euclaise/mathqa_programs huggingface dataset:
Problem: calculate the l . c . m of 5 / 6 , 4 / 7 , 9 / 10 , 8 / 9 is :
Options: a ) 560 , b ) 364 , c ) 320 , d ) 330 , e ) 360
Rationale: "required l . c . m = l . c . m . of 5 , 4 , 9 , 8 / h . c . f . of 6 , 7 , 10 , 9 = 360 / 1 = 360 answer is e"
Answer: e
Python program:
a = 5 * 4
b = 9 * 8
c = a * b
Problem: find the least positive integer divisible by each of the integers between 5 through 10 ( including 10 ) .
Options: a ) 560 , b ) 380 , c ) 900 , d ) 2560 , e ) 2520
Rationale: the integer should be divisible by : 5 , 6 , 7 , 89 , and 10 . the least common multiple of these integers is lcm = 420 . answer : 5 * 3 ^ 2 * 7 * 2 ^ 3 the answer is e )
Answer: e
Python program:
a = 2 ** 3
b = 3 ** 2
c = a * b
d = c * 5
e = 3 + 4 
f = d * e
Problem: a number when divided by a divisor leaves a remainder of 25 . when twice the original number is divided by the same divisor , the remainder is 11 . what is the value of the divisor ?
Options: a ) 12 , b ) 13 , c ) 35 , d ) 38 , e ) 59
Rationale: "let the number is n , the divisor = d , i will make the two equations - n = xd + 25 2 n = yd + 11 where x and y are integers solving them : d ( y - 2 x ) = 38 as d is also integer and 38 is a prime number , the d should be 38 to satisfy the above equation . hence answer is ' d '"
Answer: d
Python program:
a = 25 + 11
Problem: dexter and prexter are competing with each other in a friendly community competition in a pool of 50 m length and the race is for 1000 m . dexter crosses 50 m in 2 min and prexter in 3 min 15 sec . each time they meet / cross each other , they do handshake ' s . how many such handshake ' s will happen if they start from the same end at the same time ?
Options: a ) 17 , b ) 18 , c ) 19 , d ) 20 , e ) 22
Rationale: explanation : when dexter completes second round , they do handshake once . now for every round which dexter completes , there will be one hand shake as the ratio of speed is 13 : 8 . d and p will meet at the pool end only after d completes 26 rounds . in the 20 th round , d finish the race and the total handshake ' s will be : 20 − 1 = 19 . answer : c
Answer: c
Python program:
a = 1000 / 50
b = a - 1
Problem: find the average of all numbers between 6 and 34 which are divisible by 5
Options: a ) 15 , b ) 20 , c ) 25 , d ) 30 , e ) 35
Rationale: "explanation : average = ( 10 + 15 + 20 + 25 + 305 ) = 1005 = 20 answer : option b"
Answer: b
Python program:
a = 5 * 3
b = 5 * 2
c = 5 + b 
d = a + c 
e = 5 * 4
f = d + e 
g = 4 + 1 
h = g * 5
i = f + h 
j = i / 5
Problem: two numbers are less than third number by 35 % and 37 % respectively . how much percent is the second number less than by the first
Options: a ) 8 % , b ) 10 % , c ) 33 % , d ) 41 % , e ) 42 %
Rationale: "let the third number is x . then first number = ( 100 - 35 ) % of x = 65 % of x = 65 x / 100 second number is ( 63 x / 100 ) difference = 65 x / 100 - 63 x / 100 = x / 50 so required percentage is , difference is what percent of first number ( x / 50 * 100 / 65 x * 100 ) % = 33 % answer : c"
Answer: c
Python program:
a = 37 - 35
b = 100 - 35
c = a / b
d = c * 100
e = d - 10
Problem: sam ’ s car was fined when he gave joe and peter a ride , so they decided to help sam pay the fine . joe paid $ 8 more than 1 / 4 of the fine and peter paid $ 8 less than 1 / 3 of the fine , leaving pay $ 15 less than 1 / 2 the fine to complete the payment . what fraction of the fine did sam pay ?
Options: a ) $ 70 , b ) $ 72 , c ) $ 73 , d ) $ 74 , e ) $ 75
Rationale: "call the fine f . joe paid ( 1 / 4 ) f + 4 and peter paid ( 1 / 3 ) f – 4 , leaving ( 1 / 2 ) f – 5 left . if we add those three up , they should add up to f . f = [ ( 1 / 4 ) f + 8 ] + [ ( 1 / 3 ) f – 8 ] + [ ( 1 / 2 ) f – 15 ] f = ( 1 / 4 ) f + ( 1 / 3 ) f + ( 1 / 2 ) f – 15 multiply all terms by 12 to clear the fractions . 12 f = 3 f + 4 f + 6 f – 180 12 f = 13 f – 180 – f = – 180 f = 180 well , if the fine cost $ 180 , then sam paid the part not covered by joe or peter . half the fine is $ 90 , and sam paid $ 15 less than this : $ 75 answer = e"
Answer: e
Python program:
a = 1 / 2
b = 1 / 4
c = 1 / 3
d = b + c 
e = a + d 
f = e * 15
g = f + 15 
h = g * 2
i = h + 10
Problem: according to the directions on a packet of smoothie mix , 1 3 - ounce packet of smoothie mix is to be combined with 12 ounces of water to make a smoothie . how many 2 - ounce packets of smoothie mix are required to prepare 150 12 - ounce smoothies ?
Options: a ) 120 , b ) 150 , c ) 180 , d ) 240 , e ) 600
Rationale: this question was n ' t particularly grueling , but i think it ' s the first where i had the opportunity to solve it via theory andinspectionthat many on this board suggest as strategy on the gmat . it actually came to me by accident . basically , if we thought that the 3 packets of powder were included in the 12 ounces of water , that would mean we would need 150 packets of smoothie mix ( along with 12 ( 150 ) ounces of water for a total of 150 packets . however , we know , after a more careful reading of the stimulus , that the 3 ounces are not included in the 12 ounces . as such , the answer has to be less than 150 packets , since 150 would be too much powder considering you already have 150 ( 12 ) ounces of water and need less packets than water to make a smoothie . as such , the only answer less than 150 is 120 , a . does this make sense ? or am i way off base ? c
Answer: c
Python program:
a = 3 * 10
b = 150 + a
Problem: a man gains 60 % by selling an article for a certain price . if he sells it at double the price , the percentage of profit will be .
Options: a ) 130 % , b ) 320 % , c ) 150 % , d ) 160 % , e ) 170 %
Rationale: "explanation : let the c . p . = x , then s . p . = ( 160 / 100 ) x = 8 x / 5 new s . p . = 2 ( 8 x / 5 ) = 16 x / 5 profit = 16 x / 5 - x = 16 x / 5 profit % = ( profit / c . p . ) * 100 = > ( 16 x / 5 ) * ( 1 / x ) * 100 = 320 % option b"
Answer: b
Python program:
a = 60 / 100
b = 1 + a 
c = b * 2
d = c - 1
e = d * 100
f = e + 100
Problem: the difference between a two - digit number and the number obtained by interchanging the positions of its digits is 54 . what is the difference between the two digits of that number ?
Options: a ) 4 , b ) 5 , c ) 6 , d ) 8 , e ) 9
Rationale: sol . let the ten ’ s digit be x and unit ’ s digit be y , then , ( 10 x + y ) - ( 10 y + x ) = 54 ⇔ 9 ( x - y ) = 54 ⇔ x - y = 6 answer c
Answer: c
Python program:
a = 10 - 1
b = 54 / a
Problem: the ratio , by volume , of soap to alcohol to water in a certain solution is 2 : 40 : 70 . the solution will be altered so that the ratio of soap to alcohol is doubled while the ratio of soap to water is halved . if the altered solution will contain 100 cubic centimeters of alcohol , how many cubic centimeters of water will it contain ?
Options: a ) 500 , b ) 600 , c ) 650 , d ) 700 , e ) 720
Rationale: "soap : alcohol initial ratio soap : alcohol : water - - > 2 : 40 : 70 initial soap : alcohol = 2 / 40 = 2 : 40 after doubled soap : alcohol = 2 * 2 / 40 = 4 : 40 initial soap : water = 2 / 70 = 2 : 70 after halved soap : water : 1 / 2 * 2 / 70 = 1 / 70 = 1 : 70 after soap : alcohol : water - - > 4 : 40 : 280 - - > 1 : 10 : 70 given alcohol 100 cubic centimeter . ratio is 10 : 100 : 700 ( 1 : 10 : 70 ) for 100 cubic centimeter of alcohol - - - 700 cubic cm water is required . answer - d"
Answer: d
Python program:
a = volume_rectangular_prism / (
b = a / 3
c = b / 2
d = c / 4
e = d / 4
Problem: a grocery shop has a sale of rs . 6435 , rs . 6927 , rs . 6855 , rs . 7230 and rs . 6562 for 5 consecutive months . how much sale must he have in the sixth month so that he gets an average sale of rs . 6500 ?
Options: a ) 4857 , b ) 4184 , c ) 4012 , d ) 4991 , e ) 5291
Rationale: "let the sale in the sixth month = x then ( 6435 + 6927 + 6855 + 7230 + 6562 + x ) / 6 = 6500 = > 6435 + 6927 + 6855 + 7230 + 6562 + x = 6 × 6500 = > 34009 + x = 39000 = > x = 39000 − 34009 = 4991 answer : d"
Answer: d
Python program:
a = 5 + 1 
b = 6500 * a
c = 6435 + 6927 
d = 6855 + c 
e = d + 7230 
f = e + 6562 
g = b - f
Problem: if rs . 420 amount to rs . 540 in 4 years , what will it amount to in 6 years at the same rate % per annum ?
Options: a ) s . 575 , b ) s . 595 , c ) s . 590 , d ) s . 600 , e ) s . 585
Rationale: 80 = ( 420 * 4 * r ) / 100 r = 7.14 % i = ( 420 * 6 * 7.14 ) / 100 = 180 420 + 180 = 600 answer : d
Answer: d
Python program:
a = 540 - 420
b = a * 6
c = 540 - 420
d = b - c
Problem: what is the ratio of 3 / 7 to the product 2 * ( 7 / 3 ) ?
Options: a ) 3 : 7 , b ) 9 : 98 , c ) 3 : 21 , d ) 1 : 7 , e ) 3 : 49
Rationale: "3 / 7 / 14 / 3 = 9 / 98 . . . imo option b ."
Answer: b
Python program:
a = 3 / const_60
Problem: if 40 % of a number exceeds 20 % of it by 12 , then find the number ?
Options: a ) 60 , b ) 50 , c ) 47 , d ) 55 , e ) 80
Rationale: "use the elimination method to find the correct option . of all the options only 60 fits 40 % of 60 = 24 20 % of 60 = 12 24 - 12 = 12 required number is 60 . answer : a"
Answer: a
Python program:
a = 40 - 20
b = a / 100
c = 12 / b
d = c + 20
Problem: a discount electronics store normally sells all merchandise at a discount of 5 percent to 25 percent off the suggested retail price . if , during a special sale , an additional 25 percent were to be deducted from the discount price , what would be the lowest possible price of an item costing $ 300 before any discount ?
Options: a ) $ 130.00 , b ) $ 160.75 , c ) $ 168.75 , d ) $ 182.00 , e ) $ 168.00
Rationale: "original price : 300 $ max first discount = - 25 % thus : 300 â ˆ — ( 1 â ˆ ’ 25 / 100 ) = 225 second discount on the discounted price = - 25 % thus : 225 â ˆ — ( 1 â ˆ ’ 25 / 100 ) = 168.75 answer c"
Answer: c
Python program:
a = 25 + 25 
b = a / 100
c = 300 * b
Problem: a train covers a distance of 12 km in 10 minutes . if it takes 6 seconds to pass a telegraph post , then the length of the train is :
Options: a ) 120 m , b ) 140 m , c ) 240 m , d ) 300 m , e ) none
Rationale: "sol . speed = [ 12 / 10 * 60 ] km / hr = [ 72 * 5 / 18 ] m / sec = 20 m / sec . length of the train = ( speed * time ) = ( 20 * 6 ) m = 120 m . answer a"
Answer: a
Python program:
a = 100 / 0
b = a - 6
c = 100 / 0
Problem: workers decided to raise rs . 3 lacs by equal contribution from each . had they contributed rs . 50 eachextra , the contribution would have been rs . 3.20 lacs . how many workers were they ?
Options: a ) 220 , b ) 400 , c ) 500 , d ) 560 , e ) 590
Rationale: "n * 50 = ( 320000 - 300000 ) = 20000 n = 20000 / 50 = 400 b"
Answer: b
Python program:
a = 3 - 20
b = a * 1000
c = b * 100
d = c / 50
Problem: each digit 1 through 5 is used exactly once to create a 5 - digit integer . if the 1 and the 2 can not be adjacent digits in the integer , how many 5 - digit integers are possible ?
Options: a ) 48 , b ) 66 , c ) none of these , d ) 78 , e ) 90
Rationale: "number of arrangements using 5 distinct digits = 5 ! number of arrangements in which 1 and 2 are adjacent - consider 1 and 2 together as one group . now you have 4 numbers / groups to arrange which can be done in 4 ! ways . in each of these arrangements , 1 and 2 can be arranged as 12 or 21 . number of arrangements in which 3 and 4 are not adjacent = 5 ! - 2 * 4 ! = 72 answer : c"
Answer: c
Python program:
a = 5 * 2
b = a * 1
c = b * 2
d = 2 * 1
e = d * 2
f = e * 2
g = c - f
Problem: if a rectangular billboard has an area of 130 square feet and a perimeter of 46 feet , what is the length of each of the longer sides ?
Options: a ) 4 , b ) 7 , c ) 8 , d ) 13 , e ) 26
Rationale: "this question can be solved algebraically or by testing the answers . we ' re told that a rectangle has an area of 130 and a perimeter of 46 . we ' re asked for the length of one of the longer sides of the rectangle . since the answers are all integers , and the area is 130 , the shorter side will almost certainly be closer to 10 ( since 10 x 10 = 100 , but we ' re not dealing with a square ) . answer b ( 7 ) does not divide evenly into 130 , if . . . the shorter side = 10 . . . the area = 130 / 10 = 13 = the longer side perimeter = 10 + 10 + 13 + 13 = 46 d"
Answer: d
Python program:
a = 46 / 2
b = 46 / 2
c = b ** 2
d = 4 * 130
e = c - d
f = math.sqrt(e)
g = a - f
h = g / 2
Problem: a train running at the speed of 60 km / hr crosses a pole in 6 seconds . what is the length of the train ?
Options: a ) 120 metres , b ) 180 metres , c ) 100 metres , d ) 228 metres , e ) 150 metres
Rationale: "speed = 60 x 5 / 18 m / sec = 50 / 3 m / sec . length of the train = ( speed x time ) . length of the train = 50 / 3 x 6 m = 100 m . option c"
Answer: c
Python program:
a = 60 * 1000
b = a / 3600
c = b * 6
Problem: find the greatest number which on dividing 3815 and 4521 , leaves a reminder of 31 and 33 respectively
Options: a ) 88 , b ) 56 , c ) 89 , d ) 86 , e ) 96
Rationale: "explanation : in this type of question , its obvious we need to calculate the hcf , trick is hcf of ( 3815 - 31 ) and ( 4521 - 33 ) = hcf ( 3784 , 4488 ) = 88 option a"
Answer: a
Python program:
a = 3815 - 31
b = 4521 - 33
c = math.gcd(a, b)
Problem: 16 men can complete a piece of work in 28 days . in how many days can 20 men complete that piece of work ?
Options: a ) 55 days , b ) 77 days , c ) 22.4 days , d ) 88 days , e ) 44 days
Rationale: "16 * 28 = 20 * x = > x = 22.4 days answer : c"
Answer: c
Python program:
a = 28 * 16
b = a / 20
Problem: two trains , one from howrah to patna and the other from patna to howrah , start simultaneously . after they meet , the trains reach their destinations after 16 hours and 25 hours respectively . the ratio of their speeds is ?
Options: a ) 4 : 9 , b ) 4 : 3 , c ) 5 : 4 , d ) 4 : 1 , e ) 4 : 2
Rationale: "let us name the trains a and b . then , ( a ' s speed ) : ( b ' s speed ) = √ b : √ a = √ 25 : √ 26 = 5 : 4 answer : c"
Answer: c
Python program:
a = math.sqrt(25)
b = math.sqrt(16)
c = a / b
Problem: two sides of a triangle have lengths x and w and meet at a right angle . if the perimeter of the triangle is 4 x , what is the ratio of x to w ?
Options: a ) a ) 2 : 3
b ) b ) 3 : 4
c ) c ) 4 : 3
d ) d ) 3 : 2
e ) e ) 2 : 1
Rationale: ahhhh . . . . my bad . thank you , you ' re correct . 8 x = 6 w - - > x / w = 3 / 4 . actually b is the right answer .
Answer: b
Python program:
a = 4 - 1
b = a * 2
c = 4 - 1
d = c ** 2
e = d - 1
f = b / e
Problem: the credit card and a global payment processing companies have been suffering losses for some time now . a well known company recently announced its quarterly results . according to the results , the revenue fell to $ 55.0 billion from $ 69.0 billion , a year ago . by what percent did the revenue fall ?
Options: a ) 25.5 , b ) 30.4 , c ) 31.8 , d ) 32.5 , e ) 33.8
Rationale: "$ 69 - $ 55 = 14 $ ( 14 / 55 ) * 100 = 25.5 % answer : a"
Answer: a
Python program:
a = 69 - 0
b = a / 69
c = b * 100
Problem: convert 30 miles into yards ?
Options: a ) 25630 yards , b ) 35200 yards , c ) 52800 yards , d ) 42560 yards , e ) 41520 yards
Rationale: "1 mile = 1760 yards 30 miles = 30 * 1760 = 52800 yards answer is c"
Answer: c
Python program:
a = 3 + 2 
b = a * 2
c = 3 + 2 
d = c * 2
e = b * d
f = e * 30
g = 3 + 2 
h = g * 2
i = 3 + 2 
j = i * 2
k = h * j
l = f / k
Problem: a garrison of 2000 men has provisions for 65 days . at the end of 15 days , a reinforcement arrives , and it is now found that the provisions will last only for 20 days more . what is the reinforcement ?
Options: a ) 1977 , b ) 1893 , c ) 1979 , d ) 3000 , e ) 1278
Rationale: "2000 - - - - 65 2000 - - - - 50 x - - - - - 20 x * 20 = 2000 * 50 x = 5000 2000 - - - - - - - 3000 answer : d"
Answer: d
Python program:
a = 2000 * 65
b = 2000 * 15
c = a - b
d = c / 20
e = d - 2000
Problem: in what time will a railway train 70 m long moving at the rate of 36 kmph pass a telegraph post on its way ?
Options: a ) 6 sec , b ) 7 sec , c ) 8 sec , d ) 9 sec , e ) 2 sec
Rationale: "t = 70 / 36 * 18 / 5 = 7 sec answer : b"
Answer: b
Python program:
a = 36 * const_0_2778
b = 70 / a
Problem: a retail appliance store priced a video recorder at 20 percent above the wholesale cost of $ 200 . if a store employee applied the 20 percent employee discount to the retail price to buy the recorder , how much did the employee pay for the recorder ?
Options: a ) $ 198 , b ) $ 216 , c ) $ 192 , d ) $ 230 , e ) $ 240
Rationale: "wholesale cost of video recorder = 200 $ video recorder was priced at 20 percent above 200 = 240 $ % discount given by store employee = 20 emlpoyee paid = . 8 * 240 = 192 $ answer c"
Answer: c
Python program:
a = 200 / 100
b = a * 20
c = 200 + b 
d = 200 / 100
e = d * 20
f = 200 + e 
g = f / 100
h = g * 20
i = c - h
Problem: what is the sum of all 3 digit numbers that leave a remainder of ' 2 ' when divided by 5 ?
Options: a ) 897 , b ) 98,910 , c ) 64,749 , d ) 49,700 , e ) 56,720
Rationale: find the number , upon sum of 3 digits of a number gives a reminder 2 when it is divided by 5 seeing the options after dividing and finding the reminder of 2 my answer was b
Answer: b
Python program:
a = 1000 - 3
b = 3 * 3
c = b * 10
d = 3 * 3
e = c + d 
f = e + 3 
g = a - f
h = g / 5
i = h + 1 
j = i / 2
k = 1000 - 3
l = 3 * 3
m = l * 10
n = 3 * 3
o = m + n 
p = o + 3 
q = k + p 
r = j * q
Problem: the speed of a train is 72 kmph . what is the distance covered by it in 20 minutes ?
Options: a ) 20 kmph , b ) 28 kmph , c ) 25 kmph , d ) 22 kmph , e ) 24 kmph
Rationale: "72 * 20 / 60 = 24 kmph answer : e"
Answer: e
Python program:
a = 20 / const_60
b = a * 72
Problem: a math teacher has 27 cards , each of which is in the shape of a geometric figure . half of the cards are rectangles , and a third of the cards are rhombuses . if 8 cards are squares , what is the maximum possible number of cards that re circles .
Options: a ) 9
b ) 10
c ) 11
d ) 12
e ) 13
Rationale: a square is a special kind of rhombus ( sides are perpendicular ) a square is a special kind of rectangles ( sides with same length ) among the 27 cards with have : 15 rectangles 10 rhombus 8 squares among the 15 rectangles , there could be 8 special ones ( with sides of same length ) that are squares . that lets at least 7 rectangles that are not square . among the 10 rectangles , there could be 8 special ones ( with sides perpendicular ) that are squares . that lets at least 2 rhombus that are not square . we have 8 squares . so the minimum different cards that represent a square , a rhombus or a rectangle is 2 + 7 + 8 = 17 which means that the maximum number of circles that you could have is 27 - 17 = 10 answer ( b )
Answer: b
Python program:
a = 27 * 8
b = a / 10
c = b / 2
d = c - const_0_25
e = d - const_0_25
Problem: at 6 ′ o a clock ticks 6 times . the time between first and last ticks is 45 seconds . how long does it tick at 12 ′ o clock
Options: a ) 47 , b ) 76 , c ) 28 , d ) 66 , e ) 99
Rationale: "explanation : for ticking 6 times , there are 5 intervals . each interval has time duration of 45 / 5 = 9 secs at 12 o ' clock , there are 11 intervals , so total time for 11 intervals = 11 × 9 = 99 secs . answer : e"
Answer: e
Python program:
a = 6 - 1
b = 45 / a
c = 12 - 1
d = b * c
Problem: the total marks obtained by a student in mathematics and physics is 70 and his score in chemistry is 20 marks more than that in physics . find the average marks scored in mathamatics and chemistry together .
Options: a ) 40 , b ) 45 , c ) 27 , d ) 28 , e ) 22
Rationale: "let the marks obtained by the student in mathematics , physics and chemistry be m , p and c respectively . given , m + c = 70 and c - p = 20 m + c / 2 = [ ( m + p ) + ( c - p ) ] / 2 = ( 70 + 20 ) / 2 = 45 . answer : b"
Answer: b
Python program:
a = 70 + 20 
b = a / 2
Problem: the ratio of the money with ravi and giri is 6 : 7 and that with giri and kiran is 6 : 15 . if ravi has $ 36 , how much money does kiran have ?
Options: a ) $ 36 , b ) $ 42 , c ) $ 60 , d ) $ 75 , e ) $ 105
Rationale: rita : sita : kavita 6 : 7 6 : 15 36 : 42 : 105 the ratio of money with ravi , giri and kiran is 36 : 42 : 105 we see that 36 = $ 36 then 105 = $ 105 answer is e
Answer: e
Python program:
a = 36 / 6
b = a * 7
c = 36 / 6
d = b / c
e = d * 15
Problem: ( 3 x + 2 ) ( 2 x - 7 ) = ax ^ 2 + kx + n . what is the value of a - n + k ?
Options: a ) 3 , b ) 8 , c ) 9 , d ) 10 , e ) 11
Rationale: expanding we have 6 x ^ 2 - 21 x + 4 x - 14 6 x ^ 2 - 17 x - 14 taking coefficients , a = 6 , k = - 17 , n = - 14 therefore a - n + k = 6 - ( - 14 ) - 17 = 20 - 17 = 3 the answer is a .
Answer: a
Python program:
a = 3 * 2
b = 7 * 2
c = a + b 
d = 2 * 2
e = 7 * 3
f = d - e
g = c + f
Problem: how many positive integers h between 200 and 300 ( both inclusive ) are not divisible by 2 , 3 or 5 ?
Options: a ) 3 , b ) 16 , c ) 75 , d ) 24 , e ) 26
Rationale: 1 ) i figured there are 101 integers ( 300 - 200 + 1 = 101 ) . since the set begins with an even and ends with an even , there are 51 evens . 2 ) question says integers are not divisible by 2 , leaving all of the odds ( 101 - 51 = 50 integers ) . 3 ) question says integers are not divisible by 5 , removing all the integers ending in 5 ( already took out those ending in 0 ) . take out 10 integers ( 2 ? 5 , ? = 0 to 9 ) , leaving us with 40 integers . 4 ) now the painstaking part . we have to remove the remaining numbers that are multiples of 3 . those are 201 , 207 , 213 , 219 , 231 , 237 , 243 , 249 , 261 , 267 , 273 , 279 , 291 , and 297 . . . a total of 14 numbers . 26 numbers left ! 6 ) answer choice e .
Answer: e
Python program:
a = 300 - 200
b = a + 1 
c = 300 - 200
d = c + 1 
e = d / 2
f = math.floor(e)
g = f + 1 
h = 300 - 200
i = h / 3
j = math.floor(i)
k = j + 1 
l = g + k 
m = 300 - 200
n = m / 5
o = n + 1 
p = l + o 
q = 300 - 200
r = q / 2
s = r / 3
t = math.floor(s)
u = 300 - 200
v = u / 5
w = v / 3
x = math.floor(w)
y = x + 1 
z = t + y 
A = 300 - 200
B = A / 10
C = B + 1 
D = z + C 
E = p - D
F = 100 / 3
G = F / 10
H = math.floor(G)
I = H + 1 
J = E + I 
K = b - J
Problem: if the sides of a triangle are 91 cm , 84 cm and 35 cm , what is its area ?
Options: a ) 120 cm 2 , b ) 1470 cm 2 , c ) 216 cm 2 , d ) 197 cm 2 , e ) 275 cm 2
Rationale: "the triangle with sides 91 cm , 84 cm and 35 cm is right angled , where the hypotenuse is 91 cm . area of the triangle = 1 / 2 * 84 * 35 = 1470 cm 2 answer : b"
Answer: b
Python program:
a = 84 * 35
b = a / 2
Problem: for every even positive integer m , f ( m ) represents the product of all even integers from 2 to m , inclusive . for example , f ( 12 ) = 2 x 4 x 6 x 8 x 10 x 12 . what is the greatest prime factor of f ( 28 ) ?
Options: a ) 2 , b ) 7 , c ) 11 , d ) 13 , e ) 17
Rationale: "f ( 28 ) = 2 * 4 * 6 * 8 * 10 * 12 * 14 * 16 * 18 * 20 * 22 * 24 * 26 * 28 the greatest prime factor in this list is 13 . the answer is d ."
Answer: d
Python program:
a = 28 / 2
b = a - 1
Problem: mike needs 30 % to pass . if he scored 212 marks and falls short by 16 marks , what was the maximum marks he could have got ?
Options: a ) 643 , b ) 677 , c ) 760 , d ) 767 , e ) 832
Rationale: if mike had scored 16 marks more , he could have scored 30 % therefore , mike required 212 + 16 = 228 marks let the maximum marks be m . then 30 % of m = 228 ( 30 / 100 ) × m = 228 m = ( 228 × 100 ) / 30 m = 22800 / 30 m = 760 answer : c
Answer: c
Python program:
a = 212 + 16 
b = 30 / 100
c = a / b
Problem: a student completes a 3 part exam as follows . the student completes sections a in 18 minutes and takes an equal time to complete the two remaining sections . what is the ratio of time spent on section c to section a if the total duration is 1 hour ?
Options: a ) 4 : 3 , b ) 5 : 4 , c ) 6 : 5 , d ) 7 : 6 , e ) 8 : 7
Rationale: "the time spent on section b and section c is 21 minutes each . the ratio of c to a is 21 : 18 = 7 : 6 the answer is d ."
Answer: d
Python program:
a = 3 / 4
Problem: . a car covers a distance of 742 km in 7 hours . find its speed ?
Options: a ) 104 , b ) 55 , c ) 148 , d ) 150 , e ) 159
Rationale: "742 / 5 = 148 kmph answer : c"
Answer: c
Python program:
a = 742 / 7
Problem: how many bricks each measuring 20 cm x 10 cm x 8 cm , will be needed to build a wall 10 m x 8 m x 24.5 m
Options: a ) 12250 , b ) 13400 , c ) 12500 , d ) 14340 , e ) none of these
Rationale: "explanation : no . of bricks = volume of the wall / volume of 1 brick = ( 1000 x 800 x 24.5 ) / ( 20 x 10 x 8 ) = 12250 answer : a"
Answer: a
Python program:
a = 10 * 8
b = a * 24
c = 20 * 10
d = c * 8
e = d / 100
f = e / 100
g = b / f