euclaise/mathqa_programs huggingface dataset:
Problem: an army ’ s recruitment process included n rounds of selection tasks . for the first a rounds , the rejection percentage was 60 percent per round . for the next b rounds , the rejection percentage was 50 percent per round and for the remaining rounds , the selection percentage was 70 percent per round . if there were 10000 people who applied for the army and 98 were finally selected , what was the value of n ?
Options: a ) 4 , b ) 5 , c ) 6 , d ) 7 , e ) 10
Rationale: "step ( 1 ) 4000 accepted . step ( 2 ) another 40 % of 40000 = 1600 accepted . here it is quiet observable that if we further deduct candidate by 60 % it would change our probablity of easy going 2000 candidate . so i would get to second stage of recruitment where 50 % is accepted step ( 3 ) 50 % of 1600 = 800 step ( 4 ) 50 % of 800 = 400 step ( 5 ) 50 % of 400 = 200 . . . here we are done with total 5 steps 70 % of 200 = 140 and last step of accepting 70 % of 140 = 98 ( our target ) total 7 steps required . ans d"
Answer: d
Python program:
a = 1 + 4 
b = 2 + a 
c = b + 2
Problem: a walks at 30 kmph and 30 hours after his start , b cycles after him at 55 kmph . how far from the start does b catch up with a ?
Options: a ) 1200 km , b ) 1980 km , c ) 2000 km , d ) 2500 km , e ) 3600 km
Rationale: "suppose after x km from the start b catches up with a . then , the difference in the time taken by a to cover x km and that taken by b to cover x km is 30 hours . x / 30 - x / 55 = 30 x = 1980 km answer is b"
Answer: b
Python program:
a = 30 * 55
Problem: a certain protective additive increases from 20 days to 25 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 ?
Options: a ) 25 % , b ) 33 1 / 3 % , c ) 50 % , d ) 66 2 / 3 % , e ) 75 %
Rationale: "general formula for percent increase or decrease , ( percent change ) : percent = change / original ∗ 100 so , the time between maintenance checks increased by 25 − 20 / 20 ∗ 100 = 25 answer : a ."
Answer: a
Python program:
a = 25 - 20
b = a / 20
c = b * 100
Problem: a $ 500 investment and a $ 1,500 investment have a combined yearly return of 13 percent of the total of the two investments . if the $ 500 investment has a yearly return of 7 percent , what percent yearly return does the $ 1,500 investment have ?
Options: a ) 9 % , b ) 15 % , c ) 105 / 8 % , d ) 11 % , e ) 12 %
Rationale: "the equation we can form the question : return on total investment = sum of individual investments ( 500 + 1500 ) ( 13 ) = ( 500 â ˆ — 7 ) + ( 1500 x ) , where x is the return on investment of 1500 . solving the equation , we get x = 15 % ( option b ) answer : b"
Answer: b
Python program:
a = 3 * 500
b = 500 + a 
c = 13 / 100
d = b * c
e = 7 / 100
f = 500 * e
g = d - f
h = 3 * 500
i = g / h
j = i * 100
Problem: the monthly rent of a shop of dimension 20 feet × 15 feet is rs . 3600 . what is the annual rent per square foot of the shop ?
Options: a ) 43 , b ) 144 , c ) 68 , d ) 87 , e ) 92
Rationale: "sol . monthly rent per square feet = 3600 / ( 20 * 15 ) = 12 & annual rent per square feet = 12 * 12 = 144 answer : b"
Answer: b
Python program:
a = 10 + 2 
b = 3600 / rectangle_area
c = a * b
Problem: liam is pulled over for speeding just as he is arriving at work . he explains to the police officer that he could not afford to be late today , and has arrived at work only four minutes before he is to start . the officer explains that if liam had driven 5 mph slower for his whole commute , he would have arrived at work exactly on time . if liam ' s commute is 40 miles long , how fast was he actually driving ? ( assume that liam drove at a constant speed for the duration of his commute . )
Options: a ) 50 mph , b ) 45 mph , c ) 48 mph , d ) 52 mph , e ) 60 mph
Rationale: let t be the number of hours he would need to reach office on time . when he is driving with over speed , he reached office 4 min earlier ! so the equation for this is s ( t - 4 / 60 ) = 40 where s is the speed and 30 is the distance . if he decreases his speed by 5 mph then he would have reached his office on time : ( s - 5 ) t = 40 if you solve above equations , you will arrive at t = 2 / 3 hr and s = 60 mph therefore answer is e
Answer: e
Python program:
a = 5 * 4
b = 40 + a
Problem: an article costing rs . 160 is sold at 20 % discount on a mark - up price . what is the selling price after discount ?
Options: a ) 106 , b ) 116 , c ) 128 , d ) 136 , e ) 146
Rationale: 160 * 80 / 100 = 128 answer : c
Answer: c
Python program:
a = 160 * 20
b = a / 100
c = 160 - b
Problem: 75 % of x is greater than 1 / 3 rd of x by 110 . what is x ?
Options: a ) 160 , b ) 264 , c ) 360 , d ) 354 , e ) 400
Rationale: 75 x / 100 - x / 3 = 110 5 x / 12 = 110 x = 264 answer : b
Answer: b
Python program:
a = 75 / 100
b = 1 / 3
c = a - b
d = 110 / c
Problem: there are 8 stores in town that had a total of 21 visitors on a particular day . however , only 12 people went shopping that day ; some people visited more than one store . if 8 people visited exactly two stores each , and everyone visited at least one store , what is the largest number of stores anyone could have visited ?
Options: a ) 2 , b ) 3 , c ) 4 , d ) 5 , e ) 6
Rationale: "8 people visited 2 stores each for 16 visits . to maximize the number of stores that one person visited , let ' s assume that 3 people visited 1 store each . the number of remaining visits is 21 - 16 - 3 = 2 , which is the maximum that one person could have visited . the answer is a ."
Answer: a
Python program:
a = 8 * 2
b = 21 - a
c = 12 - 8
d = c - 1
e = b - d
Problem: indu gave bindu rs . 2500 on compound interest for 2 years at 4 % per annum . how much loss would indu has suffered had she given it to bindu for 2 years at 4 % per annum simple interest ?
Options: a ) 1 , b ) 2 , c ) 3 , d ) 4 , e ) 5
Rationale: "2500 = d ( 100 / 4 ) 2 d = 4 answer : d"
Answer: d
Python program:
a = 4 / 100
b = 1 + a 
c = b ** 2
d = 2500 * c
e = d - 2500
f = 4 / 100
g = 2500 * f
h = g * 2
i = e - h
Problem: 7 people average age is 30 . youngest person age is 7 . find average of the people when youngest was born .
Options: a ) 23 , b ) 24 , c ) 25 , d ) 26 , 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 - 49 = 161 so average age would be 161 / 7 = 23 answer : a"
Answer: a
Python program:
a = 30 * 7
b = 7 * 7
c = a - b
d = c / 7
Problem: how many pounds of salt at 50 cents / lb must be mixed with 40 lbs of salt that costs 35 cents / lb so that a merchant will get 20 % profit by selling the mixture at 48 cents / lb ?
Options: a ) 20 , b ) 15 , c ) 40 , d ) 50 , e ) 25
Rationale: "selling price is 48 cents / lb for a 20 % profit , cost price should be 40 cents / lb ( cp * 6 / 5 = 48 ) basically , you need to mix 35 cents / lb ( salt 1 ) with 50 cents / lb ( salt 2 ) to get a mixture costing 40 cents / lb ( salt avg ) weight of salt 1 / weight of salt 2 = ( salt 2 - salt avg ) / ( salt avg - salt 1 ) = ( 50 - 40 ) / ( 40 - 35 ) = 2 / 1 we know that weight of salt 1 is 40 lbs . weight of salt 2 must be 20 lbs . answer ( a )"
Answer: a
Python program:
a = 48 * 40
b = 100 + 20 
c = b / 100
d = 35 * 40
e = c * d
f = a - e
g = 100 + 20 
h = g / 100
i = 50 * h
j = i - 48
k = f / j
Problem: a factory that employs 1000 assembly line workers pays each of these workers $ 5 per hour for the first 40 hours worked during a week and 1 ½ times that rate for hours worked in excess of 40 . what was the total payroll for the assembly - line workers for a week in which 30 percent of them worked 10 hours , 50 percent worked 40 hours , and the rest worked 50 hours ?
Options: a ) $ 180,000 , b ) $ 185,000 , c ) $ 170,000 , d ) $ 200,000 , e ) $ 205,000
Rationale: 30 % of 1000 = 300 worked for 20 hours payment @ 5 / hr total payment = 300 * 10 * 5 = 15000 50 % of 1000 = 500 worked for 40 hours payment @ 5 / hr total payment = 500 * 40 * 5 = 100000 remaining 200 worked for 50 hours payment for first 40 hours @ 5 / hr payment = 200 * 40 * 5 = 40000 payment for next 10 hr @ 7.5 / hr payment = 200 * 10 * 7.5 = 15000 total payment = 15000 + 100000 + 40000 + 15000 = 170000 hence , answer is c
Answer: c
Python program:
a = 1 / 10
b = a + 1 
c = 3 / 2
d = 5 * 10
e = c * d
f = 40 * 5
g = e + f 
h = 3 + 5 
i = 10 - h
j = g * i
k = 40 * 5
l = k * 5
m = j + l 
n = 5 * 10
o = n * 3
p = m + o 
q = p / 10
r = 1000 * q
s = r / 1000
t = b * s
Problem: along a yard 273 metres long , 14 trees are palnted at equal distances , one tree being at each end of the yard . what is the distance between two consecutive trees
Options: a ) 18 , b ) 19 , c ) 10 , d ) 21 , e ) 12
Rationale: "explanation : 14 trees have 13 gaps between them , required distance ( 273 / 13 ) = 21 option d"
Answer: d
Python program:
a = 14 - 1
b = 273 / a
Problem: a sum of money deposited at c . i . amounts to rs . 2442 in 2 years and to rs . 2926 in 3 years . find the rate percent ?
Options: a ) 11 , b ) 20 , c ) 28 , d ) 24 , e ) 82
Rationale: "explanation : 2420 - - - 484 100 - - - ? = > 20 % answer : option b"
Answer: b
Python program:
a = 2926 - 2442
b = a / 2442
c = b * 100
Problem: a ratio between two numbers is 8 : 9 and their l . c . m . is 432 . the first number is
Options: a ) 60 , b ) 45 , c ) 50 , d ) 48 , e ) none
Rationale: sol . let the required numbers be 8 x and 9 x . then , their l . c . m . is 72 x . ∴ 72 x = 432 ⇔ x = 6 . hence , the first number is 48 . answer d
Answer: d
Python program:
a = 8 * 9
b = 432 / a
c = b * 8
Problem: jim needs $ 1000 to buy a new flat - screen tv . since he has only $ 7 , he borrows the remaining balance from his sister mary . the loan will be repaid in 3 annual installments at an interest rate of 10 % , compounded annually . the formula for calculating the monthly payment p is p = ( l x c x r ) / ( c – 1 ) where l = amount of the loan , r = annual interest rate , and c = compounding factor = ( 1 + r ) ^ n where n = number of annual payments . how much does jim have to pay mary at the end of each of the next 3 years ( rounded to the nearest penny ) ?
Options: a ) $ 357.67 , b ) $ 375.85 , c ) $ 387.40 , d ) $ 399.30 , e ) $ 433.33
Rationale: l = 993 r = 0.1 c = 1.1 ^ 3 = 1.331 insert all of these in the formula and we get p = 993 * 1.331 * 0.1 / 0.331 in order to resolve above without a calc , we need to find the approx value of 0.1331 / 0.331 ~ 0.4 ~ ~ 993 * 0.4 ~ 397 answer d
Answer: d
Python program:
a = 1000 - 7
b = 10 / 100
c = a * b
d = 10 / 100
e = 1 + d 
f = e ** 3
g = c * f
h = 10 / 100
i = 1 + h 
j = i ** 3
k = j - 1
l = g / k
Problem: there is a 35 cm line marked at each centimeter and an insect is placed at every centimeter . 9 frogs are trained to jump a constant distance . the first one jumps 2 cm in every leap , the second one jumps 3 cm and so on until the 9 th one jumps 10 cm in every leap and they eat any insect that is available at that spot . if all of them start from start line and finish the entire 35 cm , how many insects were still left after the race was over ?
Options: a ) 0 , b ) 4 , c ) 6 , d ) 7 , e ) 10
Rationale: "only the prime numbers greater than 10 and less than 35 were left . that is 11 , 13 , 17 , 19 , 23 , 29 , and 31 . the total is 7 . the answer is d ."
Answer: d
Python program:
a = 10 + 2
Problem: a searchlight on top of the watchtower makes 4 revolutions per minute . what is the probability that a man appearing near the tower will stay in the dark for at least 5 seconds ?
Options: a ) 5 / 6 , b ) 4 / 5 , c ) 3 / 4 , d ) 2 / 3 , e ) 1 / 2
Rationale: the searchlight completes one revolution every 15 seconds . the probability that the man ' s area will be lit up is 5 / 15 = 1 / 3 . the probability that he will stay in the dark is 1 - 1 / 3 = 2 / 3 the answer is d .
Answer: d
Python program:
a = 5 * 3
b = 5 / a
c = 1 - b
Problem: how many integers are between 7 and 120 / 9 , inclusive ?
Options: a ) 5 , b ) 6 , c ) 7 , d ) 9 , e ) 10
Rationale: "120 / 9 = 13 . xx we are not concerned about the exact value of 120 / 9 as we just need the integers . the different integers between 7 and 120 / 9 would be 7 , 8 , 9 , 10 , 11 , 12,13 total number of integers = 7 option c"
Answer: c
Python program:
a = 120 / 9
b = a - 7
c = b + 1
Problem: the two lines y = x and x = - 5 intersect on the coordinate plane . what is the value of the area of the figure formed by the intersecting lines and the x - axis ?
Options: a ) 7.5 , b ) 10 , c ) 12.5 , d ) 15 , e ) 17.5
Rationale: "the point of intersection is ( - 5 , - 5 ) . the triangle has a base of length 5 and a height of 5 . area = ( 1 / 2 ) * base * height = ( 1 / 2 ) * 5 * 5 = 12.5 the answer is c ."
Answer: c
Python program:
a = 5 * 5
b = a / 2
Problem: in a 100 - mile trip , the first 30 miles were completed at 60 mph . if the average speed for the whole trip was 40 mph , what was the average speed in the last 70 miles ?
Options: a ) 30 mph , b ) 32 mph , c ) 35 mph , d ) 37 mph , e ) 38 mph
Rationale: the time to complete the first 30 miles was ( 30 miles / 60 mph ) = ( 1 / 2 ) hours . the time to complete the whole trip was ( 100 miles / 40 mph ) = ( 5 / 2 ) hours . the time to complete the last 70 miles was ( 5 / 2 ) - ( 1 / 2 ) = ( 2 ) hours . the average speed in the last 70 miles was ( 70 miles / 2 hours ) = 35 mph . the answer is c .
Answer: c
Python program:
a = 100 / 40
b = 30 / 60
c = a - b
d = 70 / c
Problem: diana took out a charge account at the general store and agreed to pay 6 % simple annual interest . if she charges $ 60 on her account in january , how much will she owe a year later , assuming she does not make any additional charges or payments ?
Options: a ) $ 62.40 , b ) $ 62.80 , c ) $ 63.20 , d ) $ 63.60 , e ) $ 64.00
Rationale: "1.06 * $ 60 = $ 63.60 the answer is d ."
Answer: d
Python program:
a = 6 / 100
b = a * 60
c = 60 + b
Problem: a started a business with an investment of rs . 70000 and after 6 months b joined him investing rs . 120000 . if the profit at the end of a year is rs . 13000 , then the share of b is ?
Options: a ) 6000 , b ) 12000 , c ) 18000 , d ) 24009 , e ) 24002
Rationale: "ratio of investments of a and b is ( 70000 * 12 ) : ( 120000 * 6 ) = 7 : 6 total profit = rs . 13000 share of b = 6 / 13 ( 13000 ) = rs . 6000 answer : a"
Answer: a
Python program:
a = const_60 * 100
b = 13000 - a
Problem: if the average ( arithmetic mean ) of x , x + 2 , and x + 4 is 103 , what is the value of x ?
Options: a ) 95 , b ) 97 , c ) 101 , d ) 85 , e ) 87
Rationale: "am of x , x + 2 , and x + 4 = x + ( x + 2 ) + ( x + 4 ) / 3 = 3 x + 6 / 3 = x + 2 given that x + 2 = 103 x = 101 answer : c"
Answer: c
Python program:
a = 4 * 2
b = 2 * 2
c = a - b
Problem: divide rs . 32000 in the ratio 1 : 7 ?
Options: a ) 12000 , 20000 , b ) 12000 , 200098 , c ) 4000 , 28000 , d ) 12000 , 20006 , e ) 12000 , 20001
Rationale: "1 / 8 * 32000 = 4000 7 / 8 * 32000 = 28000 answer : c"
Answer: c
Python program:
a = 7 - 2
b = 7 - 2
c = 1 + b 
d = 32000 / c
e = a * d
Problem: the manager of a produce market purchased a quantity of tomatoes for $ 0.80 per pound . due to improper handling , 10 percent of the tomatoes , by weight , were ruined and discarded . at what price per pound should the manager sell the remaining tomatoes if she wishes to make a profit on the sale of the tomatoes equal to 10 percent of the cost of the tomatoes .
Options: a ) $ 0.94 , b ) $ 0.96 , c ) $ 0.98 , d ) $ 1.00 , e ) $ 1.20
Rationale: "assume the manager bought 100 tomatoes . cost price = 80 given : 10 % are damaged - - > available tomatoes to sell = 90 90 * x - 80 = 0.1 * 80 90 x - 80 = 8 90 x = 88 x = 88 / 90 = 44 / 45 = 0.977 x is slightly under 0.977 = 0.98 answer : c"
Answer: c
Python program:
a = 10 / 100
b = 1 + a 
c = 100 - 10
d = c / 100
e = 0 / 80
f = b * e
Problem: a rectangle having length 140 cm and width 40 cm . if the length of the rectangle is increased by thirty percent then how much percent the breadth should be decreased so as to maintain the same area .
Options: a ) 17.64 % , b ) 33.33 % , c ) 40 % , d ) 75 % , e ) none of these
Rationale: explanation : solution : ( 30 / ( 140 + 30 ) * 100 ) % = 17.64 % answer : a
Answer: a
Python program:
a = 140 * 40
b = 3 * 10
c = b * 140
d = c / 100
e = 140 + d 
f = a / e
g = f / 40
h = 1 + g 
i = h * 10
Problem: which number can we add to 722425 to get a number exactly divisible by 456 ?
Options: a ) 312 , b ) 335 , c ) 347 , d ) 361 , e ) 383
Rationale: "722425 / 456 = 1584 with a remainder of 121 . we need to add 456 - 121 = 335 the answer is b ."
Answer: b
Python program:
a = 456 - reminder
Problem: a man is walking at the rate of 8 km / hr crosses a bridge in 15 minutes . the length of the bridge is
Options: a ) 1000 meters , b ) 1050 meters , c ) 1200 meters , d ) 2000 meters , e ) none of these
Rationale: 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 = 8 â ˆ — 5 / 18 = 20 / 9 m / sec time = 15 â ˆ — 60 seconds = 900 seconds distance = time â ˆ — speed / distance = 20 / 9 â ˆ — 900 = 2000 meter option d
Answer: d
Python program:
a = 15 / const_60
b = 8 * a
c = b * 1000
Problem: a certain company reported that the revenue on sales increased 15 % from 2000 to 2003 , and increased 30 % from 2000 to 2005 . what was the approximate percent increase in revenue for this store from 2003 to 2005 ?
Options: a ) 50 % , b ) 40 % , c ) 35 % , d ) 32 % , e ) 13 %
Rationale: "assume the revenue in 2000 to be 100 . then in 2003 it would be 115 and and in 2005 130 , so from 2003 to 2005 it increased by ( 130 - 115 ) / 115 = 15 / 115 = 13 % . answer : e ."
Answer: e
Python program:
a = 30 / 100
b = 1 + a 
c = 15 / 100
d = 1 + c 
e = b - d
f = 15 / 100
g = 1 + f 
h = e / g
i = h * 100
Problem: p and q invested in a business . the profit earned was divided in the ratio 2 : 3 . if p invested rs 40000 , the amount invested by q is
Options: a ) 30000 , b ) 50000 , c ) 40000 , d ) 20000 , e ) 60000
Rationale: let the amount invested by q = q 40000 : q = 2 : 3 ⇒ 40000 × 3 = 2 q ⇒ q = ( 40000 × 3 ) / 2 = 60000 answer is e .
Answer: e
Python program:
a = 40000 / 2
b = a * 3
Problem: in the first m games of a team ' s season , the ratio of the team ' s wins to its losses was 3 : 1 . in the subsequent n games , the ratio of the team ´ s wins to losses was 1 : 4 . if m : n = 4 : 5 , what was the ratio of the team ' s wins to its losses for all m + n games ?
Options: a ) 1 : 2 , b ) 2 : 3 , c ) 3 : 4 , d ) 4 : 5 , e ) 5 : 6
Rationale: "m = 4 / 9 of total games n = 5 / 9 of total games wins = 3 / 4 * 4 / 9 + 1 / 5 * 5 / 9 = 3 / 9 + 1 / 9 = 4 / 9 losses = 1 - 4 / 9 = 5 / 9 the ratio of wins to losses is 4 : 5 . the answer is d ."
Answer: d
Python program:
a = 3 + 1 
b = 3 + 0 
c = a / b
Problem: if x dollars is invested at 10 percent for one year and y dollars is invested at 8 percent for one year , the annual income from the 10 percent investment will exceed the annual income from the 8 percent investment by $ 65 . if $ 2,000 is the total amount invested , how much is invested at 8 percent ?
Options: a ) $ 550 , b ) $ 650 , c ) $ 750 , d ) $ 850 , e ) $ 950
Rationale: "0.1 x = 0.08 ( 2000 - x ) + 65 0.18 x = 225 x = 1250 then the amount invested at 8 % is $ 2000 - $ 1250 = $ 750 the answer is c ."
Answer: c
Python program:
a = 100 * 10
b = a * 2
c = 10 * 8
d = c * 2
e = d + 65 
f = 10 / 100
g = 8 / 100
h = f + g 
i = e / h
j = b - i
Problem: ramu bought an old car for rs . 36000 . he spent rs . 15000 on repairs and sold it for rs . 62900 . what is his profit percent ?
Options: a ) 16 % , b ) 17 % , c ) 18 % , d ) 58 % , e ) 23 %
Rationale: total cp = rs . 36000 + rs . 15000 = rs . 51000 and sp = rs . 62900 profit ( % ) = ( 62900 - 51000 ) / 51000 * 100 = 23 % answer : e
Answer: e
Python program:
a = 36000 + 15000 
b = 62900 - a
c = 36000 + 15000 
d = b / c
e = d * 100
Problem: the sum of the ages of 4 children born at the intervals of 4 years each is 48 years . what is the age of the youngest child ?
Options: a ) 2 years , b ) 4 years , c ) 6 years , d ) 8 years , e ) 10 years
Rationale: "let the ages of the children be x , ( x + 4 ) , ( x + 4 ) and ( x + 12 ) years . then , x + ( x + 4 ) + ( x + 8 ) + ( x + 12 ) = 48 4 x = 24 = > x = 6 . age of youngest child = x = 6 years . answer : c"
Answer: c
Python program:
a = 4 / 4
b = 48 / a
c = 4 - 1
d = c * 4
e = b - d
f = e / 4
Problem: the two lines y = x and x = - 7 intersect on the coordinate plane . if z represents the area of the figure formed by the intersecting lines and the x - axis , what is the side length of a cube whose surface area is equal to 6 z ?
Options: a ) 16 , b ) 8 √ 2 , c ) 8 , d ) 7 / √ 2 , e ) ( √ 2 ) / 3
Rationale: "800 score official solution : the first step to solving this problem is to actually graph the two lines . the lines intersect at the point ( - 7 , - 7 ) and form a right triangle whose base length and height are both equal to 4 . as you know , the area of a triangle is equal to one half the product of its base length and height : a = ( 1 / 2 ) bh = ( 1 / 2 ) ( 7 × 7 ) = 49 / 2 ; so z = 49 / 2 . the next step requires us to find the length of a side of a cube that has a face area equal to 49 / 2 . as you know the 6 faces of a cube are squares . so , we can reduce the problem to finding the length of the side of a square that has an area of 49 / 2 . since the area of a square is equal to s ² , where s is the length of one of its side , we can write and solve the equation s ² = 49 / 2 . clearly s = √ 49 / 2 = 7 / √ 2 , oranswer choice ( d ) ."
Answer: d
Python program:
a = 7 * 7
b = a / 2
c = math.sqrt(b)
Problem: find the smallest four - digit number which is a multiple of 112
Options: a ) 137 , b ) 112 , c ) 287 , d ) 121 , e ) 191
Rationale: "explanation : the smallest four digit number is 1000 . if 1000 is divided by 112 , the remainder is 104 . 112 - 104 = 8 , if 8 is added to 1000 , it will become the smallest four digit number and a multiple of 112 . answer : b"
Answer: b
Python program:
a = 112 / 1000
b = a / 3
c = b / 3
d = c / 3
e = 112 / 1000
f = e / 3
g = f / 3
h = g / 3
i = d * h
Problem: a goods train runs at a speed of 72 kmph and crosses a 270 m long platform in 26 seconds . what is the length of the goods train ?
Options: a ) 230 m , b ) 250 m , c ) 260 m , d ) 270 m , e ) 240 m
Rationale: "s = 270 + x / t 72 * 5 / 18 = 270 + x / 26 x = 250 answer : b"
Answer: b
Python program:
a = 72 * const_0_2778
b = a * 26
c = b - 270
Problem: alex takes a loan of $ 4,000 to buy a used truck at the rate of 6 % simple interest . calculate the annual interest to be paid for the loan amount .
Options: a ) 680 , b ) 700 , c ) 240 , d ) 620 , e ) 260
Rationale: "from the details given in the problem principle = p = $ 4,000 and r = 6 % or 0.06 expressed as a decimal . as the annual interest is to be calculated , the time period t = 1 . plugging these values in the simple interest formula , i = p x t x r = 4,000 x 1 x 0.06 = 240.00 annual interest to be paid = $ 240 answer : c"
Answer: c
Python program:
a = 6 * 100
b = math.sqrt(100)
c = a * b
d = c * 6
e = d / 100
Problem: if 145 % of j is equal to 25 % of k , 160 % of k is equal to 50 % of l , and 175 % of l is equal to 75 % of m , then 40 % of m is equal to what percent of 200 % of j ?
Options: a ) 0.35 , b ) 3.5 , c ) 35 , d ) 700 , e ) 3500
Rationale: "imo answer should be 350 . . . consider j = 10 , then k = 50 , l = 150 and m = 350 . . . . 40 % of 350 , comes out to be 140 . . . . 200 % of 10 is 20 . . . . ( 140 * 100 ) / 20 = 700 . . . . ans : d"
Answer: d
Python program:
a = 145 * 160
b = a * 175
c = 25 * 50
d = c * 75
e = b / d
f = e * 40
g = f / 200
h = g * 100