options stringlengths 37 300 | correct stringclasses 5
values | annotated_formula stringlengths 7 727 | problem stringlengths 5 967 | rationale stringlengths 1 2.74k | program stringlengths 10 646 |
|---|---|---|---|---|---|
a ) 20 , b ) 150 , c ) 225 , d ) 300 , e ) 304 | e | subtract(multiply(multiply(add(4, const_1), add(4, const_1)), multiply(4, 4)), multiply(multiply(add(4, const_1), add(4, const_1)), 4)) | how many 4 digit numbers are there , if it is known that the first digit is even , the second is odd , the third is prime , the fourth ( units digit ) is divisible by 3 , and the digit 5 can be used only once ? | "4 options for the first digit : 2 , 4 , 6 , 8 ; 5 options for the second digit : 1 , 3 , 5 , 7 , 9 ; 4 options for the third digit : 2 , 3 , 5 , 7 ; 4 options for the fourth digit : 0 , 3 , 6 , 9 . four digit # possible without the restriction ( about the digit 2 ) : 4 * 5 * 4 * 4 = 320 numbers with five 5 - s , 5 x 5 x 4 * 1 * 1 * 4 = 16 . thus there are 320 - 16 = 304 such numbers . answer : e ." | a = 4 + 1
b = 4 + 1
c = a * b
d = 4 * 4
e = c * d
f = 4 + 1
g = 4 + 1
h = f * g
i = h * 4
j = e - i
|
a ) 2 / 35 , b ) 2 / 3 , c ) 6 / 35 , d ) 5 / 7 , e ) 7 / 5 | c | multiply(divide(6, 7), divide(1, 5)) | two brothers ram and ravi appeared for an exam . the probability of selection of ram is 6 / 7 and that of ravi is 1 / 5 . find the probability that both of them are selected . | "let a be the event that ram is selected and b is the event that ravi is selected . p ( a ) = 6 / 7 p ( b ) = 1 / 5 let c be the event that both are selected . p ( c ) = p ( a ) x p ( b ) as a and b are independent events : = 6 / 7 x 1 / 5 = 6 / 35 answer : c" | a = 6 / 7
b = 1 / 5
c = a * b
|
a ) - 16.16 % , b ) - 15.15 % , c ) - 14.14 % , d ) - 13.13 % , e ) - 12.12 % | c | subtract(const_100, multiply(multiply(add(const_1, divide(6, const_100)), subtract(const_1, divide(19, const_100))), const_100)) | a volunteer organization is recruiting new members . in the fall they manage to increase their number by 6 % . by the spring however membership falls by 19 % . what is the total change in percentage from fall to spring ? | "( 100 % + 6 % ) * ( 100 % - 19 % ) = 1.06 * . 81 = 0.8586 . 1 - 0.8586 = 14.14 % lost = - 14.14 % the answer is c the organization has lost 14.14 % of its total volunteers from fall to spring ." | a = 6 / 100
b = 1 + a
c = 19 / 100
d = 1 - c
e = b * d
f = e * 100
g = 100 - f
|
a ) 19 , b ) 20 , c ) 22 , d ) 21 , e ) 19.5 | b | multiply(divide(subtract(31, 1), add(1, 2)), 2) | one hour after yolanda started walking from x to y , a distance of 31 miles , bob started walking along the same road from y to x . if yolanda Γ’ s walking rate was 1 miles per hour and bob Γ’ s was 2 miles per hour , how many miles had bob walked when they met ? | "let t be the number of hours that bob had walked when he met yolanda . then , when they met , bob had walked 4 t miles and yolanda had walked ( t + 1 ) miles . these distances must sum to 31 miles , so 2 t + ( t + 1 ) = 31 , which may be solved for t as follows 2 t + ( t + 1 ) = 31 2 t + t + 1 = 31 3 t = 30 t = 10 ( hours ) therefore , bob had walked 2 t = 2 ( 10 ) = 20 miles when they met . the best answer is b ." | a = 31 - 1
b = 1 + 2
c = a / b
d = c * 2
|
a ) 333 , b ) 200 , c ) 288 , d ) 210 , e ) 1999 | d | subtract(divide(divide(5565, 26.50), const_2), multiply(const_2, 20)) | the length of a rectangular plot is 20 metres more than its breadth . if the cost of fencing the plot @ rs . 26.50 per metre is rs . 5565 , what is the length of the plot in metres ? | "let length of plot = l meters , then breadth = l - 20 meters and perimeter = 2 [ l + l - 20 ] = [ 4 l - 40 ] meters [ 4 l - 40 ] * 26.50 = 5565 [ 4 l - 40 ] = 5565 / 26.50 = 210 4 l = 250 l = 250 / 4 = 62.5 meters . answer : d" | a = 5565 / 26
b = a / 2
c = 2 * 20
d = b - c
|
['a ) 9', 'b ) 18 β 3 β 3', 'c ) 18', 'd ) 18 + 3 β 3', 'e ) 27'] | c | multiply(3, divide(multiply(multiply(3, const_2), subtract(const_3, sqrt(const_3))), subtract(const_3, sqrt(const_3)))) | if the perimeter of Ξ΄ acd is 9 + 3 β 3 , what is the perimeter of equilateral triangle Ξ΄ abc ? | the altitude of an equilateral triangle is side * β 3 / 2 . as perimeter of triangle acd is 9 + 3 β 3 , ac + cd + ad = ( side + side / 2 + side * β 3 / 2 ) = 9 + 3 β 3 or side = 6 . perimeter of equilateral triangle , abc is 3 ( side ) or 18 . answer : ( optionc ) | a = 3 * 2
b = math.sqrt(3)
c = 3 - b
d = a * c
e = math.sqrt(3)
f = 3 - e
g = d / f
h = 3 * g
|
a ) 41 , b ) 28 , c ) 43 , d ) 44 , e ) 45 | b | divide(factorial(8), multiply(factorial(subtract(8, const_2)), factorial(const_2))) | if 8 boys meet at a reunion and each boy shakes hands exactly once with each of the others , then what is the total number of handshakes | "n ( n - 1 ) / 2 = 8 * 7 / 2 = 28 answer : b" | a = math.factorial(8)
b = 8 - 2
c = math.factorial(b)
d = math.factorial(2)
e = c * d
f = a / e
|
a ) 45 hours , b ) 47 hours , c ) 48 hours , d ) 50 hours , e ) none | c | add(divide(subtract(25, 20), multiply(divide(20, 40), divide(add(const_100, 25), const_100))), 40) | a man ' s basic pay for a 40 hour week is rs . 20 . overtime is paid for at 25 % above the basic rate . in a certain week he worked overtime and his total wage was rs . 25 . he therefore worked for a total of : | explanation : basic rate per hour = rs . ( 20 / 40 ) = rs . 1 / 2 overtime per hour = 125 % of rs . 1 / 2 = 125 / 100 Γ 1 / 2 = rs . 5 / 8 suppose he worked x hours overtime . then , 20 + 5 / 8 x = 25 or 5 / 8 x = 5 x = 5 Γ 8 / 5 = 8 hours so he worked in all for ( 40 + 8 ) hours = 48 hours . correct option : c | a = 25 - 20
b = 20 / 40
c = 100 + 25
d = c / 100
e = b * d
f = a / e
g = f + 40
|
a ) 2 days , b ) 5 1 / 2 days , c ) 6 1 / 2 days , d ) 7 1 / 2 days , e ) 10 days | b | add(multiply(15, 3), divide(15, 3)) | a can complete a work in 15 days and b can do the same work in 7 days . if a after doing 3 days , leaves the work , find in how many days b will do the remaining work ? | "the required answer = ( 15 - 3 ) * 7 / 15 = 84 / 15 = 5 1 / 2 days answer is b" | a = 15 * 3
b = 15 / 3
c = a + b
|
a ) 13 , b ) 14 , c ) 15 , d ) 16 , e ) 20 | e | divide(factorial(subtract(add(const_4, 01), const_1)), multiply(factorial(01), factorial(subtract(const_4, const_1)))) | how many positive integers less than 60 have a reminder 01 when divided by 3 ? | "1 also gives the remainder of 1 when divided by 3 . so , there are total of 20 numbers . answer : e ." | a = 4 + 1
b = a - 1
c = math.factorial(b)
d = math.factorial(1)
e = 4 - 1
f = math.factorial(e)
g = d * f
h = c / g
|
a ) 13.8 , b ) 14.1 , c ) 14.4 , d ) 14.6 , e ) 14.8 | c | subtract(inverse(add(inverse(multiply(add(add(const_2, const_3), const_4), const_60)), inverse(add(multiply(const_3, const_4), const_3)))), divide(subtract(multiply(multiply(const_4, const_4), const_3), const_2), multiply(const_100, const_100))) | it takes six minutes to load a certain video on a cellphone , and fifteen seconds to load that same video on a laptop . if the two devices were connected so that they operated in concert at their respective rates , how many seconds would it take them to load the video ? | "the laptop can load the video at a rate of 1 / 15 of the video per second . the phone can load the video at a rate of 1 / ( 60 * 6 ) = 1 / 360 of the video per second . the combined rate is 1 / 15 + 1 / 360 = 25 / 360 of the video per second . the time required to load the video is 360 / 25 = 14.4 seconds . the answer is c ." | a = 2 + 3
b = a + 4
c = b * const_60
d = 1/(c)
e = 3 * 4
f = e + 3
g = 1/(f)
h = d + g
i = 1/(h)
j = 4 * 4
k = j * 3
l = k - 2
m = 100 * 100
n = l / m
o = i - n
|
a ) 122 , b ) 132 , c ) 142 , d ) 152 , e ) 162 | b | divide(add(divide(multiply(1200, 10), const_100), 1200), multiply(divide(1200, const_100), const_2)) | a computer store offers employees a 10 % discount off the retail price . if the store purchased a computer from the manufacturer for $ 1200 dollars and marked up the price 10 % to the final retail price , how much would an employee save if he purchased the computer at the employee discount ( 10 % off retail price ) as opposed to the final retail price . | "cost price = 1200 profit = 10 % = 10 % of 1200 = 120 selling price = cp + profit sp = 1320 a discount of 10 % to employees means 10 % off on 1320 so 10 % of 1320 = 132 ans b" | a = 1200 * 10
b = a / 100
c = b + 1200
d = 1200 / 100
e = d * 2
f = c / e
|
a ) 15 , b ) 18 , c ) 21 , d ) 24 , e ) 27 | e | divide(divide(12, subtract(const_1, divide(const_1, 3))), subtract(const_1, divide(const_1, 3))) | for all real numbers v , an operation is defined by the equation v * = v - v / 3 . if ( v * ) * = 12 , then v = | ( v * ) * = ( v - v / 3 ) - ( v - v / 3 ) / 3 12 = 2 v / 3 - 2 v / 9 = 4 v / 9 v = 27 the answer is e . | a = 1 / 3
b = 1 - a
c = 12 / b
d = 1 / 3
e = 1 - d
f = c / e
|
a ) 287 m , b ) 704 m , c ) 168 m , d ) 278 m , e ) 107 m | b | divide(multiply(multiply(multiply(divide(add(multiply(add(const_3, const_4), const_3), const_1), add(const_3, const_4)), 22.4), const_2), 500), const_100) | the radius of a wheel is 22.4 cm . what is the distance covered by the wheel in making 500 resolutions . | "in one resolution , the distance covered by the wheel is its own circumference . distance covered in 500 resolutions . = 500 * 2 * 22 / 7 * 22.4 = 70400 cm = 704 m answer : b" | a = 3 + 4
b = a * 3
c = b + 1
d = 3 + 4
e = c / d
f = e * 22
g = f * 2
h = g * 500
i = h / 100
|
a ) 40 % , b ) 50 % , c ) 60 % , d ) 70 % , e ) 80 % | d | multiply(divide(subtract(40, subtract(60, multiply(divide(subtract(const_100, 20), const_100), subtract(const_100, 40)))), 40), const_100) | 20 percent of the women in a college class are science majors , and the non - science majors make up 60 % of the class . what percentage of the men are science majors if 40 % of the class are men ? | science majors make up 0.4 of the class . 60 % of the class are women and 0.2 * 0.6 = 0.12 of the class are female science majors . then 0.28 of the class are male science majors . 0.4 x = 0.28 x = 0.7 = 70 % the answer is d . | a = 100 - 20
b = a / 100
c = 100 - 40
d = b * c
e = 60 - d
f = 40 - e
g = f / 40
h = g * 100
|
a ) s . 1991 , b ) s . 2991 , c ) s . 3991 , d ) s . 4991 , e ) s . 6991 | e | subtract(multiply(add(5, const_1), 8500), add(add(add(add(8435, 8927), 8855), 9230), 8562)) | a grocer has a sale of rs . 8435 , rs . 8927 , rs . 8855 , rs . 9230 and rs . 8562 for 5 consecutive months . how much sale must he have in the sixth month so that he gets an average sale of rs . 8500 ? | "explanation : total sale for 5 months = rs . ( 8435 + 8927 + 8855 + 9230 + 8562 ) = rs . 44009 . required sale = rs . [ ( 8500 x 6 ) Γ’ β¬ β 44009 ] = rs . ( 51000 Γ’ β¬ β 44009 ) = rs . 6991 . answer e" | a = 5 + 1
b = a * 8500
c = 8435 + 8927
d = c + 8855
e = d + 9230
f = e + 8562
g = b - f
|
a ) 11 , b ) 10 , c ) 8 , d ) 12 , e ) 15 | c | add(8, divide(subtract(110, 20), add(25, 20))) | two stations a and b are 110 km apart on a straight line . one train starts from a at 5 a . m . and travels towards b at 20 kmph . another train starts from b at 8 a . m . and travels towards a at a speed of 25 kmph . at what time will they meet ? | "suppose they meet x hours after 5 a . m . distance covered by a in x hours = 20 x km . distance covered by b in ( x - 1 ) hours = 25 ( x - 1 ) km . therefore 20 x + 25 ( x - 1 ) = 110 45 x = 135 x = 3 . so , they meet at 8 a . m . answer : c" | a = 110 - 20
b = 25 + 20
c = a / b
d = 8 + c
|
a ) 8.07 , b ) 7.07 , c ) 6.07 , d ) 7.0 , e ) 8.5 | b | subtract(circle_area(add(divide(40, 1100), 1100)), circle_area(divide(40, 1100))) | a circular ground whose diameter is 40 metres , has a garden of area 1100 m ^ 2 around it . what is the wide of the path of the garden ? | "req . area = Γ― β¬ [ ( 20 ) 2 Γ’ β¬ β ( r ) 2 ] = 22 Γ’ Β β 7 Γ£ β ( 400 - r ^ 2 ) [ since a 2 - b 2 = ( a + b ) ( a - b ) ] ie ) 22 / 7 ( 400 - r ^ 2 ) = 1100 , ie ) r ^ 2 = 50 , r = 7.07 m answer b" | a = 40 / 1100
b = a + 1100
c = circle_area - (
|
a ) 3 , b ) 6 , c ) 8 , d ) 9 , e ) 12 | b | divide(divide(multiply(multiply(36, 12), 4), 72), 4) | in a manufacturing plant , it takes 36 machines 4 hours of continuous work to fill 4 standard orders . at this rate , how many hours of continuous work by 72 machines are required to fill 12 standard orders ? | "the choices give away the answer . . 36 machines take 4 hours to fill 4 standard orders . . in next eq we aredoubling the machines from 36 to 72 , but thework is not doubling ( only 1 1 / 2 times ) , = 4 * 48 / 72 * 12 / 4 = 6 ans b" | a = 36 * 12
b = a * 4
c = b / 72
d = c / 4
|
a ) 130 % , b ) 140 % , c ) 150 % , d ) 160 % , e ) 170 % | b | add(multiply(subtract(multiply(add(const_1, divide(20, const_100)), const_2), const_1), const_100), const_100) | a man gains 20 % by selling an article for a certain price . if he sells it at double the price , the percentage of profit will be . | "explanation : let the c . p . = x , then s . p . = ( 120 / 100 ) x = 6 x / 5 new s . p . = 2 ( 6 x / 5 ) = 12 x / 5 profit = 12 x / 5 - x = 7 x / 5 profit % = ( profit / c . p . ) * 100 = > ( 7 x / 5 ) * ( 1 / x ) * 100 = 140 % option b" | a = 20 / 100
b = 1 + a
c = b * 2
d = c - 1
e = d * 100
f = e + 100
|
a ) 5 % , b ) 11 % , c ) 13 % , d ) 21 % , e ) 19 % | b | multiply(divide(subtract(const_100, 90), 90), const_100) | if the cost price is 90 % of the selling price , then what is the profit percent ? | "let s . p . = $ 100 c . p . = $ 90 profit = $ 10 profit % = 10 / 90 * 100 = 25 / 6 = 11 % approximately answer is b" | a = 100 - 90
b = a / 90
c = b * 100
|
a ) 30 , b ) 50 , c ) 60 , d ) 80 , e ) 150 | e | divide(200, const_10) | marginal cost is the cost of increasing the quantity produced ( or purchased ) by one unit . if the fixed cost for n products is $ 10,000 and the marginal cost is $ 200 , and the total cost is $ 40,000 , what is the value of n ? | "total cost for n products = fixed cost for n products + n * marginal cost - - > $ 40,000 = $ 10,000 + n * $ 200 - - > n = 150 . answer : e ." | a = 200 / 10
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a ) 200 , b ) 300 , c ) 400 , d ) 500 , e ) 470 | b | add(add(multiply(const_3, multiply(9, 9)), multiply(multiply(const_3, 9), const_2)), const_3) | 7 does not occur in 1000 . so we have to count the number of times it appears between 1 and 999 . any number between 1 and 999 can be expressed in the form of xyz where 0 < x , y , z < 9 . | 1 . the numbers in which 7 occurs only once . e . g 7 , 17 , 78 , 217 , 743 etc this means that 7 is one of the digits and the remaining two digits will be any of the other 9 digits ( i . e 0 to 9 with the exception of 7 ) you have 1 * 9 * 9 = 81 such numbers . however , 7 could appear as the first or the second or the third digit . therefore , there will be 3 * 81 = 243 numbers ( 1 - digit , 2 - digits and 3 - digits ) in which 7 will appear only once . in each of these numbers , 7 is written once . therefore , 243 times . 2 . the numbers in which 7 will appear twice . e . g 772 or 377 or 747 or 77 in these numbers , one of the digits is not 7 and it can be any of the 9 digits ( 0 to 9 with the exception of 7 ) . there will be 9 such numbers . however , this digit which is not 7 can appear in the first or second or the third place . so there are 3 * 9 = 27 such numbers . in each of these 27 numbers , the digit 7 is written twice . therefore , 7 is written 54 times . 3 . the number in which 7 appears thrice - 777 - 1 number . 7 is written thrice in it . therefore , the total number of times the digit 7 is written between 1 and 999 is 243 + 54 + 3 = 300 option b | a = 9 * 9
b = 3 * a
c = 3 * 9
d = c * 2
e = b + d
f = e + 3
|
a ) 3 , b ) 6 , c ) 8 , d ) 9 , e ) 7 | c | divide(16, subtract(4, 2)) | a person can swim in still water at 4 km / h . if the speed of water 2 km / h , how many hours will the man take to swim back against the current for 16 km ? | "m = 4 s = 2 us = 4 - 2 = 2 d = 16 t = 16 / 2 = 8 answer : c" | a = 4 - 2
b = 16 / a
|
a ) 3 % , b ) 5 5 / 9 % , c ) 25 % , d ) 33 1 / 3 % , e ) 60 % | b | subtract(const_100, divide(multiply(subtract(15, 12), const_100), subtract(18.8, 15.6))) | in 1982 and 1983 , company b β s operating expenses were $ 12.0 million and $ 15.0 million , respectively , and its revenues were $ 15.6 million and $ 18.8 million , respectively . what was the percent increase in company b β s profit ( revenues minus operating expenses ) from 1982 to 1983 ? | profit in 1982 = 15.6 - 12 = 3.6 million $ profit in 1983 = 18.8 - 15 = 3.8 million $ percentage increase in profit = ( 3.8 - 3.6 ) / 3.6 * 100 % = 5 5 / 9 % answer b | a = 15 - 12
b = a * 100
c = 18 - 8
d = b / c
e = 100 - d
|
a ) 4 km , b ) 5 km , c ) 6 km , d ) 7 km , e ) 8 km | c | divide(add(1, divide(24, subtract(const_100, multiply(const_4, const_10)))), add(divide(divide(1, const_3), 5), divide(divide(const_2, const_3), const_4))) | peter can cover a certain distance in 1 hr . 24 min . by covering two - third of the distance at 4 kmph and the rest at 5 kmph . find the total distance . | time = distance / speed let total distance travelled be x in 84 / 60 hrs 2 / 3 rd of x travelled in 4 km / hr 1 / 3 rd of distance travelled in 5 km / hr 2 x / ( 3 * 4 ) + x / ( 3 * 5 ) = 84 / 60 x = 6 km answer : c | a = 4 * 10
b = 100 - a
c = 24 / b
d = 1 + c
e = 1 / 3
f = e / 5
g = 2 / 3
h = g / 4
i = f + h
j = d / i
|
['a ) 20 %', 'b ) 18 %', 'c ) 36 %', 'd ) 11 %', 'e ) none of these'] | d | multiply(subtract(const_1, sqrt(divide(subtract(const_100, 20), const_100))), const_100) | if the area of a circle decreases by 20 % , then the radius of a circle decreases by | if area of a circle decreased by x % then the radius of a circle decreases by ( 100 β 10 β 100 β x ) % = ( 100 β 10 β 100 β 20 ) % = ( 100 β 10 β 80 ) % = 100 - 89 = 11 % answer d | a = 100 - 20
b = a / 100
c = math.sqrt(b)
d = 1 - c
e = d * 100
|
a ) 6 only , b ) 6 and 12 , c ) 12 only , d ) by 18 only , e ) none of these | b | add(multiply(6, const_100), multiply(2, 6)) | if n is a natural number , then ( 6 n ^ 2 + 6 n ) is always divisible by ? | "( 6 n ^ 2 + 6 n ) = 6 n ( n + 1 ) , which is always divisible by 6 and 12 both , since n ( n + 1 ) is always even . correct option : b" | a = 6 * 100
b = 2 * 6
c = a + b
|
a ) 11.52 sec , b ) 10.1 sec , c ) 10.6 sec , d ) 10.8 sec , e ) 10.2 sec | a | divide(add(140, 180), multiply(add(60, 40), const_0_2778)) | two trains 140 m and 180 m long run at the speed of 60 km / hr and 40 km / hr respectively in opposite directions on parallel tracks . the time which they take to cross each other is ? | "relative speed = 60 + 40 = 100 km / hr . = 100 * 5 / 18 = 250 / 9 m / sec . distance covered in crossing each other = 140 + 180 = 320 m . required time = 320 * 9 / 250 = 11.52 sec . answer : a" | a = 140 + 180
b = 60 + 40
c = b * const_0_2778
d = a / c
|
a ) 9 , b ) 16 , c ) 15 , d ) 32 , e ) 10 | d | add(8, const_1) | the average of first seven multiples of 8 is : | "explanation : ( 8 ( 1 + 2 + 3 + 4 + 5 + 6 + 7 ) / 7 = 8 x 28 / 7 = 32 answer : d" | a = 8 + 1
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a ) 0 , b ) 1 / 3 , c ) 1 / 2 , d ) 2 / 3 , e ) 1 | d | divide(const_2, 3) | a box contains 100 balls , numbered from 1 to 100 . if 3 balls are selected at random and with replacement from the box . if the 3 numbers on the balls selected contain two odd and one even . what is the probability j that the first ball picked up is odd numbered ? | "answer - d selecting the balls either even or odd is having probability 50 / 100 = 1 / 2 we have already selected 3 balls with 2 odd numbers and 1 even number . so we have 3 combinations ooe , oeo , eoo . we have 3 outcomes and 2 are favourable as in 2 cases 1 st number is odd . so probability j is 2 / 3 . d" | a = 2 / 3
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a ) 6 , b ) 7 , c ) 8 , d ) 9 , e ) 10 | d | divide(54, const_10) | the ratio between the perimeter and the width of a rectangle is 5 : 1 . if the area of the rectangle is 54 square centimeters , what is the length of the rectangle in centimeters ? | "perimeter = 2 ( w + l ) = 5 w 3 w = 2 l w = 2 l / 3 wl = 54 2 l ^ 2 / 3 = 54 l ^ 2 = 81 l = 9 cm the answer is d ." | a = 54 / 10
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a ) 25 , b ) 43 , c ) 42 , d ) 40 , e ) 18 | d | divide(rectangle_area(5, 24), 3) | carol and jordan draw rectangles of equal area . if carol ' s rectangle measures 5 inches by 24 inches and jordan ' s rectangle is 3 inches long , how wide is jordan ' s rectangle , in inches ? | "area of carol ' s rectangle = 24 * 5 = 120 let width of jordan ' s rectangle = w since , the areas are equal 3 w = 120 = > w = 40 answer d" | a = rectangle_area / (
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a ) 98 , b ) 78 , c ) 76 , d ) 87 , e ) 75 | e | divide(add(add(add(add(76, 65), 82), 67), 85), divide(const_10, const_2)) | dacid obtained 76 , 65 , 82 , 67 and 85 marks ( out of 100 ) in english , mathematics , physics , chemistry and biology . what are his average marks ? | "average = ( 76 + 65 + 82 + 67 + 85 ) / 5 = 375 / 5 = 75 . answer : e" | a = 76 + 65
b = a + 82
c = b + 67
d = c + 85
e = 10 / 2
f = d / e
|
a ) 48 % , b ) 52 % , c ) 54 % , d ) 60 % , e ) 70 % | c | multiply(const_100, divide(multiply(divide(90, const_100), 24), add(16, 24))) | 16 ltr of water is added with 24 ltr of a solution containing 90 % of alcohol in the water . the % of alcohol in the new mixture is ? | "we have a 24 litre solution containing 90 % of alcohol in the water . = > quantity of alcohol in the solution = 24 Γ£ β 90 / 100 now 16 litre of water is added to the solution . = > total quantity of the new solution = 24 + 16 = 40 percentage of alcohol in the new solution = 24 Γ£ β 90 / 100 40 Γ£ β 100 = 24 Γ£ β 9010040 Γ£ β 100 = 24 Γ£ β 2.25 / 100 = 54 % c" | a = 90 / 100
b = a * 24
c = 16 + 24
d = b / c
e = 100 * d
|
a ) 1 / 35 , b ) 1 / 10 , c ) 1 / 15 , d ) 1 / 20 , e ) 1 / 25 | b | divide(const_2, choose(add(3, 3), 3)) | a bag contains 3 white marbles and 3 black marbles . if each of 3 girls and 3 boys randomly selects and keeps a marble , what is the probability that all of the girls select the same colored marble ? | first , total ways to select for all boys and girls , i . e 6 ! / ( 3 ! * 3 ! ) = 6 * 5 * 4 * 3 * 2 * 1 / 3 * 2 * 1 * 3 * 2 * 1 = 20 then there are one two way girls can have all same colors , either white or black . the number of ways in which 3 girls can select 3 white balls = 3 c 3 = 1 the number of ways in which 3 girls can select 3 black balls = 3 c 3 = 1 therefore , total favorable outcomes / total outcomes = 2 / 20 = 1 / 10 b | a = 3 + 3
b = math.comb(a, 3)
c = 2 / b
|
a ) 1 : 4 , b ) 1 : 3 , c ) 1 : 2 , d ) 2 : 5 , e ) 2 : 11 | c | divide(multiply(multiply(add(const_1, const_4), divide(const_1, const_2)), const_2), multiply(add(multiply(add(const_1, const_4), divide(const_1, const_2)), const_1), const_2)) | a cube has four of its faces painted half red and half white . the other faces are completely painted white . what is the ratio between the red painted areas and the white painted areas of the cube ? | "let x be the area of each face of the cube . the area painted red is 4 ( x / 2 ) = 2 x the area painted white is 4 ( x / 2 ) + 2 x = 4 x the ratio of red to white is 2 x : 4 x which is 1 : 2 . the answer is c ." | a = 1 + 4
b = 1 / 2
c = a * b
d = c * 2
e = 1 + 4
f = 1 / 2
g = e * f
h = g + 1
i = h * 2
j = d / i
|
a ) 75 , b ) 72 , c ) 130 , d ) 70 , e ) 80 | c | divide(multiply(const_100, divide(5, const_2)), 5) | if a book is sold at 5 % profit instead of 5 % loss , it would have brought rs 13 more . find out the cost price of the book | "let c . p . of the book be rs . β x β given , 1.05 x - 0.95 x = 13 = > 0.1 x = 13 = 13 / 0.1 = rs 130 answer : c" | a = 5 / 2
b = 100 * a
c = b / 5
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a ) 2 , b ) 3 , c ) 8 , d ) 14 , e ) 56 | c | lcm(4, 8) | if 4 and 8 are factors of 60 n , what is the minimum value of n ? | 60 n / 4 * 8 should be integer = > 2 * 2 * 3 * 5 * n / 2 * 2 * 2 * 2 * 2 = 3 * 5 * n / 8 must be an integer for this to be true n must multiple of 8 , thus min of n = 8 hence c | a = math.lcm(4, 8)
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a ) 20 , b ) 18 , c ) 17 , d ) 16 , e ) 15 | e | divide(log(multiply(power(3, 7), power(3, 8))), log(3)) | if 3 ^ 8 x 3 ^ 7 = 3 ^ n what is the value of n ? | "3 ^ 8 * 3 ^ 7 = 3 ^ n or 3 ^ 8 + 7 = 3 ^ n n = 15 e" | a = 3 ** 7
b = 3 ** 8
c = a * b
d = math.log(c)
e = math.log(3)
f = d / e
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a ) 54.5 , b ) 56.5 , c ) 59.2 , d ) 61 , e ) 62 | b | divide(add(55, 58), const_2) | in karthik ' s opinion , his weight is greater than 55 kg but less than 62 kg . his brother does not agree with karthik and he thinks that karthik ' s weight is greater than 50 kg but less than 60 kg . his father ' s view is that his weight can not be greater than 58 kg . if all of them are correct in their estimation , what is the average of different probable weights of karthik ? | explanation : solution : assume karthik ' s weight be x kg . according to karthik , 55 < x < 62 according to karthik ; s brother , 50 < x < 60 . according to karthik ' s mother , x < 58 . the values satisfying all the above conditions are 56 and 57 . . ' . required average = ( 56 + 57 ) / 2 = 56.5 . answer : b | a = 55 + 58
b = a / 2
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a ) 17 sec , b ) 12 sec , c ) 16 sec , d ) 15 sec , e ) 20 sec | e | divide(multiply(200, const_2), add(speed(200, 15), speed(200, 10))) | two trains of equal lengths take 10 sec and 15 sec respectively to cross a telegraph post . if the length of each train be 200 m , in what time will they cross other travelling in opposite direction ? | "speed of the first train = 120 / 10 = 12 m / sec . speed of the second train = 120 / 5 = 8 m / sec . relative speed = 12 + 8 = 20 m / sec . required time = ( 200 + 200 ) / 20 = 20 sec . answer : e" | a = 200 * 2
b = speed + (
c = a / b
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a ) 283.8 mtrs , b ) 378.4 mtrs , c ) 478.4 mtrs , d ) 488.4 mtrs , e ) 578.4 mtrs | a | multiply(66, divide(multiply(86, 8), multiply(20, 8))) | if 20 men can build a wall 66 metres long in 8 days , what length of a similar can be built by 86 men in 8 days ? | "if 20 men can build a wall 66 metres long in 8 days , length of a similar wall that can be built by 86 men in 8 days = ( 66 * 86 * 8 ) / ( 8 * 20 ) = 283.8 mtrs answer : a" | a = 86 * 8
b = 20 * 8
c = a / b
d = 66 * c
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a ) 12 , b ) 13 , c ) 14 , d ) 15 , e ) 17 | e | add(10, const_4) | how many odd numbers between 10 and 1,300 are the squares of integers ? | "the square of an odd number is an odd number : 10 < odd < 1,000 10 < odd ^ 2 < 1,000 3 . something < odd < 31 . something ( by taking the square root ) . so , that odd number could be any odd number from 5 to 31 , inclusive : 5 , 7 , 9 , 11 , 13 , 15 , 17 , 19 , 21 , 23 , 25 , 27 , 29 , and 31 . 17 numbers . answer : e ." | a = 10 + 4
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a ) 330 , b ) 90 , c ) 270 , d ) 250 , e ) 350 | b | divide(multiply(30, 2310), 770) | the l . c . m of two numbers is 2310 and their h . c . f is 30 . if one number is 770 the other is | "the other number = l . c . m * h . c . f / given number = 2310 * 30 / 770 = 90 answer is b ." | a = 30 * 2310
b = a / 770
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a ) $ 94.03 , b ) $ 96.75 , c ) $ 98.68 , d ) $ 102.07 , e ) $ 105.3 | c | add(add(multiply(const_2, 32.20), multiply(const_1, 20.43)), multiply(const_1, 13.85)) | a garden center sells a certain grass seed in 5 - pound bags at $ 13.85 per bag , 10 - pound bags at $ 20.43 per bag , and 25 - pound bags $ 32.20 per bag . if a customer is to buy at least 65 pounds of the grass seed , but no more than 80 pounds , what is the least possible cost of the grass seed that the customer will buy ? | "there can be 2 cases 1 ) 25 + 25 + 10 + 5 = $ 98.68 or 2 ) 25 + 25 + 25 = $ 96.60 c" | a = 2 * 32
b = 1 * 20
c = a + b
d = 1 * 13
e = c + d
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a ) 3 . , b ) 7 . , c ) 10 . , d ) 12 . , e ) 15 . | c | multiply(2, 2) | the distance between west - town to east - town is 15 kilometers . two birds start flying simultaneously towards one another , the first leaving from west - town at a speed of 2 kilometers per minute and the second bird , leaving from east - town , at a speed of 1 kilometers per minute . what will be the distance , in kilometers , between the meeting point and west - town ? | "time taken by the birds to meet = 15 / ( 2 + 1 ) = 5 mins distance traveled by the bird traveling from west - town = 2 * 5 = 10 answer : c" | a = 2 * 2
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a ) 42 , b ) 36 , c ) 46 , d ) 38 , e ) 40 | d | multiply(add(subtract(10, const_1), 10), divide(22, add(subtract(6, const_1), 6))) | a certain clock marks every hour by striking a number of times equal to the hour , and the time require for a stroke is exactly equal to the time interval between strokes . at 6 : 00 the time lapse between the beginning of the first stoke and the end of the last stroke is 22 seconds . at 10 : 00 , how many seconds elapse between the beginning of the first stroke and the end of the last stroke ? | "at 6 ' o clock , there would be 6 strikes . first strike , then a short interval , the second strike , then a short interval and so on till the 6 th strike . so there would be in all 5 intervals between 6 strikes . similarly , between 10 strikes , there would be 9 intervals . according to the question , the time spent in the strike and the interval is same . at 6 ' o clock , the 6 strikes and the 5 intervals together take 22 sec so each strike and each interval takes 2 secs . at 12 ' o clock , the 10 strikes and 9 intervals will take 2 * ( 10 + 9 ) = 38 secs d d" | a = 10 - 1
b = a + 10
c = 6 - 1
d = c + 6
e = 22 / d
f = b * e
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a ) 22 , b ) 98 , c ) 60 , d ) 88 , e ) 24 | e | divide(multiply(multiply(divide(add(100, 100), multiply(20, add(const_1, const_2))), const_2), const_3600), const_1000) | two trains , each 100 m long , moving in opposite directions , cross other in 20 sec . if one is moving twice as fast the other , then the speed of the faster train is ? | "let the speed of the slower train be x m / sec . then , speed of the train = 2 x m / sec . relative speed = ( x + 2 x ) = 3 x m / sec . ( 100 + 100 ) / 20 = 3 x = > x = 10 / 3 . so , speed of the faster train = 20 / 3 = 20 / 3 * 18 / 5 = 24 km / hr . answer : e" | a = 100 + 100
b = 1 + 2
c = 20 * b
d = a / c
e = d * 2
f = e * 3600
g = f / 1000
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a ) 4 : 1 , b ) 1 : 4 , c ) 3 : 2 , d ) 2 : 3 , e ) 2 : 5 | c | divide(multiply(multiply(multiply(const_3, const_2), const_100), const_100), divide(multiply(multiply(multiply(const_3, const_2), const_100), const_100), multiply(add(const_2, const_3), const_2))) | if a and b get profits of rs . 6,000 and rs . 4,000 respectively at the end of year then ratio of their investments are | "suppose a and b is ratio of investment . so a : b = 6000 + 4000 a : b = 10000 a / ( a + b ) * 10000 = 6000 2 a = 3 b a / b = 3 / 2 i . e 3 : 2 answer : c" | a = 3 * 2
b = a * 100
c = b * 100
d = 3 * 2
e = d * 100
f = e * 100
g = 2 + 3
h = g * 2
i = f / h
j = c / i
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a ) 18 , b ) 19 , c ) 20 , d ) 21 , e ) 22 | d | floor(divide(171, 8)) | on dividing 171 by a number , the quotient is 8 and the remainder is 3 . find the divisor . | "d = ( d - r ) / q = ( 171 - 3 ) / 8 = 168 / 8 = 21 d" | a = 171 / 8
b = math.floor(a)
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a ) 780 , b ) 200 , c ) 210 , d ) 220 , e ) 230 | a | multiply(subtract(40, const_1), divide(40, const_2)) | 40 men shake hands with each other . maximum no of handshakes without cyclic handshakes . | "or , if there are n persons then no . of shakehands = nc 2 = 40 c 2 = 780 answer : a" | a = 40 - 1
b = 40 / 2
c = a * b
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a ) 2999 , b ) 2778 , c ) 7000 , d ) 2889 , e ) 6612 | c | multiply(multiply(const_1, const_12), divide(21000, add(add(multiply(const_1, const_12), multiply(subtract(const_12, 6), const_2)), multiply(subtract(const_12, 8), const_3)))) | a , b and c enter into partnership . a invests some money at the beginning , b invests double the amount after 6 months , and c invests thrice the amount after 8 months . if the annual gain be rs . 21000 . a ' s share is ? | "x * 12 : 2 x * 6 : 3 x * 4 1 : 1 : 1 1 / 3 * 21000 = 7000 answer : c" | a = 1 * 12
b = 1 * 12
c = 12 - 6
d = c * 2
e = b + d
f = 12 - 8
g = f * 3
h = e + g
i = 21000 / h
j = a * i
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a ) 8 , b ) 10 , c ) 12 , d ) 14 , e ) 16 | a | divide(subtract(100, multiply(15, const_3)), const_4) | a box has exactly 100 balls , and each ball is either red , blue , or white . if the box has 15 more blue balls than white balls , and thrice as many red balls as blue balls , how many white balls does the box has ? | "x = the number of red balls y = the number of blue balls z = the number of white balls from the first sentence we have equation # 1 : x + y + z = 100 . . . the box has 15 more blue balls than white balls . . . equation # 2 : y = 15 + z . . . thrice as many red balls as blue balls . . . equation # 3 : x = 3 y solve equation # 2 for z : z = y - 15 now , we can replace both x and z with y in equation # 1 3 y + y + ( y - 15 ) = 100 5 y - 15 = 100 5 y = 115 y = 23 there are 23 blue balls . this is 15 more than the number of white balls , so z = 8 . that ' s the answer . just as a check , x = 69 , and 69 + 23 + 8 = 100 . answer = 8 , ( a )" | a = 15 * 3
b = 100 - a
c = b / 4
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a ) 8 sec , b ) 15 sec , c ) 20 sec , d ) 10 sec , e ) 22 sec | b | divide(150, multiply(36, const_0_2778)) | how long does a train 150 m long traveling at 36 kmph takes to cross a signal post ? | d = 150 m s = 36 * 5 / 18 = 10 t = 150 * 1 / 10 = 15 sec answer : b | a = 36 * const_0_2778
b = 150 / a
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a ) 30 % , b ) 35 % , c ) 40 % , d ) 45 % , e ) 50 % | c | multiply(divide(add(multiply(40, divide(20, const_100)), multiply(80, divide(50, const_100))), add(40, 80)), const_100) | a car dealership has 40 cars on the lot , 20 % of which are silver . if the dealership receives a new shipment of 80 cars , 50 % of which are not silver , what percentage of total number of cars are silver ? | "the number of silver cars is 0.2 * 40 + 0.5 * 80 = 48 the percentage of cars which are silver is 48 / 120 = 40 % the answer is c ." | a = 20 / 100
b = 40 * a
c = 50 / 100
d = 80 * c
e = b + d
f = 40 + 80
g = e / f
h = g * 100
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a ) 18.5 , b ) 21.5 , c ) 24.5 , d ) 27.5 , e ) 30.5 | c | divide(multiply(7, 7), const_2) | the two lines y = x and x = - 7 intersect on the coordinate plane . what is the value of the area of the figure formed by the intersecting lines and the x - axis ? | "the point of intersection is ( - 7 , - 7 ) . the triangle has a base of length 7 and a height of 7 . area = ( 1 / 2 ) * base * height = ( 1 / 2 ) * 7 * 7 = 24.5 the answer is c ." | a = 7 * 7
b = a / 2
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a ) 40 , b ) 50 , c ) 60 , d ) 79 , e ) 48 | e | divide(divide(subtract(125, multiply(multiply(3, const_0_2778), 3)), 10), const_0_2778) | a train 125 m long passes a man , running at 3 km / hr in the same direction in which the train is going , in 10 sec . the speed of the train is ? | "speed of the train relative to man = 125 / 10 = 25 / 2 m / sec . = 25 / 2 * 18 / 5 = 45 km / hr let the speed of the train be x km / hr . then , relative speed = ( x - 3 ) km / hr . x - 3 = 45 = > x = 48 km / hr . answer : option e" | a = 3 * const_0_2778
b = a * 3
c = 125 - b
d = c / 10
e = d / const_0_2778
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a ) 2 , b ) 3 , c ) 4 , d ) 6 , e ) 7 | e | divide(14, const_2) | if 16 ^ y = 4 ^ 14 , what is y ? | 16 ^ y = 4 ^ 2 y = 4 ^ 14 2 y = 14 y = 7 the answer is e . | a = 14 / 2
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a ) 15 , b ) 16 , c ) 17 , d ) 18 , e ) 19 | a | divide(add(sqrt(add(multiply(multiply(105, const_2), const_4), const_1)), const_1), const_2) | if each participant of a chess tournament plays exactly one game with each of the remaining participants , then 105 games will be played during the tournament . find the number of participants . | "let p be the number of participants . pc 2 = 105 ( p ) ( p - 1 ) = 210 = 15 * 14 p = 15 the answer is a ." | a = 105 * 2
b = a * 4
c = b + 1
d = math.sqrt(c)
e = d + 1
f = e / 2
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a ) 150 meter , b ) 100 meter , c ) 105 meter , d ) 120 meter , e ) 130 meter | a | multiply(divide(multiply(90, const_1000), const_3600), 6) | a train running at the speed of 90 km / hr crosses a pole in 6 seconds . find the length of the train . | "speed = 90 * ( 5 / 18 ) m / sec = 25 m / sec length of train ( distance ) = speed * time ( 25 ) * 6 = 150 meter answer : a" | a = 90 * 1000
b = a / 3600
c = b * 6
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a ) 2 / 7 , b ) 3 / 7 , c ) 4 / 7 , d ) 9 / 14 , e ) 11 / 14 | c | divide(subtract(7, 3), 7) | jen has a jar of jam , and she ate 1 / 3 of the jam for lunch . if jen ate 1 / 7 of the remaining jam for dinner , what fraction of the jam was left after dinner ? | let x be the amount of jam at the beginning . after lunch , the remaining jam was ( 2 / 3 ) x . after dinner , the remaining jam was ( 6 / 7 ) ( 2 / 3 ) x = ( 4 / 7 ) x . the answer is c . | a = 7 - 3
b = a / 7
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a ) $ 94.03 , b ) $ 96.75 , c ) $ 98.78 , d ) $ 98.77 , e ) $ 105.3 | d | add(add(multiply(const_2, 32.25), multiply(const_1, 20.42)), multiply(const_1, 13.85)) | a garden center sells a certain grass seed in 5 - pound bags at $ 13.85 per bag , 10 - pound bags at $ 20.42 per bag , and 25 - pound bags $ 32.25 per bag . if a customer is to buy at least 65 pounds of the grass seed , but no more than 80 pounds , what is the least possible cost of the grass seed that the customer will buy ? | "there can be 2 cases 1 ) 25 + 25 + 10 + 5 = $ 98.77 or 2 ) 25 + 25 + 25 = $ 96.75 d" | a = 2 * 32
b = 1 * 20
c = a + b
d = 1 * 13
e = c + d
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a ) 82.9 % , b ) 84.2 % , c ) 81.0 % , d ) 80.6 % , e ) 81.6 % | e | subtract(power(7, const_2), power(3, const_2)) | the radius of the two circular fields is in the ratio 3 : 7 the area of the first field is what percent less than the area of the second ? | "r = 3 Γ― β¬ r 2 = 9 r = 7 Γ― β¬ r 2 = 49 49 Γ― β¬ Γ’ β¬ β 40 Γ― β¬ 100 - - - - ? = > 81.6 % . answer : e" | a = 7 ** 2
b = 3 ** 2
c = a - b
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a ) 3 . , b ) 7 . , c ) 10 . , d ) 16 . , e ) 15 . | d | multiply(4, const_4) | the distance between west - town to east - town is 20 kilometers . two birds start flying simultaneously towards one another , the first leaving from west - town at a speed of 4 kilometers per minute and the second bird , leaving from east - town , at a speed of 1 kilometers per minute . what will be the distance , in kilometers , between the meeting point and west - town ? | time taken by the birds to meet = 20 / ( 4 + 1 ) = 4 mins distance traveled by the bird traveling from west - town = 4 * 4 = 16 answer : d | a = 4 * 4
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a ) 3,500 , b ) 24,500 , c ) 25,500 , d ) 26,500 , e ) 27,500 | a | floor(divide(divide(subtract(550, multiply(6,000, divide(8, const_100))), subtract(divide(10, const_100), divide(8, const_100))), 6,000)) | angelo and isabella are both salespersons . in any given week , angelo makes $ 550 in base salary plus 8 percent of the portion of his sales above $ 6,000 for that week . isabella makes 10 percent of her total sales for any given week . for what amount of weekly sales would angelo and isabella earn the same amount of money ? | "official solution : the problem asks for the amount of weekly sales it takes for angelo and isabella to earn the same amount of money . you can write an equation that sets angelo β s and isabella β s weekly earnings equal to each other , with x representing weekly sales . weekly earnings for each salesperson equal base salary plus commission . so angelo β s earnings are 550 + ( 0.08 ) ( x β 6,000 ) , and isabella β s are 0.10 x . set up the equation and solve : 550 + ( 0.08 ) ( x β 6,000 ) = 0.10 x distribute the 0.08 : 550 + 0.08 x β 480 = 0.10 x combine terms and subtract 0.08 x from both sides : 70 = 0.02 x divide both sides by 0.02 : 3,500 = x your answer is a ." | a = 8 / 100
b = 6 * 0
c = 550 - b
d = 10 / 100
e = 8 / 100
f = d - e
g = c / f
h = g / 6
i = math.floor(h)
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a ) 1 / 10 , b ) 1 / 5 , c ) 2 / 5 , d ) 3 / 5 , e ) 3 / 10 | b | divide(subtract(subtract(divide(add(13, sqrt(subtract(power(13, const_2), multiply(const_4, 40)))), const_2), subtract(13, divide(add(13, sqrt(subtract(power(13, const_2), multiply(const_4, 40)))), const_2))), const_1), 10) | if p ^ 2 β 13 p + 40 = s , and p is a positive integer between 1 and 10 , inclusive , what is the probability that s < 0 ? | p 2 β 13 p + 40 = s so ( p β 8 ) ( p β 5 ) = s for q to be negative , the expressions ( p β 8 ) and ( p β 5 ) must have opposite signs . which integers on the number line will yield opposite signs for the expressions ( p β 8 ) and ( p β 5 ) ? those integers in the range 5 < p < 8 ( notice 5 and 8 are not included because they would both yield a value of zero and zero is a nonnegative integer ) . that means that there are only two integer values for p , 6 and 7 , that would yield a negative q . with a total of 10 possible p values , only 2 yield a negative q , so the probability is 2 / 10 or 1 / 5 . the correct answer is b . | a = 13 ** 2
b = 4 * 40
c = a - b
d = math.sqrt(c)
e = 13 + d
f = e / 2
g = 13 ** 2
h = 4 * 40
i = g - h
j = math.sqrt(i)
k = 13 + j
l = k / 2
m = 13 - l
n = f - m
o = n - 1
p = o / 10
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a ) 3.75 days , b ) 3.78 days , c ) 3.25 days , d ) 3.15 days , e ) 2.75 days | a | inverse(add(inverse(6), inverse(10))) | a and b complete a work in 6 days . a alone can do it in 10 days . if both together can do the work in how many days ? | "1 / 6 + 1 / 10 = 8 / 30 = 4 / 15 15 / 4 = 3.75 days answer : a" | a = 1/(6)
b = 1/(10)
c = a + b
d = 1/(c)
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a ) 0 , b ) 2 , c ) 5 , d ) 7 , e ) 9 | b | divide(subtract(add(add(add(multiply(5, const_100), 2), multiply(const_1, const_10)), multiply(const_1, const_10)), add(multiply(5, const_100), 2)), multiply(const_1, const_10)) | 5 * 2 is a 3 digit number with * is a missing digit . if the number is divisible by 6 , the missing digit is | sol . let the number be 5 x 2 . clearly , it is divisible by 2 . now , 5 + x + 2 = ( 7 + x ) must be divisible by 3 . so , x = 2 . answer b | a = 5 * 100
b = a + 2
c = 1 * 10
d = b + c
e = 1 * 10
f = d + e
g = 5 * 100
h = g + 2
i = f - h
j = 1 * 10
k = i / j
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a ) 2 , b ) 5 , c ) 8 , d ) 15 , e ) 25 | c | divide(subtract(multiply(48, 40), multiply(divide(add(const_100, 20), const_100), multiply(38, 40))), subtract(multiply(50, divide(add(const_100, 20), const_100)), 48)) | how many pounds of salt at 50 cents / lb must be mixed with 40 lbs of salt that costs 38 cents / lb so that a merchant will get 20 % profit by selling the mixture at 48 cents / lb ? | selling price is 48 cents / lb for a 20 % profit , cost price should be 40 cents / lb ( cp * 6 / 5 = 48 ) basically , you need to mix 38 cents / lb ( salt 1 ) with 50 cents / lb ( salt 2 ) to get a mixture costing 40 cents / lb ( salt avg ) weight of salt 1 / weight of salt 2 = ( salt 2 - saltavg ) / ( saltavg - salt 1 ) = ( 50 - 40 ) / ( 40 - 38 ) = 5 / 1 we know that weight of salt 1 is 40 lbs . weight of salt 2 must be 8 lbs . answer ( c ) | a = 48 * 40
b = 100 + 20
c = b / 100
d = 38 * 40
e = c * d
f = a - e
g = 100 + 20
h = g / 100
i = 50 * h
j = i - 48
k = f / j
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a ) 438 , b ) 446 , c ) 452 , d ) 462 , e ) 470 | a | multiply(multiply(multiply(600, subtract(1, divide(1, 10))), subtract(1, divide(1, 10))), subtract(1, divide(1, 10))) | in a certain animal population , for each of the first 3 months of life , the probability that an animal will die during that month is 1 / 10 . for a group of 600 newborn members of the population , approximately how many would be expected to survive the first 3 months of life ? | "number of newborns that can die in first month = 1 / 10 * 600 = 60 survived = 540 number of newborns that can die in second month = 1 / 10 * 540 = 54 survived = 486 number of newborns that can die in third month = 1 / 10 * 486 = 48 survived = 438 answer : a" | a = 1 / 10
b = 1 - a
c = 600 * b
d = 1 / 10
e = 1 - d
f = c * e
g = 1 / 10
h = 1 - g
i = f * h
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['a ) 8', 'b ) 2', 'c ) 6', 'd ) 0', 'e ) 12'] | d | subtract(add(add(15, 17), 20), 40) | three interviewers , a , b , and c are interviewing 40 applicants . only with three interviewers ' admission can an applicant be admitted . if interviewer b admitted 15 applicants , a admitted 17 applicants , and c admitted 20 applicants , at least how many applicants get the admission ? | if b admitted 15 are overlapping with a admission of 17 but c does not overlap with anybody . then no student will get nod from all the 3 . hence 0 student will get admission . answer : d | a = 15 + 17
b = a + 20
c = b - 40
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a ) 25 , b ) 35 , c ) 45 , d ) 65 , e ) 55 | e | subtract(negate(14), multiply(subtract(1, 5), divide(subtract(1, 5), subtract(0, 1)))) | 0 , 1 , 5 , 14 , 30 , ____ | "0 , 1,5 , 14 , 30 , . . . . . 0 + 1 * 1 = 1 1 + 2 * 2 = 5 5 + 3 * 3 = 14 14 + 4 * 4 = 30 so 30 + 5 * 5 = 55 answer : e" | a = negate - (
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a ) 120 , b ) 240 , c ) 360 , d ) 720 , e ) 1440 | b | multiply(multiply(4, const_3), divide(factorial(add(4, const_1)), factorial(const_3))) | the security gate at a storage facility requires a 4 - digit lock code . if the lock code must consist only of digits from 1 through 7 , inclusive , with no repeated digits , and the first and last digits of the code must be odd , how many lock codes are possible ? | x - x - x - x - x - - > there are 4 odd digits from 1 to 7 , inclusive thus options for the first and the last x ' s are : 4 - x - x - 3 . other x ' s can take following values : 4 - 5 - 4 - 3 - - > 4 * 5 * 4 * 3 = 240 . answer : b . | a = 4 * 3
b = 4 + 1
c = math.factorial(b)
d = math.factorial(3)
e = c / d
f = a * e
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a ) 3 , b ) 9 , c ) 15 , d ) 19 , e ) 28 | e | add(add(power(4, const_2.0), multiply(2, 2)), 4) | if [ [ x ] ] = x ^ 2 + 2 x + 4 , what is the value of [ [ 4 ] ] ? | "[ [ x ] ] = x ^ 2 + 2 x + 4 [ [ 4 ] ] = 4 ^ 2 + 2 * 4 + 4 = 28 . option e" | a = 4 ** 2
b = 2 * 2
c = a + b
d = c + 4
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a ) 150 , b ) 750 , c ) 1,250 , d ) 1,500 , e ) 2,500 | d | multiply(50, 5) | in a forest 110 deer were caught , tagged with electronic markers , then released . a week later , 50 deer were captured in the same forest . of these 50 deer , it was found that 5 had been tagged with the electronic markers . if the percentage of tagged deer in the second sample approximates the percentage of tagged deer in the forest , and if no deer had either left or entered the forest over the preceding week , what is the approximate number of deer in the forest ? | "the percentage of tagged deer in the second sample = 5 / 50 * 100 = 10 % . so , 150 tagged deers comprise 10 % of total # of deers - - > total # of deers = 110 * 10 = 1,100 . answer : d ." | a = 50 * 5
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a ) 20 , b ) 200 , c ) 50 , d ) 400 , e ) 140 | c | subtract(divide(divide(4240, 26.50), const_2), multiply(const_2, 20)) | the length of a rectangular plot is 20 metres more than its breadth . if the cost of fencing the plot @ rs . 26.50 per metre is rs . 4240 , what is the length of the plot in metres ? | "let length of plot = l meters , then breadth = l - 20 meters and perimeter = 2 [ l + l - 20 ] = [ 4 l - 40 ] meters [ 4 l - 40 ] * 26.50 = 4240 [ 4 l - 40 ] = 4240 / 26.50 = 160 4 l = 200 l = 200 / 4 = 50 meters . answer : c" | a = 4240 / 26
b = a / 2
c = 2 * 20
d = b - c
|
a ) 7.5 % , b ) 9.1 % , c ) 10.9 % , d ) 16.67 % , e ) 15 % | d | multiply(divide(20, add(20, const_100)), const_100) | in the new budget the price of milk rose by 20 % . by how much percent must a person reduce his consumption so that his expenditure on it does not increase ? | reduce in consumption = r / ( 100 + r ) * 100 % = 20 / 120 * 100 = 16.67 % answer is d | a = 20 + 100
b = 20 / a
c = b * 100
|
a ) 800 , b ) 500 , c ) 505 , d ) none of these , e ) 506 | a | divide(const_100.0, divide(08, 64)) | evaluate 64 / . 08 | "explanation : 64 / . 08 = 6400 / 8 = 800 option a" | a = 8 / 64
b = 100 / 0
|
a ) 412 , b ) 332 , c ) 400 , d ) 483 , e ) 566 | a | sqrt(subtract(power(multiply(283, 2), 2), power(multiply(206, 2), 2))) | two airplanes take off from one airfield at noon . one flies due east at 206 miles per hour while the other flies directly northeast at 283 miles per hour . approximately how many miles apart are the airplanes at 2 p . m . ? | "a in two hours : the plane flying east will be 412 miles away from airport . the other plane will be 566 miles away from airport . 566 / 412 = ~ 1.4 = ~ sqrt ( 2 ) this means that planes formed a right isocheles triangle = > sides of such triangles relate as 1 : 1 : sqrt ( 2 ) = > the planes are 412 miles apart . a" | a = 283 * 2
b = a ** 2
c = 206 * 2
d = c ** 2
e = b - d
f = math.sqrt(e)
|
a ) 0.2 , b ) 0.5 , c ) 0.6 , d ) 0.75 , e ) 1.0 | c | divide(multiply(divide(multiply(8, 5), const_100), 96), const_100) | 96 % of 5 / 8 = | "should be simple . 0.96 * 5 / 8 = 4.8 / 8 = 0.6 correct option : c" | a = 8 * 5
b = a / 100
c = b * 96
d = c / 100
|
a ) 0 kmph , b ) 4 kmph , c ) 16 kmph , d ) 2.5 kmph , e ) 3 kmph | e | divide(subtract(14, 8), const_2) | a man goes downstream at 14 kmph , and upstream 8 kmph . the speed of the stream is | speed of the stream = 1 / 2 ( 14 - 8 ) kmph = 3 kmph . correct option : e | a = 14 - 8
b = a / 2
|
a ) 2 : 1 , b ) 4 : 7 , c ) 8 : 77 , d ) 4 : 121 , e ) none | d | power(divide(2, 11), 2) | the ratio of radius of a circle and the side of a square is 2 : 11 . find the ratio of their areas : | "radius / side = 2 / 11 β area of circle / area of square = 4 / 121 answer : d" | a = 2 / 11
b = a ** 2
|
a ) 45 m , b ) 50 m , c ) 54 m , d ) 72 m , e ) none of these | b | multiply(9, subtract(subtract(multiply(multiply(4, const_0_2778), 10), multiply(9, multiply(2, const_0_2778))), multiply(2, const_0_2778))) | a train overtakes two person who are walking in the same direction in which the train is going , at the rate of 2 kmph and 4 kmph and passes them completely in 9 and 10 seconds respectively . the length of the train is : | let actual speed of train = s m / sec and length of train = l m . then , s - 2 Γ 5 / 18 = l 9 β 9 s = l + 5 . . . β¦ ( i ) and s - 4 Γ 5 β 18 = l β 10 β 90 s = 9 l + 100 . . . . . ( ii ) by ( i ) & ( ii ) , we get l = 50 m . answer b | a = 4 * const_0_2778
b = a * 10
c = 2 * const_0_2778
d = 9 * c
e = b - d
f = 2 * const_0_2778
g = e - f
h = 9 * g
|
a ) 25 days , b ) 26 days , c ) 23 days , d ) 45 days , e ) 27 days | e | multiply(add(const_1, const_2), 18) | a is twice as good a workman as b and together they finish a piece in 18 days . in how many days will a alone finish the work ? | "sol . ( a β s 1 day β s work ) : ) ( b β s 1 days work ) = 2 : 1 . ( a + b ) ' s 1 day ' s work = 1 / 18 divide 1 / 18 in the ratio 2 : 1 . : . a β s 1 day ' s work = ( 1 / 18 * 2 / 3 ) = 1 / 27 hence , a alone can finish the work in 27 days . ans : e" | a = 1 + 2
b = a * 18
|
a ) 2 , b ) 3 , c ) 4 , d ) 5 , e ) 6 | a | multiply(subtract(divide(power(26, const_2), 56), floor(divide(power(26, const_2), 56))), 56) | on dividing a number by 56 , we get 26 as remainder . on dividing the same number by 8 , what will be the remainder ? | "number = 56 x + 26 ( β΅ since the number gives 26 as remainder on dividing by 56 ) = ( 7 Γ 8 Γ x ) + ( 3 Γ 8 ) + 2 hence , if the number is divided by 8 , we will get 2 as remainder . answer : a" | a = 26 ** 2
b = a / 56
c = 26 ** 2
d = c / 56
e = math.floor(d)
f = b - e
g = f * 56
|
a ) 11 , b ) 14 , c ) 16 , d ) 12 , e ) 19 | c | divide(1240, multiply(multiply(const_2, divide(add(add(multiply(const_3, const_100), multiply(const_1, const_10)), const_4), const_100)), 12)) | if the wheel is 12 cm then the number of revolutions to cover a distance of 1240 cm is ? | "2 * 22 / 7 * 12 * x = 1240 = > x = 16 answer : c" | a = 3 * 100
b = 1 * 10
c = a + b
d = c + 4
e = d / 100
f = 2 * e
g = f * 12
h = 1240 / g
|
a ) 1.5 , b ) 4.5 , c ) 7.5 , d ) 9.5 , e ) 8.7 | b | divide(add(2, 7), 2) | ( ab ) x β 2 = ( ba ) x β 7 . what is the value of x ? | explanation : ( a / b ) x β 2 = ( b / a ) x β 7 β ( a / b ) x β 2 = ( a / b ) β ( x β 7 ) β x β 2 = β ( x β 7 ) β x β 2 = β x + 7 β x β 2 = β x + 7 β 2 x = 9 β x = 92 = 4.5 option b | a = 2 + 7
b = a / 2
|
a ) 12 days , b ) 18 days , c ) 15 days , d ) 21 days , e ) 22 days | c | inverse(subtract(inverse(6), inverse(10))) | a and b together can do a piece of work in 6 days and a alone can do it in 10 days . in how many days can b alone can do it ? | "explanation : a and b can do work 1 / 6 in 1 day a alone can do 1 / 10 work in 1 day b alone can do ( 1 / 6 - 1 / 10 ) = 1 / 15 work in 1 day = > complete work can be done in 15 days by b answer : option c" | a = 1/(6)
b = 1/(10)
c = a - b
d = 1/(c)
|
a ) 87 , b ) 89 , c ) 90 , d ) 93 , e ) 102 | e | subtract(multiply(4, add(94, 2)), multiply(94, 3)) | jerry β s average ( arithmetic mean ) score on the first 3 of 4 tests is 94 . if jerry wants to raise his average by 2 points , what score must he earn on the fourth test ? | total score on 3 tests = 94 * 3 = 282 jerry wants the average to be = 96 hence total score on 4 tests should be = 96 * 4 = 384 score required on the fourth test = 384 - 282 = 102 option e | a = 94 + 2
b = 4 * a
c = 94 * 3
d = b - c
|
a ) 100 , b ) 200 , c ) 300 , d ) 400 , e ) 500 | b | divide(multiply(multiply(const_1000, const_100), 0.036), divide(18000, const_1000)) | in the biology lab of ` ` jefferson ' ' high school there are 0.036 * 10 ^ 5 germs , equally divided among 18000 * 10 ^ ( - 3 ) petri dishes . how many germs live happily in a single dish ? | "0.036 * 10 ^ 5 can be written as 3600 18000 * 10 ^ ( - 3 ) can be written as 18 required = 3600 / 18 = 200 answer : b" | a = 1000 * 100
b = a * 0
c = 18000 / 1000
d = b / c
|
a ) 2788 , b ) 5500 , c ) 7282 , d ) 2782 , e ) 2729 | b | multiply(subtract(12, 7), divide(4400, subtract(7, 3))) | an amount of money is to be divided between p , q and r in the ratio of 3 : 7 : 12 . if the difference between the shares of p and q is rs . 4400 , what will be the difference between q and r ' s share ? | 4 - - - 4400 5 - - - ? = > 5500 answer : b | a = 12 - 7
b = 7 - 3
c = 4400 / b
d = a * c
|
a ) 25 minutes . , b ) 30 minutes . , c ) 40 minutes . , d ) 55 minutes , e ) 1 hour and 20 minutes | c | multiply(divide(subtract(const_1, add(divide(const_1, 3), divide(const_1, 2.5))), divide(const_1, 2.5)), const_60) | it takes avery 3 hours to build a brick wall while tom can do it in 2.5 hours . if the two start working together and after an hour avery leaves , how much time will it take tom to complete the wall on his own ? | "avery ' s efficiency is 100 / 3 = 33 % tom ' s = 100 / 2.5 = 40 % they worked together for 1 hour and finished 73 % of the job remaining = 27 % tom will complete 40 % in 60 minutes , 20 % in 30 minutes and , 7 % in 60 * 7 / 40 minutes = 10.5 minutes time taken by tom to finish the remaining on his own = 30 + 10.5 = 40.5 minutes ( adjusting for the 0.333 ) ~ 40 minutes answer : c" | a = 1 / 3
b = 1 / 2
c = a + b
d = 1 - c
e = 1 / 2
f = d / e
g = f * const_60
|
a ) 127 , b ) 688 , c ) 200 , d ) 121 , e ) 123 | c | divide(subtract(350, 340), divide(5, const_100)) | if 5 % more is gained by selling an article for rs . 350 than by selling it for rs . 340 , the cost of the article is ? | "let c . p . be rs . x . then , 5 % of x = 350 - 340 = 10 x / 20 = 10 = > x = 200 answer : c" | a = 350 - 340
b = 5 / 100
c = a / b
|
a ) a ) 7.24 , b ) b ) 2 , c ) c ) 8.5 , d ) d ) 6.67 , e ) e ) 3 | a | divide(power(3, 2), 2) | the current of a stream runs at the rate of 3 kmph . a boat goes 6 km and back to the starting point in 2 hours , then find the speed of the boat in still water ? | "s = 3 m = x ds = x + 3 us = x - 3 6 / ( x + 3 ) + 6 / ( x - 3 ) = 2 x = 7.24 answer : a" | a = 3 ** 2
b = a / 2
|
a ) 198 , b ) 200 , c ) 204 , d ) 207 , e ) 210 | d | add(180, multiply(180, divide(15, const_100))) | an article with cost price of 180 is sold at 15 % profit . what is the selling price ? | "sp = 1.15 * 180 = 207 answer : d" | a = 15 / 100
b = 180 * a
c = 180 + b
|
a ) rs . 3601 , b ) rs . 3618 , c ) rs . 4200 , d ) rs . 3619 , e ) rs . 3610 | c | subtract(multiply(add(1800, 150), add(15, const_1)), multiply(1800, 15)) | the average monthly salary of 15 employees in an organisation is rs . 1800 . if the manager ' s salary is added , then the average salary increases by rs . 150 . what is the manager ' s monthly salary ? | "manager ' s monthly salary = rs . ( 1950 * 16 - 1800 * 15 ) = rs . 4200 answer : c" | a = 1800 + 150
b = 15 + 1
c = a * b
d = 1800 * 15
e = c - d
|
a ) 2 , b ) 3 , c ) 4 , d ) 6 , e ) 8 | c | subtract(divide(multiply(8, add(const_4, const_1)), 24), add(const_4, const_1)) | 8 machines , each working at the same constant rate , together can complete a certain job in 24 days . how many additional machines , each working at the same constant rate , will be needed to complete the job in 16 days ? | "another solution which is faster is since each machine works at a constant rate . the time needs to bought down from 24 to 16 . so the new time is 2 / 3 of the original time . thus to achieve this we need the rate to be 3 / 2 of original . so 3 / 2 * 8 = 12 so we need 12 - 8 = 4 more machines . answer : c" | a = 4 + 1
b = 8 * a
c = b / 24
d = 4 + 1
e = c - d
|
a ) 27 , b ) 28 , c ) 29 , d ) 30 , e ) 31 | a | multiply(divide(subtract(52, divide(multiply(40, 62.5), const_100)), subtract(const_100, 40)), const_100) | a group of boy scouts and girls scouts is going on a rafting trip . 52 % of the scouts arrived with signed permission slips . if 40 % of the scouts were boy scouts and 62.5 % of the boy scouts arrived with signed permission slips , then what percentage of the children were girl scouts who arrived with signed permission slips ? | "we do n ' t know how many scouts went on the trip , so let ' s assume 100 scouts went on the trip ( since we only are concerned with percents in the answer ) 40 % were boy scouts so 40 % of 100 = 40 were boy scouts 62.5 % of the boy scouts brought their permission slips signed , so . 625 * 40 = 25 boy scouts had signed slips 15 boy scouts did not 52 % of all the scouts had signed slips , so . 52 * 100 = 52 in total had signed slips thus 52 - 25 = 27 girl scouts had signed slips thus the percentage of scouts who were girl scouts arriving with signed permission slips is 27 / 100 = . 27 = 27 % a" | a = 40 * 62
b = a / 100
c = 52 - b
d = 100 - 40
e = c / d
f = e * 100
|
a ) 10 % , b ) 33 1 / 3 % , c ) 40 % , d ) 50 % , e ) 66 2 / 3 % | b | divide(subtract(30, 25), subtract(divide(40, const_100), divide(25, const_100))) | seed mixture x is 40 percent ryegrass and 60 percent bluegrass by weight ; seed mixture y is 25 percent ryegrass and 75 % fescue . if a mixture of x and y contains 30 % ryegrass , what percent of the weight of the mixture is x ? | "assuming the weight of the mixture to be 100 g * * , then the weight of ryegrass in the mixture would be 30 g . also , assume the weight mixture x used in the mixture is xg , then the weight of mixture y used in the mixture would be ( 100 - x ) g . so we can now equate the parts of the ryegrass in the mixture as : 0.4 x + 0.25 ( 100 - x ) = 30 0.4 x + 25 - 0.25 x = 30 0.15 x = 5 x = 5 / 0.15 = 500 / 15 = 100 / 3 so the weight of mixture x as a percentage of the weight of the mixture = ( weight of x / weight of mixture ) * 100 % = ( 100 / 3 ) / 100 * 100 % = 33 % answer : b" | a = 30 - 25
b = 40 / 100
c = 25 / 100
d = b - c
e = a / d
|
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