euclaise/mathqa_programs huggingface dataset:
Problem: in a kilometer race , a beats b by 48 meters or 6 seconds . what time does a take to complete the race ?
Options: a ) 22 , b ) 119 , c ) 110 , d ) 109 , e ) 12
Rationale: "time taken by b run 1000 meters = ( 1000 * 6 ) / 48 = 125 sec . time taken by a = 125 - 6 = 119 sec . answer : b"
Answer: b
Python program:
a = 1 * 1000
b = 48 / 6
c = a / b
d = c - 6
Problem: a shopkeeper sells 20 % of his stock at 10 % profit ans sells the remaining at a loss of 5 % . he incurred an overall loss of rs . 200 . find the total worth of the stock ?
Options: a ) 20029 , b ) 20000 , c ) 10000 , d ) 20027 , e ) 20026
Rationale: "let the total worth of the stock be rs . x . the sp of 20 % of the stock = 1 / 5 * x * 1.1 = 11 x / 50 the sp of 80 % of the stock = 4 / 5 * x * 0.95 = 19 x / 25 = 38 x / 50 total sp = 11 x / 50 + 38 x / 50 = 49 x / 50 overall loss = x - 49 x / 50 = x / 50 x / 50 = 200 = > x = 10000 answer : c"
Answer: c
Python program:
a = 5 / 100
b = 100 - 20
c = b / 100
d = a * c
e = 10 / 100
f = 20 / 100
g = e * f
h = d - g
i = 200 / h
Problem: the average weight of 10 person ' s increases by 5 kg when a new person comes in place of one of them weighing 60 kg . what is the weight of the new person ?
Options: a ) 85.5 , b ) 86.5 , c ) 87.5 , d ) 110 , e ) 89.5
Rationale: "total increase in weight = 10 × 5 = 50 if x is the weight of the new person , total increase in weight = x − 60 = > 50 = x - 60 = > x = 50 + 60 = 110 answer : d"
Answer: d
Python program:
a = 10 * 5
b = a + 60
Problem: the speed at which a man can row a boat in still water is 15 kmph . if he rows downstream , where the speed of current is 3 kmph , what time will he take to cover 60 metres ?
Options: a ) 22 seconds , b ) 65 seconds , c ) 78 seconds , d ) 12 seconds , e ) 21 seconds
Rationale: "speed of the boat downstream = 15 + 3 = 18 kmph = 18 * 5 / 18 = 5 m / s hence time taken to cover 60 m = 60 / 5 = 12 seconds . answer : d"
Answer: d
Python program:
a = 15 + 3 
b = a * const_0_2778
c = 60 / b
Problem: solution a is 10 % salt and solution b is 80 % salt . if you have 30 ounces of solution a and 60 ounces of solution b , in what ratio could you mix solution a with solution b to produce 50 ounces of a 50 % salt solution ?
Options: a ) 6 : 4 , b ) 6 : 14 , c ) 3 : 4 , d ) 4 : 6 , e ) 3 : 7
Rationale: "forget the volumes for the time being . you have to mix 20 % and 80 % solutions to get 50 % . this is very straight forward since 50 is int he middle of 20 and 80 so we need both solutions in equal quantities . if this does n ' t strike , use w 1 / w 2 = ( a 2 - aavg ) / ( aavg - a 1 ) w 1 / w 2 = ( 80 - 50 ) / ( 50 - 10 ) = 3 / 4 so the volume of the two solutions will be equal . answer has to be 3 : 4 . c"
Answer: c
Python program:
a = 80 / 100
b = 50 * a
c = 50 / 100
d = 50 * c
e = b - d
f = 80 / 100
g = 10 / 100
h = f - g
i = e / h
j = 80 / 100
k = 50 * j
l = 50 / 100
m = 50 * l
n = k - m
o = 80 / 100
p = 10 / 100
q = o - p
r = n / q
s = 50 - r
t = i / s
Problem: at what price must an article costing rs . 47.50 be marked in order that after deducting 12 % from the list price . it may be sold at a profit of 25 % on the cost price ?
Options: a ) 62.5 , b ) 67.5 , c ) 62.7 , d ) 62.2 , e ) 62.9
Rationale: "cp = 47.50 sp = 47.50 * ( 125 / 100 ) = 59.375 mp * ( 88 / 100 ) = 59.375 mp = 67.5 answer : b"
Answer: b
Python program:
a = 47 * 50
b = a / 100
c = 47 + 50 
d = c * 100
e = 100 - 12
f = d / e
Problem: if p ( a ) = 2 / 15 , p ( b ) = 4 / 15 , and p ( a â ˆ ª b ) = 6 / 15 find p ( b | a )
Options: a ) 1 / 2 , b ) 2 / 3 , c ) 3 , d ) 4 / 5 , e ) 4 / 7
Rationale: p ( b | a ) = p ( a â ˆ ª b ) / p ( a ) p ( b | a ) = ( 6 / 15 ) / ( 2 / 15 ) = 3 . c
Answer: c
Python program:
a = 6 / 15
b = 2 / 15
c = a / b
Problem: if x + y = 9 and x – y = 3 , then x ^ 2 - y ^ 2 =
Options: a ) - 4 , b ) 4 , c ) 10 , d ) 27 , e ) 40
Rationale: the fastest approach has already been shown . here ' s one more option . given : x + y = 9 x – y = 3 add the two equations to get : 2 x = 12 , which means x = 6 if x = 6 , we can plug that value into either equation , to conclude that y = 3 if x = 6 and y = 3 , then x ² - y ² = 6 ² - 3 ² = 27 answer : d
Answer: d
Python program:
a = 9 - 3
b = a ** 2
c = 3 ** 2
d = b - c
Problem: in a primary school , the ratio of the number of girls to boys is 5 : 8 . if there are 160 girls , the total number of students in the college is :
Options: a ) 100 , b ) 250 , c ) 260 , d ) 300 , e ) 350
Rationale: let the number of girls and boys be 5 x and 8 x . total number of students = 13 x = 13 x 32 = 416 . answer : d
Answer: d
Python program:
a = 160 / 8
b = 5 * a
c = 5 * 8
d = 160 + c 
e = b + d
Problem: a confectioner decides to sell all of his pastry due to the coming holiday . his pastry goods are equally divided among a group of 35 regular customers . if only 49 customers come to the bakery , each one will receive 6 less pastry goods . how much pastry does the confectioner needs to sell ?
Options: a ) 525 . , b ) 412 . , c ) 432 . , d ) 502 . , e ) 522 .
Rationale: "pastry is divided in 35 customers equally . so , total number of pastry must be a multiple of 35 only option a satisfies the condition , and hence is the answer"
Answer: a
Python program:
a = 49 * 6
b = 49 - 35
c = a / b
d = c * 35
Problem: ( 74 + 75 + 76 + 77 + . . . . . + 149 + 150 ) = ?
Options: a ) 8624 , b ) 8634 , c ) 8654 , d ) 8644 , e ) 8677
Rationale: "explanation : sum of first n natural numbers = ( 1 + 2 + 3 + . . . . . + n ) = n ( n + 1 ) / 2 ( 74 + 75 + 76 + . . . . . + 150 ) = ( 1 + 2 + . . . . + 73 + 74 + 75 + . . . . . + 150 ) - ( 1 + 2 + . . . . + 73 ) = ( 1 / 2 x 150 x 151 ) - ( 1 / 2 x 73 x 74 ) = 11325 - 2701 = 8624 answer : option a"
Answer: a
Python program:
a = 77 + 1 
b = 77 * a
c = b / 2
d = 74 - 1
e = d * 74
f = e / 2
g = c - f
Problem: an item is being sold for $ 10 each . however , if a customer will “ buy at least 3 ” they have a promo discount of 17 % . also , if a customer will “ buy at least 10 ” items they will deduct an additional 8 % to their “ buy at least 3 ” promo price . if sam buys 10 pcs of that item how much should he pay ?
Options: a ) $ 92.00 , b ) $ 88.00 , c ) $ 87.04 , d ) $ 80.96 , e ) $ 75.00
Rationale: "without any discount sam should pay 10 * 10 = $ 100 . now , the overall discount would be slightly less than 27 % , thus he must pay slightly more than $ 73 . only answer choice e fits . answer : e"
Answer: e
Python program:
a = 17 * 8
b = a / 100
c = 10 - b
d = c * 10
Problem: a leak in the bottom of a tank can empty the full tank in 6 hours . an inlet pipe fills water at the rate of 3 liters per minute . when the tank is full in inlet is opened and due to the leak the tank is empties in 8 hours . the capacity of the tank is ?
Options: a ) 5729 , b ) 5760 , c ) 2889 , d ) 2870 , e ) 4320
Rationale: "1 / x - 1 / 6 = - 1 / 8 x = 24 hrs 24 * 60 * 3 = 4320 . answer : e"
Answer: e
Python program:
a = 8 * const_60
b = 3 * a
c = 8 * const_60
d = 6 * const_60
e = c / d
f = e - 1
g = b / f
Problem: a feed store sells two varieties of birdseed : brand a , which is 65 % millet and 35 % sunflower , and brand b , which is 40 % millet and 60 % safflower . if a customer purchases a mix of the two types of birdseed that is 50 % millet , what percent of the mix is brand a ?
Options: a ) 40 % , b ) 45 % , c ) 50 % , d ) 60 % , e ) 55 %
Rationale: "yes there is a simple method : consider the following method brand a : 65 % millet and 35 % sunflower brand b : 40 % millet and 60 % safflower mix : 50 % millet here the weighted average is 50 % , now brand a has 65 % millet , which is 15 % more than the weighted average of mix = + 0.15 a - - - - - - - - - - - - - - - i similarly , brand b has 40 % millet , which is 10 % less than the weighted average of mix = - 0.10 b - - - - - - - - - - - - ii now , both brand a and brand b are combined to give a 50 % mix containing millet , so equate i and ii implies , 0.15 a = 0.10 b therefore a / b = 0.10 / 0.15 = 2 / 3 a : b : ( a + b ) = 2 : 3 : ( 3 + 2 ) = 2 : 3 : 5 we have to find , percent of the mix is brand a i . e . a : ( a + b ) = 2 : 5 = ( 2 / 5 ) * 100 = 40 % here is a pictorial representation : brand a = 65 % - - - - - - - - - - - - - - - - - - - - - - - - 15 % or 0.15 above average , a times - - - - - - - - - - - - - - - - - total below = + 0.15 a - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - average = 50 % or 0.50 brand b = 40 % - - - - - - - - - - - - - - - - - - - - - - - - - - 10 % or 0.10 below average , b times - - - - - - - - - - - - - - - - - total above = - 0.10 b since the amount below the average has to equal the average above the average ; therefore , 0.15 a = 0.10 b a / b = 2 / 3 a : b : total = 2 : 3 : 5 therefore a / total = 2 : 5 = 40 %"
Answer: a
Python program:
a = 3 + 2 
b = 3 / a
c = b * 100
Problem: of 60 children , 30 are happy , 10 are sad , and 20 are neither happy nor sad . there are 16 boys and 44 girls . if there are 6 happy boys and 4 sad girls , how many boys are neither happy nor sad ?
Options: a ) 2 , b ) 4 , c ) 6 , d ) 8 , e ) 10
Rationale: venn diagrams are useful for multiple values of a single variable e . g . state of mind - happy / sad / neither . when you have two or more variables such as here where you have gender - boy / girl too , it becomes unwieldy . in this case , either use the table or logic . table method is shown above ; here is how you will use logic : there are 6 happy boys . there are 4 sad girls but total 10 sad children . so rest 6 sad children must be sad boys . we have 6 happy boys and 6 sad boys . total we have 16 boys . so 16 - 6 - 6 = 4 boys must be neither happy nor sad . answer ( b )
Answer: b
Python program:
a = 10 - 4
b = 16 - a
c = b - 6
Problem: pipe p can drain the liquid from a tank in 1 / 4 the time that it takes pipe q to drain it and in 2 / 3 the time that it takes pipe r to do it . if all 3 pipes operating simultaneously but independently are used to drain liquid from the tank , then pipe q drains what portion of the liquid from the tank ?
Options: a ) 9 / 29 , b ) 3 / 23 , c ) 3 / 8 , d ) 17 / 29 , e ) 3 / 4
Rationale: "suppose q can drain in 1 hr . so , rq = 1 / 1 = 1 so , rp = 1 / [ ( 1 / 4 ) rq ] = 4 also , rp = rr / ( 2 / 3 ) = > 4 = rr / ( 2 / 3 ) = > rr = 8 / 3 let h is the time it takes to drain by running all 3 pipes simultaneously so combined rate = rc = 1 / h = 1 + 4 + 8 / 3 = 23 / 3 = 1 / ( 3 / 23 ) thus running simultaneously , pipe q will drain 3 / 23 of the liquid . thus answer = b ."
Answer: b
Python program:
a = 1 * 1
b = 4 * 1
c = b * 2
d = 1 * 1
e = c + d 
f = a / e
Problem: a box contains 10 apples , 9 of which are red . an apple is drawn from the box and its color is noted before it is eaten . this is done a total of n times , and the probability that a red apple is drawn each time is less than 0.5 . what is the smallest possible value of n ?
Options: a ) 3 , b ) 4 , c ) 5 , d ) 6 , e ) 7
Rationale: "when you choose ( and then eat ) the first apple , the probability of that apple being red is 9 / 10 . so if we do the activity 1 times , the probability of it being red is 9 / 10 . for 2 times , it is ( 9 / 10 ) * ( 8 / 9 ) for 3 times , it is ( 9 / 10 ) * ( 8 / 9 ) * ( 7 / 8 ) you can notice that the numerator of the first term cancels with the denominator of the second . so we can see that the probability becomes 0.5 when the last term is 5 / 6 & it becomes less than 0.5 when the last term is 4 / 5 . 9 accounts for n = 1 , so 4 will account for n = 6 , answer . d"
Answer: d
Python program:
a = 0 * 5
b = a + 1
Problem: if a - b = 10 and a 2 + b 2 = 210 , find the value of ab .
Options: a ) 68 , b ) 42 , c ) 55 , d ) 18 , e ) 44
Rationale: "2 ab = ( a 2 + b 2 ) - ( a - b ) 2 = 210 - 100 = 110 ab = 55 . answer : c"
Answer: c
Python program:
a = 10 ** 2
b = 210 - a
c = b / 2
Problem: in a 150 member association consisting of men and women , exactly 10 % of men and exactly 20 % women are homeowners . what is the least number of members who are homeowners ?
Options: a ) 22 , b ) 21 , c ) 20 , d ) 19 , e ) 18
Rationale: solution simple out of 150 10 % are male i . e 15 and 20 % are female i . e 30 , so total homeowner is 45 . now min number homeowner is 15 and max is 30 so question ask us to find least and 18 has least value among all option . so ans is 18 . ans : e
Answer: e
Python program:
a = 20 / 100
b = a * 10
c = 20 / 100
d = c * 10
e = b * d
f = 150 - 10
g = f / 10
h = e + g
Problem: the length of the longest rod that can fit in a cubical room of 4 m side is ?
Options: a ) 6.978 m
b ) 6.928 m
c ) 6.829 m
d ) 6.248 m
e ) 6.982 m
Rationale: the length of the longest rod = 4 sq . root of 3 = 6.928 m answer : b
Answer: b
Python program:
a = math.sqrt(2)
b = a * 4
c = b ** 2
d = 4 ** 2
e = c + d 
f = math.sqrt(e)
Problem: if $ 5,000 is invested in an account that earns 16 % interest compounded semi - annually , then the interest earned after one year would be how much greater than if the $ 5,000 had been invested at 8 % simple yearly interest ?
Options: a ) $ 4 , b ) $ 8 , c ) $ 12 , d ) $ 16 , e ) $ 432
Rationale: "solution amount ( ci ) = p + ( 1 + r / n ) ^ nt = 5000 + ( 1 + 0.16 / 2 ) ^ 2 = 5416 amount ( si ) = p + ptr / 100 = 5000 + ( 5000 * 1 * 16 / 100 ) = 5400 difference = 5416 - 5400 = 16 $ d"
Answer: d
Python program:
a = 16 * 1
Problem: a rectangular paper , when folded into two congruent parts had a perimeter of 34 cm for each part folded along one set of sides and the same is 38 cm when folded along the other set of sides . what is the area of the paper ?
Options: a ) 140 cm
b ) 240 cm 2
c ) 560 cm 2
d ) none of these
e ) can not be determined
Rationale: solution when folded along breadth , we have : 2 ( l / 2 + b ) = 34 or l + 2 b = 34 when folded along length , we have : 2 ( l / 2 + b ) = 38 or 2 l + b = 38 solving ( i ) and ( ii ) , we get : l = 14 and b = 10 . ∴ area of the paper = ( 1410 ) cm 2 = 140 cm 2 answer a
Answer: a
Python program:
a = 38 * 2
b = a - 34
c = b / 3
d = 38 * 2
e = d - 34
f = e / 3
g = f * 2
h = 38 - g
i = c * h
Problem: after giving a discount of rs . 50 the shopkeeper still gets a profit of 20 % , if the cost price is rs . 180 . find the markup % ?
Options: a ) 0.5 , b ) 0.6 , c ) 0.48 , d ) 0.65 , e ) 0.45
Rationale: "cost price = 180 s . p = 180 * 120 / 100 = 216 disc = 50 so . . . mark price = 216 + 50 = 266 . . . . . . mark up % = 266 - 180 / 180 = 86 / 180 = . 48 or 48 % answer : c"
Answer: c
Python program:
a = 100 / 20
b = 180 / a
c = 180 + b 
d = c + 50 
e = d - 180
f = e / 180
Problem: the water level in a rectangular swimming pool measuring 60 feet by 10 feet is to be lowered by 6 inches . how many gallons of water must be removed ? ( 1 cu ft = 7.5 gallons )
Options: a ) 100 , b ) 2250 , c ) 750 , d ) 1200 , e ) 5625
Rationale: "6 inches = 1 / 2 feet ( there are 12 inches in a foot . ) , so 60 * 10 * 1 / 2 = 300 feet ^ 3 of water must be removed , which equals to 300 * 7.5 = 2250 gallons . answer : b"
Answer: b
Python program:
a = 10 + 2 
b = 6 / a
c = volume_rectangular_prism * (
Problem: a leak in the bottom of a tank can empty the tank in 6 hrs . an pipe fills water atthe rate of 4 ltrs / min . when the tank is full in inlet is opened and due to the leak the tank is empties in 8 hrs . the capacity of the tank is ?
Options: a ) 4670 , b ) 4546 , c ) 4556 , d ) 4675 , e ) 5760
Rationale: 1 / x - 1 / 6 = - 1 / 8 x = 24 hrs 24 * 60 * 4 = 5760 e
Answer: e
Python program:
a = 6 * 4
b = a * const_60
c = b * 4
Problem: what is the least number of squares tiles required to pave the floor of a room 2 m 25 cm long and 1 m 35 cm broad ?
Options: a ) 15 , b ) 20 , c ) 40 , d ) 44 , e ) 48
Rationale: "length of largest tile = h . c . f . of 225 cm and 135 cm = 45 cm . area of each tile = ( 45 x 45 ) cm 2 . required number of tiles = 225 x 135 / ( 45 ^ 2 ) = 15 . answer : a"
Answer: a
Python program:
a = 2 * 100
b = 25 * 100
c = rectangle_area / (
Problem: 7 people average age is 30 . youngest person age is 8 . find average of the people when youngest was born .
Options: a ) 23 , b ) 24 , c ) 25 , d ) 22 , e ) 27
Rationale: "average age of people = 30 so have total age = 210 before 7 years we have to deduct each person age by seven years 210 - 56 = 154 so average age would be 154 / 7 = 22 answer : d"
Answer: d
Python program:
a = 30 * 7
b = 8 * 7
c = a - b
d = c / 7
Problem: 24 people can write 48 book in 6 days working 8 hour a day . then in how many day 192 can be written by 50 people ?
Options: a ) 223 / 26 , b ) 288 / 27 , c ) 309 / 22 , d ) 288 / 26 , e ) 288 / 25
Rationale: work per day epr hour per person = 48 / ( 6 * 8 * 24 ) / / eq - 1 people = 50 ; let suppose day = p ; per day work for 8 hours acc . to condition work per day epr hour per person = 192 / ( p * 8 * 50 ) / / eq - 2 eq - 1 = = eq - 2 ; p = 288 / 25 answer : e
Answer: e
Python program:
a = 48 * 6
b = 50 / 2
c = a / b
Problem: john makes $ 60 a week from his job . he earns a raise andnow makes $ 75 a week . what is the % increase ?
Options: a ) 16.12 % , b ) 25 % , c ) 16.56 % , d ) 17.66 % , e ) 18.1 %
Rationale: "increase = ( 15 / 60 ) * 100 = ( 1 / 4 ) * 100 = 25 % . b"
Answer: b
Python program:
a = 75 - 60
b = a / 60
c = b * 100
Problem: at a supermarket , john spent 1 / 2 of his money on fresh fruits and vegetables , 1 / 3 on meat products , and 1 / 10 on bakery products . if he spent the remaining $ 5 on candy , how much did john spend at the supermarket ?
Options: a ) $ 75 , b ) $ 80 , c ) $ 90 , d ) $ 120 , e ) $ 180
Rationale: "let ' s let t = total number of dollars spent at the supermarket . with this variable we can set up an equation and determine t . we are given that john spent 1 / 2 of his money on fresh fruits and vegetables , or ( 1 / 2 ) t , 1 / 3 on meat products , or ( 1 / 3 ) t , and 1 / 10 on bakery products , or ( 1 / 10 ) t . we are also given that he spent the remaining $ 5 on candy . since we know where all his money was allocated , we can sum these values together and set the sum to t . so we have : ( 1 / 2 ) t + ( 1 / 3 ) t + ( 1 / 10 ) t + 5 = t to get rid of the fractions we can multiply the entire equation by 30 , and we obtain : 15 t + 10 t + 3 t + 150 = 30 t 28 t + 150 = 30 t 150 = 2 t t = 75 john spent $ 7 at the supermarket . answer : a"
Answer: a
Python program:
a = 1 / 10
b = 1 / 3
c = a + b 
d = 1 / 2
e = c + d 
f = 1 - e
g = 5 / f
Problem: a bus started its journey from chennai and reached mumbai in 50 min with its average speed of 60 km / hr . if the average speed of the bus is increased by 6 km / hr , how much time will it take to cover the same distance ?
Options: a ) 45 min . , b ) 55 min . , c ) 65 min . , d ) 60 min . , e ) 50 min .
Rationale: sol . distance between mumbai and pune = ( 60 * 50 ) / 60 = 50 average speed of the bus is increased by 6 km / hr then the speed of the bus = 66 km / hr required time = 50 * 66 / 60 = 55 min . b
Answer: b
Python program:
a = 50 / 60
b = a * 60
c = 60 - 6
d = b / c
e = d * 60
Problem: two goods trains each 500 m long are running in opposite directions on parallel tracks . their speeds are 45 km / hr and 30 km / hr respectively . find the time taken by the slower train to pass the driver of the faster one ?
Options: a ) 22 sec , b ) 88 sec , c ) 48 sec , d ) 18 sec , e ) 9 sec
Rationale: "relative speed = 45 + 30 = 75 km / hr . 75 * 5 / 18 = 125 / 6 m / sec . distance covered = 500 + 500 = 1000 m . required time = 1000 * 6 / 125 = 48 sec . answer : c"
Answer: c
Python program:
a = 45 + 30
Problem: the ratio between the present ages of a and b is 4.5 : 3 respectively . the ratio between a ' s age 4 years ago and b ' s age 4 years hence is 1 : 1 . what is the ratio between a ' s age 4 years hence and b ' s age 4 years ago ?
Options: a ) 3 : 4 , b ) 3 : 0 , c ) 3 : 1 , d ) 7 : 3 , e ) 3 : 7
Rationale: "let the present ages of a and b be 4.5 x and 3 x years respectively . then , ( 4.5 x - 4 ) / ( 3 x + 4 ) = 1 / 1 1.5 x = 8 = > x = 5.33 required ratio = ( 5 x + 4 ) : ( 3 x - 4 ) = 28 : 12 = 7 : 3 . answer : d"
Answer: d
Python program:
a = 4 + 5 
b = 4 - 5
c = a / b
d = 4 * 5
e = d + 4 
f = 4 + 5 
g = 4 - 5
h = f / g
i = 3 * h
j = i - 4
k = e / j
Problem: the average weight of a , b and c is 46 kg . if the average weight of a and b be 40 kg and that of b and c be 43 kg , then the weight of b is :
Options: a ) 17 kg , b ) 20 kg , c ) 26 kg , d ) 31 kg , e ) 22 kg
Rationale: "let d sum of a , b , c is 3 * 46 = 144 and sum of a and b s 2 * 40 = 80 sum of b and c is 3 * 43 = 86 hence 80 + 86 - 144 = 22 ans = 22 answer : e"
Answer: e
Python program:
a = 40 * 2
b = 43 * 2
c = a + b 
d = 46 * 3
e = c - d
Problem: the rate of spin of a certain gyroscope doubled every 10 seconds from the moment a particular stopwatch started . if after a minute and a half the gyroscope reached a speed of 6400 meters per second , what was the speed , in meters per second , when the stopwatch was started ?
Options: a ) 25 / 2 , b ) 25 / 4 , c ) 25 / 8 , d ) 25 / 16 , e ) 25 / 32
Rationale: "let x be the original speed when the stopwatch was started . in 90 seconds , the speed doubled 9 times . 2 ^ 9 * x = 6400 x = ( 2 ^ 8 * 25 ) / 2 ^ 9 = 25 / 2 the answer is a ."
Answer: a
Python program:
a = const_60 / 2
b = a + const_60 
c = b / 10
d = c - 1
e = 2 ** d
f = 6400 / e
g = f / 2
Problem: if two integers x , y ( x > y ) are selected from - 5 to 6 ( inclusive ) , how many cases are there ?
Options: a ) 62 , b ) 66 , c ) 70 , d ) 74 , e ) 78
Rationale: "there are 12 integers from - 5 to 6 inclusive . 12 c 2 = 66 . the answer is b ."
Answer: b
Python program:
a = 6 + 5 
b = 6 + 2 
c = a + b 
d = 6 + 1 
e = c + d 
f = e + 6 
g = f + 5 
h = g + 2 
i = h + 1
Problem: what is the remainder when 2 ^ 20 is divided by 10 ?
Options: a ) 0 , b ) 2 , c ) 4 , d ) 6 , e ) 8
Rationale: "2 ^ 20 = 2 ^ 10 x 2 ^ 10 and 2 ^ 10 = 1024 4 * 4 = 16 , so the unit digit of this multiplication is 6 the remainder is 6 answer : d"
Answer: d
Python program:
a = 10 / 2
b = 2 * 2
c = a - b
Problem: what will be the cost of building a fence around a square plot with area equal to 289 sq ft , if the price per foot of building the fence is rs . 56 ?
Options: a ) s . 3944 , b ) s . 3948 , c ) s . 3942 , d ) s . 3808 , e ) s . 3929
Rationale: "let the side of the square plot be a ft . a 2 = 289 = > a = 17 length of the fence = perimeter of the plot = 4 a = 68 ft . cost of building the fence = 68 * 56 = rs . 3808 . answer : d"
Answer: d
Python program:
a = math.sqrt(289)
b = square_perimeter * (
Problem: the average weight of a group of boys is 20 kg . after a boy of weight 34 kg joins the group , the average weight of the group goes up by 1 kg . find the number of boys in the group originally ?
Options: a ) 12 , b ) 14 , c ) 18 , d ) 13 , e ) 10
Rationale: "let the number off boys in the group originally be x . total weight of the boys = 20 x after the boy weighing 34 kg joins the group , total weight of boys = 20 x + 34 so 20 x + 34 = 21 ( x + 1 ) = > x = 13 . answer : d"
Answer: d
Python program:
a = 20 + 1 
b = 34 - a
c = b + 1
Problem: in a certain school , 20 % of students are below 8 years of age . the number of students above 8 years of age is 2 / 3 of the number of students of 8 years of age which is 12 . what is the total number of students in the school ?
Options: a ) 72 , b ) 80 , c ) 25 , d ) 150 , e ) 100
Rationale: "explanation : let the number of students be x . then , number of students above 8 years of age = ( 100 - 20 ) % of x = 80 % of x . 80 % of x = 12 + 2 / 3 of 12 80 / 100 x = 20 x = 25 . answer : option c"
Answer: c
Python program:
a = 2 / 3
b = 12 * a
c = 12 + b 
d = 20 / 100
e = 1 - d
f = c / e
Problem: if w is a positive integer and 10 ^ w – 74 in decimal notation has digits whose sum is 440 , what is the value of w ?
Options: a ) 40 , b ) 44 , c ) 45 , d ) 46 , e ) 50
Rationale: answer e = 50 we have ( 10 ^ w ) - 74 , where the sum of the digits is 440 . 100 - 74 = 26 , so we already have 2 + 6 = 8 from the 440 . because we have a power of 10 , we will have numbers like 100 , 1000 , 10000 and so on . this minus 74 rests 26 and a lot of 9 s . e . g : 1000 - 74 = 9926 . so dividing the 432 / 9 = 48 , that ` s the number of 9 s . and we have 2 other numbers ( 2 and 6 ) wich were 00 before the subtraction . so we have 48 + 2 as an w = 50
Answer: e
Python program:
a = 440 / 10
b = 74 - a
c = 10 * 2
d = b + c