) 3 = 40000 ( 111 / 100 ) 3 = 40000 × 111 × 111 × 111 / 100 × 100 × 100 = 4 × 111 × 111 × 111 / 100 = 54705.24 compound interest = 54705.24 - 40000 = rs . 14705.24 answer : option a
Answer: a
Python program:
a = 4 * 100
b = a * 100
c = 11 / 100
d = 1 + c 
e = d ** 3
f = b * e
g = 4 * 100
h = g * 100
i = f - h
Problem: a train 640 m in length crosses a telegraph post in 16 seconds . the speed of the train is ?
Options: a ) 22 kmph , b ) 77 kmph , c ) 144 kmph , d ) 71 kmph , e ) 88 kmph
Rationale: "s = 640 / 16 * 18 / 5 = 144 kmph answer : c"
Answer: c
Python program:
a = 640 / 16
b = const_3_6 * a
Problem: if bill can buy 3 pairs of jeans and 2 shirts for $ 69 or 2 pairs of jeans and 3 shirts for $ 76 , how much does one shirt cost ?
Options: a ) $ 10 , b ) $ 12 , c ) $ 13.20 , d ) $ 15 , e ) $ 18
Rationale: "3 j + 2 s = 69 2 j + 3 s = 76 - - - - - - - - - - - - - - - - 5 j + 5 s = 145 - - - - ( divide by 5 ) - - - > j + s = 29 3 j + 2 s = j + 2 ( j + s ) = j + 58 = 69 - - - > j = 11 3 * 11 + 2 s = 69 33 + 2 s = 69 2 s = 36 s = 18 answer : e"
Answer: e
Python program:
a = 76 * 3
b = 69 * 2
c = a - b
d = 3 * 3
e = 2 * 2
f = d - e
g = c / f
Problem: in a certain deck of cards , each card has a positive integer written on it , in a multiplication game a child draws a card and multiplies the integer on the card with the next large integer . if the each possible product is between 15 and 270 , then the least and greatest integer on the card would be
Options: a ) 3 and 15 , b ) 3 and 20 , c ) 4 and 13 , d ) 4 and 16 , e ) 5 and 14
Rationale: "given : 15 < x ( x + 1 ) < 270 . now , it ' s better to test the answer choices here rather than to solve : if x = 4 then x ( x + 1 ) = 20 > 15 - - > so , the least value is 4 . test for the largest value : if x = 16 then x ( x + 1 ) = 16 * 17 = 272 > 270 answer : d ."
Answer: d
Python program:
a = math.sqrt(15)
b = math.floor(a)
c = b + 1 
d = c * 100
e = math.sqrt(270)
f = math.floor(e)
g = f - 1
h = d + g
Problem: a total of 320 chocolates were distributed among 100 boys and girls such that each boy received 2 chocolates and each girl received 3 chocolates . find the respective number of boys and girls ?
Options: a ) 10,10 , b ) 30,40 , c ) 70 , 50 , d ) 20,20 , e ) 10,15
Rationale: "let the number of boys be x . number of girls is 100 - x . total number of chocolates received by boys and girls = 2 x + 3 ( 100 - x ) = 320 = > 300 - x = 320 = > x = 20 . so , the number of boys or girls is 20 . answer : d"
Answer: d
Python program:
a = 3 * 100
b = 320 / 10
c = a - b
Problem: harry started a 7 - mile hike with a full 11 - cup canteen of water and finished the hike in 3 hours with 2 cup of water remaining in the canteen . if the canteen leaked at the rate of 1 cup per hour and harry drank 3 cups of water during the last mile , how many cups did he drink per mile during the first 6 miles of the hike ?
Options: a ) 2 / 6 , b ) 3 / 6 , c ) 4 / 6 , d ) 6 / 4 , e ) 5 / 6
Rationale: "no of cups leaked during the trip = 3 cups . no of cups harry drank = 6 cups . no of cups harry drank during the first 6 miles = 3 . drink / mile = 3 / 6 answer : b"
Answer: b
Python program:
a = 11 - 3
b = a - 3
c = b - 2
d = c / 6
Problem: there are 810 male and female participants in a meeting . half the female participants and one - quarterof the male participants are democrats . one - third of all the participants are democrats . how many of the democrats are female ?
Options: a ) 75 , b ) 100 , c ) 125 , d ) 135 , e ) 225
Rationale: "let m be the number of male participants and f be the number of female articipants in the meeting . thetotal number of participants is given as 810 . hence , we have m + f = 810 now , we have that half the female participants and one - quarter of the male participants are democrats . let d equal the number of the democrats . then we have the equation f / 2 + m / 4 = d now , we have that one - third of the total participants are democrats . hence , we have the equation d = 810 / 3 = 270 solving the three equations yields the solution f = 270 , m = 540 , and d = 270 . the number of female democratic participants equals half the female participants equals 270 / 2 = 135 . answer : d"
Answer: d
Python program:
a = 810 / 3
b = a * 4
c = b - 810
d = c / 2
Problem: a square is drawn by joining the mid points of the sides of a given square in the same way and this process continues indefinitely . if a side of the first square is 4 cm , determine the sum of the areas all the square .
Options: a ) 32 cm 2
b ) 16 cm 2
c ) 20 cm 2
d ) 64 cm 2
e ) none of these
Rationale: solution : side of the first square is 4 cm . side of second square = 2 √ 2 cm . side of third square = 2 cm . and so on . i . e . 4 , 2 √ , 2 , √ 2 , 1 . . . . . . thus , area of these square will be , = 16 , 8 , 4 , 2 , 1 , 1 / 2 . . . . . . . hence , sum of the area of first , second , third square . . . . . . = 16 + 8 + 4 + 2 + 1 + . . . . . = [ 16 / { 1 - ( 1 / 2 ) } ] = 32 cm 2 . answer : option a
Answer: a
Python program:
a = 4 ** 2
b = 1 / 2
c = a / b
Problem: find the greatest number of 5 digits which is exactly divisible by 12 , 15 and 18 ?
Options: a ) a ) 13050 , b ) b ) 12960 , c ) c ) 10025 , d ) d ) 11080 , e ) e ) 12080
Rationale: the largest five digit numbers are 13050 , 12960,12080 13050 is not divisible by 12 12960 is divisible by 18 , 12 and 15 answer : b
Answer: b
Python program:
a = 12 * 15
b = a * 18
c = 4 * b
Problem: kim has 4 pairs of shoes ; each pair is a different color . if kim randomly selects 2 shoes without replacement from the 8 shoes , what is the probability that she will select 2 shoes of the same color ?
Options: a ) 1 / 7 , b ) 1 / 8 , c ) 1 / 9 , d ) 1 / 10 , e ) 1 / 25
Rationale: "total pairs = 8 c 2 = 28 ; same color pairs = 4 c 1 * 1 c 1 = 4 ; prob = 1 / 7 ans a"
Answer: a
Python program:
a = math.comb(8, 2)
b = 4 / a
Problem: the number 110 can be written as the sum of the squares of 3 different positive integers . what is the sum of these 3 integers ?
Options: a ) 18 , b ) 16 , c ) 15 , d ) 14 , e ) 13
Rationale: "7 ^ 2 + 5 ^ 2 + 6 ^ 2 = 49 + 25 + 36 = 110 7 + 5 + 6 = 18 hence answer is a"
Answer: a
Python program:
a = 4 + 3 
b = 3 + 2 
c = a + b 
d = c + 3
Problem: in an examination , 20 % of total students failed in hindi , 70 % failed in english and 10 % in both . the percentage of these who passed in both the subjects is :
Options: a ) 10 % , b ) 20 % , c ) 30 % , d ) 40 % , e ) 50 %
Rationale: "pass percentage = 100 - ( 20 + 70 - 10 ) = 100 - 80 = 20 answer : b"
Answer: b
Python program:
a = 20 + 70 
b = a - 10
c = 100 - b
Problem: the tax on a commodity is diminished by 25 % and its consumption increased by 13 % . the effect on revenue is ?
Options: a ) 18 , b ) 16 , c ) 10 , d ) 15 , e ) 14
Rationale: "100 * 100 = 10000 75 * 113 = 8475 - - - - - - - - - - - 10000 - - - - - - - - - - - 1525 100 - - - - - - - - - - - ? = > 15 % decrease answer : d"
Answer: d
Python program:
a = 13 / 100
b = 1 + a 
c = 25 / 100
d = 1 - c
e = b * d
f = e * 100
g = 100 - f
Problem: the famous denali star train starts from anchorge & travels towards fair banksat speed 50 mph . after some time another train glacier discovery train ( at parallel track ) at fair banks and moves towards anchorge at a speed of 70 mph . both the trains denali star & glacier discovery have a length 1 / 6 miles each . after the trains meet how many seconds will faster train take to overtake the slower one ?
Options: a ) 10 sec , b ) 11 sec , c ) 12 sec , d ) 13 sec , e ) 14 sec
Rationale: total distance = ( 1 / 6 ) + ( 1 / 6 ) = 1 / 3 miles relative speed = ( 50 + 70 ) mph = 120 mph time taken = ( 1 / 3 ) / ( 120 ) hours = 10 seconds answer : a
Answer: a
Python program:
a = 1 / 6
b = 1 / 6
c = a + b 
d = 50 + 70 
e = c / d
f = e * 3600
Problem: how many positive integers between 1 and 300 are there such that they are multiples of 21 ?
Options: a ) 14 , b ) 16 , c ) 17 , d ) 13 , e ) 15
Rationale: "multiples of 21 = 21 , 42,63 , - - - - - 294 number of multiples of 21 = > 21 * 14 = 294 answer is a"
Answer: a
Python program:
a = 300 - 1
b = a / 21
Problem: if p , q , and r are distinct positive digits and the product of the two - digit integers pq and pr is 221 , what is the sum of the digits p , q , and r ?
Options: a ) 5 , b ) 11 , c ) 13 , d ) 21 , e ) 23
Rationale: factor out 221 221 = 13 * 17 thus pq = 13 & pr = 17 or vice versa thus p = 1 , q = 3 & r = 7 sum = 1 + 3 + 7 = 11 answer : b
Answer: b
Python program:
a = 1 + 12 
b = 221 / a
c = reminder + (
Problem: p and q invested in a business . the profit earned was divided in the ratio 3 : 4 . if p invested rs 50000 , the amount invested by q is
Options: a ) 30000 , b ) 66666 , c ) 40000 , d ) 20000 , e ) 60000
Rationale: "let the amount invested by q = q 50000 : q = 3 : 4 ⇒ 50000 × 4 = 3 q ⇒ q = ( 50000 × 4 ) / 3 = 66666 answer is b ."
Answer: b
Python program:
a = 50000 / 3
b = a * 4
Problem: the end of a blade on an airplane propeller is 20 feet from the center . if the propeller spins at the rate of 1,320 revolutions per second , how many miles will the tip of the blade travel in one minute ? ( 1 mile = 5,280 feet )
Options: a ) 200 π , b ) 240 π , c ) 600 π , d ) 480 π , e ) 1,200 π
Rationale: "distance traveled in 1 revolution = 2 π r = 2 π 20 / 5280 revolutions in one second = 1320 revolutions in 60 seconds ( one minute ) = 1320 * 60 total distance traveled = total revolutions * distance traveled in one revolution 1320 * 60 * 2 π 20 / 5280 = 600 π c is the answer"
Answer: c
Python program:
a = 2 * 100
b = 2 + 3 
c = b * 1000
d = a + c 
e = 20 / d
f = e * 2
g = 2 * 10
h = 2 + g 
i = 3 + 4 
j = h / i
k = f * j
l = k * 1
m = l * const_60
Problem: car a runs at the speed of 65 km / hr & reaches its destination in 8 hr . car b runs at the speed of 70 km / h & reaches its destination in 4 h . what is the respective ratio of distances covered by car a & car b ?
Options: a ) 10 : 4 , b ) 10 : 7 , c ) 13 : 7 , d ) 14 : 6 , e ) 13 : 9
Rationale: "sol . distance travelled by car a = 65 × 8 = 520 km distance travelled by car b = 70 × 4 = 280 km ratio = 520 / 280 = 13 : 7 c"
Answer: c
Python program:
a = 65 * 8
b = 70 * 4
c = a / b
Problem: two cards are drawn together from a pack of 52 cards . the probability that one is a spade and one is a heart , is :
Options: a ) 2 / 109 , b ) 7 / 109 , c ) 8 / 223 , d ) 14 / 263 , e ) 13 / 102
Rationale: "n ( s ) = ( 52 x 51 ) / ( 2 x 1 ) = 1326 . let e = event of getting 1 spade and 1 heart . n ( e ) = number of ways of choosing 1 spade out of 13 and 1 heart out of 13 = ( 13 x 13 ) = 169 . p ( e ) = n ( e ) / n ( s ) 169 / 1326 = 13 / 102 answer e"
Answer: e
Python program:
a = 52 / 4
b = 52 / 4
c = a * b
d = 52 * 52
e = c / d
f = e * 2
Problem: how many positive integers less than 50 are there such that they are multiples of 9 ?
Options: a ) 5 , b ) 6 , c ) 4 , d ) 8 , e ) 3
Rationale: "number of multiples of 9 = > 45 - 9 / 9 + 1 = 5 answer is a"
Answer: a
Python program:
a = 4 + 9 
b = a - 1
c = math.factorial(b)
d = math.factorial(9)
e = 4 - 1
f = math.factorial(e)
g = d * f
h = c / g
Problem: pat , kate and mark charged a total of 189 hours to a certain project . if pat charged twice as much time to the project as kate and 1 / 3 as much times as mark , how many more hours did mark charge to the project than kate .
Options: a ) 18 , b ) 36 , c ) 72 , d ) 90 , e ) 105
Rationale: "let kate charge for x hours , then pat charged for 2 x and mat - for 6 x . so , 2 x + 6 x + x = 189 - total hours charged for , x = 21 . mat charged 6 x - x or 5 x for more hours than kate , or for 105 hours . e is correct"
Answer: e
Python program:
a = 1 + 2 
b = 2 * 3
c = a + b 
d = 189 / c
e = 2 * 3
f = e - 1
g = d * f
Problem: a part of certain sum of money is invested at 9 % per annum and the rest at 18 % per annum , if the interest earned in each case for the same period is equal , then ratio of the sums invested is ?
Options: a ) 4 : 2 , b ) 2 : 1 , c ) 4 : 3 , d ) 4 : 0 , e ) 4 : 9
Rationale: "18 : 9 = 2 : 1 answer : b"
Answer: b
Python program:
a = 18 / 100
b = a * 9
Problem: find the amount on rs . 5000 in 2 years , the rate of interest being 10 % per first year and 12 % for the second year ?
Options: a ) 3377 , b ) 6160 , c ) 5460 , d ) 1976 , e ) 1671
Rationale: 5000 * 110 / 100 * 112 / 100 = > 6160 answer : b
Answer: b
Python program:
a = 100 + 10 
b = 5000 * a
c = b / 100
d = 100 + 12 
e = c * d
f = e / 100
Problem: ray writes a two digit number . he sees that the number exceeds 4 times the sum of its digits by 3 . if the number is increased by 18 , the result is the same as the number formed by reversing the digits . find the sum of the digits of the number .
Options: a ) 2 , b ) 8 , c ) 9 , d ) 3 , e ) 5
Rationale: "let the two digit number be xy . 4 ( x + y ) + 3 = 10 x + y - - - ( 1 ) 10 x + y + 18 = 10 y + x - - - ( 2 ) solving 1 st equation , 4 x + 4 y + 3 = 10 x + y 3 y + 3 = 6 x 6 x – 3 y = 3 therefore , 2 x – y = 1 - - - ( 3 ) solving 2 nd equation , xy + 18 = yx ⇒ ⇒ ( 10 x + b ) + 18 = 10 y + x ⇒ ⇒ 18 = 9 y – 9 x ⇒ ⇒ 2 = y – x we get y - x = 2 - - - ( 4 ) adding 3 and 4 , we get x = 3 by substituting in ( 4 ) , we get y = 5 so the given number is 35 . sum of the digits = 8 . answer : b"
Answer: b
Python program:
a = 18 - 3
b = a / 3
Problem: 1000 men have provisions for 15 days . if 200 more men join them , for how many days will the provisions last now ?
Options: a ) 10.5 , b ) 12.5 , c ) 13.5 , d ) 11.5 , e ) 11
Rationale: "1000 * 15 = 1200 * x x = 12.5 answer b"
Answer: b
Python program:
a = 15 * 1000
b = 1000 + 200 
c = a / b
Problem: a circle graph shows how the budget of a certain company was spent : 15 percent for transportation , 9 percent for research and development , 5 percent for utilities , 4 percent for equipment , 2 percent for supplies , and the remainder for salaries . if the area of each sector of the graph is proportional to the percent of the budget it represents , how many degrees of the circle are used to represent salaries ?
Options: a ) 216 ° , b ) 222 ° , c ) 228 ° , d ) 234 ° , e ) 240 °
Rationale: "the percent of the budget for salaries is 100 - ( 15 + 9 + 5 + 4 + 2 ) = 65 % 100 % of the circle is 360 degrees . then ( 65 % / 100 % ) * 360 = 234 degrees the answer is d ."
Answer: d
Python program:
a = 15 + 9 
b = a + 5 
c = b + 4 
d = c + 2 
e = d * 360
f = e / 100
g = 360 - f
Problem: the area of a rectangular field is equal to 750 square meters . its perimeter is equal to 110 meters . find the width of this rectangle .
Options: a ) 5
b ) 10
c ) 15
d ) 20
e ) 25
Rationale: l * w = 750 : area , l is the length and w is the width . 2 l + 2 w = 110 : perimeter l = 55 - w : solve for l ( 55 - w ) * w = 750 : substitute in the area equation w = 25 and l = 30 correct answer e
Answer: e
Python program:
a = 110 / 2
b = 110 / 2
c = 110 / 2
d = b * c
e = 4 * 750
f = d - e
g = math.sqrt(f)
h = a - g
i = h / 2
Problem: a number increased by 10 % gives 660 . the number is ?
Options: a ) 200 , b ) 300 , c ) 500 , d ) 600 , e ) 400
Rationale: "formula = total = 100 % , increase = ` ` + ' ' decrease = ` ` - ' ' a number means = 100 % that same number increased by 10 % = 110 % 110 % - - - - - - - > 660 ( 110 ã — 6 = 660 ) 100 % - - - - - - - > 600 ( 100 ã — 6 = 600 ) option ' d '"
Answer: d
Python program:
a = 10 / 100
b = 1 + a 
c = 660 / b
Problem: working simultaneously and independently at an identical constant rate , 10 machines of a certain type can produce a total of x units of product p in 4 days . how many of these machines , working simultaneously and independently at this constant rate , can produce a total of 3 x units of product p in 6 days ?
Options: a ) 14 , b ) 15 , c ) 18 , d ) 20 , e ) 22
Rationale: "the rate of 10 machines is rate = job / time = x / 4 units per day - - > the rate of 1 machine 1 / 10 * ( x / 4 ) = x / 40 units per day ; now , again as { time } * { combined rate } = { job done } then 6 * ( m * x / 40 ) = 3 x - - > m = 20 . answer : d ."
Answer: d
Python program:
a = 10 * 3
b = 4 / 6
c = a * b
Problem: the average of first five prime numbers greater than 3 is ?
Options: a ) 32.2 , b ) 10.6 , c ) 32.3 , d ) 32.8 , e ) 32.4
Rationale: "5 + 7 + 11 + 13 + 17 = 53 / 5 = 10.60 answer = b"
Answer: b
Python program:
a = 3 + 1
Problem: the length of a train and that of a platform are equal . if with a speed of 90 k / hr , the train crosses the platform in one minute , then the length of the train ( in meters ) is ?
Options: a ) 299 , b ) 266 , c ) 299 , d ) 750 , e ) 261
Rationale: "speed = [ 90 * 5 / 18 ] m / sec = 25 m / sec ; time = 1 min . = 60 sec . let the length of the train and that of the platform be x meters . then , 2 x / 60 = 25 è x = 25 * 60 / 2 = 750 answer : d"
Answer: d
Python program:
a = 90 * 1000
b = const_60 / 1
c = a / b
d = c / 2
Problem: the average age of students of a class is 15.7 years . the average age of boys in the class is 16.4 years and that of the girls is 15.4 years . the ration of the number of boys to the number of girls in the class is ?
Options: a ) 3 : 7 , b ) 7 : 3 , c ) 2 : 5 , d ) 2 : 1 , e ) 2 : 4
Rationale: "let the ratio be k : 1 . then , k * 16.4 + 1 * 15.4 = ( k + 1 ) * 15.7 = ( 16.4 - 15.7 ) k = ( 15.7 - 15.4 ) = k = 0.3 / 0.7 = 3 / 7 required ratio = 3 / 7 : 1 = 3 : 7 . answer : a"
Answer: a
Python program:
a = 15 - 7
b = 16 - 4
c = a / b
Problem: in the rectangular coordinate system , points ( 5 , 0 ) and ( – 5 , 0 ) both lie on circle c . what is the maximum possible value of the radius of c ?
Options: a ) 2 , b ) 4 , c ) 8 , d ) 16 , e ) none of the above
Rationale: "the answer is b it takes 3 distinct points to define a circle . only 2 are given here . the two points essentially identify a single chord of the circle c . since no other information is provided , however , the radius of the circle can essentially be anything . all this information tell us is that the radius isgreater 5 b"
Answer: b
Python program:
a = 5 ** 2
b = math.sqrt(a)
Problem: train a leaves the station traveling at 30 miles per hour . two hours later train в leaves the same station traveling in the same direction at 42 miles per hour . how many miles from the station was train a overtaken by train b ?
Options: a ) 150 , b ) 170 , c ) 190 , d ) 210 , e ) 230
Rationale: "after two hours , train a is ahead by 60 miles . train b can catch up at a rate of 12 miles per hour . the time to catch up is 60 / 12 = 5 hours . in 5 hours , train a travels another 30 * 5 = 150 miles for a total of 210 miles . the answer is d ."
Answer: d
Python program:
a = 30 * 2
b = 42 - 30
c = a / b
d = c * 42
Problem: what sum of money will produce rs . 70 as simple interest in 5 years at 3 1 / 2 percent ?
Options: a ) 400 , b ) 500 , c ) 367 , d ) 368 , e ) 339
Rationale: "70 = ( p * 5 * 7 / 2 ) / 100 p = 400 answer : a"
Answer: a
Python program:
a = 1 / 2
b = 3 + a 
c = 5 * b
d = c / 100
e = 70 / d
Problem: what is the hcf of 2 / 3 , 5 / 9 and 6 / 5
Options: a ) 1 / 45 , b ) 2 / 45 , c ) 4 / 15 , d ) 8 / 45 , e ) 9 / 45
Rationale: "explanation : hcf of fractions = hcf of numerators / lcm of denominators = ( hcf of 2 , 5 , 6 ) / ( lcm of 3 , 9 , 5 ) = 1 / 45 answer : option a"
Answer: a
Python program:
a = 2 / 5
Problem: the h . c . f . of two numbers is 38 and the other two factors of their l . c . m . are 12 and 10 . the larger of the two numbers is :
Options: a ) 678 , b ) 456 , c ) 234 , d ) 476 , e ) 432
Rationale: ": explanation : clearly , the numbers are ( 38 x 12 ) and ( 38 x 10 ) . { \ color { blue } \ therefore } larger number = ( 38 x 12 ) = 456 . answer : b ) 456"
Answer: b
Python program:
a = 38 * 10
Problem: robert ate 9 chocolates , nickel ate 2 chocolates . how many more chocolates did robert ate than nickel ?
Options: a ) a ) 4 , b ) b ) 7 , c ) c ) 9 , d ) d ) 5 , e ) e ) 2
Rationale: 9 - 2 = 7 . answer is b
Answer: b
Python program:
a = 9 - 2
Problem: the area of a circle is increased by 800 % . by what percent has the diameter of the circle increased ?
Options: a ) 100 % , b ) 200 % , c ) 300 % , d ) 600 % , e ) 800 %
Rationale: "a diameter of 2 it ' s radius = 1 it ' s area = ( 1 ^ 2 ) pi = 1 pi answer a : if we increase that diameter 100 % , we have . . . . a diameter of 4 it ' s radius = 2 it ' s area = ( 2 ^ 2 ) pi = 4 pi this area has increased ( 4 pi - 1 pi ) / 1 pi = 3 pi / 1 pi = 3 = 300 % answer b : if we increase the diameter 200 % , we have . . . a diameter of 6 it ' s area = 3 it ' s area = ( 3 ^ 2 ) pi = 9 pi this area has increased ( 9 pi - 1 pi ) / 1 pi = 8 pi / 1 pi = 8 = 800 % answer : e"
Answer: e
Python program:
a = 2 / 2
b = 100 * a
Problem: 3 boys are ages 4 , 6 and 7 respectively . 3 girls are ages 5 , 8 and 9 , respectively . if two of the boys and two of the girls are randomly selected and the sum of the selected children ' s ages is q , what is the difference between the probability that q is even and the probability that q is odd ?
Options: a ) 1 / 9 , b ) 1 / 6 , c ) 2 / 9 , d ) 1 / 4 , e ) 1 / 2
Rationale: age of boys q : 4 , 6 , 7 sum of ages taken 2 at a time : 10 , 13,11 ages of girls : 5 , 8 , 9 sum of ages taken 2 at a time : 13 , 17,14 9 combinations of sum between sets ( 10 , 12,11 ) ( 13 , 17,14 ) = 23 , 27,24 - 16 , 30,17 - 24 , 28,25 prob ( even ) = 5 / 9 prob ( odd ) = 4 / 9 answer = 5 / 9 - 4 / 9 = 1 / 9
Answer: a
Python program:
a = 5 / 9
b = 4 / 9
c = a - b
Problem: if 4 xz + yw = 4 and xw + yz = 8 , what is the value of the expression ( 2 x + y ) ( 2 z + w ) ?
Options: a ) 22 , b ) 20 , c ) 24 , d ) 26 , e ) 28
Rationale: ( 2 x + y ) * ( 2 z + w ) = 4 + 2 ( 8 ) = 20 answer : b
Answer: b
Python program:
a = 8 * 2
b = 4 + a
Problem: some of 50 % - intensity red paint is replaced with 25 % solution of red paint such that the new paint intensity is 40 % . what fraction of the original paint was replaced ?
Options: a ) 1 / 30 , b ) 1 / 5 , c ) 2 / 5 , d ) 3 / 4 , e ) 4 / 5
Rationale: "40 % is 15 % - points above 25 % and 10 % - points below 50 % . thus the ratio of 25 % - solution to 50 % - solution is 2 : 3 . 2 / 5 of the original paint was replaced . the answer is c ."
Answer: c
Python program:
a = 40 / 100
b = 50 / 100
c = a - b
d = 25 / 100
e = 50 / 100
f = d - e
g = c / f