euclaise/mathqa_programs huggingface dataset:
Problem: on selling 20 balls at rs . 720 , there is a loss equal to the cost price of 5 balls . the cost price of a ball is :
Options: a ) s . 48 , b ) s . 50 , c ) s . 55 , d ) s . 60 , e ) s . 70
Rationale: "( c . p . of 20 balls ) - ( s . p . of 20 balls ) = ( c . p . of 5 balls ) c . p . of 15 balls = s . p . of 20 balls = rs . 720 . c . p . of 1 ball = rs . 720 / 15 = rs . 48 . answer : option a"
Answer: a
Python program:
a = 20 - 5
b = 720 / a
Problem: the average of first 13 natural numbers is ?
Options: a ) 5.2 , b ) 5.5 , c ) 7 , d ) 9 , e ) 10
Rationale: "sum of 13 natural no . = 182 / 2 = 91 average = 91 / 13 = 7 answer : c"
Answer: c
Python program:
a = 13 + 1
Problem: tom opened a shop investing rs . 30000 . jose joined him 2 months later , investing rs . 45000 . they earned a profit of rs . 54000 after completion of one year . what will be jose ' s share of profit ?
Options: a ) 20000 , b ) 24000 , c ) 34000 , d ) 35000 , e ) 30000
Rationale: sol = ~ s - so anju ’ s share = [ 5 / 9 ] x 54000 = 30000 e
Answer: e
Python program:
a = 2 * 3
b = 2 * a
c = 30000 * b
d = 2 * 3
e = 2 * d
f = e - 2
g = 45000 * f
h = 2 * 3
i = 2 * h
j = 30000 * i
k = g + j 
l = c / k
m = 1 - l
n = 54000 * m
Problem: fresh grapes contain 75 % water by weight and raisins obtained by drying fresh grapes contain 25 % water by weight . how many kgs of fresh grapes are needed to get 25 kgs of raisins ?
Options: a ) 75 kgs , b ) 64 kgs , c ) 72 kgs , d ) 65 kgs , e ) 70 kgs
Rationale: "the weight of non - water in 20 kg of dried grapes ( which is 100 - 25 = 75 % of whole weight ) will be the same as the weight of non - water in x kg of fresh grapes ( which is 100 - 75 = 25 % of whole weight ) , so 25 * 0.75 = x * 0.25 - - > x = 75 . answer : a ."
Answer: a
Python program:
a = 100 - 25
b = 25 * a
c = b / 100
d = c + 75
Problem: every year an amount increases by 1 / 8 th of itself . how much will it be after two years if its present value is rs . 64000 ?
Options: a ) 81000 , b ) 22887 , c ) 26877 , d ) 26771 , e ) 17121
Rationale: 64000 * 9 / 8 * 9 / 8 = 81000 answer : a
Answer: a
Python program:
a = 1 / 8
b = a * 64000
c = 64000 + b 
d = 1 / 8
e = 1 / 8
f = e * 64000
g = 64000 + f 
h = d * g
i = c + h
Problem: a train covers a distance of 12 km in 10 min . if it takes 5 sec to pass a telegraph post , then the length of the train is ?
Options: a ) 298 m , b ) 188 m , c ) 120 m , d ) 160 m , e ) 189 m
Rationale: "speed = ( 12 / 10 * 60 ) km / hr = ( 72 * 5 / 18 ) m / sec = 20 m / sec . length of the train = 20 * 8 = 160 m . answer : d"
Answer: d
Python program:
a = 12 / 10
b = a - 5
c = 12 / b
Problem: victor gets 95 % marks in examinations . if these are 285 marks , find the maximum marks .
Options: a ) 334 , b ) 500 , c ) 376 , d ) 288 , e ) 300
Rationale: let the maximum marks be m then 95 % of m = 285 ⇒ 95 / 100 × m = 285 ⇒ m = ( 285 × 100 ) / 95 ⇒ m = 28500 / 95 ⇒ m = 300 therefore , maximum marks in the examinations are 300 . answer : e
Answer: e
Python program:
a = 95 / 100
b = 285 / a
Problem: last month , john rejected 0.5 % of the products that he inspected and jane rejected 0.9 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 ?
Options: a ) 1 / 6 , b ) 1 / 2 , c ) 5 / 8 , d ) 5 / 6 , e ) 15 / 16
Rationale: "x - fraction of products jane inspected ( 1 - x ) - fraction of products john inspected 0.9 ( x ) + 0.5 ( 1 - x ) = 0.75 0.4 x = 0.75 - 0.5 x = 0.25 / 0.4 x = 5 / 8 therefore the answer is c : 5 / 8 ."
Answer: c
Python program:
a = 0 - 75
b = 0 - 9
c = a / b
Problem: a company wants to spend equal amounts of money for the purchase of two types of computer printers costing $ 375 and $ 150 per unit , respectively . what is the fewest number of computer printers that the company can purchase ?
Options: a ) 3 , b ) 4 , c ) 5 , d ) 6 , e ) 7
Rationale: the smallest amount that the company can spend is the lcm of 375 and 150 , which is 750 for each , which is total 1500 . the number of 1 st type of computers which costing $ 375 = 750 / 375 = 2 . the number of 2 nd type of computers which costing $ 150 = 750 / 150 = 5 . total = 2 + 5 = 7 answer is e .
Answer: e
Python program:
a = math.lcm(375, 150)
b = a / 375
c = math.lcm(375, 150)
d = c / 150
e = b + d
Problem: how many integerskgreater than 100 and less than 1200 are there such that if the hundreds and the units digits ofkare reversed , the resulting integer is k + 99 ?
Options: a ) 50 , b ) 60 , c ) 70 , d ) 80 , e ) 100
Rationale: "numbers will be like 102 = > 201 = 102 + 99 203 = > 302 = 103 + 99 so the hundereth digit and units digit are consecutive where unit digit is bigger than hundred digit . there will be ten pairs of such numbers for every pair there will 10 numbers like for 12 = > 102 , 112,132 , 142,152 , 162,172 , 182,192 . total = 10 * 10 = 100 hence e"
Answer: e
Python program:
a = 100 / 10
b = 2 * 4
c = a * b
d = 100 / 10
e = c + d
Problem: a batch of cookies was divided amomg 3 tins : 2 / 3 of all the cookies were placed in either the blue or the green tin , and the rest were placed in the red tin . if 1 / 5 of all the cookies were placed in the blue tin , what fraction of the cookies that were placed in the other tins were placed in the green tin
Options: a ) 21 / 31 , b ) 9 / 4 , c ) 5 / 9 , d ) 7 / 5 , e ) 9 / 7
Rationale: "this will help reduce the number of variables you have to deal with : g + b = 2 / 3 r = 1 / 3 b = 1 / 5 we can solve for g which is 7 / 10 what fraction ( let it equal x ) of the cookies that were placed in the other tins were placed in the green tin ? so . . x * ( g + r ) = g x * ( 7 / 10 + 1 / 3 ) = 7 / 10 x = 21 / 31 answer : a"
Answer: a
Python program:
a = 2 / 3
b = 1 - a
c = 2 / 3
d = 1 / 5
e = c - d
f = b + e
Problem: a grocer is storing soap boxes in cartons that measure 30 inches by 42 inches by 60 inches . if the measurement of each soap box is 7 inches by 6 inches by 5 inches , then what is the maximum number of soap boxes that can be placed in each carton ?
Options: a ) 360 , b ) 252 , c ) 280 , d ) 300 , e ) 420
Rationale: "however the process of dividing the volume of box by the volume of a soap seems flawed but it does work in this case due to the numbers dimensions of the box = 30 * 42 * 60 dimensions of the soap = 5 * 6 * 7 we get = 6 x 6 x 10 = 360 so the question is why this particular arrangement , in order to maximize number of soaps we need to minimize the space wasted and this is the only config where we dont waste any space so we can expect the maximum number the answer is ( a )"
Answer: a
Python program:
a = 30 * 42
b = a * 60
c = 7 * 6
d = c * 5
e = b / d
Problem: if ( a - b - c + d = 13 ) and ( a + b - c - d = 5 ) , what is the value of ( b - d ) ^ 2 ?
Options: a ) 4 . , b ) 8 . , c ) 12 . , d ) 16 , e ) 64
Rationale: a - b - c + d = 13 - - equation 1 a + b - c - d = 5 - - equation 2 adding 1 and 2 , we get 2 a - 2 c = 18 = > a - c = 9 - - equation 3 using equation 3 in 2 , we get b - d = 5 - 9 = - 4 = > ( b - d ) ^ 2 = 16 answer d
Answer: d
Python program:
a = 13 + 5 
b = a / 2
c = 5 - b
d = c ** 2
Problem: a train 225 m in length crosses a telegraph post in 15 seconds . the speed of the train is ?
Options: a ) 37 kmph , b ) 34 kmph , c ) 32 kmph , d ) 38 kmph , e ) 76 kmph
Rationale: "s = 225 / 25 * 18 / 5 = 32 kmph answer : c"
Answer: c
Python program:
a = 225 / 15
b = const_3_6 * a
Problem: find the value of 3 x [ ( 3.6 x 0.48 x 2.50 ) / ( 0.12 x 0.09 x 0.5 ) ]
Options: a ) 800 , b ) 500 , c ) 900 , d ) 1600 , e ) 2400
Rationale: "answer 3 x [ ( 3.6 x 0.48 x 2.50 ) / ( 0.12 x 0.09 x 0.5 ) ] = 3 x [ ( 36 x 48 x 250 ) / ( 12 x 9 x 5 ) ] = 3 x 4 x 4 x 50 = 2400 correct option : e"
Answer: e
Python program:
a = 3 * 6
b = a * 2
c = 0 * 12
d = c * 0
e = b / d
f = e * 3
Problem: sara bought both german chocolate and swiss chocolate for some cakes she was baking . the swiss chocolate cost $ 3.5 per pound , and german chocolate cost $ 2.8 per pound . if the total the she spent on chocolate was $ 28 and both types of chocolate were purchased in whole number of pounds , how many total pounds of chocolate she purchased ?
Options: a ) 9 , b ) 8 , c ) 10 , d ) 12 , e ) 15
Rationale: "if there were all the expensive ones , 3.5 . . . . there would be 28 / 3.5 or 8 of them but since 2.8 $ ones are also there , answer has to be > 8 . . if all were 2.8 $ ones , there will be 28 / 2.8 or 10 . . . so only 9 is left answer a . ."
Answer: a
Python program:
a = 3 + 5 
b = a / 2
c = 28 / b
Problem: if 16 men can reap 80 hectares in 24 days , then how many hectares can 36 men reap in 30 days ?
Options: a ) 127 , b ) 225 , c ) 287 , d ) 450 , e ) 281
Rationale: "explanation : let the required no of hectares be x . then men - - - hectares - - - days 16 - - - - - - - - - 80 - - - - - - - - - 24 36 - - - - - - - - - x - - - - - - - - - 30 more men , more hectares ( direct proportion ) more days , more hectares ( direct proportion ) x = 36 / 16 * 30 / 24 * 80 x = 225 answer : b"
Answer: b
Python program:
a = 36 * 30
b = 16 * 24
c = b / 80
d = a / c
Problem: a shop sells 1 chocolate at the rate rupee 1 each . you can exchange 3 warppers for one chocolate . if you have rs . 15 , what is the maximum number of chocolates you can get ?
Options: a ) 21 , b ) 22 , c ) 23 , d ) 24 , e ) 25
Rationale: rs . 15 = 15 chocolates 15 wrappers = 5 chocolates 5 wrappers = 1 chocolate ( u have 2 wrappers with you . . ) count this wrapper with already existing wrappers = 15 + 5 + 1 + 1 = 22 chocolates . . answer : b
Answer: b
Python program:
a = 15 / 3
b = a + 1 
c = b + 1 
d = c + 15
Problem: jim is now twice as old as fred , who is 9 years older than sam . 6 years ago , jim was 5 times as old as sam . how old is jim now ?
Options: a ) 42 , b ) 46 , c ) 50 , d ) 54 , e ) 58
Rationale: j = 2 f = 2 ( s + 9 ) = 2 s + 18 j - 6 = 5 * ( s - 6 ) ( 2 s + 18 ) - 6 = 5 s - 30 s = 14 and so j = 46 the answer is b .
Answer: b
Python program:
a = 6 * 5
b = a - 6
c = 9 * 2
d = b + c 
e = 9 - 6
f = d / e
g = f + 9 
h = g * 2
Problem: a person lent a certain sum of money at 4 % per annum at simple interest and in 8 years the interest amounted to rs . 204 less than the sum lent . what was the sum lent ?
Options: a ) 228 , b ) 278 , c ) 300 , d ) 500 , e ) 821
Rationale: p - 204 = ( p * 4 * 8 ) / 100 p = 300 answer : c
Answer: c
Python program:
a = 4 * 8
b = a / 100
c = 1 - b
d = 204 / c
Problem: the l . c . m . of 2 numbers is 48 . the numbers are in the ratio 2 : 3 . find their sum ?
Options: a ) 36 , b ) 40 , c ) 48 , d ) 32 , e ) 56
Rationale: "let the numbers be 2 x and 3 x l . c . m . = 6 x 6 x = 48 x = 8 the numbers are = 16 and 24 required sum = 16 + 24 = 40 answer is b"
Answer: b
Python program:
a = 48 * 2
b = 2 / a
c = b * 2
d = 48 * 2
e = 2 / d
f = e * 48
g = c + f
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 $ 42.0 billion from $ 69.0 billion , a year ago . by what percent did the revenue fall ?
Options: a ) 20.8 , b ) 30.4 , c ) 31.8 , d ) 39.1 , e ) 33.8
Rationale: "$ 69 - $ 42 = 27 $ ( 27 / 69 ) * 100 = 39.13 % answer : d"
Answer: d
Python program:
a = 69 - 0
b = a / 69
c = b * 100
Problem: how many positive integers less than 100 have a remainder of 2 when divided by 13 ?
Options: a ) 5 , b ) 7 , c ) 8 , d ) 9 , e ) 6
Rationale: "take the multiples of 13 and add 2 0 x 13 + 2 = 2 . . . . 13 x 7 + 2 = 93 there are 14 numbers answer c"
Answer: c
Python program:
a = 4 + 2 
b = a - 1
c = math.factorial(b)
d = math.factorial(2)
e = 4 - 1
f = math.factorial(e)
g = d * f
h = c / g
Problem: convert 60 miles into yards ?
Options: a ) 105600 yards , b ) 35200 yards , c ) 39520 yards , d ) 42560 yards , e ) 41520 yards
Rationale: "1 mile = 1760 yards 60 miles = 60 * 1760 = 105600 yards answer is a"
Answer: a
Python program:
a = 3 + 2 
b = a * 2
c = 3 + 2 
d = c * 2
e = b * d
f = e * 60
g = 3 + 2 
h = g * 2
i = 3 + 2 
j = i * 2
k = h * j
l = f / k
Problem: the price of a bushel of corn is currently $ 3.20 , and the price of a peck of wheat is $ 10.80 . the price of corn is increasing at a constant rate of 5 x cents per day while the price of wheat is decreasing at a constant rate of x ( 2 ^ 1 / 2 ) - x cents per day . what is the approximate price when a bushel of corn costs the same amount as a peck of wheat ?
Options: a ) $ 4.50 , b ) $ 10.2 , c ) $ 5.30 , d ) $ 5.50 , e ) $ 5.60
Rationale: i tried using time / rate approach : - initial price difference = 10.80 - 3.20 = 7.60 price of corn increasing by 5 x price of wheat decreasing by x ( 1.4 ) - x = . 4 x since both the quantities are moving towards reducing the price gap hence : - relative increase = 5 x + . 4 x let t be the time by which gap is filled so , 7.6 = t ( 5.4 x ) - > t = ( 7.6 ) / 5.4 x final price = 3.20 + 5 x * t - > 3.20 + 5 * 7.6 / 5.4 = 10.2 answer b .
Answer: b
Python program:
a = 10 - 8
b = math.sqrt(2)
c = b - 1
d = 5 + c 
e = a / d
f = e * 5
g = 3 + 2
Problem: how many positive integers e 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 / 2
e = d + 1 
f = 300 - 200
g = f / 3
h = g + 1 
i = 5 * 3
j = i + 2 
k = h - j
l = math.floor(k)
m = l + 1 
n = e + m 
o = 300 - 200
p = o / 5
q = p + 1 
r = 5 * 3
s = q - r
t = n + s 
u = b - t
Problem: the hcf of two numbers is 23 and the other two factors of their lcm are 13 and 14 . what is the largest number ?
Options: a ) 280 , b ) 284 , c ) 292 , d ) 320 , e ) 322
Rationale: hcf of the two numbers = 23 since hcf will be always a factor of lcm , 23 is a factor of the lcm . given that other two factors in the lcm are 13 and 14 . hence factors of the lcm are 23 , 13 , 14 so , numbers can be taken as ( 23 × 13 ) and ( 23 × 14 ) = 299 and 322 hence , largest number = 322 e )
Answer: e
Python program:
a = 23 * 14
Problem: in a throw of dice what is the probability of ge æ « ng number greater than 2
Options: a ) 1 / 2 , b ) 2 / 3 , c ) 1 / 5 , d ) 1 / 6 , e ) none of these
Rationale: explanation : number greater than 2 is 3 , 4 , 5 & 6 , so only 4 number total cases of dice = [ 1,2 , 3,4 , 5,6 ] so probability = 4 / 6 = 2 / 3 answer : b
Answer: b
Python program:
a = 6 - 2
b = a / 6
Problem: a retailer purchases shirts from a wholesaler and then sells the shirts in her store at a retail price that is 50 percent greater than the wholesale price . if the retailer decreases the retail price by 30 percent this will have the same effect as increasing the wholesale price by what percent ?
Options: a ) 15 , b ) 20 , c ) 10 , d ) 5 , e ) 8
Rationale: answer : d = 5 . assume rs . 100 to be the price at which the retailer buys from wholesaler . 50 % increase makes retail price = 150 . now 30 % decrease - > ( 1 - 30 / 100 ) * 150 = 105 . now compared to the wholesale price of 100 , 5 % increase is what will have the same effect as increasing the wholesale price .
Answer: d
Python program:
a = 50 / 100
b = 1 + a 
c = 30 / 100
d = 1 - c
e = b * d
f = e - 1
g = f * 100
Problem: on dividing 172 by a number , the quotient is 10 and the remainder is 2 . find the divisor .
Options: a ) 9 , b ) 11 , c ) 13 , d ) 15 , e ) 17
Rationale: "d = ( d - r ) / q = ( 172 - 2 ) / 10 = 170 / 10 = 17 e"
Answer: e
Python program:
a = 172 / 10
b = math.floor(a)
Problem: in what time a sum of money double itself at 4 % per annum simple interest ?
Options: a ) 25 % , b ) 33 1 / 3 % , c ) 83 1 / 3 % , d ) 33 4 / 3 % , e ) 73 1 / 3 %
Rationale: "p = ( p * 4 * r ) / 100 r = 25 % answer : a"
Answer: a
Python program:
a = 100 * 100
b = 4 * 100
c = a / b
Problem: a big container is 35 % full with water . if 48 liters of water is added , the container becomes 3 / 4 full . what is the capacity of the big container in liters ?
Options: a ) 80 , b ) 90 , c ) 100 , d ) 110 , e ) 120
Rationale: "48 liters is 40 % of the capacity c . 48 = 0.4 c c = 48 / 0.4 = 120 liters . the answer is e ."
Answer: e
Python program:
a = 3 / 4
b = 35 / 100
c = a - b
d = 48 / c
Problem: in a box , there are 8 orange , 7 black and 6 white balls . if one ball is picked up randomly . what is the probability that it is neither orange nor white ?
Options: a ) 2 / 3 , b ) 3 / 4 , c ) 7 / 19 , d ) 8 / 21 , e ) 10 / 21
Rationale: total balls are 21 and neither black nor white . so favor case will be only 8 c 1 and total case 21 c 1 probability will be 8 c 1 / 21 c 1 = 8 / 21 answer : d
Answer: d
Python program:
a = 8 + 7 
b = a + 6 
c = 8 / b
Problem: suraj has a certain average of runs for 12 innings . in the 13 th innings he scores 96 runs thereby increasing his average by 5 runs . what is his average after the 13 th innings ?
Options: a ) 48 , b ) 64 , c ) 36 , d ) 72 , e ) 27
Rationale: "to improve his average by 5 runs per innings he has to contribute 12 x 5 = 60 runs for the previous 12 innings . thus , the average after the 13 th innings = 96 - 60 = 36 . answer : c"
Answer: c
Python program:
a = 12 * 5
b = 96 - a
c = 13 - 12
d = b / c
Problem: total number of boys and girls in a school is 150 . if the number of boys is x , then girls become x % of the total number of students . the number of boys is
Options: a ) 50 , b ) 60 , c ) 70 , d ) 80 , e ) 90
Rationale: explanation : clearly , x % of 150 = 150 - x [ as x is number of boys ] = > x + x / 100 ∗ 150 = 150 = > 5 / 2 x = 150 = > x = 60 option b
Answer: b
Python program:
a = 150 * 100
b = 150 + 100 
c = a / b
Problem: $ 20000 will become $ 60000 at 20 % p . a . find the time ?
Options: a ) 2 years , b ) 5 years , c ) 7 years , d ) 8 years , e ) 10 years
Rationale: "si = simple interest = a - p = 60000 - 20000 = $ 40000 r = 100 si / pt = 100 * 40000 / 20000 * 20 = 10 years answer is e"
Answer: e
Python program:
a = 60000 - 20000
b = 20 / 100
c = 20000 * b
d = a / c
Problem: a certain car dealership sells economy cars , luxury cars , and sport utility vehicles . the ratio of economy to luxury cars is 6 : 2 . the ratio of economy cars to sport utility vehicles is 5 : 3 . what is the ratio of luxury cars to sport utility vehicles ?
Options: a ) 9 : 8 , b ) 8 : 9 , c ) 6 : 2 , d ) 2 : 3 , e ) 1 : 2
Rationale: the ratio of economy to luxury cars is 6 : 2 - - > e : l = 6 : 2 = 30 : 10 . the ratio of economy cars to sport utility vehicles is 5 : 3 - - > e : s = 5 : 3 = 30 : 18 . thus , l : s = 10 : 18 = 5 : 6 . answer : b .
Answer: b
Python program:
a = 4 * 3
b = 3 * 3
c = a / b
d = 3 * 4
e = 2 * 4
f = d / e
g = c / f
Problem: what is the smallest integer that satisfies the inequality ( ( x - 3 ) / ( x ^ 2 - 8 x - 20 ) ) > 0 ?
Options: a ) - 2 , b ) 10 , c ) - 1 , d ) 3 , e ) 0
Rationale: let us factorize the denominator and rewrite the expression as ( x â ˆ ’ 3 ) / ( ( x â ˆ ’ 10 ) ( x + 2 ) ) > 0 equate each of the terms of the expression to zero to identify the values of x that are relevant to test whether the inequality holds good . the values that are relevant to us are x = 3 , x = 10 and x = - 2 . let us arrange these values in ascending order : - 2 , 3 and 10 . the quickest way to solve inequalities questions after arriving at these values is verifying whether the inequality holds good at the following intervals . interval 1 : x < - 2 . pick a value in that range and check whether the inequality holds good . let us take x = - 10 . when x = - 10 , ( x â ˆ ’ 3 ) / ( ( x â ˆ ’ 10 ) ( x + 2 ) ) < 0 ; the inequality does not hold good in this interval . interval 2 : - 2 < x < 3 . let us take x = 0 . when x = 0 , ( x â ˆ ’ 3 ) / ( ( x â ˆ ’ 10 ) ( x + 2 ) ) = ( 0 â ˆ ’ 3 ) / ( ( 0 â ˆ ’ 10 ) ( 0 + 2 ) ) > 0 ; the inequality holds good in this interval . the least integer value that x can take if x > - 2 is x = - 1 . answer : c .
Answer: c
Python program:
a = negate - (
b = a / 3
Problem: the average ( arithmetic mean ) of 20 , 40 , and 60 is 5 more than the average of 10 , 80 , and what number ?
Options: a ) 35 , b ) 30 , c ) 25 , d ) 20 , e ) 15
Rationale: a 1 = 120 / 3 = 40 a 2 = a 1 - 5 = 35 sum of second list = 35 * 3 = 105 therefore the number = 105 - 90 = 15 e
Answer: e
Python program:
a = 20 + 40 
b = a + 60 
c = 5 * 3
d = c + 10 
e = d + 80 
f = b - e
Problem: if a = 105 and a ^ 3 = 21 * 49 * 45 * b , what is the value of b ?
Options: a ) 25 , b ) 42 , c ) 45 , d ) 49 , e ) 54
Rationale: "first step will be to break down all the numbers into their prime factors . 105 = 3 * 5 * 7 21 = 7 * 3 49 = 7 * 7 45 = 3 * 3 * 5 so , ( 105 ) ^ 3 = 3 * 7 * 7 * 7 * 3 * 3 * 5 * b therefore ( 3 * 5 * 7 ) ^ 3 = 3 ^ 3 * 5 * 7 ^ 3 * b therefore , b = 3 ^ 3 * 5 ^ 3 * 7 ^ 3 / 3 ^ 3 * 5 * 7 ^ 3 b = 5 ^ 2 = 25 correct answer a ."
Answer: a
Python program:
a = 105 ** 3
b = 21 * 49
c = b * 45
d = a / c
Problem: james took a 3 - hour bike ride . in the second hour he traveled 30 miles , which was 20 percent farther than he traveled the first hour . if he traveled 25 percent farther in the third hour than he did in the second hour , how many miles did jose travel during the entire ride ?
Options: a ) 54.0 , b ) 54.9 , c ) 92.5 , d ) 57.0 , e ) 63.0
Rationale: let the distance travelled in the first hour be x . thus , 1.2 x = 30 , x = 25 . now , the distance travelled in the 3 rd hour = 30 + 1 / 4 â ˆ — 30 = 37.5 the only option ending with a 0.5 in the decimal place is c . answer : c
Answer: c
Python program:
a = 100 - 20
b = a / 100
c = b * 30
d = c + 30 
e = 100 + 25 
f = e / 100
g = f * 30
h = d + g
Problem: calculate the value of n from the below equation : n ^ 3 â ˆ ’ 10 n + 20 = 44
Options: a ) 1 , b ) 5 , c ) 3 , d ) 2 , e ) 4
Rationale: "use elimination method to find the correct option . you find that of all the options when 4 is the correct value for n answer : e"
Answer: e
Python program:
a = 44 - 20
b = 10 + 20 
c = a / b
d = 3 - c
Problem: due to construction , the speed limit along an 9 - mile section of highway is reduced from 45 miles per hour to 35 miles per hour . approximately how many minutes more will it take to travel along this section of highway at the new speed limit than it would have taken at the old speed limit ?
Options: a ) a ) 5.61 , b ) b ) 3.42 , c ) c ) 10 , d ) d ) 15 , e ) e ) 24
Rationale: "old time in minutes to cross 9 miles stretch = 9 * 60 / 45 = 9 * 4 / 3 = 12 new time in minutes to cross 9 miles stretch = 9 * 60 / 35 = 9 * 12 / 7 = 15.42 time difference = 3.42 ans : b"
Answer: b
Python program:
a = 45 + 9 
b = a - 1
c = 9 / 35
d = 9 / 45
e = c - d
f = b * e
g = max(f)
Problem: a number x is multiplied by 5 , and this product is then divided by 3 . if the positive square root of the result of these two operations equals x , what is the value of x if x ≠ 0 ?
Options: a ) 25 / 9 , b ) 9 / 5 , c ) 5 / 3 , d ) 3 / 5 , e ) 9 / 25
Rationale: "sqrt ( 5 x / 3 ) to be perfect square x has to 5 / 3 ans : c"
Answer: c
Python program:
a = 5 / 3
Problem: what amount does an investor receive if the investor invests $ 4000 at 10 % p . a . compound interest for two years , compounding done annually ?
Options: a ) $ 4720 , b ) $ 4840 , c ) $ 4920 , d ) $ 5080 , e ) $ 5160
Rationale: "a = ( 1 + r / 100 ) ^ n * p ( 1.1 ) ^ 2 * 5000 = 1.21 * 5000 = 4840 the answer is b ."
Answer: b
Python program:
a = 10 / 100
b = 1 + a 
c = b ** 2
d = 4000 * c