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 ) 250 , e ) 316 | 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 3 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 6 ) : 4 * 5 * 4 * 4 = 320 numbers with three 3 - s , 3 x 3 x 3 4 * 1 * 1 * 1 = 4 thus there are 320 - 4 = 316 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 ) 35.67 % , b ) 64.75 % , c ) 68.00 % , d ) 69.57 % , e ) none of these | c | multiply(divide(subtract(subtract(multiply(const_2, multiply(const_100, const_10)), multiply(divide(32, const_100), subtract(multiply(const_2, multiply(const_100, const_10)), 900))), multiply(divide(32, const_100), 900)), multiply(const_2, multiply(const_100, const_10))), const_100) | in an examination , there were 2,000 candidates , out of which 900 candidates were girls and rest were boys . if 32 % of the boys and 32 % of the girls passed , then the total percentage of failed candidates is ? | "girls = 900 , boys = 1100 passed = ( 32 % of 1100 ) + ( 32 % of 900 ) = 352 + 288 = 640 failed = 2000 - 640 = 1360 failed % = [ ( 1360 / 2000 ) x 100 ] % = 68 % . answer : c" | a = 100 * 10
b = 2 * a
c = 32 / 100
d = 100 * 10
e = 2 * d
f = e - 900
g = c * f
h = b - g
i = 32 / 100
j = i * 900
k = h - j
l = 100 * 10
m = 2 * l
n = k / m
o = n * 100
|
a ) 24 , b ) 25 , c ) 26 , d ) 27 , e ) 29 | c | divide(add(multiply(multiply(divide(3, 2), 2), 7), 5), subtract(multiply(divide(3, 2), 2), 2)) | find ( 7 x + 5 y ) / ( x - 2 y ) if x / 2 y = 3 / 2 ? | "x / 2 y = 3 / 2 = > x = 6 y / 2 = 3 y = > ( 7 x + 5 y ) / ( x - 2 y ) = ( ( 7 * ( 3 y ) ) + 5 y ) / ( 3 y - 2 y ) = > 26 y / y = 26 answer : c" | a = 3 / 2
b = a * 2
c = b * 7
d = c + 5
e = 3 / 2
f = e * 2
g = f - 2
h = d / g
|
a ) 55 , b ) 56 , c ) 57 , d ) 58 , e ) 59 | c | add(45, multiply(add(59, const_1), divide(200, const_1000))) | when a student weighing 45 kgs left a class , the average weight of the remaining 59 students increased by 200 g . what is the average weight of the remaining 59 students | explanation : let the average weight of the 59 students be a . so the total weight of the 59 of them will be 59 * a . the questions states that when the weight of this student who left is added , the total weight of the class = 59 a + 45 when this student is also included , the average weight decreases by 0.2 kgs 59 a + 45 / 60 = a β 0.2 = > 59 a + 45 = 60 a - 12 = > 45 + 12 = 60 a - 59 a = > a = 57 answer : option c | a = 59 + 1
b = 200 / 1000
c = a * b
d = 45 + c
|
a ) 26.7 , b ) j = 30.0 , c ) j = 40.0 , d ) j = 53.3 , e ) 60.0 | c | divide(640, add(add(multiply(divide(divide(640, const_2), 80), const_2), divide(divide(640, const_2), 80)), divide(divide(640, const_2), 80))) | mike drives his new corvette from san francisco to las vegas , a journey of 640 miles . he drives the first half of the trip at an average rate of 80 miles per hour , but has to slow down for the second half of his journey . if the second half of the trip takes him 200 percent longer than the first half , what is his average rate j in miles per hour for the entire trip ? | veritas prepofficial solution correct answer : c using the formula : time = distance / rate , we find that mike takes 4 hours to cover the first 320 miles of his trip . since the 2 nd 320 miles take 200 % longer than the first , it takes mike 8 hours longer , or 12 hours . ( note : 200 % longer than the first half is not 200 % of the first half . ) the overall time is 4 hours + 12 hours or 16 hours . since the definition of average rate = total distance traveled / total time of travel , mike ' s average rate = 640 / 16 or 40 miles per hour . answer choice c is correct . | a = 640 / 2
b = a / 80
c = b * 2
d = 640 / 2
e = d / 80
f = c + e
g = 640 / 2
h = g / 80
i = f + h
j = 640 / i
|
a ) 2 , b ) 3 , c ) 4 , d ) 6 , e ) 8 | b | add(divide(power(2, 2), 2), const_1) | if f ( x ) = 12 - x ^ 2 / 2 and f ( 2 k ) = 3 k , what is one possible value for k ? | first of all , see thisgmat blog postand check the related lesson linked below for some background on function notation . we can plug anything in for x and get a result . you can find f ( 1 ) , for example , by plugging in 1 where x is , and you would get 12 - 1 / 2 = 11.5 . or we could find f ( 2 ) , which would be 12 - 4 / 2 = 10 . so the notation f ( 2 k ) means that we are going to plug a 2 k in for x everywhere in the formula for f ( x ) . that would be : f ( 2 k ) = 12 - ( 2 k ) ^ 2 / 2 = 12 - 2 k ^ 2 . remember that we have to square both the 2 and the k , to get 4 k 2 . now , this expression , the output , we will set equal to 2 k . 12 - 2 k ^ 2 = 2 k - - > k = - 4 or k = 3 . all the answers are positive , so we choose k = 3 . answer = b | a = 2 ** 2
b = a / 2
c = b + 1
|
a ) 48 , b ) 34 , c ) 44 , d ) 54 , e ) 64 | a | divide(multiply(56, 12), 14) | two numbers n and 14 have lcm = 56 and gcf = 12 . find n . | "the product of two integers is equal to the product of their lcm and gcf . hence . 14 Γ n = 56 Γ 12 n = 56 Γ 12 / 14 = 48 correct answer a" | a = 56 * 12
b = a / 14
|
a ) 201 mps , b ) 114 mps , c ) 118 mps , d ) 115 mps , e ) 111 mps | d | multiply(const_0_2778, 414) | express a speed of 414 kmph in meters per second ? | "414 * 5 / 18 = 115 mps answer : d" | a = const_0_2778 * 414
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a ) 1 / 2 , b ) 1 / 4 , c ) 2 / 4 , d ) 1 / 4 , e ) 1 / 4 | a | multiply(subtract(const_1, multiply(add(divide(const_1, 10), divide(const_1, 15)), 3)), 15) | two pipes p and q can fill a cistern in 10 and 15 minutes respectively . both are opened together , but at the end of 3 minutes the first is turned off . how much longer will the cistern take to fill ? | "3 / 10 + x / 15 = 1 x = 10 1 / 2 answer : a" | a = 1 / 10
b = 1 / 15
c = a + b
d = c * 3
e = 1 - d
f = e * 15
|
a ) 1400 , b ) 1600 , c ) 1800 , d ) 1500 , e ) 2000 | e | divide(multiply(divide(100, const_100), multiply(multiply(80, 150), 10)), 60) | the malibu country club needs to drain its pool for refinishing . the hose they use to drain it can remove 60 cubic feet of water per minute . if the pool is 80 feet wide by 150 feet long by 10 feet deep and is currently at 100 % capacity , how long will it take to drain the pool ? | "volume of pool = 80 * 150 * 10 cu . ft , 100 % full = 60 * 100 * 10 * 1 cu . ft water is available to drain . draining capacity = 60 cu . ft / min therefore time taken = 80 * 150 * 10 * 1 / 60 min = 2000 min e" | a = 100 / 100
b = 80 * 150
c = b * 10
d = a * c
e = d / 60
|
a ) 5 min , b ) 6 min , c ) 7 and 1 / 2 min , d ) 8 min , e ) 10 min | c | multiply(subtract(divide(divide(multiply(multiply(subtract(15, 10), divide(15, const_60)), const_60), 10), const_2), const_0_25), 10) | tom and john traveled in the same direction along the equal route at their constant speed rates of 15 km per hour and 10 km per hour , respectively . after 15 minutes tom passed john , tom reaches a certain gas station , how many r minutes it takes john to reach the station ? | since the question states β after 15 minutes β , we can say tom traveled 15 / 4 km for 15 minutes as he can travel 15 km per hour . hence , using the same logic , we can say john traveled 10 / 4 km as he travels 10 km per hour . so , john has to travel ( 15 / 4 ) - ( 10 / 4 ) km = 5 / 4 km more . since john β s speed is 10 km / hour , which means 1 km / 6 minutes . as he has to travel 5 / 4 km more , it is going to take him 6 ( 5 / 4 ) minutes . hence , r = 6 ( 5 / 4 ) = 15 / 2 minutes . the correct answer is c . | a = 15 - 10
b = 15 / const_60
c = a * b
d = c * const_60
e = d / 10
f = e / 2
g = f - const_0_25
h = g * 10
|
a ) $ 132,000 , b ) $ 50,000 , c ) $ 82,500 , d ) $ 92,000 , e ) $ 100,000 | a | divide(subtract(add(add(150000, multiply(150000, add(const_1, divide(20, const_100)))), multiply(multiply(150000, add(const_1, divide(20, const_100))), add(const_1, divide(20, const_100)))), add(add(add(100000, 50000), multiply(100000, add(const_1, divide(20, const_100)))), multiply(multiply(100000, add(const_1, divide(20, const_100))), add(const_1, divide(20, const_100))))), const_1000) | a professional athlete was offered a 3 - year contract to play with team k that provided for an annual salary of $ 100000 in the first year , an increase in annual salary of 20 % over the previous year for the next two years , and a bonus of $ 50000 on signing . team l offered a 3 - year contract providing for an annual salary of $ 150000 in the first year , an increase in annual salary of 20 % over the previous year for the next two years , and no signing bonus . if he accepts the offer of team l and fulfills the 3 - year contract terms , the athlete will receive how much more money by choosing team l over team k ? | team k ' s contract = $ 100,000 + $ 100,000 * 1.2 + $ 100,000 * 1.2 * 1.2 + $ 50,000 = $ 414,000 team l ' s contract = $ 150,000 + $ 150,000 * 1.2 + $ 150,000 * 1.2 * 1.2 = $ 546,000 the difference = $ 132,000 . answer : a . | a = 20 / 100
b = 1 + a
c = 150000 * b
d = 150000 + c
e = 20 / 100
f = 1 + e
g = 150000 * f
h = 20 / 100
i = 1 + h
j = g * i
k = d + j
l = 100000 + 50000
m = 20 / 100
n = 1 + m
o = 100000 * n
p = l + o
q = 20 / 100
r = 1 + q
s = 100000 * r
t = 20 / 100
u = 1 + t
v = s * u
w = p + v
x = k - w
y = x / 1000
|
a ) 1710 , b ) 1920 , c ) 2440 , d ) 2860 , e ) 3260 | a | divide(multiply(multiply(19, subtract(19, const_1)), 10), const_2) | there are 19 teams in the hockey league , and each team faces all the other teams 10 times each . how many games are played in the season ? | "the number of ways to choose two teams is 19 c 2 = 19 * 18 / 2 = 171 the total number of games in the season is 10 * 171 = 1710 . the answer is a ." | a = 19 - 1
b = 19 * a
c = b * 10
d = c / 2
|
a ) 20 , b ) 11 , c ) 9 , d ) 31 , e ) 21 | a | add(11, 9) | in a family 11 people eat only vegetarian , 6 people eat only non veg . , 9 people eat both veg and non veg . . how many people eat veg in the family ? | "total people eat veg = only veg + both veg and non veg total = 11 + 9 = 20 answer = a" | a = 11 + 9
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a ) 30 seconds , b ) 20 seconds , c ) 40 seconds , d ) 10 seconds , e ) none | a | divide(add(divide(divide(400, divide(multiply(7.2, const_1000), const_3600)), const_2), divide(400, divide(multiply(7.2, const_1000), const_3600))), const_10) | a cyclist climbs a hill with a length of 400 m with a speed of 7.2 km / h . when descending , the speed is two times greater . how much time is necessary for the cyclist to climb and descend the hill ? | 7.2 km = 7200 m . 1 h = 3600 s . the speed will be 7200 m / 3600 s = 2 m / s . the necessary time to climb will be 20 seconds . when descending , if the speed is two times greater , the necessary time will be two times smaller , so 10 seconds . the total necessary time is 20 s + 10 s = 30 seconds . answer a | a = 7 * 2
b = a / 3600
c = 400 / b
d = c / 2
e = 7 * 2
f = e / 3600
g = 400 / f
h = d + g
i = h / 10
|
a ) 32.7 , b ) 32.4 , c ) 22.4 , d ) 34.9 , e ) 35.1 | d | add(divide(circumface(6.8), const_2), multiply(6.8, const_2)) | the radius of a semi circle is 6.8 cm then its perimeter is ? | "36 / 7 r = 6.8 = 34.9 answer : d" | a = circumface / (
b = a + 2
|
a ) 0.35 , b ) 0.3505 , c ) 0.3509 , d ) 0.65 , e ) 0.3527 | d | multiply(divide(6.513, 10.02), const_100) | 6.513 / 10.02 = | "6.513 / 10.02 6.513 / 1002 = 6.5 move the comma two places to the left as we have 2 decimal places from the divisor : 0.65 . answer : d" | a = 6 / 513
b = a * 100
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a ) 18 , b ) 28 , c ) 48 , d ) 56 , e ) 60 | c | multiply(divide(divide(add(add(multiply(multiply(const_4, const_2), const_10), multiply(multiply(const_4, const_2), const_100)), multiply(const_12, const_1000)), 230), 7), 6) | the ratio between the number of sheep and the number of horses at the stewart farm is 6 to 7 , if each horse is fed 230 ounces of horse food per day and the farm needs a total 12,880 ounces of horse food per day , what is the number of sheep in the farm ? | "let the number of sheeps and horses be 4 x and 7 x . now total number of horses = total consumption of horse food / consumption per horse = 12880 / 230 = 56 , which is equal to 7 x . = > x = 8 sheeps = 6 x = 6 * 8 = 48 . hence c ." | a = 4 * 2
b = a * 10
c = 4 * 2
d = c * 100
e = b + d
f = 12 * 1000
g = e + f
h = g / 230
i = h / 7
j = i * 6
|
a ) 1 , b ) 6 , c ) 3 , d ) 5 , e ) 0 | e | divide(1, 11) | what is the 23 th digit to the right of the decimal point in the decimal form of 1 / 11 ? | "to solve , we first have to use some long division . long division allows us to get 1 / 11 in decimal form , which is 0.090909 β¦ where β 09 β is repeating . we see that the 1 st , 3 rd , 5 th digit to the right of the decimal point is a 0 and that the 2 nd , 4 th , 6 th digit to the right of the decimal point is a 9 . in other words , each odd - positioned digit is a 0 , and each even - positioned digit is a 9 . then the 23 th digit to the right of the decimal point and we see that 23 is odd , then 23 th digit is a 0 . answer e ." | a = 1 / 11
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a ) 25 , b ) 56 , c ) 45 , d ) 36 , e ) 44 | e | add(multiply(divide(subtract(subtract(add(multiply(const_4, const_2), 20), 4), 4), const_2), 4), 4) | the present age of the father is 4 years more than 4 times the age of his son . 4 years hence , father ' s age will be 20 years more than twice the age of the son . find the present age of the father ? | let the son ' s present age be x years father ' s present age = ( 4 x + 4 ) 4 x + 4 + 4 = 2 ( x + 4 ) + 10 4 x + 8 = 2 x + 18 x = 5 father ' s present age = 4 x + 4 = 4 * 10 + 4 = 44 years answer is e | a = 4 * 2
b = a + 20
c = b - 4
d = c - 4
e = d / 2
f = e * 4
g = f + 4
|
a ) - 1 , b ) - 4 , c ) - 3 , d ) 0 , e ) - 5 | c | divide(1, 3) | find the slope of the line perpendicular to the line y = ( 1 / 3 ) x - 7 | "two lines are perpendicular if the product of their slopes is equal to - 1 . the slope of the given line is equal to 1 / 3 . if m is the slope of the line perpendicular to the given line , then m Γ ( 1 / 3 ) = - 1 solve for m m = - 3 correct answer c ) - 3" | a = 1 / 3
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a ) 60 minutes , b ) 72 minutes , c ) 75 minutes , d ) 76 minutes , e ) 77 minutes | a | divide(3600, 60) | a scuba diver descends at a rate of 60 feet per minute . a diver dive from a ship to search for a lost ship at the depth of 3600 feet below the sea level . . how long will he take to reach the ship ? | time taken to reach = 3600 / 60 = 60 minutes answer : a | a = 3600 / 60
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a ) 35 , b ) 36 , c ) 37 , d ) 38 , e ) 39 | b | floor(divide(multiply(32, 8), 7)) | in a certain company , the ratio of the number of managers to the number of non - managers in any department must always be greater than 7 : 32 . in the company , what is the maximum number of non - managers in a department that has 8 managers ? | "8 / 7 * 32 = 36.6 the answer is b ." | a = 32 * 8
b = a / 7
c = math.floor(b)
|
a ) 9 , b ) 16 , c ) 15 , d ) 25 1 / 3 , e ) 28 1 / 2 | c | multiply(30, divide(multiply(3, 2), multiply(4, 3))) | a paint store mixes 3 / 4 pint of red paint and 2 / 3 pint of white paint to make a new paint color called perfect pink . how many pints of red paint would be needed to make 30 pints of perfect pink paint ? | 3 / 4 pint is required to make 3 / 4 + 2 / 3 = 17 / 12 pint of perfect pink so 17 / 12 pint requires 3 / 4 pint of red . . 1 pint will require 3 / 4 * 12 / 17 = 9 / 17 . . 30 pints will require 9 / 17 * 30 = 15 pints . . c | a = 3 * 2
b = 4 * 3
c = a / b
d = 30 * c
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a ) 7 , b ) 8 , c ) 9 , d ) 10 , e ) 12 | e | multiply(divide(multiply(const_10, 180), add(180, 230)), const_2) | a certain elevator has a safe weight limit of 2,500 pounds . what is the greatest possible number of people who can safely ride on the elevator at one time with the average ( arithmetic mean ) weight of half the riders being 180 pounds and the average weight of the others being 230 pounds ? | "lets assume there are 2 x people . half of them have average weight of 180 and other half has 230 . maximum weight is = 2500 so 180 * x + 230 * x = 2500 = > 410 x = 2500 = > x is approximately equal to 6 . so total people is 2 * 6 = 12 answer e ." | a = 10 * 180
b = 180 + 230
c = a / b
d = c * 2
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a ) 9 : 6 , b ) 3 : 2 , c ) 118 : 126 , d ) 122 : 193 , e ) 201 : 132 | d | divide(add(divide(2, add(3, 2)), divide(1, add(2, 1))), add(add(divide(2, add(3, 2)), divide(1, add(2, 1))), divide(3, add(4, 3)))) | there are 3 vessels of equal capacity . vessel a contains milk and water in the ratio 4 : 3 ; vessel b contains milk and water in the ratio 2 : 1 and vessel c contains milk and water in the ratio 3 : 2 . if the mixture in all the 3 vessels is mixed up . what will be the ratio of water to milk ? | 4 : 3 = > 4 x + 3 x = 7 x 2 : 1 = > 2 y + 1 y = 3 y 3 : 2 = > 3 z + 2 z = 5 z 7 x = 3 y = 5 z take lcm of 7 , 3,5 = 105 or simply ; x = 3 * 5 = 15 y = 7 * 5 = 35 z = 3 * 7 = 21 so , ratio of water : milk = ( 3 x + y + 2 z ) / ( 4 x + 2 y + 3 z ) = 122 / 193 ans : d | a = 3 + 2
b = 2 / a
c = 2 + 1
d = 1 / c
e = b + d
f = 3 + 2
g = 2 / f
h = 2 + 1
i = 1 / h
j = g + i
k = 4 + 3
l = 3 / k
m = j + l
n = e / m
|
a ) 2304 , b ) 2305 , c ) 2309 , d ) 2310 , e ) 2311 | a | divide(5625, power(add(divide(1, 4), 1), 4)) | each year for 4 years , a farmer increased the number of trees in a certain orchard by 1 / 4 of the number of trees in the orchard of the preceding year . if all of the trees thrived and there were 5625 trees in the orchard at the end of 4 year period , how many trees were in the orchard at the beginning of the 4 year period . | "trees increase by 1 / 4 the number of trees in preceding year . hence , correct answer must be divisible by 4 . based on divisibility rules , if last 2 digits are divisible by 4 then the number is divisible by 4 . thus , we can eliminate b , c , d , e the answer to be a again , trees increase by 1 / 4 the number of trees in preceding year . hence , the number of trees increase by 5 / 4 times the number of trees the preceding year . if x = initial number of trees = 2304 year 1 = 5 / 4 x year 2 = ( 5 / 4 ) ( 5 / 4 ) x year 3 = ( 5 / 4 ) ( 5 / 4 ) ( 5 / 4 ) x year 4 = ( 5 / 4 ) ( 5 / 4 ) ( 5 / 4 ) ( 5 / 4 ) x only for answer d : ( 5 / 4 ) ( 5 / 4 ) ( 5 / 4 ) ( 5 / 4 ) 2304 = 5625 hence , correct answer = a" | a = 1 / 4
b = a + 1
c = b ** 4
d = 5625 / c
|
a ) 43 , b ) 58 , c ) 60 , d ) 70 , e ) 80 | b | divide(add(negate(10), sqrt(subtract(power(negate(10), 2), multiply(const_4, negate(divide(multiply(800, 10), 2)))))), 2) | the time it took car p to travel 800 miles was 2 hours less than the time it took car r to travel the same distance . if car p β s average speed was 10 miles per hour greater than that of car r , what was car r β s average speed , in miles per hour ? | "let speed of car r be = x then speed of car p = x + 10 a / q , ( 800 / x ) - ( 800 / ( x + 10 ) ) = 2 solving for x = 58 miles \ hr . b" | a = negate + (
b = negate ** (
c = b - 2
d = 800 * 10
e = d / 2
f = 4 * negate
g = math.sqrt(c)
h = a / g
|
a ) 1 hour , b ) 1 1 / 2 hours , c ) 2 hours , d ) 2 1 / 2 hours , e ) 3 hours | d | subtract(50, 40) | a flamboyant comic book villain has abducted a bystander ! captain valiant is alerted to the crime and reaches the start of the villain ' s trail 30 minutes later . the villain is in a getaway car going 40 kmph , and captain valiant can fly at 50 kmph . how long will the bystander have to wait for rescue ? | distance covered by the villain in 1 / 2 hour = 20 km now , 10 km is compensated in 1 hour therefore 20 km will be compensated in 2 hours added to the half hour head start , the bystander has been kidnapped for 2 1 / 2 hours . correct answer : d | a = 50 - 40
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a ) 15 , b ) 17 , c ) 20 , d ) 8 , e ) 9 | c | divide(multiply(5, 4), subtract(5, 4)) | a man can do a piece of work in 5 days , but with the help of his son , he can do it in 4 days . in what time can the son do it alone ? | "son ' s 1 day ' s work = ( 1 / 4 ) - ( 1 / 5 ) = 1 / 20 the son alone can do the work in 20 days answer is c" | a = 5 * 4
b = 5 - 4
c = a / b
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a ) 150 meter , b ) 876 meter , c ) 167 meter , d ) 450 meter , e ) 169 meter | d | multiply(divide(multiply(60, const_1000), const_3600), 27) | a train running at the speed of 60 km / hr crosses a pole in 27 seconds . find the length of the train ? | "speed = 60 * ( 5 / 18 ) m / sec = 50 / 3 m / sec length of train ( distance ) = speed * time ( 50 / 3 ) * 27 = 450 meter answer : d" | a = 60 * 1000
b = a / 3600
c = b * 27
|
a ) 19 , b ) 17 , c ) 13 , d ) 9 , e ) 8 | b | add(const_12, multiply(10, const_4)) | find the greatest number that will divide 400 , 435 and 541 leaving 9 , 10 and 14 as remainders respectively | "explanation : answer will be hcf of ( 400 - 9 , 435 - 10 , 541 - 14 ) hcf of ( 391 , 425 , 527 ) = 17 option b" | a = 10 * 4
b = 12 + a
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a ) 9900 , b ) 9999 , c ) 9988 , d ) 9944 , e ) 9966 | d | multiply(floor(divide(power(const_10, 4), 88)), 88) | what is the largest 4 digit number exactly divisible by 88 | "explanation : largest 4 digit number is 9999 after doing 9999 Γ· 88 we get remainder 55 hence largest 4 digit number exactly divisible by 88 = 9999 - 55 = 9944 answer : option d" | a = 10 ** 4
b = a / 88
c = math.floor(b)
d = c * 88
|
a ) 30 % gain , b ) 30 % loss , c ) 40 % gain , d ) 40 % loss , e ) 50 % loss | d | multiply(const_100, divide(subtract(const_100, divide(multiply(const_100, 25), 15)), divide(multiply(const_100, 25), 15))) | if the cost price of 15 articles is same as the selling price of 25 articles . find the gain or loss percentage ? | "explanation : 15 cp = 25 sp cost price cp = 25 selling price sp = 15 formula = ( sp - cp ) / cp * 100 = ( 15 - 25 ) / 25 * 100 = 40 % loss answer : option d" | a = 100 * 25
b = a / 15
c = 100 - b
d = 100 * 25
e = d / 15
f = c / e
g = 100 * f
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a ) 1.0875 days , b ) 0.1875 days , c ) 0.0675 days , d ) 0.0875 days , e ) 0.0775 days | d | inverse(add(inverse(16), inverse(40))) | a and b complete a work in 16 days . a alone can do it in 40 days . if both together can do the work in how many days ? | "1 / 16 + 1 / 40 = 0.0875 days answer : d" | a = 1/(16)
b = 1/(40)
c = a + b
d = 1/(c)
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a ) 188 cm 2 , b ) 165 cm 2 , c ) 168 cm 2 , d ) 198 cm 2 , e ) 987 cm 2 | b | multiply(multiply(divide(const_1, const_2), add(6, 9)), 22) | find the area of the quadrilateral of one of its diagonals is 22 cm and its off sets 9 cm and 6 cm ? | "1 / 2 * 22 ( 9 + 6 ) = 165 cm 2 answer : b" | a = 1 / 2
b = 6 + 9
c = a * b
d = c * 22
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a ) 22 , b ) 30 , c ) 88 , d ) 71 , e ) 11 | b | divide(multiply(multiply(3, const_2), 10), subtract(8, multiply(3, const_2))) | a work which could be finished in 8 days was finished 3 days earlier after 10 more men joined . the number of men employed was ? | "x - - - - - - - 8 ( x + 10 ) - - - - 6 x * 8 = ( x + 10 ) 6 x = 30 \ answer : b" | a = 3 * 2
b = a * 10
c = 3 * 2
d = 8 - c
e = b / d
|
a ) 25 % , b ) 20 % , c ) 50 % , d ) 66 2 / 3 % , e ) 75 % | b | multiply(divide(subtract(30, 25), 25), const_100) | a certain protective additive increases from 25 days to 30 days the time between required maintenance checks on an industrial vehicle . by what percent is the time between maintenance checks increased by using the additive ? | "general formula for percent increase or decrease , ( percent change ) : percent = change / original β 100 so , the time between maintenance checks increased by 30 β 25 / 25 β 100 = 20 answer : b ." | a = 30 - 25
b = a / 25
c = b * 100
|
a ) 72 , b ) 83 , c ) 45 , d ) 53 , e ) 64 | a | subtract(multiply(8, 61), subtract(multiply(13, 58), multiply(57, 7))) | the average of 13 numbers is 58 . average of the first 7 of them is 57 and that of the last 7 is 61 . find the 8 th number ? | "sum of all the 13 numbers = 13 * 58 = 754 sum of the first 7 of them = 7 * 57 = 399 sum of the last 7 of them = 7 * 61 = 427 so , the 8 th number = 427 + 399 - 754 = 72 . answer : a" | a = 8 * 61
b = 13 * 58
c = 57 * 7
d = b - c
e = a - d
|
a ) 8 : 5 , b ) 8 : 9 , c ) 2 : 2 , d ) 8 : 2 , e ) 2 : 8 | a | divide(divide(1, 40), power(divide(1, 2), 2)) | the volumes of two cones are in the ratio 1 : 40 and the radii of the cones are in the ratio of 1 : 2 . what is the length of the wire ? | "the volume of the cone = ( 1 / 3 ) Ο r 2 h only radius ( r ) and height ( h ) are varying . hence , ( 1 / 3 ) Ο may be ignored . v 1 / v 2 = r 1 ^ 2 . h 1 / r 2 ^ 2 . h 2 = > 1 / 40 = ( 1 ) ^ 2 h 1 / ( 2 ) ^ 2 h 2 = > h 1 / h 2 = 8 / 5 i . e . h 1 : h 2 = 8 : 5 answer : a" | a = 1 / 40
b = 1 / 2
c = b ** 2
d = a / c
|
a ) 7.5 % , b ) 9.1 % , c ) 10.9 % , d ) 12.6 % , e ) 15 % | c | multiply(divide(10, add(10, const_100)), const_100) | in the new budget the price of milk rose by 10 % . 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 % = 10 / 110 * 100 = 9.1 % answer is c" | a = 10 + 100
b = 10 / a
c = b * 100
|
a ) 90 , b ) 2,700 , c ) 4,500 , d ) 5,400 , e ) 2,850 | e | divide(multiply(add(40, 55), const_60), const_2) | a copy machine , working at a constant rate , makes 40 copies per minute . a second copy machine , working at a constant rate , makes 55 copies per minute . working together at their respective rates , how many copies do the two machines make in half an hour ? | together the two machines make 40 + 55 = 95 copies per minute . so , in half an hour they will make 95 * 30 = 2,850 copies . answer : e . | a = 40 + 55
b = a * const_60
c = b / 2
|
a ) 24 , b ) 18 , c ) 16 , d ) 12 , e ) 8 | e | multiply(multiply(4, 2), divide(6, 6)) | working simultaneously and independently at an identical constant rate , 4 machines of a certain type can produce a total of x units of product p in 6 days . how many of these machines , working simultaneously and independently at this constant rate , can produce a total of 2 x units of product p in 6 days ? | "4 machines do x units in 6 days we have x / 6 = > rate of the 4 machines we know that we need to have 2 x units in 4 days therefore , we need to get to 2 x / 4 rate of the machines . rate of one machine is x / 6 * 1 / 4 = x / 24 . now , we need to know how many machines need to work simultaneously , to get 2 x done in 6 days . 2 x / 6 work needs to be done by machines that work at x / 24 rate . let ' s assign a constant y for the number of machines : ( x / 24 ) * y = 2 x / 6 y = 2 x / 6 * 24 / x cancel 6 with 24 , and x with x and get - > 8 . answer choice e" | a = 4 * 2
b = 6 / 6
c = a * b
|
a ) 40 , b ) 42 , c ) 44 , d ) 46 , e ) 48 | b | add(17, sqrt(subtract(divide(multiply(10, 7), 5), 7))) | evaluate : 17 + sqrt ( - 7 + 10 Γ£ β 6 Γ£ Β· 5 ) = ? | "according to order of operations , inner brackets first where 10 x 6 Γ£ Β· 5 is first calculated since it has a multiplication and a division . 10 x 6 Γ£ Β· 5 = 60 Γ£ Β· 5 = 12 hence 17 + sqrt ( - 7 + 10 Γ£ β 6 Γ£ Β· 5 ) = 17 + sqrt ( - 7 + 12 ) = 17 + sqrt ( 5 ) = 17 + 25 = 42 correct answer b ) 42" | a = 10 * 7
b = a / 5
c = b - 7
d = math.sqrt(c)
e = 17 + d
|
a ) 290 / 289 , b ) 1 / 289 , c ) 290 / 90 , d ) 362 / 361 , e ) none of these | d | add(power(divide(const_1, const_1), const_2), power(divide(const_1, 19), const_2)) | product of two natural numbers is 19 . then , the sum of reciprocals of their squares is | explanation : if the numbers are a , b , then ab = 19 , as 17 is a prime number , so a = 1 , b = 19 . 1 / a 2 + 1 / b 2 = 1 / 1 ( 2 ) + 1 / 19 ( 2 ) = 362 / 361 option d | a = 1 / 1
b = a ** 2
c = 1 / 19
d = c ** 2
e = b + d
|
a ) - 4 , b ) - 6 , c ) - 2 , d ) - 10 , e ) - 8 | c | add(divide(120, const_10), divide(120, divide(120, const_10))) | if a ( a + 2 ) = 120 and b ( b + 2 ) = 120 , where a β b , then a + b = | "i . e . if a = 10 then b = - 12 or if a = - 12 then b = 10 but in each case a + b = - 12 + 10 = - 2 answer : c" | a = 120 / 10
b = 120 / 10
c = 120 / b
d = a + c
|
['a ) 22 / 7 x 24 / 35', 'b ) 22 / 7 x 36 x 4', 'c ) 22 / 7 x 36 / 5', 'd ) 22 / 7 x 37 / 21', 'e ) 22 / 7 x 32 / 21'] | a | divide(subtract(volume_cylinder(6, add(10, 4)), volume_cylinder(6, 10)), multiply(multiply(5, 6), 7)) | a rectangular block has the dimensions 5 x 6 x 7 cm it is dropped into a cylindrical vessel of radius 6 cm and height 10 cm . if the level of the fluid in the cylinder rises by 4 cm , what portion of the block is immersed in the fluid ? | explanation : since level of water increased in cylinder by height 4 . this is because of the rectangular block . therefore , area of rectangular block immersed in water is = 22 / 7 x ( 6 ) ^ 2 x 4 thats why portion of block immersed in water is = ( 22 / 7 x 36 x 4 ) / total vol . of rectangle = ( 22 / 7 x 36 x 4 ) / ( 7 x 5 x 6 ) = 22 / 7 x 24 / 35 . answer is a | a = 10 + 4
b = volume_cylinder - (
c = b / volume_cylinder
|
a ) 35 , b ) 36 , c ) 37 , d ) 38 , e ) 39 | b | multiply(divide(630, multiply(63, const_1000)), const_3600) | a train 630 m long , running with a speed of 63 km / hr will pass a tree in ? | "speed = 63 * 5 / 18 = 35 / 2 m / sec time taken = 630 * 2 / 35 = 36 sec answer : option b" | a = 63 * 1000
b = 630 / a
c = b * 3600
|
a ) 5 / 9 , b ) 3 / 15 , c ) 26 / 100 , d ) 43 / 60 , e ) 53 / 90 | c | divide(add(multiply(multiply(1, 3), 3), 2), multiply(2, multiply(5, 1))) | of the female students at barkely university , 1 / 6 are on the honor roll . of the male students , 2 / 5 are on the honor roll . if 3 / 5 of the students are female , what fraction of all the students are on the honor roll ? | "let the total students be 100 given 3 / 5 of the students are females = 60 then males = 2 / 5 = 40 1 / 6 of the females are on honor roll = 10 males on the honor roll = 2 / 5 = 16 total students on honor roll = 10 + 16 = 26 fraction = 26 / 100 c" | a = 1 * 3
b = a * 3
c = b + 2
d = 5 * 1
e = 2 * d
f = c / e
|
a ) 20 . , b ) 21 . , c ) 22 . , d ) 23 . , e ) 24 . | c | add(divide(1430, add(divide(1430, add(add(const_10, const_10), const_2)), 45)), 9) | a basket of 1430 apples is divided equally among a group of apple lovers . if 45 people join the group , each apple lover would receive 9 apples less . how many u apples did each person get before 45 people joined the feast ? | "before solving it algebraically , let us prime factorize 1430 = 2 * 5 * 11 * 13 . since number of apples per person * total persons u = 1430 , the answer should be a factor of 1430 . only c is . and that ' s your answer . c" | a = 10 + 10
b = a + 2
c = 1430 / b
d = c + 45
e = 1430 / d
f = e + 9
|
a ) 5037 , b ) 5447 , c ) 5867 , d ) 6297 , e ) 6617 | d | add(lcm(lcm(18, 70), lcm(100, 21)), 3) | what is the smallest number which when increased by 3 is divisible by 18 , 70 , 100 and 21 ? | "when increased by 3 , the number must include at least 2 ^ 2 * 3 ^ 2 * 5 ^ 2 * 7 = 6300 the answer is d ." | a = math.lcm(18, 70)
b = math.lcm(100, 21)
c = math.lcm(a, b)
d = c + 3
|
a ) 343 , b ) 199 , c ) 121 , d ) 69 , e ) 249 | a | power(add(multiply(2, power(add(multiply(2, power(add(1, multiply(2, 0)), 0)), 1), 1)), 1), power(add(multiply(2, power(add(1, multiply(2, 0)), 0)), 1), 1)) | if a ( k ) = ( 2 k + 1 ) ^ k , and k = 0 , what is the value of a ( a ( a ( k ) ) ) ? | a ( a ( a ( 0 ) ) ) = a ( a ( 1 ) ) = a ( 3 ) = ( 6 + 1 ) ^ 3 = 343 . thus , the answer is a . | a = 2 * 0
b = 1 + a
c = b ** 0
d = 2 * c
e = d + 1
f = e ** 1
g = 2 * f
h = g + 1
i = 2 * 0
j = 1 + i
k = j ** 0
l = 2 * k
m = l + 1
n = m ** 1
o = h ** n
|
a ) 21 , b ) 22 , c ) 23 , d ) 25 , e ) 24 | e | divide(subtract(add(add(27, 3), 27), subtract(11, 2)), subtract(11, subtract(11, 2))) | the cricket team of 11 members is 27 yrs old & the wicket keeper is 3 yrs older . if the ages ofthese 2 are excluded , the average age of theremaining players is 1 year less than the average age of the whole team . what is the average age of the team ? | "let the average age of the whole team be x years . 11 x - ( 27 + 30 ) = 9 ( x - 1 ) = > 11 x - 9 x = 48 = > 2 x = 48 = > x = 24 . so , average age of the team is 24 years . e" | a = 27 + 3
b = a + 27
c = 11 - 2
d = b - c
e = 11 - 2
f = 11 - e
g = d / f
|
a ) 15 , b ) 20 , c ) 13 , d ) 17 , e ) 22 | d | add(divide(subtract(89, 1), 5), const_1) | how many multiples of 5 are there between 1 and 89 ? | "5 multiples are 5 , 10,15 , - - - - - - - - - , 80,85 it should be mentioned whether 1 and 89 are inclusive . the answer is ( 85 - 5 ) / 5 + 1 = 17 answer is d" | a = 89 - 1
b = a / 5
c = b + 1
|
a ) 6 , b ) 7 , c ) 8 , d ) 9 , e ) 10 | b | add(floor(divide(subtract(subtract(40, 12), subtract(20, 5)), const_2)), 1) | the scoring system in a certain football competition goes as follows : 3 points for victory , 1 point for a draw , and 0 points for defeat . each team plays 20 matches . if a team scored 12 points after 5 games , what is the least number of the remaining matches it has to win to reach the 40 - point mark by the end of the tournament ? | "to get 40 points as end of season we need another 28 points or more from remaining 15 matches : option a = 6 * 3 + 9 * 1 = 27 option b = 7 * 3 + 8 * 1 = 29 hence option b - 7" | a = 40 - 12
b = 20 - 5
c = a - b
d = c / 2
e = math.floor(d)
f = e + 1
|
a ) 7 , b ) 6 , c ) 5 , d ) 4 , e ) 3 | e | floor(divide(log(divide(31,000, 3.134)), log(10))) | if x is an integer and 3.134 Γ 10 ^ x is less than 31,000 what is the greatest possible value for x ? | "if x = 4 3.134 Γ 10 ^ 4 = 31340 > 31000 so , x = 3 answer : e" | a = 31 / 0
b = math.log(a)
c = math.log(10)
d = b / c
e = math.floor(d)
|
a ) 10 hours , b ) 12 hours , c ) 14 hours , d ) 15 hours , e ) none of these | d | add(divide(40, subtract(6, 2)), divide(40, add(6, 2))) | in a river flowing at 2 km / hr , a boat travels 40 km upstream and then returns downstream to the starting point . if its speed in still water be 6 km / hr , find the total journey time . | "explanation : speed of the boat = 6 km / hr speed downstream = ( 6 + 2 ) = 8 km / hr speed upstream = ( 6 - 2 ) = 4 km / hr distance travelled downstream = distance travelled upstream = 40 km total time taken = time taken downstream + time taken upstream = ( 40 / 8 ) + ( 40 / 4 ) = 15 d" | a = 6 - 2
b = 40 / a
c = 6 + 2
d = 40 / c
e = b + d
|
a ) 45 min , b ) 60 min , c ) 55 min , d ) 70 min , e ) 80 min | b | divide(multiply(48, divide(50, const_60)), divide(40, const_60)) | a train covers a distance in 50 min , if it runs at a speed of 48 kmph on an average . the speed at which the train must run to reduce the time of journey to 40 min will be | "time = 50 / 60 hr = 5 / 6 hr speed = 48 mph distance = s * t = 48 * 5 / 6 = 40 km time = 40 / 60 hr = 2 / 3 hr new speed = 40 * 3 / 2 kmph = 60 kmph answer : b ." | a = 50 / const_60
b = 48 * a
c = 40 / const_60
d = b / c
|
a ) 1 , b ) 50 , c ) 19 , d ) 20 , e ) 21 | b | subtract(multiply(divide(100, 2), add(divide(100, 2), 1)), multiply(divide(add(99, 1), 2), add(divide(subtract(99, 1), 2), 1))) | ifaequals the sum of the even integers from 2 to 100 , inclusive , andbequals the sum of the odd integers from 1 to 99 , inclusive , what is the value of a - b ? | "this is a solution from beatthegmat : even numbers : ( 100 - 2 ) / 2 + 1 = 50 even integers . ( 100 + 2 ) / 2 = 51 is the average of the even set . sum = avg * ( # of elements ) = 51 * 50 = 2550 = a odd numbers : ( 99 - 1 ) / 2 + 1 = 50 odd integers . ( 99 + 1 ) / 2 = 50 is the average of the odd set . sum = avg * ( # of elements ) = 50 * 50 = 2500 = b a - b = 2550 - 2500 = 50 . ( b )" | a = 100 / 2
b = 100 / 2
c = b + 1
d = a * c
e = 99 + 1
f = e / 2
g = 99 - 1
h = g / 2
i = h + 1
j = f * i
k = d - j
|
a ) 26 , b ) 28 , c ) 29 , d ) 30 , e ) 27 | e | add(divide(subtract(102, add(add(const_1, const_2), 3)), 4), 3) | the sum of 4 consecutive numbers is 102 . the greatest among these 3 number is : | let the numbers be x , x + 1 , x + 2 and x + 3 then , x + ( x + 1 ) + ( x + 2 ) + ( x + 3 ) = 102 4 x = 96 x = 24 greatest number , ( x + 3 ) = 27 answer : e | a = 1 + 2
b = a + 3
c = 102 - b
d = c / 4
e = d + 3
|
a ) 14 , b ) 16 , c ) 18 , d ) 20 , e ) 22 | e | multiply(divide(add(multiply(3, const_10), const_3), 3), const_2) | the sum of all possible two digit numbers formed from 3 different one digit natural numbers when divided by the sum of the original 3 numbers is equal to ? | let the one digit numbers x , y , z sum of all possible two digit numbers = ( 10 x + y ) + ( 10 x + z ) + ( 10 y + x ) + ( 10 y + z ) + ( 10 z + x ) + ( 10 z + y ) = 22 ( x + y + z ) therefore sum of all possible two digit numbers when divided by sum of one digit numbers gives 22 . answer e | a = 3 * 10
b = a + 3
c = b / 3
d = c * 2
|
a ) 13.25 , b ) 14.36 , c ) 15.85 , d ) 12.27 , e ) 11.25 | d | divide(multiply(subtract(const_100, 10), 18), add(const_100, 32)) | if a man lost 10 % by selling oranges at the rate of 18 a rupee at how many a rupee must he sell them to gain 32 % ? | "90 % - - - - 18 132 % - - - - ? 90 / 132 * 18 = 12.27 answer : d" | a = 100 - 10
b = a * 18
c = 100 + 32
d = b / c
|
a ) 26.7 , b ) z = 30.0 , c ) z = 40.0 , d ) z = 53.3 , e ) 60.0 | c | divide(640, add(add(multiply(divide(divide(640, const_2), 80), const_2), divide(divide(640, const_2), 80)), divide(divide(640, const_2), 80))) | mike drives his new corvette from san francisco to las vegas , a journey of 640 miles . he drives the first half of the trip at an average rate of 80 miles per hour , but has to slow down for the second half of his journey . if the second half of the trip takes him 200 percent longer than the first half , what is his average rate z in miles per hour for the entire trip ? | "veritas prepofficial solution correct answer : c using the formula : time = distance / rate , we find that mike takes 4 hours to cover the first 320 miles of his trip . since the 2 nd 320 miles take 200 % longer than the first , it takes mike 8 hours longer , or 12 hours . ( note : 200 % longer than the first half is not 200 % of the first half . ) the overall time is 4 hours + 12 hours or 16 hours . since the definition of average rate = total distance traveled / total time of travel , mike ' s average rate = 640 / 16 or 40 miles per hour . answer choice c is correct ." | a = 640 / 2
b = a / 80
c = b * 2
d = 640 / 2
e = d / 80
f = c + e
g = 640 / 2
h = g / 80
i = f + h
j = 640 / i
|
a ) $ 1010 , b ) $ 1100 , c ) $ 1110 , d ) $ 1101 , e ) $ 1200 | b | divide(12100, 11) | john is going with 10 friends on a trip to sidney for spring break . airfare and hotel costs a total of $ 12100.00 for the group of 11 friends . how much does each person have to pay for their hotel and airfare ? | answer = b the total cost of the trip ( $ 12100.00 ) divided by 11 equals $ 1100.00 . | a = 12100 / 11
|
a ) 20 , b ) 25 , c ) 30 , d ) 40 , e ) 50 | d | divide(80, const_2) | a soccer store typically sells replica jerseys at a discount of 30 percent to 50 percent off list price . during the annual summer sale , everything in the store is an additional 20 percent off the original list price . if a replica jersey ' s list price is $ 80 , approximately what r percent of the list price is the lowest possible sale price ? | let the list price be 2 x for min sale price , the first discount given should be 50 % , 2 x becomes x here now , during summer sale additional 20 % off is given ie sale price becomes 0.8 x it is given lise price is $ 80 = > 2 x = 80 = > x = 40 and 0.8 x = 32 so lowest sale price is 32 , which r is 40 % of 80 hence , d is the answer | a = 80 / 2
|
a ) 1 / 6 , b ) 1 / 2 , c ) 5 / 8 , d ) 5 / 4 , e ) 15 / 16 | d | divide(subtract(0.75, 0.5), subtract(0.7, 0.5)) | last month , john rejected 0.5 % of the products that he inspected and jane rejected 0.7 percent of the products that she inspected . if total of 0.75 percent of the products produced last month were rejected , what fraction of the products did jane inspect ? | x - fraction of products jane inspected ( 1 - x ) - fraction of products john inspected 0.7 ( x ) + 0.5 ( 1 - x ) = 0.75 0.2 x = 0.75 - 0.5 x = 0.25 / 0.2 x = 5 / 4 therefore the answer is d : 5 / 4 . | a = 0 - 75
b = 0 - 7
c = a / b
|
['a ) 978', 'b ) 789', 'c ) 999', 'd ) 778', 'e ) 787'] | c | multiply(multiply(subtract(multiply(sqrt(3136), const_4), multiply(const_2, const_1)), 1.5), const_3) | the area of a square field 3136 sq m , if the length of cost of drawing barbed wire 3 m around the field at the rate of rs . 1.50 per meter . two gates of 1 m width each are to be left for entrance . what is the total cost ? | a 2 = 3136 = > a = 56 56 * 4 * 3 = 672 β 6 = 666 * 1.5 = 999 answer : c | a = math.sqrt(3136)
b = a * 4
c = 2 * 1
d = b - c
e = d * 1
f = e * 3
|
a ) 5 , b ) 10 , c ) 12 , d ) 20 , e ) 25 | d | multiply(divide(50, subtract(multiply(34, 2), 63)), 2) | a firm is comprised of partners and associates in a ratio of 2 : 63 . if 50 more associates were hired , the ratio of partners to associates would be 1 : 34 . how many partners are currently in the firm ? | the ratio 1 : 34 = 2 : 68 so the ratio changed from 2 : 63 to 2 : 68 . 68 - 63 = 5 which is 1 / 10 of the increase in 50 associates . the ratio changed from 20 : 630 to 20 : 680 . thus the number of partners is 20 . the answer is d . | a = 34 * 2
b = a - 63
c = 50 / b
d = c * 2
|
a ) 7 , b ) 9 , c ) 12 , d ) 14 , e ) 18 | d | subtract(divide(multiply(multiply(divide(4, add(4, 3)), 42), 4), 3), multiply(divide(3, add(4, 3)), 42)) | a certain drink of type a is prepared by mixing 4 parts milk with 3 parts fruit juice . another drink of type b is prepared by mixing 4 parts of fruit juice and 3 parts of milk . how many liters of fruit juice must be added to 42 liters of drink a to convert it to drink b ? | in 42 liters of drink a , there are 24 liters of milk and 18 liters of juice . with 24 liters of milk , we need a total of 32 liters of juice to make drink b . we need to add 14 liters of juice . the answer is d . | a = 4 + 3
b = 4 / a
c = b * 42
d = c * 4
e = d / 3
f = 4 + 3
g = 3 / f
h = g * 42
i = e - h
|
a ) 18 , b ) 28 , c ) 40 , d ) 56 , e ) 58 | c | multiply(divide(divide(12880, 230), 7), 5) | the ratio between the number of sheep and the number of horses at the stewar farm is 5 to 7 . if each of horse is fed 230 ounces of horse food per day and the farm needs a total 12880 ounces of horse food per day . what is number sheep in the form ? ? | "et no of sheep and horses are 5 k and 7 k no of horses = 12880 / 230 = 56 now 7 k = 56 and k = 8 no of sheep = ( 5 * 8 ) = 40 answer : c" | a = 12880 / 230
b = a / 7
c = b * 5
|
a ) 1.5 , b ) 2 , c ) 2.4 , d ) 3 , e ) 3.6 | e | divide(multiply(6, const_3), add(const_3, const_2)) | working alone , tom finishes cleaning half the house in a third of the time it takes nick to clean the entire house alone . tom alone cleans the entire house in 6 hours . how many hours will it take nick and tom to clean the entire house if they work together ? | answer is 3.6 hours . tom does the complete house in 6 hours while nick does it in 9 hours . 1 / ( 1 / 6 + 1 / 9 ) = 3.6 answer is e | a = 6 * 3
b = 3 + 2
c = a / b
|
a ) 80 , b ) 160 , c ) 240 , d ) 360 , e ) 400 | e | add(divide(360, 9), 360) | of the people who responded to a market survey , 360 preferred brand x and the rest preferred brand y . if the respondents indicated a preference for brand x over brand y by ratio of 9 to 1 , how many people responded to the survey ? | "ratio = 9 : 1 = > 9 x respondents preferred brand x and x preferred brand y since , no . of respondents who preferred brand x = 360 = > 9 x = 360 = > x = 40 hence total no . of respondents = 360 + 40 = 400 hence e is the answer ." | a = 360 / 9
b = a + 360
|
a ) 80 litres , b ) 90 litres , c ) 120 litres , d ) 180 litres , e ) none of these | d | multiply(1200, multiply(800, divide(90, multiply(800, 600)))) | 90 litres of diesel is required to travel 600 km using a 800 cc engine . if the volume of diesel required to cover a distance varies directly as the capacity of the engine , then how many litres of diesel is required to travel 800 km using 1200 cc engine ? | "explanatory answer to cover a distance of 800 kms using a 800 cc engine , the amount of diesel required = 800 / 600 * 90 = 120 litres . however , the vehicle uses a 1200 cc engine and the question states that the amount of diesel required varies directly as the engine capacity . i . e . , for instance , if the capacity of engine doubles , the diesel requirement will double too . therefore , with a 1200 cc engine , quantity of diesel required = 1200 / 800 * 120 = 180 litres . answer d" | a = 800 * 600
b = 90 / a
c = 800 * b
d = 1200 * c
|
a ) a . 0.156 , b ) b . 0.01506 , c ) c . 0.0156 , d ) d . 0.0001566 , e ) e . 0.00001566 | c | divide(add(divide(divide(multiply(1000, 60), 40), 50), 9), add(divide(multiply(1000, 60), 40), 1000)) | machine β a produces 40 % of the total output and machine - b produces 60 % of the total output . an average of 9 units out of a 1000 goods manufactured by machine - a and one unit of 50 units produced by machine - b prove to be defective . what is the probability that a unit chosen at random from the total daily output of the factory is defective ? | let total production be 10000 units . . . . a produces 4000 units and 36 units are defective b produces 6000 units and 120 units are defective so , out of total 10,000 units 156 units are defective . . . so the required probability = 156 / 10000 = > 0.0156 answer will be ( c ) | a = 1000 * 60
b = a / 40
c = b / 50
d = c + 9
e = 1000 * 60
f = e / 40
g = f + 1000
h = d / g
|
a ) 41.1 sec , b ) 64.8 sec , c ) 31.8 sec , d ) 50.4 sec , e ) none of the above | b | divide(add(470, 520), multiply(55, const_0_2778)) | a 470 m long train is running at a speed of 55 km / hr . it crossed a platform of length 520 m in ? | "speed = 55 km / hr ( to convert km / hr in to m / s ) = 55 x 5 / 18 m / s distance = 470 m + 520 m ( if questions is about train crossing a post you need to consider only the length of train , ) = 990 m time = distance / speed = 990 x 18 / ( 5 x 55 ) = 64.8 sec ans is : b" | a = 470 + 520
b = 55 * const_0_2778
c = a / b
|
a ) 18 , b ) 28 , c ) 32 , d ) 56 , e ) 58 | d | multiply(divide(divide(12880, 230), 7), 7) | the ratio between the number of sheep and the number of horses at the stewar farm is 7 to 7 . if each of horse is fed 230 ounces of horse food per day and the farm needs a total 12880 ounces of horse food per day . what is number sheep in the form ? ? | "et no of sheep and horses are 7 k and 7 k no of horses = 12880 / 230 = 56 now 7 k = 56 and k = 8 no of sheep = ( 7 * 8 ) = 56 answer : d" | a = 12880 / 230
b = a / 7
c = b * 7
|
a ) 3 : 2 , b ) 1 : 2 , c ) 4 : 1 , d ) 5 : 2 , e ) 4 : 3 | c | divide(subtract(9, 5), subtract(10, 9)) | gold is 10 times as heavy as water and copper is 5 times as heavy as water . in what ratio should these be mixed to get an alloy 9 times as heavy as water ? | "g = 10 w c = 5 w let 1 gm of gold mixed with x gm of copper to get 1 + x gm of the alloy 1 gm gold + x gm copper = x + 1 gm of alloy 10 w + 5 wx = x + 1 * 9 w 10 + 5 x = 9 ( x + 1 ) x = 1 / 4 ratio of gold with copper = 1 : 1 / 4 = 4 : 1 answer is c" | a = 9 - 5
b = 10 - 9
c = a / b
|
a ) 88 , b ) 108 , c ) 110 , d ) 90 , e ) 93 | a | subtract(subtract(subtract(182, 22), subtract(73, const_1)), const_4) | veena ranks 73 rd from the top in a class of 182 . what is her rank from the bottom if 22 students have failed the examination ? | "total student = 182 failed = 22 paasd student = 182 - 22 = 160 from bottom her rank is = 160 - 73 + 1 = 88 answer : a" | a = 182 - 22
b = 73 - 1
c = a - b
d = c - 4
|
a ) 315 , b ) 350 , c ) 325 , d ) 335 , e ) none of them | b | multiply(multiply(const_100.0, divide(12, 1176)), 3) | what annual installment will discharge a debt of rs . 1176 due in 3 years at 12 % simple interest ? | "let each installment be rs . x then , ( x + ( ( x * 12 * 1 ) / 100 ) ) + ( x + ( ( x * 12 * 2 ) / 100 ) ) + x = 1176 = ( ( 28 x / 25 ) + ( 31 x / 25 ) + x ) = 1176 Γ― Ζ βΊ ( 28 x + 31 x + 25 x ) = ( 1176 * 25 ) x = ( 1176 * 25 ) / 84 = rs . 350 . therefore , each installment = rs . 350 . answer is b ." | a = 12 / 1176
b = 100 * 0
c = b * 3
|
a ) 117 % , b ) 120 % , c ) 121 % , d ) 133 % , e ) 140 % | d | multiply(power(add(1, divide(divide(12, const_100), const_2)), add(const_2, const_3)), const_100) | michelle deposited a certain sum of money in a savings account on july 1 st , 2007 . she earns an 12 % interest compounded semiannually . the sum of money in the account on december 31 st , 2009 is approximately what percent of the initial deposit ? | "since michelle earns 12 % interest compounded semiannually , then she earns 6 % interest every 6 months . now , the simple interest earned in 5 periods ( 30 months = 5 * 6 months ) would be 6 % * 5 = 30 % . but , since the interest iscompoundedevery 6 months , then there would be interest earned on interest ( very small amount ) thus the actual interest earned would be a little bit more than 30 % , only answer choice d fits . answer : d" | a = 12 / 100
b = a / 2
c = 1 + b
d = 2 + 3
e = c ** d
f = e * 100
|
a ) 12 / 25 , b ) 13 / 25 , c ) 3 / 5 , d ) 6 / 7 , e ) 7 / 8 | a | divide(divide(9, 15), divide(divide(add(50, const_100), const_100), divide(subtract(const_100, 20), const_100))) | if the numerator of a fraction is increased by 50 % and denominator by 20 % , the fraction become 9 / 15 . what was the original fraction ? | "explanation : let the fraction be x / y we have 150 x / 120 y = 9 / 15 = x / y = 12 / 25 answer : option a" | a = 9 / 15
b = 50 + 100
c = b / 100
d = 100 - 20
e = d / 100
f = c / e
g = a / f
|
a ) 2 / 3 , b ) 1 / 4 , c ) 7 / 9 , d ) 1 / 5 , e ) 8 / 11 | a | divide(add(subtract(const_1, add(divide(1, 2), divide(1, 3))), multiply(subtract(const_1, divide(1, 3)), divide(1, 2))), add(add(subtract(const_1, add(divide(1, 2), divide(1, 3))), multiply(subtract(const_1, divide(1, 3)), divide(1, 2))), multiply(subtract(const_1, divide(1, 4)), divide(1, 3)))) | every student of a certain school must take one and only one elective course . in last year , 1 / 2 of the students took p . e . as an elective , 1 / 3 of the students took theatre as an elective , and all of the other students took music . in this year , 1 / 3 of the students who took p . e . and 1 / 4 of the students who took theatre left school , other students did not leave , and no fresh student come in . what fraction of all students took p . e . or music ? | lets pick smart numbers . total number of students : 12 p . e . ( 1 / 2 ) : 6 theatre ( 1 / 3 ) : 4 music ( 1 / 6 ) : 2 after leaving school p . e . : 4 theatre : 3 music : 2 new total number of students : 9 p . e . and music : 6 answer 2 / 3 or a | a = 1 / 2
b = 1 / 3
c = a + b
d = 1 - c
e = 1 / 3
f = 1 - e
g = 1 / 2
h = f * g
i = d + h
j = 1 / 2
k = 1 / 3
l = j + k
m = 1 - l
n = 1 / 3
o = 1 - n
p = 1 / 2
q = o * p
r = m + q
s = 1 / 4
t = 1 - s
u = 1 / 3
v = t * u
w = r + v
x = i / w
|
a ) 230 , b ) 175 , c ) 225 , d ) 315 , e ) none of these | d | subtract(multiply(1500, power(add(const_1, divide(10, const_100)), 2)), 1500) | what is the compound interest paid on a sum of rs . 1500 for the period of 2 years at 10 % per annum . | "solution = interest % for 1 st year = 10 interest % for 2 nd year = 10 + 10 % of 10 = 10 + 10 * 10 / 100 = 11 total % of interest = 10 + 11 = 21 total interest = 21 % 1500 = 1500 * ( 21 / 100 ) = 315 answer d" | a = 10 / 100
b = 1 + a
c = b ** 2
d = 1500 * c
e = d - 1500
|
a ) rs . 575 , b ) rs . 600 , c ) rs . 625 , d ) rs . 485 , e ) rs . 590 | a | add(divide(600, add(const_1, divide(20, const_100))), multiply(divide(15, const_100), divide(600, add(const_1, divide(20, const_100))))) | if sharon ' s weekly salary increased by 20 percent , she would earn $ 600 per week . if instead , her weekly salary were to increase by 15 percent , how much would she earn per week ? | "soln : - ( 600 / 120 ) 115 = 575 in this case long division does not take much time . ( 5 / 1 ) 115 = rs . 575 answer : a" | a = 20 / 100
b = 1 + a
c = 600 / b
d = 15 / 100
e = 20 / 100
f = 1 + e
g = 600 / f
h = d * g
i = c + h
|
a ) 6 hours , b ) 9 hours , c ) 14 hours , d ) 24 hours , e ) 32 hours | b | multiply(3, const_3) | jamshid can paint a fence in 50 percent less time than taimour can when each works alone . when they work together , they can paint the fence in 3 hours . how long would it take taimour to paint the fence alone ? | "i believe the answer is b . please see below for explanation . if jamshid can paint a dence in 50 percent less time then taimour we can infer the following rate j = 2 t if working together they can do the job in 8 hours we can infer 1 = 2 t + t * 3 = > 1 / 9 working alone taimour can do the job in 1 = 1 / 9 * hours = > 9 answer b" | a = 3 * 3
|
a ) 1000 meters , b ) 1050 meters , c ) 2200 meters , d ) 2250 meters , e ) none of these | d | multiply(multiply(9, divide(15, const_60)), const_1000) | a man is walking at the rate of 9 km / hr crosses a bridge in 15 minutes . the length of the bridge is | "explanation : we need to get the answer in meters . so we will first of change distance from km / hour to meter / sec by multiplying it with 5 / 18 and also change 15 minutes to seconds by multiplying it with 60 . speed = 9 Γ’ Λ β 5 / 18 = 5 / 2 m / sec time = 15 Γ’ Λ β 60 seconds = 900 seconds distance = time Γ’ Λ β speed / distance = 5 / 2 Γ’ Λ β 900 = 2250 meter option d" | a = 15 / const_60
b = 9 * a
c = b * 1000
|
a ) 20 , b ) 24 , c ) 26 , d ) 25 , e ) 22 | b | add(divide(subtract(99, 1), 4), const_1) | how many multiples of 4 are there between 1 and 99 ? | "4 multiples are 4 , 8,12 , - - - - - - - - - , 92,96 it should be mentioned whether 1 and 99 are inclusive . the answer is ( 96 - 4 ) / 4 + 1 = 24 answer is b" | a = 99 - 1
b = a / 4
c = b + 1
|
a ) 0.75 , b ) 0.8 , c ) 1.375 , d ) 1.4 , e ) 1.85 | c | inverse(divide(80, add(80, 30))) | patrick purchased 80 pencils and sold them at a loss equal to the selling price of 30 pencils . the cost of 80 pencils is how many times the selling price of 80 pencils ? | say the cost price of 80 pencils was $ 80 ( $ 1 per pencil ) and the selling price of 1 pencil was p . selling at a loss : 80 - 80 p = 30 p - - > p = 8 / 11 . ( cost price ) / ( selling price ) = 1 / ( 8 / 11 ) = 11 / 8 = 1.375 . answer : c . | a = 80 + 30
b = 80 / a
c = 1/(b)
|
a ) 70 % , b ) 60 % , c ) 30 % , d ) 10 % , e ) 20 % | c | subtract(divide(multiply(add(const_100, 23.5), const_100), subtract(const_100, 5)), const_100) | a shopkeeper sold an article offering a discount of 5 % and earned a profit of 23.5 % . what would have been the percentage of profit earned if no discount was offered ? | "explanation : let c . p . be rs . 100 . then , s . p . = rs . 123.50 let marked price be rs . x . then , 95 / 100 x = 123.50 x = 12350 / 95 = rs . 130 now , s . p . = rs . 130 , c . p . = rs . 100 profit % = 30 % . answer c" | a = 100 + 23
b = a * 100
c = 100 - 5
d = b / c
e = d - 100
|
a ) 10 , b ) 15 , c ) 20 , d ) 25 , e ) 30 | b | multiply(divide(multiply(subtract(28, 7), divide(5, const_60)), 7), const_60) | the hiker walking at a constant rate of 7 miles per hour is passed by a cyclist traveling in the same direction along the same path at 28 miles per hour . the cyclist stops to wait for the hiker 5 minutes after passing her , while the hiker continues to walk at her constant rate , how many minutes must the cyclist wait until the hiker catches up ? | "for the 5 minutes the cyclist continues to overtake the hiker , she is going at 21 miles per hour faster than the hiker . once the cyclist stops , the hiker is going at 7 miles per hour while the cyclist is at rest so the amount of time the hiker will take to cover the distance between them is going to be in the ratio of the relative speeds . 21 / 7 * 5 or 15 minutes answer is ( b )" | a = 28 - 7
b = 5 / const_60
c = a * b
d = c / 7
e = d * const_60
|
a ) 281 , b ) 284 , c ) 288 , d ) 255 , e ) 180 | e | multiply(18, 10) | find the area of a parallelogram with base 18 cm and height 10 cm ? | "area of a parallelogram = base * height = 18 * 10 = 180 cm 2 answer : e" | a = 18 * 10
|
a ) 77.14 cm , b ) 47.14 cm , c ) 84.92 cm , d ) 94.94 cm , e ) 31.42 cm | e | divide(circumface(divide(square_edge_by_perimeter(rectangle_perimeter(24, 16)), const_2)), const_2) | the parameter of a square is equal to the perimeter of a rectangle of length 24 cm and breadth 16 cm . find the circumference of a semicircle whose diameter is equal to the side of the square . ( round off your answer to two decimal places ) | "let the side of the square be a cm . parameter of the rectangle = 2 ( 24 + 16 ) = 80 cm parameter of the square = 80 cm i . e . 4 a = 80 a = 20 diameter of the semicircle = 20 cm circimference of the semicircle = 1 / 2 ( β ) ( 20 ) = 1 / 2 ( 22 / 7 ) ( 20 ) = 440 / 14 = 31.42 cm to two decimal places answer : e" | a = square_edge_by_perimeter / (
b = circumface / (
|
a ) 76 % . , b ) 66 % . , c ) 89 % . , d ) 140 % . , e ) 91 % . | d | 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 the sells it at double the price , the percentage of profit will be ? | "let c . p . = rs . x . then , s . p . = rs . ( 12 % of x ) = rs . 6 x / 5 new s . p . = 2 * 6 x / 5 = rs . 12 x / 5 profit = 12 x / 5 - x = rs . 7 x / 5 profit = 7 x / 5 * 1 / x * 100 = 140 % . answer : d" | a = 20 / 100
b = 1 + a
c = b * 2
d = c - 1
e = d * 100
f = e + 100
|
a ) 48,000 , b ) 51,000 , c ) 54,000 , d ) 57,000 , e ) 60,000 | c | subtract(divide(multiply(15, const_3600), const_1000), const_3) | mars travels around the sun at a speed of approximately 15 miles per second . the approximate speed is how many miles per hour ? | 15 * 3600 = 54,000 the answer is c . | a = 15 * 3600
b = a / 1000
c = b - 3
|
a ) $ 15300 , b ) $ 14300 , c ) $ 15337.50 , d ) $ 16300 , e ) $ 15800 | c | subtract(multiply(950, subtract(50, 20.75)), 12450) | acme β s manufacturing costs for sets of horseshoes include a $ 12450 initial outlay , and $ 20.75 per set . they can sell the sets $ 50 . if profit is revenue from sales minus manufacturing costs , and the company producessells 950 sets of horseshoes , what was their profit ? | total manufacturing cost = 12,450 + 950 * 20.75 = 32162.5 total selling cost = 950 * 50 = 47500 profit = 47500 - 32162.50 = 15337.50 answer : c | a = 50 - 20
b = 950 * a
c = b - 12450
|
a ) 46 , b ) 59 , c ) 63 , d ) 75 , e ) 88 | b | subtract(multiply(5, 100), subtract(multiply(9, 104), multiply(99, 5))) | the average of 9 numbers is 104 . average of the first 5 of them is 99 and that of the last 5 is 100 . find the 5 th number ? | sum of all the 9 numbers = 9 * 104 = 936 sum of the first 5 of them = 5 * 99 = 495 sum of the last 5 of them = 5 * 100 = 500 so , the 5 th number = 495 + 500 - 936 = 59 . answer : b | a = 5 * 100
b = 9 * 104
c = 99 * 5
d = b - c
e = a - d
|
a ) 123 , b ) 106 , c ) 100 , d ) 101 , e ) 240 | d | subtract(101.25, divide(1, 4)) | the cash realised on selling a 14 % stock is rs . 101.25 , brokerage being 1 / 4 % is | "explanation : cash realised = rs . ( 101.25 - 0.25 ) = rs . 101 . answer : d" | a = 1 / 4
b = 101 - 25
|
a ) 60 m , b ) 20 m , c ) 43 m , d ) 20 m , e ) 23 m | d | subtract(500, divide(multiply(subtract(500, 140), 4), 3)) | in a 500 m race , the ratio of the speeds of two contestants a and b is 3 : 4 . a has a start of 140 m . then , a wins by : | "to reach the winning post a will have to cover a distance of ( 500 - 140 ) m , i . e . , 360 m . while a covers 3 m , b covers 4 m . while a covers 360 m , b covers 4 x 360 m = 480 m . 3 thus , when a reaches the winning post , b covers 480 m and therefore remains 20 m behind . a wins by 20 m . answer : d" | a = 500 - 140
b = a * 4
c = b / 3
d = 500 - c
|
a ) 7 , b ) 7.68 , c ) 8 , d ) 9 , e ) 10 | b | divide(subtract(sqrt(add(multiply(multiply(30, 10), const_4), power(30, const_2))), 30), const_2) | tom read a book containing 100 pages by reading the same number of pages each day . if he would have finished the book 10 days earlier by reading 30 pages a day more , how many days did tom spend reading the book ? | actually u can set up 2 equation p - - stands for the pages d - - stands for the days 1 ) p * d = 100 ( we want to find the days , sop = 100 / d ) 2 ) ( p + 30 ) ( d - 10 ) = 100 = > pd - 10 p + 30 d - 300 = 100 as the 1 ) stated u can put 1 ) into 2 ) = > 100 - 10 p + 30 d - 300 = 100 = > 30 d - 10 p = 100 put the bold one into it = > 30 d - 10 ( 100 / d ) = 100 the we get the final equation 30 d ^ 2 - 1000 = 100 d ( divide 16 ) = > d ^ 2 - 5 d - 150 = 0 ( d - 15 ) ( d + 10 ) = 0 so d = 7.68 days . ans : ( b ) | a = 30 * 10
b = a * 4
c = 30 ** 2
d = b + c
e = math.sqrt(d)
f = e - 30
g = f / 2
|
a ) 20 , b ) 11 , c ) 21 , d ) 41 , e ) none of these | c | add(multiply(sqrt(divide(subtract(241, 100), const_2)), const_100), sqrt(subtract(241, divide(subtract(241, 100), const_2)))) | the sum of the squares of three numbers is 241 , while the sum of their products taken two at a time is 100 . their sum is : | "x ^ + y ^ 2 + z ^ 2 = 241 xy + yz + zx = 100 as we know . . ( x + y + z ) ^ 2 = x ^ 2 + y ^ 2 + z ^ 2 + 2 ( xy + yz + zx ) so ( x + y + z ) ^ 2 = 241 + ( 2 * 100 ) ( x + y + z ) ^ 2 = 441 so x + y + z = 21 answer : c" | a = 241 - 100
b = a / 2
c = math.sqrt(b)
d = c * 100
e = 241 - 100
f = e / 2
g = 241 - f
h = math.sqrt(g)
i = d + h
|
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